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THE NEW YORK
POBUC LIBRARY
Q
O
it
O
S
I
r
WATER POWER ENGINEERING
THE THEORY. INVESTIGATION AND DEVELOPMENT
OF WATER POWERS.
BY
Daniel w. mead.
Member American Society Civil Enginan
Consul/ f fig" Engineer
Professor of Hydraulic and Sanitary Engineering
University of Wisconsin
First E'lition.
NEW YORK
McGraw-Hill Book Co,
19O8
THE NEW YORK
PUBLIC LIBRARY
63248^
•iTO« LC«tUR AMD
Copyrighted 1907-1908
BY
Daniel W. Mead
:': ••• •. .•
*• •*•*! •*.
Btatm JouaiTAL yRonam CourAgrt
Ma»i«on, WiaooMnr
PREFACE
In the development of a water power project the engineer is fre-
qently called upon to do more than design and construct the power
plant. He may be required to report on.the adequacy of the supply,
the head and power available and the probable variations in the
same, the plan for development, the cost of construction and opera-
tion, and the advisability of the investment. A study of the entire
project, therefore, becomes essential, and each factor must be care-
fully considered in detail to assure ultimate success. Each of the
features of the development is of equal importance to the commer-
cial success of the project. The majority of the failures in water
power development have occurred from causes other than structural
defects, and a knowledge of these other important and controlling
factors is therefore quite as essential as a knowledge of design and
construction. It must be said, however, that in respect to some of
these controlling factors current practice has not been what it should
l>e. This has resulted in many over-developments and illy advised
installations, from which the power generated has not been equal
to that anticipated, and in many poor financial investments amount-
ing frequently to practical failures. The engineer has given much
attention to design and construction but too little attention to the
other fundamental considerations mentioned above on which the
success of the project depends to an equal extent.
In the preparation of this book the author has endeavored to con-
sider, briefly at least, all fundamental principles and to point out the
basis on which successful .^'Mer power-, cqvelopment depends. The
method of study and inyestig^tipn outlined herein was developed by
the author during tweuty^five year'$ of professional practice and in
his efforts to illustrate the. principles underlying the subject in his
lectures to the senior ^•class^iji.wateJ*. power engineering at the Uni-
versity of Wisconsin. A somewhat extended acquaintance with the
literature relating to water power engineering leads the author to
believe that in a number of features the principles and methods de-
scribed in this book are ^mewhat in advance of present practice.
VI
Preface,
In current practice, the hydraulic engineer, to determine the ex-
tent of a proposed hydraulic development, commonly depends on a
study of the monthly averages of stream flow and of observed maxi-
mum and minimum Oows. He usually assumes from his previous
knowledge and study that the development should be based on a
certain minimum or average stream discharge per square mile of
drainage area. The value of this method depends on the breadth of
the engineer's local knowledge of rainfall and run-oflf relations.
With a sufficient knowledge of these conditions, this method may
form a safe basis for water power development but it fails to give
the complete information which is essential for a full comprehension
of the subject. In other cases the development is predicted on a
single, or on a very few, measurements of what is believed, or as-
sumed to be, the low water flow of the stream. This method, evettfl
when accompanied by careful study of rainfall records, is a danger*
ous one to employ as many over-developed water power projects
demonstrate. Neither of these methods compares favorably with
the more exact method of studying flow by actual or comparative^
hydrographs as is described in Chaps. IV, V, VI 11 and IX. "
In current practice the head available is usually determined for
average conditions, or, perhaps, occasionally for low, average and
high water conditions, and no detailed study of the daily e fleet on
power is attempted* In Chaps. IV and V this subject is presented
in detail and a method of the investigation of this important subject,
under all conditions of flow and all conditions of use, is outlined.
On the basis of the kno%vledge gained from the study of flow and
head, the study of the power that can be developed for each day ini
the year and during each year for which actual or comparative hy-J
drographs are available, is outlined. An outline of a method for
the consideration of possible variations in flow during periods for]
which no measurements arc available based on the available rain-J
fall records, is also given*, ii>f:haj]^,-VJ.:VM •and VIIL A study of
the effect of pondage OTv'pfiier' k mc^tMmpc>rtant matter, though
not always carefully considcrel^, pr ^{^J-er^sftcd, is also discussed in —
considerable detail in Chaps. lV,:V^"na'^XxVl. |
In the selection of turbines,4fi)j:a'\vs(6en power project* the current
practice has been for the erfgtntir; Whilfe rtfawing certain conclu-
sions from the tables of manufacturers' catalogues, to present to the
manufacturer the conditions under which the power is to be devel-^
oped and to rely largely or entirely on the manufacturer for advice]
Preface. vii
as to machinery to be used. In such cases he is dependent for re-
sults on guarantees which are usually quite indefinite in character
and seldom verified by actual tests, under working conditions, be-
fore the wheels are accepted and paid for. This has resulted in
many cases in the installation of wheels which are entirely unsuited
to the particular conditions under which they are installed.
Practical turbine analysis has not been treated except in the most
general way in any publications except the various German treatises
on the turbine in which the subject is discussed from the basis of
turbine design. The author has developed the method of turbine
analysis and selection, outlined in Chapters XIV and XVI.
which applies to all wheels when tests of wheels of the series or
class considered are available. These methods are based on the
practical operating conditions of actual tests and are both theoreti-
cally and practically correct. The engineer should be able to intel-
ligently select the turbines needed for the particular conditions of his
installation and to determine, with a considerable degree of accuracy,
the results on which he can depend during all conditions of head
and flow.
It is believed that this treatment of the subject is sufficiently
complete to place the selection of turbines on a better footing and
that, when adopted, it will lead to the selection of better and more
improved designs and assure more satisfactory results.
The subject of turbine governing has, for electrical reasons, be-
come an important one. While a number of important papers have
appeared on this subject, there is, so far as the author knows, no
discussion in English which offers the engineer a basis for a com-
plete consideration of this subject. Chap. XVIII, on the principles
of turbine governing together with appendixes A, B and C, offer,
it is believed, suggestions for the consideration of this subject which
may prove of value to water power engineers.
The report on a water power project should involve a careful
and complete investigation of the entire subject, and should be
based on the broadest considerations of the project in all its rela-
tions. Many reports which have come to the author's attention
bave been too limited in scope and have included only general opin-
ions which have not. to his mind, been sufficiently specific or based
on sufficient information to warrant approval without extended in-
vestigations. In Chap. XXVIII the author has outlined his idea
viii Preface.
of the extent and scope of such investigation and report, which h
believes is essential for an intelligent investigation and a reliabl
opinion on this subject.
ACKNOWLEDGMENTS.
There can be little which is strictly new or original in any technics
work, and in offering this book to the profession, the author wishes t
acknowledge his indebtedness to the large number of technical ai
tides that have already appeared on various phases of the subjecl
Many references to such literature have been given at the end of th
various chapters.
Many illustrations have been taken, with more or less chang
from Engineering News, Engineering Record, Cassier's Magazin
and Electrical World and Engineer. Various manufacturers hav
furnished photographs and, in some cases, cuts of their wheels, go\
ernors and apparatus, in connection with which their names appeal
Tlie author has been greatly aided by his assistants, both of hi
own private office and of the University staff. He wishes especiall
to acknowledge the assistance of Mr. L. F. Harza to whoi
Chap. XVIII on The Speed Regulation of Turbine Water Wheel
and appendixes A, B and C are largely due. Mr. Harza has als
been of much assistance in the editorial work of publication. Ej
pecial acknowledgment is also due to Professor G. J. Davis, Ji
for the preparation of the diagrams of friction of water in pipes an
of Bazin's and Kutter's coefficients, etc. Mr. Robert Ewald assistc
in the selection of material for illustrations, in the investigation <
German literature, and the preparation of various graphical diagram
including the first development of the characteristic curve.
The author also desires to acknowledge his indebtedness to h
principal assistant, Mr. C. V. Seastone, for advice and assistance i
the arrangement of many of the chapters in this work and assis
ance in the editorial work of publication.
The sources of various other tables, illustrations, etc., are a
knowledged in their proper places. D. W. M.
Madison, Oct. i, 1908.
CONTENTS
CHAPTER I.
Introduction.
The Hwtory of Water Power Development— Every Development of
Water Power — ^The EiarlieBt Type of Water Wheel — ^The Undershot
Wheel — The Overshot and Breast Water Wheel — ^The Development
of the Turhine— Fundamental Ideas of the Turhlne— The Modem
Turhin&— The American or Francla Turbine — ^Modern Changes in
Turbine Practice — Historical Notes on Water Power Development —
Development of Water Power in the United States — ^Literature. ••• 1
CHAPTER IL
Power.
The Development of Potential Energy — Definition of Energy — Solar
Energy the Ultimate Source — ^No Waste of Energy in Nature— Laws
of Energy Conservation — Efficiency — Natural Limit to Efficiency — •
Practical Limits to Efficiency — Efficiency of a Combined Plant-
Capacity of Each Part of a System not Identical — The Analysis of
Losses — The Losses In a Hydro-Electric Plant— Units of Energy'—
Conversion of Energy Units — ^Kinetic Energy — Uniform Motion —
Uniform Varied Motion — Compound Motiour-Qraphlcal Representa-
tion of the Laws of Motion — ^Transformation — ^Literature 19
CHAPTER IIL
Hydraulics.
Basis of Hydraulics — Mathematical Expression for Energy— Velocity
Head*— Entrance Head — Submerged Orifices — Friction Head — Kut-
ter's Formula — Bazin's Formula — ^Efficiency of Section — ^Determina-
tion of Canal Cross-Section — The Back Water Curve — Flow of
Water in Pipes — The Flow of Water Through Orifices — Flow over
Weirs — ^Literature 40
CHAPTER IV.
Wateb Powis.
The Study of the Power of a Stream as Affected by Flow— Source of
Water Power — Factors of Stream Flow — Broad Knowledge of
Contents.
Stream Plow Neceasary— The Hydrograph— The Use of Local
Hydrography— Use of Comparative Hydrographs— Reliability of
Comparauve Hydrographfl— When no Hydrographs are Available—
The Hydrograph as a Power Curve 7S^
CHAPTER V.
Wateb Poweb (Continued)
The Study of the Power of a Stream as Affected by Head— Variations
in Head — The Rating or Discharge Curve— The Tail Water Curve —
The Head Water Curve— Graphic Representation of Head — Effects
of Design of Dam on Head — Effect of Head on the Power of the
Plant — Graphical Representation of the Relations of Power, Head
and Plow — Graphical Study of Power at Kilbourn — Power of the
Kilbourn Wheels Under Variations in Flow— Effects of Low Water
Flow — Effects of Number of Wheels on Head and Power • 9 J
CHAPTER VL
Rainfall.
Importance of Rainfall Study — Distribution of Rainfall — The Rainfall
Must be Studied in Detail — ^Local Variation in Annual Rainfalls—
Local Variations in Periodical Distribution of Annual Rainfall —
. Accuracy of Rainfall Maps and Records — Rainfall and Altitude —
Value of Extended Rainfall Records — Accuracy in Rainfall Obser-
vation*—District Rainfall — Study of Rainfall as Affecting Run-off —
Literature.. ..c 111-
CHAPTER VII.
The Disposal of the Rainfall.
Pactors of Disposal — The Rate or Intensity of Rainfall— Condition of
Receiving Surfaces and Geological Strata — Effects of Wind — Effects
of Vegetation — Percolation— Evaporation — Evaporation Relations —
Practical Consideration of Losses — Literature 133-
CHAPTER VIII.
Run-off.
Ron-oCf — Influence of Various Factors — Relations of Annual Rainfall
and Run-off of Water Year — Relation of Periodic Rainfall to Run-
off— ^Monthly Keiatlon of Rainfall and Run-off — ^Maximum iStream
Flow— Estimate of Stream Flow 146;
Contents. zi
CHAPTER IX.
RuN-OFF» ( Continued )
Relation of Run-off to Topographical Conditions — Tweets of Geological
Condition on the Run-off— The Influence of Storage on the Distri-
bution of Run-off— Effects of Area on the Run-off — ^The Study of a
Stream from Its Hydrographs — Comparative Run-off and Compara-
tive Hydrographs — Comparative Hydrographs from Different
Hydrologlcal Divisions of the United Statest— Literature 17S
CHAPTER X.
Stream Flow.
Plow in Open Channels — Changes in Value of B^tors with Changes
in Flow — Effects of Variable Flow on the Hydraulic Gradient —
Effects of a* Rising or a Falling Stream on Gradient — Effects of
Channel Condition on Gradient — Effect of Change in Grade and of
Obstructions — Relation of Gauge Heights to Flow — Variations in
Velocity in the Cross-Section of a Stream — Effects of Ice-Covering
on the Distribution of Velocities 1»«.
CHAPTER XI.
The Measurement of Stream Flow.
Necessity for Stream Flow Measurements — ^Methods for the Estimate
or Determination of Flow in Open Channels--Estimates from
Cross-Section and Slope — Weir Measurement — Measurement of
Flow by the Determination of Velocity — The Use of the Current
Meter — Current Meter Ob?ervatons and Com putatlon'— Float
Measurements — The Application of Stream Gaugings — Literature. 21 Jl:
CHAPTER XII.
Water Whescls.
Classification of Water Wheels — Gravity Wheels— Reaction Wheels —
Impulse Wheels — ^Use of Water Wheels — Classification of Tvtr-
bines— Conditions of Operation — Relative Advantage of Reaction
and Impulse Turbines — Relative Turbine Efficiencies — Turbine De-
velopment in the United States — The American Fourneyron Tur-
bine—The American Jonval Turbine — The American Type of Re-
action Turbine — The Double LefTel Turbine — Other American
Wheels — ^Early Development of Impulse Wheels — American Im-
pulse Wheels — Turbine Development In Europe 23 T
:xxi
Contenta,
CHAPTER Xtll,
Th§ Runner — Its Material and Manufacture — Diameter af tte Run*
jier— The Detalli oC the Runiter — Vertical Turblae Bearlnga^— Hoii*
fontal Turbine Bearings — Thrusts-Bearing In Snoqualmle Fall*
Turblus— The Chute Case — Turbine Gates— The Draft Tube. 2S4
tJHAPTER XIV.
Htdbacxics of the TtniBirffi.
"practical Hydraulics of the Turbine^NoniencIature Used la Chapter—
First Principies^lmpuise and Keactlon— The impulse Wheel—
irffect of Angle of Discharge on Efficiency^ — Reaction Wheel-
Graphical Relation of Energy and Velocity In Reaction Turbine*
Turbine Relations— Relation of Turbine Speed to Diameter and
Head— Graphical Expression of Speed Relations— Relations of fp
and Efficiency — Discharge of Turbine at Fixed Gats Openings
Power of a Turbine — The Relation of Diacbarge to the Diameter of
a Turbine — The Relation of Power to the Diameter of a Turbine —
Relation of Bpeed to Di:?charge of Turbines.— Relations of Speed to
Power or Turbines^ Value of Turbine Constants— Literature,,.,
CHAPTER XT.
TunaiKE Testinq.
The Importanrc of Testing Machinery — The Testing of Water Wheeli^—
Smeatoa's Experiments — The Barly Testing of Turbine Water
Wheels — The Testing of Turbines hy James Emerson— The Kolyoke
Testing Flume — The Value of Tests — Purpose of Turbine Testings
P^tors that Influence the Results of a Test — Measurement of Dl»>
Charge — Measurement of Head — Measurement of Spetd of Rota-
tion— Measurement of Power — Efficiency — Illustration of Methods
and Apparatus for Testing Water Wheela— Tests of Wheels In
Place— Literature ,,.* , ..^ ».., Sfl
CHAPTER XVL
The Seiactioh of the Tuhbie^i^
Eflert of Condttons of Operation — Baals for the Selection of the Tur-
bines-Selection of the Turbine for Uniform Head and Power— Ths
Selection of a Turbine for a Given Speed and Power to Work under
a Given Fixed Head— To Estimate the Operating Results of a Tur-
bine under one Head from Test Results Secured at Another Head —
To Estimate the Operating Results of a Turbine of one Diameter
from Test Results of Another Diameter of the Same Series— To
Estimate the Operating Results of a Turbine under Variable
Contents. xiii
Heads from a Test Made under a Fixed Head — A More Exact
Graphical Method fi)r Calculation^— The Construction of the Char*
acteristlc Curves of a Turhlne — The Consideration of the Turbine
from its Characterletlc Curve — Other Characteristic Curves —
Graphical Analysis as Proposed by Mr. W A. Waters 884
CHAPTER XVII.
The Load Cubvb' and Load Factoes, and Theib Influence on thb Design or
THE Power Plant.
Variation In Load — Load Curves of Light and Power Plants.— Factory
Load Curves — ^Load Curve of London Hydraulic Supply Company —
Railway Load Curves — ^Load Conditions for Maximum Returns*— The
Load Curve in Relation to Machine Selection — Influence of Manage-
ment on Load Curve — Relation of Load Curve to Stream Flow and
Auxiliary Power — Literature • 420
CHAPTER XVIIL
The Spied Regxtlation of Turbine Water Wheels.
The Relation of Resistance and Speed — Self-Regulation in a Plant with
Variable Speed and Resistance — ^The Relations Necessary for Con-
stant Speed — ^The Ideal Governor — Present Status — Value of Uni-
form Speed — ^The Problem — ^Energy Required to Change the Pen-
stock Velocity — Hunting or Racing — ^Nomenclature — Shock of
Water Hammer Due to Sudden Changes In Velocity — ^Permissible
Rates of Gate Movement — ^Regulation of Impulse Wheels — Influences
Opposing Speed Regulatiour- Change of Penstock Velocity — Effect
of Slow Acceleration on Water Supplied to Wheel — Value of Racing
or Gate Over-Run — Energy Required to Change the Penstock Velo-
city—Effect of Sensitiveness and Rapidity of Governor — The Fly-
wheel— ^The Stand-Pipe — ^The Air Chamber — Predetermination of
Speed Regulation for Wheel set In open Penstocks — Predetermina-
tion of Speed Regulation, Plant with Closed Penstock, — Predeter-
mination of Speed Regulation, Plant with Standpipe — Application
of Method. Closed Penstock — ^Application of Method, Open Penstock
—Application of Method, Plant with Standpipe— Literature 440
CHAPTER XIX.
The Wateb Wheel Go\'ebnob.
Types of Water Wheel Governors — Simple Mechanical Governors — ^Anti-
racing Mechanical Governors — Details and Applications of Wood-
ward Govemora— The Lombard-Replogle Mechanical Governors —
Essential Features of an Hydraulic Governor— Details of Lombard
Hydraulic Govemor^Operatlng Results with Lombard Governor —
The Sturgess Hydraulic Governor — Test Results with Sturgess Gov-
xiv . Contents.
ernor — Control from Swltchboarfl — Connection of Governors to
Gatea— Relief Valves — Lombard Hydraulic Relief Valves — Sturgess
Relief Valves ...c 470
CHAPTER XX.
ABBAI7GEMENT OF THE REACTION WheEL.
General Conditions — Necessary Submergence of Reaction Wheels^— Ar-
rangement of Vertical Shaft Turbine — ^Arrangement of Horizontal
Turbines— Classification of Wheels — ^Vertical Wheels and Their Con-
nection— Some Installations of Vertical Water Wheels — Some In-
stallations of Vertical Wheels In Series — Some Installations of
Horizontal Water Wheels — Some Installations of Multiple Tandem
Horizontal Wheels — ^Unbalanced Wheels 500
CHAPTER XXI.
The Selection of Machinery and Design of Plant.
Plant Capacity — Influence of Choice of Machinery on Total Capacity-
Effect of Size of Units on Cost — Overload — ^E#conomy In Operation-
Possibilities in Prime Movers — Capacity of Prime Movers — The In-
stallation of Tandem Water Wheels — Power Connection — ^Various
Methods of Connection in Use— Use of Shafting— The Wheel Pit —
Turbine Support— Trash Racks 525
CHAPTER XXII.
Examples of Watee Power Plants.
Sterling Plant— Plant of York-Haven Water Power Company — Plant of
South Bend Electric Company — Spier Falls Plant of the Hudson
River Power Transmission Company — Plant of Columbus Power
Company — Plant of the Dolgevllle Electric Light and Power Co. —
Plant of the Shawlnigan Water and Power Company — Plant of the
Concord Electric Company — Plant of Winnipeg Electric Railway
Co. — Plant of Nevada Power, Mining, and Milling Co. — Literature. . 637
CHAPTER XXIII.
The Relation of Dam and Poweb Station.
Ceneral Consideration — Classification of Types of Development — Con-
centrated Fall — Examples of the Distribution of Water at Various
Plants — Head Races only— Plants Located in Dam— High Head De-
velopments • 661
Contents. xv
CaEIAPTER XXIV,
PsmoiFLiB or CoNBTBucnoN or Dams.
Object of Construction— Dams for Water Power Purposes^-Helght of
Dam — ^Ayallable Head — 'Vhe Principles of Oonstmction of Damfr^
The Foundations of Dams — Strength of Dams — Flood Flowsr^Im?
pervious Ctonstructionr-The Stability of Masonry Dam»— Calcula^
tions for Stability — Further Considerations— Types and Details of
Dams— Literature 579
CHAPTER XXV.
Appendages to Dams.
Movable Dams — Flood Gates — Flash Boards — Head Gates and Gate
Hoists — Flshways — ^Logways — ^Literature 603
CHAPTER XXVI.
Pondage and Storage.
Effect of Pondage on Power — ^Effect of Limited Pondage on the Power
Curve — ^Power Hydrograph at Sterling, Illinois — Effect of Pondage
on other Powers— Effect of Limited Storage — ^Effect of Large Stor-
age— Effect of Auxiliary Power — ^EJffect of Maximum Storage — Cal-
culation for Storage — ^Method of Storage Calculation — ^Analytical
Method— Literature 624
CHAPTER XXVII.
Cost, Value and Sale of Poweik.
¥*inancia] Consideration — Purpose of Development — Cost of Water Pow-
er— Depreciation — ^Annual Cost of Developed Power— Cost of Distri-
bution—Effect of Partial Loads on Cost of Power— Cost of Auxil-
iary Power or Power Generated from other than Water Power
Sources — Market Price of Water Pow^r — Sale of Power — ^An Equi-
table Basis for the Sale of Power— Value of Improvements Intended
to Bffect Economy— Value of a Water Power Property— Literature. 646
CHAPTER XXVIII.
The Investigation of Water Power Projects.
The ESztent of the Investigationr— Preliminary Investigation and Re-
port—Study of Kun-off- Study of Rainfall— Study of Topographi-
cal and Geological Conditions — Study of Flood-flow — Study of
Back Water Curve— Study of Head— Study of Storage and Pond-
age— Study of Probable Load Curve — Study of Power Development
Study of Auxiliary Power— Study of Site of Dam and Power Sta-
tion— Study of Plant Designr— The Estimate of Cost — The Report. . 675
I
xvi Contents.
APPENDICES.
A. Water Hammer — B. Speed Regulation, a more Detailed Analysis
than in Chapter XVIII— C. The Stand-Pipe — D. Test Data of Turbine
Water Wheels— E. Elffect of an Umbrella upon Formation of Vor-
tices—P, EJvaporatlon Tables— G. Two New Water Wheel Governors
— H. Miscellaneous Tables Including: Equivalent Measures and
Weights of Water— Equivalent Units of EJnergy— Velocities in Feet
per Second Due to Heads from 0 to 50 Feet— Three Halves Powers
of Numbers, 0 to 100 — Five Halves Powers of Numbers, 0 to 50 — ^Re-
lation of mean Rainfall to Maximum and Minimum Discharge
of Various Rivers — Rainfall, Run-oft and Evaporation for Storage.
Growing and Replenishing Periods or 12 Streams of the United
States *.. 685-757
WATER POWER ENGINEERING.
CHAPTER L
INTRODUCTION.
THE HISTORY OF WATER POWER DEVELOPMENT.
I. Early Development of Water Power. — Most methods of
power generation can be traced to an origin at no very remote
period. Their development has been within historic times. The
first development of water power, however, antedates history.
Its origin is lost in remote antiquity.
Air and water, both physical agents most essential to life, have
ever been the most obvious sources of potential energy and have
each been utilized for power purposes since the earliest times.
Beside the Nile, the Euphrates, and the Yellow Rivers, thou-
sands of years ago the primitive hydraulic engineer planned and
constructed his simple forms of current wheels and utilized the
energy of the river current to raise its waters and irrigate the
otherwise arid wastes into fertility. Such primitive wheels were
also utilized for the grinding of corn and other simple power
purposes. From these simple forms and primitive applications
have gradually been developed the modern water power installa-
tions of to-day.
2. The Earliest Type of Water Wheel— The crude float wheel
driven directly by the river current developed but a small por-
tion of the energy of the passing stream. The Chinese Nora,
built of bamboo with woven paddles, is still in use in the east
(see Fig. i), and was probably the early form of development of
^his type of wheel. The type is by no means obsolete for it is
yet used for minor irrigation purposes in all countries. These
^vheels, while inefficient, served their purpose and were exten-
sively developed and widely utilized. One of the greatest de-
velopments of which there is record was the float wheel installa-
Introduction.
Pig. 1, — Chinese Nora, or
Float Wlieel Used
Present.
From Earliest Times to
lion used to operate the pumps at London Bridge for the first
water supply system of the city of London, and constructed
about 1581 (see Fig. 2). In all such wheels the paddles dip into
the unconfined current which, when impeded by the wheel, heads
up and passes around the sides of the wheel and thus allows^
only a small part of the current energy to be utilized. H
3. The Undershot Wheal, — The introduction of a channel con-
fining the water and conducting it to a point where it could be
applied directly to the undershot wheel, was an improvement that
permitted the utilization of about thirty per cent, of the theo-J
rig. E. — Float Wbeel Opemttng; Fiunps for Water Supply ot London 1S8
(From Matthews' Hydraulia Loud. 1835.)
The Overshot and Breast Water Wheel. 3
retical power of the water. This form of water wheel was most
widely used for power development until the latter half of the
eighteenth century.
In the float and undershot wheels the energy of water is ex-
erted through the impact due to its velocity. The heading up
of the water, caused by the interference of the wheel, results
also iii the exertion of pressure due to the weight of the water,
but this action has only a minor effect. The conditions of the
application of the energy of water through its momentum is not
favorable to the high efficiency of this type of wheels and the
determination of this fact by Smeaton's experiments undoubt-
edly was an important factor in the introduction and adoption of
the overshot water wheel.
.s^i^^i
Fig. S.— Breast Wheel Used From About 1780 to About 1870.
4. The Overshot and Breast Water Wheel. — In the overshot
water wheel the energy of water is applied directly through its
weight by the action of gravity, to which application the design
of the wheel is readily adapted. Such wheels when well con-
structed have given efficiencies practically equal to the best
modem turbine, but on account of their large size and the serious
effects of back-water and ice conditions, they are unsatisfactory
for modern power plants (see Fig. 11).
Following the work of Smeaton, the breast wheel (see Fig. 3)
was developed in England largely through the work of Fairbairn
^^^ Rennie. The latter in 1784 erected a large wheel of this
^ype to which he applied the sliding gate from which the water
flowed upon the wheel instead of issuing through a sluice as
formerly. About this time the fly-ball governor, which had been
^^igned and adapted as a governor for steam engines by Watt,
^^ applied to the governing of these wheels and by means of
these governors the speed of the wheel under varying loads was
iDLroduclioo.
Fig, 4.— Breast Wheel About 1790 Showing Early Application of Governor,
(After Glynn.)
kept sufficiently constant for the purpose to which they were
then applied, (See Fig* 4*)
Another mode of applying water to wheels under low falls was
introduced by M. Poncelet, (See Fig< 5.) Various changes and
improvements in the form of buckets, in their ventilation so as
to permit of complete filling and prompt emptying, and in their
structure, tcxjk place from time to time, and until far into the
middle of the nineteenth century these forms of wheels were
widely used for water power purposes.
Fig. 5.— Poticelet's Wheel
5. The Development of the Turbine. — The invention of any
important machine or device is rarely the work of a single mind.
In general such inventions are the result of years of experience
of many men which may be simply correlated by some designer.
Fundamental Idea of the Turbine.
to 'whom often undue credit is g^ven* To the man who has
gathered together past experiences and embodied them in a new
and useful invention and perhaps through whose energy practical
applications are made of such inventions, the credit is frequently
assigned for ideas which have been lying dormant, perhaps
through centuries of time. Every inventor or promotor of val-
uable improvements in old methods and old construction is en-
titled to due credttj but the fact should nevertheless be recalled
that even in the greatest inventions very few radical changes are
embodied, but old ideas are utilized and rearranged and a new
and frequently much more satisfactory combination results. Im-
provements in old ideas are the improvements which are the
most substantial. Inventions which are radically new and strictly
original are apt to be faulty and of little practical value*
I
^FH5. 6, — Anctent Indian Water WheeK (After Glynn J ContalnEng FuB^
dameutal Suggest ion of Both Turbine and Impulse Wlieela.
6, Fundamental Ideas of the Turbine. — ^The embryo turbine
may be distinguished in the ancient Indian water mill (see Fig. 6).
A similar early type of vertical wheel used in Europe in the six-
teenth century, the illustration of which was taken from an an-
cient print (see Sci. Am. Sup* Feb. 17, '06) is shown in Fig- J.
Barkers mill in its original form or in the form improved by
M* Mathon de Cour, embodied the principal idea of the pressure
6 Introduction*
turbine, and was used to a considerable extent for mill purposes.
In 1845 James Whitlaw suggested an improved form which was
used in both England and Gennany early in the nineteenth cen-
tury. (See Fig. 8.) Many elements of the modern turbine were
conceived by Benjamin Tyler, who received letters patent for
what he termed the "Wry Fly" wheel in 1804. T!ie description of
this wheel as contained in the patent specifications is as follows :
Fig. 7,— Early Vertical Wheel.
Containing fundamental auggeatioii of tli»
Turbine.
'The Wr>' Fly is a wheel which, built upon the lower end of a
perpendiciilar shaft in a circular form, resembles that of a tub.
It is made fast by the insertion of two or more short cones,
which, passing through the shaft, extend to the outer side of the
wheel. The outside of the wheel is made of plank, jointed and
fitted to each other, doweled at top and bottom, and hooped by
three bands of iron, so as to make it water-tight ; the top must
be about one-fifth part larger than the bottom in order to drive
4
Barker's MiU. 7
the hoops, but this proportion may be varied, or even reversed,
according to the situation of place, proportion of the wheel, and
quantity of water. The buckets are made of winding timber, and
placed inside of the wheel, made fast by strong wooden pins
drove in an oblique direction ; they are fitted to the inside of the
tttb or wheel, in such a manner as to form an acute angle from
the wheel, the inner edge of the bucket inclining towards the
w^ter, which is poured upon the top, or upper end of it about
twelve and a half degrees ; instead of their standing perpendicular
with the shaft of the wheel they are placed in the form of a
screw, the lower ends inclining towards the water, and against
the course of the stream, after the rate of forty-five degrees ; this,
however, may be likewise varied, according to the circumstances
of the place, quantity of water, and size of the wheel."
Elevation.
Plan and Partial Section.
Fig. & — Early Vertical Wheel. Containinjir Fundamental Suggestion of the
Tnrbine. (After Glynn. )
Inlroduction*
Fig. 9. — ^Roue A* CurveB (After Glimii).
From the description it will be noted that, with the exception
of the chuteSp the principal features of the modern turbine were
here anticipated. The "Wry Fly" wheel was an improvement on
the "tub" wheel which was then in use to a considerable extend
in the country.
These various early efforts received their first practical con-
summation and modern solution ihrough various French in-
ventors early in the nineteenth century. The "Roue a Ciives*'
(Fig. 9) and the **Roue Volant" {Fig. 10) had long been used
in France, and were the subject of extensive tests by MM* Pio-
bert and Tardy at Toulouse. Those various wheels received the
water tangentially through an opening or spout, being practically
an improvement on the old Indian mill by the addition of a rim
and the modification of the form of buckets.
7. The Modem Turbine, — The next improvement in the United
States consisted in the addition of a spiral or scroll case to the
wheel, by means of which the water was applied equally to all
parts of the circumference passing inward and downward through
the wheel. To the French inventors, Koechlin, Foumeyron and
Jonval, is largely due the design of the turbine in a more modern
and practical form. By the middle of the nineteenth century
these wheels had met with wide application in France and been
■
I
4
The Modern Turbine.
I
Fig. 10. — Roue Volant (After Glynn).
adopted and considerably improved by American and German
engineers, but were scarcely known in England. (See "Power
of Water," by Jos. Glynn, 1852.) The turbine was introduced
into the United States about 1843 ^Y Elwood Morris, of Penn-
sylvania, but was developed and brought to public attention more
largely through the inventions of Uriah A. Boyden, who in 1844
designed a seventy-five horse-power turbine for use at Lowell,
Mass, (See Fig. 132, page 251.) The great advantage of the
turbine over the old style water wheel may be summarized as fol-
lows: (See Figs. 11 and 12).
First: Turbines occupy a much smaller space.
Second: On account of their comparatively high speed they
"CJin'frequently be used for power purposes without gearing and
with a consequent saving in power.
Third: They will work submerged.
Fourth: They may be utilized under any head or fall of water.
(Turbines are in use under heads as low as sixteen inches and
as high as .several hundred feet.)
Fifth: Their efficiency, when the wheel is properly constructed,
« comparatively high.
Sxth: They permit a greater variation in velocity without ma-
terial change in efficiency.
to
Imroduclion.
The Francis Turbine.
zx
Seventh: They are more readily protected from ice interfer-
ence.
8, The American or Francis Turbine. — ^Through the efforts of
Uriah A. Boyden and James B. Francis (1849), ^^e Fouraeyron
turbine became the leading wheel in New England for many
years.
In 1838 Samuel B. Howd of Geneva, New York, patented the
"inward flow" wheel, in which the action of the Fourneyron tur-
bine was reversed. This seems to have been the origin of the
American type of turbine, and the Howd wheel was followed by
a large number of variations of the same general design on
which American practice has been based for many years. About
^849, James B. Francis designed an inward flow turbine of the
same general t3rpe as the Howd wheel. Two of these wheels
IS. — Inward Flow Wheel by S. B. Howd t After Francis).
^'cre constructed by the Lowell Machine Sliop for the Boott
Cotton Mills. In the Lowell hydraulic experiments (page 61)
^Jr. Francis refers to the previous patent of Howd and says :
"Under this patent a large number of wheels have been con-
structed and a great many of them are now running in diflferent
I?
Introduction.
parts of the country. They are known in some places as the^
Howd wheels in others as the United States wheel. They have
uniformly been constructed in a very simple and cheap manner
in order to meet the demands of the numerous classes of millers
and manufacturers who must have cheap wheels if they have
any." M
Fig. 13 shows a plan and vertical section of the Howd wheels
as constructed by the owners of the patent rights for a portion
of the New England states. In this cut g indicates the wooden
Fig, 14, — Original Francis Turblna
guides by which the water is directed on to the buckets; W ifi
dicates the wheel which is composed of buckets of cast iroi!
fastened to the upper and lower crowns of the wheel by bolts.
The upright crown is connected with the vertical shaft S by arms.
The regulating gate is placed outside of the guides and is made
of wood. The upright shaft S runs on a step at the bottom (noi
shown in the cut). The projections on one side of the buckets.
it was claimed, increased the efficiency of the wheel by diminish^
ing the waste of the water. f
The wheel designed by Francis was on more scientific lines, of
lietter meclianical construction (see Fig. 14) and is regarded bi
Modem Changes in Turbine Practice.
13
many as the origin of the American turbine. The credit of this
design is freely awarded to Francis by German engineers, this
type of wheel being known in Germany as the Francis Turbine.
The Francis wheel was followed by other inward flow wheels of
a more or less similar type. The Swain wheel was designed by
A. M. Swain in 1855. The American turbine of Stout, Mills and
Temple (1859), ^^^ Leffel wheel, designed by James Leflfel in
i860, and the Hercules wheel, designed by John B. McCormick
in 1876, are among the best known and earliest of the wheels of
this class.
9. Modem Changes in Turbine Practice. — A radical change has
taken place in later years in the design of turbines by the adop-
tion of deeper, wider and fewer buckets which has resulted in a
great increase of power as shown by the following table from a
paper by Samuel Webber (Transactions of Am. Soc. M. E.
Vol. XVII) :
T1811 h— Showing Size, Capacity and Power of Varimis Txirbinee Under
a ee-foot Head.
Inches
Diameter.
Cubic Feet
Water per
Second.
Horse
Power.
Boyden-Fourneyron . .
Ri«lon
Bisdon "L. C."
B»don"L. D."
LeHel, Standard
Wfel, Special
Tyler..
SviiiL
Hunt, "Swain bucket'
Hnnt, New Style
lAl, ••Samson"
"Htttsoles"
'TieU»'»
^ 8wtin
36
:^6
36
36
35
36
36
36
36
35
36
25
86
22.95
35.45
48.27
80.
40.46
60.
40.7
58.2
48.8
98.
109.1
107.6
108.8
89.5
55
89
121
199
96
148
95.8
140
121
289.74
264
253.5
266
215
By 1870 the turbine had largely superseded the water wheel
for manufacturing purposes at the principal water power plants
in this country. The old time water wheel has since become of
comparatively small importance, but it is still used in many iso-
'^ places where it is constructed by local talent, and adapted
to local conditions and necessities.
14 Introduction.
The current wheel is still widely used for irrigation purposes
and in many instances is a useful and valuable machine.
10. Historical Notes on Water Power Development. — ^Water
mills were introduced at Rome about seventy years B. C. (see
Strabo Lib. XII), and were first erected on the Tiber. Vitruvius
describes their construction as similar in principle to the Egyp-
tian Tympanum. To their circumference were fixed floats or
paddles which when acted upon by the current of the stream
drove the wheel around. Attached to this axis was another ver-
tical wheel provided with cogs or teeth. A large horizontal wheel
toothed to correspond with it worked on an axis, the upper head
of which was attached to the mill stone. The use of such water
wheels became very common in Italy and in other countries sub-
ject to Roman rule.
Some of the early applications of water power are of interest.
In 1 581 a pump operated by a float wheel was established at
London Bridge to supply the city of London with water. In
1675 ^ri elaborate pumping plant driven by water wheels was
established on the Seine river near Saint Germain. For this
plant a dam was constructed across the river and chutes were
arranged to conduct the water to the undershot water wheels.
Thcse were twelve .pr more in number, each operating a pump
that raised the waters of the Seine into certain reservoirs and
aqueducts for distribution.
The pumping of water for agricultural irrigation and drainage,
domestic supplies and mine drainage, was undoubtedly the first
application of water power, and still constitutes an important
application of water. Fig. 15, from an article by W. F. Dupfec,
published in Cassier's Magazine of March, 1899, illustrates a
primitive application of the water wheel to the pumping of water
from mines. The frontispiece also shows the great Laxy over-
shot water wheel in the Isle of Man which is still used for mine
drainage. The wheel is about seventy feet in diameter and the
water is brought froin the hills a considerable distance for power
purposes.
11. Development of Water Power in the United States. — ^In
this country one of the first applications of water power was the
old tidal mill on Mill Creek near Boston, constructed in 1631,
which was followed by the extensive developments of small
powers wherever settlements were made and water power was
Development of Water Power.
IS
available. Often availability of water power determined the
location of the early settlement.
About 1725 the first power plant was established along the
Niagara River. This was a water-driven saw-mill constructed
Ckronologieal Development of Water Power of the United States to 1898.
Year.
Lowell, Mass
Nwhoa, N. H
<5ohoee,N. Y
Norwich, Conn
ADgQBta,Me. ,
Mmchester.N. H ,
Hooksett, N. H
Liwienoe, Mass.
Aopirta,Ga
Holyoke, Mass
Uvnston, Me.
Oolomboa, Ga
Bocbeeter, N. Y
St. Anthony Falls, Minn. .
Kiagara,N. Y. (Hy. canal)
Turner's Falls. Conn
FoxRiver, Wis
KiminghaiD, Conn
Bingor, Me.
Augusta, Ga
timer's Falls. N. Y
Mechanicsville, N. Y
^ Cload, Minn
little Falls. Minn
Spokane, Wash
Howland, Me
^wtt Falls, Mont
Aiatln, Texas.
gwhSte. Marie, Ont
Johom, Cal
^id,N.H
JWenajMont
Junneapolis, Minn
Mechanicsville, N. Y
1822
1823
1826
1828
1834
1835
1841
1845
1847
1848
1849
1850
185(>
1857
18()1
1866
1866
1870
1876
1876
1882
1882
1885
1887
1888
1888
18<»0
1891
1S91
1891
1894
1894
1896
1897
1897
:898
Fall
Ft.
36
36
104
16
17
52
14
30
50
50
50
25
236
50
90
35
185
22
9
50
30
20
14
14
70
22
42
60
18
55
13
170
446
32
18
18
Minimum
Horse
Power.
11,845
1,200
9,450
700
3,5U0
12,000
1,81'0
11,000
8,500
14,000
11,900
10,000
8,000
15,500
15,000
10,000
1,000
1,767
8,500
1,125
3,636
4,500
4,000
18,000
6,000
16,000
10,000
10,000
6,200
5,000
50,000
2,U40
10,000
6,000
3,270
Drainage
AreaSq.
Miles.
4,088
516
3,490
1,240
5,907
2,839
2,791
4,625
8,830
8,000
3,200
14,900
2,474
19,736
271,000
6,000
6,449
2,000
7,200
6,830
2,650
4,476
13,250
11,084
4,180
22,000
40,000
51,600
2,350
271,000
360
14,900
19,737
4,478
^7 the French to furnish lumber for Fort Niagara. Mr. J. T.
Fanning gives the following list of the dates of establishing some
^ the principal water powers of the United States :
The last few years have witnessed a still more rapid develop-
ment. The increase in manufacturing industries and other de-
i6
Inti'oduclJoo
mands for power and energy, I lie increased cosi of coal, am
improvement in electrical methods of generation and tram
sion have all united to accelerate the development of water p
plants. Water powers once valueless on account of their
tance from centers of manufacturing and population are
accessible and such powers are rapidly being developed and
energy brought into the market.
rig.
IS.— Earl f Application of Undershot Water Wheel to Mtne
Date Unknown (from C&ssiers Mag. March, 1S99J
Dri
LITERATURE.
I
AppletoTi*a Cy doped la of Applied Merhanlcs* Modem Me Chan la
S, pp* 891-901. Description of the development of the
Spon*s Dictionary of Knglneerlng. Barker's Mill, pp. 230-23&.
do. Float Water Wheels (includtng undershot wheels), pp. 15
do, Overshot Water Whet^ls, p, 2557.
do. PoDcelet*s Water Wheels, p 2G(J0. ^H
do. Turbine Water Wheels, pp. 3014-3023, ^|
Knights Mechanical Dictionary, Vol. 3, Water Wheels, p. 27*
bines, pp. 2C56-2C^8.
i
Literature. i7
4. Emerson, James. Hydrodynamics. Published by author. Willimansett,
Mass. 1892. Describes several types of American turbines.
5. Matthews, William. Hydraulia. London, 1836. (Description of London
Bridge Water Wheels, p. 28.)
6. Palrbairn. William. Machinery and Mill work. Description of undershot
water wheel, pp. 145-150; description of earlier types (^ tur-
bines, pp. 151-173.
7. Francis, James B. Lowell Hydraulic Experiments, pp. 1-70. Descrip-
tion and tests of Boyden-Fpurneyron Tremond Turbines; also
the Boyden-Francls "Center-Vent" Turbine, in which the Flow
was Radially Inward. New York, D. Van Nostrand, 1883.
& Welsbach, P. J. Mechanics of Engineering, vol. XL Hydraulics and
Hydraulic Motors. Translated by A. J. DuBois. New York.
J. Wiley & Sons.
9. Morin, Arthur. Experiments on Water Wheels having a Vertical Axis,
Called Turbines, 1838. Translated by EUwood Morris in Jour.
Franklin Inst, 3d ser.. vol. 6, 1843. pp. 234-246, 289-302. 370-377.
370-377.
10. Morris, ESlwood. Remarks on Reaction Water Wheels Used in the
United States and on the Turbine of M. Foumeyron. Jour.
Franklin Inst, 3d ser.. Vol. 4, 1842, pp. 219-227, 289-304.
11. Morris, EUwood. Experiments on the Useful Effect of Turbines in the
United States. Jour. Franklin Inst., 3d ser.. Vol. 6, 1843,
pp. 377-384.
12. Wbitelaw, James. Observations of Mr. EUwood Morris's Remarks on
Water Wheels. Jour. Franklin Inst, 3d ser.. Vol. 8, 1844.
pp. 73-80.
13. Franklin Institute. The Koechlin Turbine. Jour. Franklin Inst, 3d
ser.. Vol. 20, 1850, pp. 189-191. (Report of experiments made
by members of the institute at the request of Emile Qeyelin,
who introduced the Koechlin turbine at Dupont's powder mill.)
H. Ewbank, Thos. Hydraulic and Other Machines for Raising Water. New
York, 1847.
15. Qeyelin, Emile. Experiments on Two Hydraulic Motors, Showing the
Comparative Power Between an Overshot Wheel and a Jonval
Turbine made for Troy, N. Y. Jour. Franklin Inst. 3d ser..
Vol. 22, 1851, pp. 418, 419.
16 Glynn, Joseph. Power of Water. London, 1850. pp. 39-97. Weales
Scientific Series.
17. Webber, Samuel. Ancient and Modem Water Wheels. Eng. Mag., Vol. 1,
1891, pp. 324-331.
18. Frlzell, J. P. The Old-Time Water Wheela of America. Trans. Am. Soc
C. E., Vol. 28, 1893, pp. 237-249.
^5- Aldrlch, H. L. Water Wheels. Description of Various Types of Ameri-
can Wheels. Power, Vol. 19, No. 11, 1894.
20. Francis, James. Water Power in New England. Eng. Rec, Vol. SS»
1896. pp. 418, 419.
1
1 8 Introduction.
21. Geyelin, Emile. First Pair of Horizontal Turbines ever Built Working
on a Ck>nimon Axis. Proc. Eng. Club, Philadelphia, Vol. 12,
1895. pp. 213, 214.
22. Francis, James. Water Power in New England. Eng. Rec. Vol. 33,
1896, pp. 418, 419.
23. Webber, Samuel. Water Power, its Generation and Transmission. Trans.
Am. Soc. Mech. Eng., Vol. 17, 1896, pp. 41-57.
24. Tyler, W. W. The BJvolution of the American Type of Water WhoeL
Jour. West Soc. Eng., Chicago, Vol. 3, 1898, pp. 879-901.
25. Johnson, W. C. Power Development at Niagara. Jour. Asso. Eng. Soc,
July, 1899, pp. 78-90. Hist of early development of power at
Niagara.
26. Christie W. W Some Old-Time Water Wheels. Description of Various
old wheels in Eastern U. S. Eng. News, Vol. 42, 1899, pp.
394-395.
27. Ruchel, E. Turbines at the World's Fair, Paris, 1900. Review of Tur-
bine development in various countries. Zeitschr. d ver Deutsch,
Ing. p. 657. 1900.
28. Foster, H. A. The Water Power at Holyoke. Jour. Asso. Eng. Soc., Vol.
25, 1900, pp. 67-34.
29. Thomas. R. Development of Turbine Construction. Zeitschr. d ver
Deutsch. Ing. p. 409, 1901.
30. Rice, A. C. Notes on the History of Turbine Development in America.
Eng. News, Vol. 48, 1902, pp. 208-209.
31. Fanning, J. T. History of the Development of American Water Powers.
Rept 22d Ann. Meeting, Am. Paper and Pulp Asso., 1898, pp.
16-24. Progress in Hydraulic Power Development Eng. Rec-
ord, Vol. 47, 1903, pp. 24-25.
32. Fanning, J. T. Progress in Hydraulic Power Development BJng. Rec-
ord, Jan. 3d, 1903.
33. Slckman, A. F. The Water Power at Holyoke. Jour. N. E. W. W. Afi80.»
Vol. 18, 1904, pp. 337-351. Historical.
CHAPTER II.
POWER.
12. The Development of Potential Energy. — ^The development
of natural sources of potential energy, the transformation of such
energy into forms which can be utilized for power, and its trans-
mission to points where it can be utilized for commercial pur-
poses, constitutes a large portion of the work of the engineer.
The water power engineer primarily deals with energy in the
form of flowing or falling water, but his knowledge must extend
much further for he encounters other forms of energy at every
turn. Much of the energy available from the potential source
will be lost by friction in bringing the water to and taking it
from the wheel. Much is lost in hydraulic and mechanical fric-
tion in the wheel ; additional losses are sustained in every trans-
formation, and, if electric or other forms of transmission are
used or auxiliary power is necessary for maintaining continuous
operation, the engineer will be brought in contact with energy
in many other forms.
13. Definition of Energy. — Energy is the active principle of
nature. It is the basis of all life, all action, and all physical
phenomena. It is the ability to exert force, to overcome resist-
ance, to do work. All physical and chemical phenomena are but
"manifestations of energy transformations, and all nature would
DC rendered inactive and inanimate without these changes.
14. Solar Energy the Ultimate Source. — A brief consideration
<^f the various sources of potential energy makes the fact mani-
fest that solar energy is the ultimate source from which all other
forms are directly or indirectly derived. The variations in solar
heat on the earth's surface produces atmospheric currents often
^f tremendous power. This form of energy may be utilized, in
*ts more moderate form, to drive the sailing vessel and the wind-
n^JI, and in other ways to be of service to man. The energy of
fuel is directly traceable to solar action. Through present and
past ages it has been the active cause of chemical and organic
20 Power
change and growth. From this has resulted fuel supplies avail-
able in the original form of wood, or in the altered forms, from
ancient vegetation to the forms of coal, oil and gas, and from
which a large portion of the energy utilized commercially is
derived.
A brief study of meteorological conditions shows that through
the agency of solar heat, and the resulting atmospheric move-
ment, a constant circulation of water is produced on and near
the earth's surface. Hundreds of tons of water are daily evapor-
ated from the seas, lakes, rivers and moist land surface, rise as
vapor into the atmosphere, circulate with the winds, and, under
favorable conditions, are dropped again upon the earth's surface
in the rainfall. Those portions of the rain that fall upon the
land tend to flow toward the lower places in the earth's crust,
where lie the seas and oceans, and such portions of these waters
as are not absorbed by the strata, evaporated from the surface
or utilized in plant gfrowth, ultimately find their way to theSe
bodies of water to again pass through this cycle of changes which
is constantly in progress. Thus we find water always in motion,
and always an active agent in nature's processes. Due to its
peculiar physical properties and chemical relations, it is one of
the essential requisites of life, and is also of great importance in
nature's processes through the energy of which it is the vehicle.
15. No Waste of Energy in Nature. — Active continuous en-
ergy transformation is^a most important natural phenomenon.
Changes from one form to another are constantly in progress.
In nature's transformations energy is always fully utilized. As
the running stream plunges over the fall, the potential energy,
due to its superior elevation, is transformed into the kinetic en-
ergy of matter in motion, and through the shock or impact the
kinetic energy is transformed into thermal energy due to a higher
temperature, which again may be partially changed in form by
radiation or vaporization. Thus the quantity of energy is con-
tinually maintained, while its quality or conditions constantly
vary. There is, and can be, no waste or loss of energy as far as
nature itself is concerned. Wasted or lost energy are terms that
apply only to energy as utilized in the service of man. Nature
itself never seems to utilize the entire quantity of energy from
one source for the development of energy of a single form, but
always differentiates from one form into a number of other forms.
When the engineer therefore attempts to utilize any source of
Laws of Energy Conservation. 2i
potential energy for a single purpose, he at once encounters this
natural law of differentiation and finds it impossible to utilize
more than a portion of the energy used in the manner in which
he desires to utilize it. Much of this loss may be due to the form
of energy available, much to the medium of transformation and
transmission, and much to physical difficulties which it is im-
possible to overcome.
i6. Laws of Energy Conservation. — Primarily it should be
fully understood and clearly appreciated that matter and energy
can neither be created nor destroyed. Both may be changed in
form or they may be dissipated or lost so far as their utilization
for commercial needs is concerned. But in one form or another
they exist, and their total amount in universal existence is al-
ways the same. In any development for the utilization, trans-
formation or transmission of energy, the following fundamental
axioms must be thoroughly understood and appreciated:
First : That the amount of energy which can be actually utilized
in any machine or system can never be greater than the amount
available from the potential source.
Second: That the amount of energy which can be utilized in
any such system can never be greater than the difference be-
tween the amount entering the system and the amount passing
from the system as waste in the working medium.
17. Efficiency. — Efficiency is the ratio or percentage of energy
utilized to energy applied in any system, part of a system, ma-
chine or in any combination of machines.
The efficiency df a given machine or mechanism, or the per-
centage of available energy which can be obtained from a given
system of generation and transmission therefore can never be
greater than represented by the equation :
E E'
Efficiency or amount of available energy = — =; — in which
E equals the energy in the working medium entering the machine
E' equals the energy in the working medium passing from the machine.
18. Natural limit to efficiency. — The total energy in a workins;
medium such as water, steam, air, etc., is the energy measured
from the basis of the absolute zero for the medium which is
being considered. For example, the average surface of I_^ke
Michigan is 580 feet above sea level ; each pound of water, there-
fore, at lake level contains 580 foot pounds of potential energy.
This amount of energy must therefore be expended in some man-
22 Power.
ner by each pound of water passing from the lake level to the
ocean level, which may be regarded as the absolute zero refer-
ence plane for water power. This energy cannot be utilized at
Chicago for there no fall is available. A small portion of this
energy is now utilized in the power plants at the falls of Niagara.
Some energy will be ultimately utilized on the Chicago Drainage
Canal, where a fall of some thirty-four feet is available from the
controlling works to Joliet. Perhaps ultimately in its entire
course one hundred and seventy feet of fall may be utilized by
the waters of the drainage canal, in which case the absolute avail-
able energy of each pound of water cannot be greater than shown
by the following equation :
Available energy = ^ — = ^^ = .2931, or 29.31 per cent.
With any other form of energy the same conditions also pre-
vail. Consider a pound of air at 760 degrees absolute tempera-
ture Fahr., and at 75 pounds absolute pressure. The number of
heat units contained will be given by the equation :
Heat units = temperature X weight X specific heat.
B. T. U. = 760 degrees XIX .1«^> = 128.
To Utilize all of the energy in this air, it would be necessary
to expand it down to a temperature of absolute zero and exhaust
it against zero pressure. In any machine for utilizing com-
pressed air, it will be necessary to exhaust it against atmospheric
pressure. This will expand the air 3.10 times, and if expanded
adiabatically it will have a final temperature of 474 degrees. The
heat units in the exhaust will therefore be as follows :
B. T. U. = 474 degrees X 1 X .169 = 80,
and the available energy will be as follows :
228 80 48
Available energy = — = -^ = .375, or 37.5 percent.
In this case also the temperatures vary directly as the heat
units, and are therefore a measure of available energy:
A -1 ui 760 — 474 rt-»r o- m
Available energy = ^r-r-r — = .375 or 3/. 5 per cent.
/oU
In the ideally perfect furnace the efficiency is somewhat higher.
The fuel may be consumed at a temperature of about 4,000 Fahr.
absolute, and the gas may be cooled before escaping to about 600
Fahr. In this case the possible efficiency or available energy is:
Practical Limits to Efficiency, 23
4000 660
Available energy = -^^ — = .832 or 83.2 per cent.
The above examples show, therefore, the limits which nature
itself places on the proportion of energy which it is theoretically
possible to utilize. For such losses the engineer is not account-
able except for the selection of the best methods for utilizing
such energy. The problem for his solution is, what amount of
this available energy can be utilized by efficient machines and
scientific methods.
19, Practical Limits to Efficiency. — The preceding equations
are the equations of ideally perfect machines. Of this available
energy only a portion can be made actually available. In practice
we are met with losses at every turn. Some energy will be lost
in friction, as radiated heat, some in the slip by pistons, or as
leakage from defective joints. In many other ways the energy
applied may be dissipated and lost. From this it follows :
The amount of energy which can be utilized can never be
greater than the difference between the amount supplied to any
given machine or mechanism, and the amount lost or consumed
in such machines by friction, radiation or in other ways. Hence
it follows that the efficiency of a given machine, or the percent-
age of energy available, or which can be obtained from the ma-
chine, can never be greater than the following:
!,« . E — fE' +E' + E"-fE"etc.). , . .
Efficiency = ^ • ^ ' in which
B 8 total energy available
E* E' E" etc. = the energy lost in friction and in various other ways, in
the machine or system, and rejected in the exhaust from the same.
Every transmission or transformation of energy entails a loss,
hence, starting with a given quantity of energy, it gradually dis-
appears by the various losses involved in the mechanism or ma-
chines used. Other things being equal, the simpler the trans-
niission or transformation, the greater the quantity of the orig-
inal amount of energy that can be utilized.
The term efficiency as here applied represents always the ratio
"Ctween the energy obtainable from the mechanism or machine
and the actual energy applied to it.
Therefore the efficiency of a pumping engine is the ratio be-
tween the energy of the water leaving the pump and the energy
^ the steam applied to the engine.
24
Power.
The efficiency of a hydro-electric plant is the ratio between the
energy in the electric current delivered at the switch board and
the energy in the water entering the water wheel.
The efficiency of the dynamo in the same plant is the ratio be-
tween the energy furnished by the dynamo and the energy ap-
plied to it.
If a shaft receives from an engine lOO horse power and de-
livers 90, ten horse power being lost in friction, etc., the efficiency
of the shaft transmission is 90 per cent.
If a steam engine receives 1,000,000 heat units from the steam
it uses, and is able to deliver only the equivalent of 10,000 heat
units; i. e., 7,780,000 foot pounds of work, the efficiency of the
engine is only one per cent.
20. Efficiency of a Combined Plant. — In any plant or connected
arrangement of mechanisms and machines for the transforma-
tion or transmission of energy the efficiency of the plant is the
product of the efficiency of each of its parts.
Hence, to estimate total efficiencies, the efficiency of each part
may be estimated, and the combined efficiency then obtained.
From the same calculation, the necessary relations between the
input and the output of energy can be obtained. Thus, if a
boiler has an efficiency of 50 per cent., and an engine has an
efficiency of 10 per cent., the combined efficiency will be .50X.10
=.05 or five per cent.
In the following examples the loss and efficiency of the unit
and the combined efficiency of the various units in the system
are shown.
FIRST EXAMPLE.
Example of Energy Loss in Well-Designed Steam Power Plant.
Per Cent
Lost.
Per Cent
Efficiency
Furnace
Ik)iler
Steam Pipe
Enjijine
Belt
Shafting, Belts and Counter Shafts
Lathes or other Machine Tools
Percentage of original energy utilized
useful work
20
15
5
94
5
40
60
80
85
95
0
95
(K)
50
Net Effi-
ciency from
Potential
Source.
80
68
64.5
3.87
3.67
2.2
1.1
1 1
Efficiency of a Combined Plant.
25
SECOND EXAMPLE.
Exampie of Energy Lo9B in Ilydfnulie Plant for Electric Lighting,
Per Cent
Lost.
Percent
Efficiency
Net Effi-
ciency from
Potential
Source.
H4^ And Tnil Raree . .
5
20
15
6
5
8
10
20
80
95
80
85
95
95
92
90
80
20
95
Turbine.
76
Gearing
64 6
Shaft .'.;
60 37
Belt
57 35
Generator
52.76
Line Loss
47 48
Tranftformer .•
87.98
JjAinp ...c ..*.x
7 00
Percentage of original energy utilized in
oaef ul work .*
7.60
THIRD EXAMPLE.
Example of Energy Lost in Steam and Electric Pumping Plant
Per Cent
Loet.
Per Cent
Efficiency
Net Effi-
ciency from
Potential
Source.
Boiler and Furnaco.
bteam Pipe
Eneine
Belt
Generator.
Line
Motor
Pomp.
Suction and Discharge Pipe
PercentRge of original energy utilized in
oseful work
30
5
90
5
20
10
10
26
20
70
95
10
95
80
90
90
75
80
70
66.6
6.65
6.82
5.05
4.55
4.09
3.06
2.45
2.45
21. Capacity of Each Part of a System Not IdenticaL — In each
of the transmission systems outlined above a much larger
amount of energy enters the first unit of the system than is de-
livered by the last. Each unit in the system receives a decreas-
ing amount of energy.
In consequence, the first units in the system must be of greater
proportional capacity, and in practice each unit must be selected
of a size or capacity suited for its position in the system. Thus
in the first example, for each 100 units of energy rereived by the
furnace, the engine receives but 64.5, and the shafting but 4.
26 Power,
aa. The Analysis of Losses. — In estimating power losses the
loss in each step from the generation to the utilization of the
power should be carefully examined. Four steps may ordinarily
be considered in any system :
1. Generation of power from potential source.
2. Conversion of power into form for transmission.
3. Transmission of power.
4. Utilization of power.
An analysis of the first three items is shown in Table 11. In
Table III is shown the ordinary maximum and minimum ef-
ficiencies obtained from various motors and machines in prac-
tical work. Higher efficiencies are sometimes obtained under
test conditions where great attention is g^ven to secure favorable
conditions, and, in many places where careless work is permitted,
neglect and unsatisfactory conditions will result in much lower
efficiencies than the minimum shown.
as. The Losses in a Hydro-electric Plant — ^To emphasize and
point out in greater detail the various losses encountered in the
generation and transmission of energy, especially as applied to
hydro-electric plants, attention is called to Fig. 16. In this
diagram is traced the losses from the potential energy of the
water in the head race of the power plant to the power avail-
able at the point where it is used. In each case considered it is
assumed that 1,000 horse-power of energy is applied to the par-
ticular work considered.
First, consider the transmission of power for traction pur-
poses. If a certain head is available when no water is flowing
in the raceways, that head becomes reduced at once when the
wheels begin to operate. A certain amount of head is also lost
in order to overcome the friction of flow through raceways, racks
and gateways. In the problem here considered it is assumed
that the above losses are five per cent, of the total energy avail-
able in the head-race, and that this loss occurs before the water
reaches the turbines : hence, 95 per cent, of the potential energy
is available at the turbine. The turbine loss is here assumed to
be about 20 per cent. First-class turbines under three-quarter
to full load conditions, will commonly give 80 per cent, efficiency,
or a little better.
Professor Unwin, in his "Development and Transmission of
Power," page 104, gives the following percentage of loss in tur-
bines :
The Losses in a Hydro-Electric Plant.
27
Shafting, friction and leakage 3 to 5 per cent
Unutilized energy 8 to 7 per cent
Friction in shaft, guides and passages 10 to 15 per cent.
Total loss of energy IG to 27 per cent
TABLE II.
Method of Generation.
z
J*
0
z
0
•-i
X
<
H
z
<^
z
0
<
z
Fuel.
'Internal Coinhustion Engine
Gas — Oil Engine losses.
( Direct (Vacuum Pump) C Furnace.
Steam ] i Boiler.
( Indirect I Piping.
(Direct (Ram) Ram losses.
Indirect (Wheels) ) ^WoL^.'-'
h
a H
2
''I
a
o
I
i
i
<
h
O
c
o
' i
Water
Power.
Minor
Sources.
Electric (Primary Batteries) .
Wind (Mills)
Waves (Motors)
^Sun Heat (Solar Engines) . . .
" Various mechani-
cal and other
losses due to
method used.
" Internal Combustion Engine Included in engine
Steam.
Electrical .
Engine and con-
nection losses.
Dynamos and wire
losses.
Hydraulic Pump 1
Pneumatic Compressor losses.
f Direct connected,— Shaft f
Mechan- i Cables, Ropes, Ch:iins ) Various losses due
ical I Electric ] to method need.
tCombination (,
(Entrance head.
Pipe friction.
Mmor losses.
Connections.
Electrical .
Pnenmatic .
fTran former losses.
j Wire losses.
I Motor losses.
[Connections.
(Pipe friction.
Air cooling.
Motor lossep.
Connections.
The Losses in a Hydro-electric Plant. 29
The next loss shown on the diagram is the loss in transmitting
the energy through the bevel gear and the shafting to the gen-
erator. The loss in gearing, shafting, etc, is shown as 10 per
cent., which is probably much less than actually takes place in
most plants of this kind, but may be considered as representing
the results of good practice.
The loss in the transformation of power in the generator is
given as 8 per cent. The generator is an alternator, and the cur-
rent generated would be at about 2,300 volts. This current must
be raised to a higher voltage, by means of transformers, for
long distance transmission. These transformers would g^ve an
efficiency of about 96 per cent. The line loss is dependent on the
size of the copper used, but would probably not exceed 10 per
cent. At the distributing point, where the energy is to be used,
the high voltage current must be transformed again into suit-
able voltage for distribution. The same energy loss is estimated,
for these transformers. If the current is to be used for traction
purposes, it will be necessary to convert it into direct current
by means of a rotary converter, the efficiency of which is esti-
mated at 92 per cent. The voltage from the general distribution
system would probably be too high for direct use in the rotary
converter, and would have to be transformed to a lower voltage
before passing into the converter. A loss of about 6 per cent.,
therefore, should be allowed for this transformation.
The current from the rotary converter is subject to a line loss
which may be again assumed at 10 per cent. The loss in the car
vQxAor may be estimated at 7 per cent. The percentage of loss
and the percentage of efficiency for each unit in this generation
and transmission system is based, of course, on the actual energy
supplied by the unit next previous to it in the system, so that
the percentages mentioned are not based on the total potential
power available in the head-race but on the power actually reach-
ing the machine.
In the solution of any actual problems of this character it is
necessary to determine the efficiencies of the various units of
4c plant under the condition of actual service. The efficiency
will be found to vary under various conditions of load. It may
therefore be desirable to determine the probable losses under
various working conditions.
In the selection of the various machines which are to form a
part of such a system of transmission, the choice should be
30
Power,
based on an effort to establish a plant which will give the maxi-
mum economy when all conditions of loading are considered.
The losses in the transmission of power for traction purposes,
as shown on the diagram, may be traced through in tabular
form as follows:
Total Energy
Available.
Per Cent
Lose.
Per Cent
Efficiency
1,000 HOBSK
Power.
LoBsin
horsepower
Head race
Turbine
Shaft and gearing
Generator
TransformerB.
Transmission line.
.Step-down Transformers.
Secondary Transformers.
Rotary Converters
Line
Traction Motor
5
20
10
«
4
10
4
6
8
10
7
95
80
90
92
96
90
96
94
92
90
93
50
UK)
76
64.7
25.2
60.4
21.7
31.3
39.3
45.1
28.4
Power utilized for operating the cars, or 37J per cent of the
original energy 374 .5 Horse Power.
In the generation and transmission of power for lighting pur-
poses, the losses will be similar to those above mentioned, up
to and including the step-down transformers at the point of dis-
tribution. In this case, however, no secondary transformers or
rotary converters would be necessary. The only loss between
the step-down transformers and the light will be the line loss
assumed at 5 per cent. The loss in the individual transformer
for the light will be about 8 per cent., leaving the available en-
ergy for actual use in the lamp at about 456.2 horse power, or a
little less than 46 per cent, of the total energy in the head-race.
In the case of the utilization of this energy for manufacturing
purposes, the loss would be the same up to and including the
step-down transformers at the point of distribution. The line
loss in the distribution from the transformer house to the manu-
facturing establishment may be assumed at 5 per cent. The
motor, if properly selected, may be run at the line voltage, and
no transformer losses need be considered. The motor efficiency
is here shown at 92 per cent., although in most cases the per-
centage of efficiency would be considerably less.
The belt loss in transmitting the power from the motor to the
line shafting is estimated at 5 per cent.
Efficiency of Generators and Motors.
Tablb m. — Ordinarif Ejfloiency of Oenerators and Motors,
31
Glass or Maceinsbt.
Cent at Fcll
Load,
mum.
Mini-
mum«
Water Wbeds.
CoDdesaiii^ - - * - {
gleam Engines . { **""
Kon-CondeneSng )
Steam Engines.. }**""
BefttEngmei. i> *#««
Gteom Air Compreadon .
^llotor
Bectrical Macbintry . , .
Tnmamitting Mechaix-
TmuDusaioD Methods.
f Overaliot WJieels. ♦ -
Bn^flSi Wheels' .
Undershot Wheels .
Tarbhiw
Impulse Wheela. > . .
i Boilers ^ - « . <
\ Steam Pipe
f Triple Expansion Corlij^
Compfitind GorUBS
.Simple CorliBa
Compound High Speed * .
f Cbtnponnd Corllea
1 Simple CorlisB
Compound tliurh Speed,
Simple Uif^h^peed. . ., ,
Simple Slide Val?e . . . . .
iGas or Oil Engines .
Diesel Motor
'Compound Con. Corliss*
Simple Con. Corliss .
Simple Corliss*,***. ***,
High Pressure
^SmallStraijfht Line. ....
5 Air^ cold
( Air J reheated.
r Dynamos ....
! Motor, large..
\ MotoFi email ,
[Trans I or user..
fBelt .•.,..
Hope . *
Cable. .- ...,,
Direct connection
Shafting **
Gearing -
Bevel Gefiring
Pneumatic r per mile ,
Hydraulici |^r mile *
ElectriCr usual
75
iS5
40
S5
85
75
18
15
12
12
12
7
7
20
30
12
2
3
60
7U
92
90
85
95
^7
tm
ln>
S5
75
97
ys
»5
65
60
25
60
75
60
75
15
12
10
10
10
7
7
6
5
10
25
10
7
5
3
IS
SO
60
SO
80
75
50
85
90
75
95
70
50
60
9^
90
85
32 Power.
The shafting necessary for the general distribution of power
through the factory is estimated at 75 per cent, efficiency.
The belt loss from the shaft to the individual machine is esti-
mated at an additional 5 per cent., leaving the total energy avail-
able for use in the machine at 308.8 horse power, or about 31 per
cent, of the original energy in the head-race.
It should be noted that in each of the three transmission sys-
tems mentioned above, the actual power utilized at the point of
application is less than half of the energy available in the head-
race. It is the function of the engineer to see that these losses
are reduced to the greatest practicable extent. These losses
must be limited in both directions. They must not be too great,
nor too small. Tliey must be adjusted at the point where true
economy would dictate. This limit is the point where the cap-
italized value of the annual power lost is equal to the capitalized
cost of effecting further saving. In other words, true economy
means the construction of a plant that will save all the power
or energy which it is financially desirable to save, and will per-
mit such waste of energy as true economy directs.
24. Units of Energy. — Energy is known by many names and
exists in many forms which seem more or less independent. The
principal forms of energy are measured by various units. Those
most commonly considered in power development and trans-
mission are as follows:
Work is energy applied to particular purposes. In general it
is energy overcoming resistance, mechanically it is .the exertion
of force through space.
Power is the rate of work, or the relative amount of work done
in a given space of time.
The unit of work is the foot pound, or the amount of work
required to raise one pound one foot. One pound raised one
foot, one-tenth pound raised ten feet, ten pounds raised one-
tenth of a foot, or any other sub-division of pounds and feet
whose product will equal one requires one foot-pound of work
to perform it.
The unit of power is based on the unit of work, and is called
"horse power.'* It is work performed at the rate of 550 foot
pounds per second, or 33,000 foot pounds per minute.
Units of Heat. The unit of heat is the amount of heat which
will raise one pound of water from 39 degrees Fahr. to 40 degrees
Fahr. at atmospheric pressure. It is called the British Thermal
Unit, and is indicated by the initials B. T. U.
Conversion of Energy Units. 33
Electric Unit. The unit of quantity of electricity is the coulomb.
One coulomb per second is called an ampere, and one ampere un-
der a volt pressure is equal to a watt, the unit of electric power.
Water Power. Water power is the power obtained from a
weight of water moving through a certain space. In water power
the unit of quantity may be the gallon or the cubic foot ; the unit of
head may be the foot; and the unit of time may be the second or
minute. The weight of water, unless highly mineralized, at ordi-
nary temperature, varies from 62.3 to 62.5 pounds per cubic foot.
As these weights vary from each other less than one-third of one
per cent., the difference is insignificant in practical problems where
the errors and uncertainties are often large. In the further discus-
sion of this subject, therefore, the weight of 62.5 pounds is used as
the most convenient in calculation.
Steam Power. The unit of steam power in ordinary use is the
pound of steam, its pressure, and rate of use. It is, however, based
on the heat unit, and must be so considered for detailed examina-
tion.
Definite quantities of work are also designated by the **horse
power hour," equivalent to 1,980,000 foot pounds, and the "kilowatt
hour," equivalent to 2,654,150 foot pounds.
The pound of steam may be considered as containing an aver-
age of 1,000 British thermal units, which may be utilized for power.
This is equivalent to 778,000 foot pounds.
35. Conversion of Energy Units. — The various forms of energy
as expressed by the units named are convertible one into another in
certain definite ratios which have been determined by the most
careful laboratory methods. In considering these ratios, however,
it must be remembered that, as shown in the preceding examples,
in the transformation from one form of energy into another the
ratios given cannot be attained in practice on account of losses
wliich can not be practically obviated. Such losses must be, in
good practice, reduced to a minimum, and the ratios given are,
therefore, the end or aim toward which good practice strives to at-
tain as nearly as practicable when all conditions and facts are duly
considered.
Energy must be considered in two conditions as well as in the
above named forms, viz.: passive and active or potential and
kinetic
Potential energy is energy stored and does not necessarily in-
volve the idea of work. Kinetic energy is energy in action and
34 Power.
involves the idea of work done or power exerted and for its meas-
urement must be considered in relation to time.
The most common units of potential energy and their equiva-
lents are as follows:
The footpound (one pound raised one foot).
=1/62.5 or .016 foot cubic foot (of water),
=1/8.34 or .12 foot gallon (of water).
=1/2655.4 or .0003766 volt coulombs.
=1/778 or .001285 British thermal units.
The foot cubic foot (one cubic foot of water raised one foot).
=62.5 foot pounds.
:=7.48 foot gallons.
=.08 British thermal units.
=.02353 volt coulombs.
The foot gallon (one gallon of water raised one foot)
s=8.34 ^^^^ pounds.
=.01072 British thermal units
=.00314 volt coulombs.
=.1334 foot cubic feet.
The volt coulomb
=2655.4 foot pounds.
=42.486 foot cubic feet.
=318.39 foot gallons.
=3.414 British thermal units.
The British thermal unit
=778 foot pounds.
=12.448 foot cubic feet.
==93.28 foot gallons.
=.2929 volt coulombs.
Quantities of energy available, used or to be used, and eithe«"
potential or kinetic may be measured in the above units.
When the rate of expenditure is also stated these units express
units of power. Some of the equivalent values of power are as fol-
lows, those most commonly used being printed in black-face type :
The horse power
=1980000 foot potinds per hour.
=33000 foot pounds per minute.
=550 foot pounds per second.
=31680 foot cubic feet per hour.
=528 foot cubic feet per minute.
Conversion of Energy Units, 35
=8.8 foot cubic feet per second.
=237600 foot gallons per hour.
=3960 foot gallons per minute.
==66 foot gallons per second.
^=74^ watts.
=2545 British thermal units per hour.
. ^=42.41 British thermal units per minute.
=.707 British thermal units per second.
The foot pound per minute
=1/33000 or .0000303 horse power.
=1/778 or .00129 British thermal units per minute;
=.0226 watts.
=i/8.34=.i2 foot gallons per minute.
=i/62.5=.oi6 foot cubic feet per second.
The foot cubic foot per minute
=62.5 foot lbs. per minute.
=i/528=.ooi89 horse power.
=1412 watts.
=748 foot gallons per minute.
=.0803 British thermal units per minute.
The foot cubic foot per second
=3750 foot lbs. per minute.
=62.5 foot lbs. per second.
=i/8.8=.ii36 horse power.
=^48.8 foot gallons per minute.
=7.48 foot gallons per second.
=4.820 British thermal units per minute.
=.0803 British thermal units per second.
Th* watt
=44.24 ft. lbs. per minute.
=.00134 horse power.
=.0568 British thermal units per minute.
=5.308 gallons feet per minute.
•=.7089 ft cu. ft. per minute.
Thf British thermal units per minute
^78 ft. lbs. per minute.
^=.02357 horse power.
=17.58 watts.
=93.28 ft gal. per minute.
=12.48 ft. cu. ft per minute.
36 Power.
26. Motion in General — In moving a body against a given force or
resistance the work done in foot pounds is the product of the space
passed through (in feet) and the resistance (in pounds). Thus in
raising a ten-pound weight 100 feet high, 1,000 foot-pounds of work
is performed. But this is not the only work performed. To pro-
duce motion in a body or to bring a body to a state of rest neces-
sitates a transfer of energy. For all moving bodies are endowed
with kinetic energy — the energy of motion — and this energy must
be given to them to produce motion, and must be taken from them
to produce a state of rest.
Hence, Newton's laws of motion:
1. "Every body continues in a state of rest, or of uniform mo-
tion in a straight line except in so far as it may be com-
pelled by impressed forces to change that state."
2. "Change of motion is proportional to the impressed force
and takes place in the direction of the straight line in
which the force acts."
3. "To every action there is always an equal and contrary reac-
tion."
The acceleration of gravity is the acceleration due to the weight
of a body acting on its mass.
The weight of a body W (on account of centrifugal effect of the
earth's revolution) varies, being least at the equator and greatest
at the poles. From Newton's second law it follows that the accel-
eration in motion designated by g and caused by the weight of any
body acting on its mass will be proportional to its weight, i. e., g^=
constant X W, and hence the weight of a body divided by the ac-
celeration will always be constant. This constant quotent desig-
nated by the letter M is termed the mass of the body.
(.)M=:^
Let W=The weight of a body.
M=Mass.
g^=Acceleration due to gravity=velocity of a falling body at
end of first second, and is ordinarily taken as 32.2 ft.
per sec. per sec.
A=Acceleration of moving body=velocity of body at end
of first second.
W'^=Weight acting.
W"=Weight acted on.
Kinetic Energy. 37
V=Velocity at end of time L
Va=Average velocity.
t?=Time force has acted.
S=Space passed through.
h=Height passed through by falling body.
V'=Initial velocity.
S'=Initial space passed through.
27. Uniform Motion. — In uniform motion the moving body
passes through equal spaces in any equal divisions of time.
Hence by definition :
The space passed through (S) equals the product of the velocity
(V) and the time (t).
(2) S=Vt
(3) V=-|
28. Uniformly Varied Motion. — If the velocity of a body is in-
creased or diminished uniformly, the motion is termed uniformly
varied motion and is termed uniformly accelerated motion in the
first case and uniformly retarded motion in the latter case.
In all such cases the following relations hold:
(4) A=^g.
(5) V=At=^g t
(6)Va=4i
(7)S=Vat=--=-
(8) V=VTXs.
With falling bodies:
S=h.
A=g.
From which equation (8) becomes
(9) V=V 2gh, ^hc well known basis of hydraulic calcu-
lations.
(10) Work==W h=W VV2g=-=M VV2.
>9. Compotmd Motion. — ^\Vhen bodies are already in motion and
additional force is applied, the following relations hold :
(11) V=V'+At.
(12) S=S'+V't+^
38 Power.
30. Graphical Representation of the Laws of Motion. — In each
case—
The vertical ordinates represent velocity
Abscissas represent time.
Areas represent space passed through.
SPACE
WNiroitM Monof*
^.^-.-'-^
a»Ace
^^^^t*"*^
*\.^\
TIM«
MNirOAM ACCBUCRATCO MOTION
^
00*4^0UN0 MOTION - UMI^tMI-lkV ACCCkCnATCO
>Htr** IMITIAU VCLOCiTV
^T =s constant
S = Vt
V = At = ,^ gt
W
v. = 4^
S = V^t =
V=t/2AS"
At«
2 " lA
V = V + At
At*
8= S' + V t + ^
Pig. 17. — Graphical Representation of the Laws of Motive.
31. Transformation. — ^The transformation of potential to kinetic
energy is well illustrated by water acting upon a water wheel. The
energy in a body is always constant whatever its form, except as
said energy be given up to other bodies or lost and wasted in vari-
ous ways. Consequently the sum of the potential and kinetic en-
ergies in any body is a constant quantity unless the difference be
accounted for by energy loss or transfer as above noted.
Water that has fallen to sea level has lost all the energy it may
have once possessed, its energy having been expended in perform-
ing some kind of work.
If, in a hydraulic plant, we have an available fall of 8.8 ft. every
cubic foot of water falling each second should produce 350 ft. lbs.
of work per second or one horse power. After the water has
passed through a well designed turbine it flows sluggishly away,
having used up nearly all its energy in the turbine to which
Literature. 39
It has transferred its energy. If, however, on account of bad de-
sign the water flows away at a rapid rate, say at lo feet per second,
the head lost, fc=vV2g i. e. h=ioV644=i-55 ft. of vertical fall.
Under these conditions the energy due to this fall still remains in
the water, after it has left the wheel, and is lost, the loss being
17.8 per cenL of the original energy.
LITERATURE.
1. Thurston, Robert H. Conversion Tables of Weights and Measures. NeW
York. J. Wiley ft Sons. 1883.
2. Oldberg, Oscar. A Manual of Weights and Measures. Chicago. O. J.
Johnson. 1887.
8. Everett, J. D. Illustrations of the C. G. S. System of Units. New York:
MacMillan ft Co. 1891.
4. Anderson, William. On the Conversion of Heat into Work. Discussion
of energy conversion. London. Whittaker & Co. 1893.
5. Unwin, W. C. On the Development and Transmission of Power. Long-
man ft Co. London. 1894.
6. Oswald, Wilhelnu Manual of Physics, — Chemical Measurements. New
York. The MacMillan Co. 1894.
7. Peabody, Cecil H. Tables of the Properties of Saturated Steam. New
York. J. Wiley ft Sons. 1895.
8. Richards, Frank. Compressed Air. New York. J. Wiley ft Sons. 1895.
9. Bolton, Reginald. Motive Powers and Their PracticaJ Selection. New
York. Longmans, Green & Co. 1895.
10. Holman, Silas W. Matter, Energy, Force and Work. New York*. The
MacMillan Co. 1898.
IL Kent, Wm. Notes of the Definition of Some Mechanical Units. Am.
Asso. Adv. of Sci. 1898. See also Eng. News, Vol. 40, p. 348.
U Mead, Daniel W. Commercial Transformation of Energy. Trans. 111.
Soc. Eng. 14th report, 1899.
U. Reeve, Sidney A. The Steam Table. New York. The MacMillan Co.
1903.
11 Kohlrausch, F. An Introduction to Physical Measurements. New York.
D. Appleton & Co. 1903.
15. Carpenter. R. C. E3xperimental Engineering. New York. John Wiley
ft Sons. 1903.
11 Herwig, Carl. Conversion Factors. New York. J. Wiley ft Sons. 1904.
17. Smithsonian Institution. Physical Tables. 3d Edition. 1904.
11 American Institute of Electrical Engineering. Report of Committee on
Standardization. 1907. Proc. Am. Inst. E. E. Vol. 26, pp. 107&-
llOC
CHAPTER IIL
HYDRAULICS.
32. Basis of Hydraulics. — ^The science of hydraulics is an empir-
ical, not an exact science, but is based on the exact sciences of
hydrostatics and dynamics. Its principal laws are therefore founded
on theory, but on account of the multitude of modifying influences
and of our necessarily imperfect theoretical knowledge of their
varying characters and extent, the formulas used must be derived
.from or at least modified by observation and experience and can-
not be founded solely on theoretical considerations. The condi-
tions under which hydraulic laws must be applied are so varied in
both number and kind that the application of the laws must be
modified to suit those various conditions and for this reason their
successful application depends largely on the practical experience
of the engineer.
In the following discussion the letters used will have the signifi-
cance shown below :
E=Energy (abstract).
P=Horse power.
W=Total weight of water.
h=The total available head in feet
hi=The velocity head.
h2=The entrance head or influx head.
hs=The friction head.
q=The quantity of water (in cubic feet per second).
w=The weight of each unit of water (cu. ft.=62.5 lbs.).
a=Area (in square inches) against which pressure is ex-
erted.
s=The space (in lineal feet) through which the area moves
under pressure.
v=The velocity of flow (in feet per second).
gi=Acceleration due to gravity (32.2 feet per second per sec-
ond.)
t=The time in seconds.
33. Mathematical Expression for Energy. — Mechanically, energy
is the exertion of force through space. The amount of available
Mathematical Expression for Energy. 41
energy of water that may be theoretically utilized is measured by
its weight (the force available) multiplied by the available head
(the space through which the force is to be exerted), 1. e., (i) E=:
Wh. From this it will be noted that the energy of water is in
direct proportion to both the head and quantity. Tliis energy may
be exerted in three ways which may be regarded as more or less
distinct but which are usually exercised, to some extent at least,
in common. The exertion of this energy in the three ways men-
tioned, expressed in terms of horse power, are as follows :
First: By its weight which is exerted when a definite quantity
of water passes from a higher to a lower position essentially with-
out velocity. This method of utilization is represented by the
equation
^ ' 560
Second: By the pressure of the water column on a given area
exerted through a definite space. This method of utilization is rep-
resented by the equation ^
^'^ ^ 650r"
Third: By the momentum of the water exerted under the full
velocity due to the head. The energy of a moving body is repre-
sented by the formula :
Wv»
(4) E = ^
The equation for the horse power of water under motion is there-
fore represented by the equation :
^ ' 560 X 2g
An analysis of these formulas will show that under any given
conditions the theoretical power exerted will be the same in each
case.
34. Velocity Head (hj). — It has already been pointed out (chap-
ter II) that energy must be expended in order to produce motion
in any body and that the head (hj necessary to produce a ve-
locity (v) is
(«) K = S
This proportion (hj/h) of the available head h has to be ex-
pended to produce and keep in motion the flow of water. This
teid (hi) is not necessarily lost (it has simply been converted into
42 Hydraulics.
kinetic energy, and it may be re-cohverted into potential energy by
correct design or it may be utilized in some other way, as, for
example, by pressure or impact in hydraulic motors).
Whatever head (hx) is necessary to maintain the velocity (v)^
with which the water leaves the plant, will be lost to the plant.
It is, therefore, desirable to keep v at this point as low as may be
found practicable when other conditions are considered.
Sudden enlargements or contractions in pipes or passages may
wholly or partially destroy the velocity and cause the permanent
loss of the corresponding head (hj).
In this case an additional amount of the available head (h^) must
be used to again generate the velocity (v) required to convey the
water through the remainder of its course. Gradual change in the
cross-section of all channel conduits or passages is, therefore, de-
sirable in order that the transformation from kinetic to potential
energy, and the reverse, shall be made without material loss.
Not only the head (hj) but still other portions of the total avail-
able head (h) may be lost in the channels and passages of a ma«
chine or plant by improper design.
35- Entrance Head. — The loss of head (hg) which occurs at en-
trance into a raceway, pipe or passage may be called the "influac
head." The amount of this loss differs considerably with the shape-
and arrangement of the end of the pipe or passage. In general, the-
influx head may be determined by the formula:
(7) h, =1^- — 1 |-2^(Merriman*8 Hydraulics, Art. 66)
In this formula the coefficient can be obtained from table IV, lit
which the variations of the constant under various conditions, with
reference to a pipe inlet, are shown, and from which it will be noted
that its magnitude depends on the shape and arrangement of the
inlet,
TABLE IV.
Arrangements of a pipe uUet with corresponding coefficients.
Arrangement of Pipe.
c
^-
A. Proiectinflf into reservoir
.716
.825
.950
.990
.956
B. Mouth flush with side of reservoir
.469
.106
C. Bell shaped month ' ;j^°™
.020
Submerged Orifices.
43
To find the value of h^, the value of -i- — i corresponding to the
given conditions, is to be selected from Table IV and substituted
in formula (7). The ordinary arrangement of suction pipes is for
a square ended pipe to project di-
rectly into the suction pit. In res-
ervoirs the pipe may be flush with
ry..'.,,'..'ym. thi^ masonry or project as in the
,, , ^ ^^g^ ^£ suction pipes. With condi-
tion (A) formula (7) becomes
^\}$f:\/ik\iykttji^^
(8)
h, = .956
2«
0m
^-^ - -^ ^^ ^
•**>*
' — -^— _-^ir_ ^T-- "-i:
^2
The value of h, can be readily
obtained from equation (8), as it
will be 95.6 per cent, of the veloc-
3 ity head.
With the mouth of the pipe flush,
with the side of the reservoir the
loss would be 46.9 per cent, of the
velocity head, and with a bell
mouth pipe the loss would be de-
creased to from two per cent. to.
^10.8 per cent, accoi'ding to the de-
sign of the bell mouth entrance.
The arrangements of inlet pipes
as referred to in Table IV are
^^" ^^- shown in Fig. 18.
36. Submerged Orifices. — A similar loss is sustained in the flow
through gates or submerged openings or in the flow past any form
of obstruction which may be encountered by the water in its flow
through channels, pipes or other forms of passages. Openings or
obstructions with square edges may cause a serious loss of head
which may, however, be reduced.
First: By increasing the opening, thus causing a reduction in
velocity and consequently a saving in head, or
Second : By rounding the corners of the opening or obstruction,,
thus causing a gradual change in velocity and a partial recovery
of any head necessarily used for creating greater velocity through
such passage or past such obstruction.
But few experiments have been made on submerged orifices and
tubes. These indicate a coefficient of about .62 for complete con-
traction which increases to .98 or even .99 with the contraction
44
Hydraulics,
completely suppressed. Certain experitucnts have recently been
made at the hydraulic laboratory of the University of Wisconsin,
on the discharge through orifices and tubes four feet square and of ■
various thicknesses or lengths and with various conditions of con-
traction. The values of the coefficients as determined in these ex-
periments with various losses of head and various conditions of
entrance, are shown in Table V.*
The FormM of Entrance and Outlet Used for the Tubes in tM &Fperimeni
were as follows:'
A- Entrfincej all corner 90**
OutleL; tube projecting into wftt«r on down stream side of bolkbesuL
a Entrance; contraction eupptet^sed on bottom.
Outlet; ttibe projecting; into water on down stream side of bulkhead.
b Entrance; contractioD Buppres^ied on bottoii and one side. ^
Outlet; tube projecting into wat«r on down stream aide of bulkhead* ^M
C Eiiinmce; contraction sup pressed on bottom and two sides.
Outlet; tube projecting into water on down etream side of bulkhead.
d' Entrance; contract] on euppreseed on bottom and two eidm*
Outlet: square cornet^ with bulkhead to sides of channel presenting J
the return current alon^ the aides of the tube.
d Entrance; contraction suppre^sBed on bottom, two sides and top*
Outlet; tube projecting into water on down itream side of bulkhead.
I
From this tabic it will be noted that a partial suppression of con-
traction does not always improve results, and that by complete sup-
pression, the coefficient is greatly increased with a corresponding
decrease in head lost. fl
37, Friction Head (h^) — In raceways and short pipes the velocity
head (hj) and the influx head (h^) are frequently the sources of the
/i^eatest losses of head. In canals and pipes of considerable length
the friction of flow may become the most serious sotirces of energy
loss>
The principles of flow in such channels may be considered as
follows :
First Principle: In any fnctionless pipe, conduit^ channel or pas-^
sage of any length the flow may be expressed by the formula;
(»)
lll = ^ or T ■* V2gh
In practice, however, we find friction is always present and a
friction factor must be introduced in the above formula in order to
i
♦Prom experiments by Mr, C, B.
tilt University of Wisconsin*
Stewart at tlie Hrdraulle Laboratory ot
J
^^^
Friction Head. 45 ■
1 represent the actual conditions of practice. (9) therefore becomes: ^|
(10
hj=q' Z_ or ▼ » c VSgh ^^^B
TABLE V. ^^H
Value of the Co^Usieni 0/ Di^^arg^ for flow through horUontal mibmergoi ^^H
lufie; 4 f^^t square, for vanous lengths, lanes of head artd forme of enfraitee ^^^|
and ouikL
^H
Lo«of
Forms
of En-
Length of tube, in feet ^|
■
bead^b»
tt%UQ&
O.Sl
0.62
1.25
2,60
6.00
10.0
14.0 ■
in feet*
and
Ontbt
■
Valne of the coefficieat, c. ^|
.0§*. «*•»•<•
A
.650
.672
.769
.742
.807
.810
.621
.838 H
.848 ■
b
,740
.7139
.S32
.862 H
c
,H34
.7139
.875
.690 H
c'
,87& ■
d
.948
,943
.940
.927
,931 H
: .10.-,
A
.611
.631
.647
.718
,783
,780
.79^ H
a
.636
.698
.771
.801 ■
b
.685
.718
.791
.813 ■
0
.772
.718
.828
.841 V
c'
M^ ^
d
M2
.911
.899
.892
M%
.IS,*,*.....
A
a
,609
.630
,628
.644
.70S
.689
,75a
.767
,779
,794
.803
b
.677
.708
.767
,814
c
.765
.708
.828
.839
c'
.82^
d
.936
,010
,899
.893
.894
M
A
a
.609
.630
.647
.711
.694
.788
.777
.794
,809
.814^
b
,678
,711
.796
.8:^3
c
.771
.711
.838
.85a
c'
,84^
d
1 .048
.923
,911
.906
.905
1 J5 ,,
A
a
.610
.634
,631
.662
.720
.705
.782
.790
.812
.828
b
.683
.720
.809
e
.779
.720
.854
d
,966
.938
.028
[,» — ^
A
b
e
d
.014
.639
.689
.788
.9i$4
.639
.660
.731
.796
,832
,66a
^^^
46
Hydraulics.
The formulas (9) and (10) represent one of the important funda-
mental principles from which many hydraulic formulas arc de-
veloped.
Second Principle: In any pipe, conduit, channel or passage we
may fairly assume:
First: From axiomatic considerations the resistance to the flow
of water may be regarded as directly proportional to the area of
The surface in contact with the water.
Second : From observed conditions the resistance is found to be
directly proportional to the square of the velocity of flow.
Third: Experience leads to the conclusion that the resistance to
flow is inversely proportional to the cross-section of the stream.
These conclusions may be expressed by the following equation:
P . __ (Yelocity)*X area of cont-act
"" area ot section
Fig. 19.
Tlie area of the surface of a channel is the product of the wetted
section or wetted perimeter (p) times the length of the section, or»
to p X 1. (See Fig. 19.) The velocity is represented by v and the
cross-section by a. Hence, from the above considerations, we may
write for the friction head :
(11) hg = ^^-^ and by transposition v* = -— ^
That is to say, the square of the velocity is in direct proportion
to the area of the section and to the friction head and inversely
proportional to the wetted perimeter and to the length of the sec-
tion.
In practice it is found that there are numerous factors which
Kutter's Formula. 47
affect the theoretical conditions, as above set forth, which must
therefore be modified in accordance with the conditions which ob-
tain. In formula (11) therefore it is necessary to apply a coeffi-
cient (c') which represents the summation of such other influences.
The form in which this last equation is ordinarily written is
Ordinarily this form is somewhat abbreviated by substituting for
a/p the hydraulic radius which represents this ratio. That is to say,
area of cross section __ a _
wetted perimeter ~ p ~
The "hydraulic radius" is also sometimes termed the "mean
<icpth" or the "mean radius." For the ratio of the resistance head
to the length of section the equivalent slope s is substituted.
That is to say:
Resistance head __ h, _
Length of section "* 1 ""
With these substitutions the formula (12) assumes the final
form of:
(13) V = ci/rs"
In the use of this formula three factors must be determined by
measurement or estimate in order to derive the fourth, v, r and s
<^ be determined experimentally or measured directly. The
factor c is the most difficult to ascertain as it depends upon a very
^cat variety of conditions which can only be known and appre-
ciated by a thorough knowledge of the conditions under considera-
tion, and by comparison of such conditions with similar observed
conditions. Various attempts have been made to derive a formula
which would give the value of c in accordance with the varying
conditions. The principal formulas for the values of c are those of
Ganguillet and Kutter and of Bazin. Ganguillet and Kutter's form-
ula for the value of c is as follows :
38. Kutter's Formula. —
4i.fl + l:^ + 2:«^l
a*) c = "
,+(..e+<L«^)_,L-
From this formula it will be seen that Ganguillet and Kutter as-
sume c to vary with the slope, with the square root of the hydraulic
^dius and with a new factor "n" which is termed the coefficient
48
Hydraulics.
VELOCITY "^V -iM FEET PER SECOND
-J
Fig. 20.
Kutter's Formula*
49
Fig. 21.
so Hydraulics.
of roughness. The value of this coefficient as determined by these
experiments is as follows:
For large pipe with the following characteristics:
Exceptionally smooth cast iron pipe n= .Oil
Ordinary new cast iron or wooden pipe .0125
New riveted pipes and pipes in use .014
Pipes in long use .019
For open channels of uniform sections :
For planed timber sides and bottom n= .009
For neat cement or glazed pipe .01
For unplaned timber xyi2
For brick work .013
For rubble masonry joiy
For irregular channels of fine gravel X)2
For canals and rivers of good section .025
For canals and rivers with stones and weeds . . . .030
For canals and rivers in bad order .035
The relation of the above factors may be determined by the dia-
grams, Figs. 20 and 21. If with a known slope and a known value
of n (for example, let n=o.i5 and s=.ooo2, as at A, Fig. 20), a
straight line be drawn on this diagram to the scales of the hydraulic
radius (at B) it will show at the intersection with the scale for the
coefficient (c) the relative value of this coefficient for these condi-
tions, or with a known c and the known hydraulic radius and the
given slope the value of n of a channel may be likewise determined.
After a line has once been drawn connecting these four known
values the velocity can be determined by drawing a line from the
hydraulic radius scale (B) to the proper point on the scale of slope
or hydraulic gradient at x, and then from the point of intersection
of the line A B with the coefficient scale at x' drawing a line par-
allel with xB which will intersect the velocity scale at the point B',
giving the velocity (in this case equal to 1.34 ft. per second). These
formulas only apply with accuracy where the channels or passages
are uniform and if applied to channels or passages which are not
uniform the sections .selected must be fairly representative. If the
sections selected are not fairly representative the value of c or n
determined from observations and experiments may vary consid-
erably from the values which would otherwise be anticipated. That
is to say, the calculations based on c and n will take into account
irregularities in channels and other unknown or unrecognized con-
ditions, including curves, bends and obstructions which may not
Bazin's Formula.
S-
^^'■~~"
/
1
T-iei
Baiin'fi ForiDulaior the
T«tiie of c in the foriiuil&
T=ci^rs iSf in Eiigjish
/
/
1
/
/
1
/
/
/
1
/
/
/
J
/
/
/
/
" **
S7
/
/
/-
— -
0 =
rr^
I
1
f
/
.5.2 + ^-
B]=0,06forimooth plank
or matched boards.
niM^,16 for plauka and
brick*
m=0.4G for nmflonrjr,
m=0.85 for r^ular eanh
beds.
m^L30 for canaU in
good order.
/
J
/
/
I
/
/
/
/
1
_^
1 ■
'5
/
/
/
/
J
1
/
/-
-/
/
f
H
■ '
/
f
/
-/
/
/
I
/
/
1
3
J
/
J
/
/
1
*t
iQ^L75 ia very bad
order*
^
*/
—
'::
a
5
<
OE
ft
u
li
r^
i
f
\
91
dI
J
fj
1
1
/
/
/
y
iVk
i^
0
/
/
y
r
/
/ "^
1
/
/
/
r
/
i
f
-v. 1/
^^
i*^
/
J-
/
1
1/.
- >/'
/
/
^
7^~
/
/ —
/
1%
- J4
— — fk
/
.^
y
^
X
z
^ wy
^
^
^
ip^^
-
^
^
* e e c
G
1 1
OEr
■ 1
f 4
ricii
3 <
[NT
3 <
IN
a 1
■ (
roH
a 1
■ 1
MULi
3
\ V
n
'=C1
a 1
/rs
» 4
9 0
S 12
5
Pig. 22. — ^Diagram For Solution of Baz!n's Formula.
GRAPHICAL 5DLUTI
V-VCLDCITY IN FCCT PCH ICCONQ.
C ^EOEFFIUIENT.
R- HYDRAULIC RADIUS LR PCCT = -^,
■ -BINE DT BLDPC
- Jl
V = c V
P-
h-i
VALU 1
u
n
.§ .7 a 9 iQ
V = VELD[:iTIES
V
F CHEZYS FORMULA
= cv¥T
p I
ym BQ rccT or channel bcctidn
rtED PCnrMCTER DF CHANNEL BCCTION IN LINEAL FEtT.
I. IN rCET BETWEEN FDINT8 CONBIDERCO.
IBTH OR DISTANCE. BETWEEN POINTS CDNBIOCHED. IN LINEAL FECT.
FEET PER SECDNO
54 Hydraulics.
have been considered at the time the original observations were
made.
39. Bazin's Formula. — It has been questioned by many observers
whether the slope of the channel has any material influence on the
value of the coefficient c. Bazin has derived a formula based on
his examination of this subject in which he assumes that c does not
vary with the slope. His formula, which is intended for the calcula-
tion of flow in open channels is shown, together with a gfraphical
table based thereon, in Fig. 22. This figure illustrates the law of
variation of c and is applicable in principle in a general way to all
channels and passages.
The graphical diagram. Fig. 23, which was prepared by the writer
in connection with Mr. J. W. Alvord, affords a ready method of
solving Chezy's formula (13).
40. Efficiency of Section. — From equations (12) and (13)
(16) q « velocity X area = va
or q = ca|/r8~= ca^5»
With c and s constant q varies as a|/r or as^/? —
\p
From this the conclusion may be drawn that other things being
equal the maximum quantify of water will pass through any sec-
tion of any river or other channel in which the hydraulic radius is
a maximum or the wetted perimeter a minimum. Where a choice
exists as to the class of material with which the channel is to be
lined c becomes a variable and q will vary as
ca y'r or as c ^5 —
That is to say, under circumstances where different characters of
lining may be used the maximum quantity will pass a given sec-
tion with c and r maximum or with c a maximum and p a minimum
for given a.
41. Determination of Canal Cross-section. — ^The velocity of the
water in any artificial channel must be limited by the class of ma-
terial used in its construction and the head which it is found prac-
ticable to use. As noted above the efficiency of a section is greatest
with the value of p minimum. Therefore, the semi-circular sec-
tion is the most advantageous cross-section that can be used in a
channel where resistance alone is considered and when the canal
Determination of Canal Cross-section.
55
IS to be lined with material which can be readily shaped into this
form. If the canal is to be lined with stone masonry it is fre-
quently more advantageous to make the face perpendicular and
to place the batter of the wall at the back. Where the canal is cut
from stone or shales which will not readily disintegrate in contact
with the water, a slope of 90"* to 40** may be sometimes used.
Quite steep slopes can also be used with dry masonry walls. In
material which can be handled with pick and shovel, slopes may be
used from i to 1.25 to i to 1.50. With artificial banks of dirt and
gravel a less slope angle is necessary and the slope must frequently
be made as low as one to two.
Table VI, which is taken partially from "Uber Wasserkraft und
Wasser Versorgungsanlagen," by Ferdinand Schlotthauer, is of
considerable value in determining the most advantageous cross-
section in various sections which may be adopted in the construc-
tion of a canal. As seen in the discussion above, the most advan-
tageous cross-section, other things being equal, is that in which the
Fig. 24.
wetted perimeter is a minimum or the hydraulic radius is a maxi-
mum. The following general discussion of the relations is based
on Fig. 24. From this figure it will be seen that
(16) a = bd + d'cota
(17) p = b -f- 2d cosec a
The transposition of (17) gives
(18) b = p — 2d coeec a
Substituting (18) in (16)
(19) « ss dp — 2d* coseca -f- d'cotor
The above equation now contains the area, depth, wetted peri-
meter and functions of the slope angle, in this case a constant.
'Hie conditions of maximum efficiency of a canal section require
56 Hydraulics.
that the wetted perimeter be a minimum or what amounts to t\
same thing with a given wetted perimeter the area a must becon
a maximum. The value of d which makes a the maximum is d
termined by putting ^i^ = o
(20) ^^ = p — 4d cosec a + 2d cota
(21) 0 = p — 4d cosec a + 2d cota
(22) d = 5
4 coseca — 2 cota
Substituting for p its value in (17)
,oQx J _ b -f 2d cosec a
""4 cosec a — 2 cota
Equation (16) transposed reads
(24) b = ^-^y^
d
Substituting this value in (23) we have
-pk— d cota -f 2d cosec a
(25) d = -5—^ 5—-
4 cosec a — 2 cota
Clearing:
(26) 4d«co8ec a — 2d«cota = a — d*cota + 2d*co8eoa
Transposing :
(27) d« =
2coseca — cota
Transforming trigonometric functions
(28) d« = 2
-: cos a cosec a
Bin a
(29) = 2 — sin a cos a cosec a
sin a
(30)
Finally.
a sin a
2 — cos a
(31) d = .JI^
• coaa
Equation (24) may be written
(32) b = -g- — dcota
Table VI is calculated from the formulas:
(31) d = J/«"^^
^ \2 — COS a
Determination of Canal Cross-section.
57
<
it
08 .a
•si
OS
O
'SI
i a
•2 t.*
O w
•5& S
©53 ^
SI*
o
c
C
08
c
^
•2
2
o
01
a
5-
I
Q O
n ^ a
^ e 1
I a 3
3
I
o
M
o
!« leS l« !<• I<« l<t
"5^ ^ "5^ > ^ ^
CO Q OS 60 -^ GO
S - - -
let
Id let let \tt l(t Id
"5* ^ "5^ ^ "5^ >
S 8 S S ? i
CO t' r* Ci •-• K
c^ c^ csi c^
lo3 lot Ia8 |a8 Ie8 loS
S g ^ 5 CO $9
r^ 00 o ^
§^
u
1 08
L
U
u
u
I08
•%
V
V
"*^
5
r«-
1
^
^
^
1
C^ Cq C^ CS|
T08 Tea Tea Toa Toa Us^
^ ^^ ^^ ^ V V
■^ csi CO 25 00 Q
loS 1 08 loS le
l€8
lot
1^
[t» let l(t
> > ^
C^ S
I 15
8
1-H ^ .-I C^
I 2 ^ ^ 5 S
g o^ ? ? ?■ P
8 S « S §5 §
g ^
•— 1-^ ^i i-H ^ ,ph , g
58 Hydraulics.
(32) b = -j^ — dcota
(33) B = b + 2dcota
(34) p = b+^
^ ' *^ ' sin a
In the above, a=cross-section area ; d=depth of water in channel ;
b=bottom width ; B=width at water level ; p=wetted perimeter ;
c=the length of slope which is equal to -; —
In Table VI the relation of these functions, for the slopes ordi-
narily used in practice have been calculated as well as for the semi-
circular section. The use of the table may be illustrated as fol-
lows: The quantity of water which it is desired to deliver is de-
termined by the conditions of the problem or by measurement The
velocity to be maintained in the channel is determined by the ex-
isting slope, the nature of material encountered, or the friction
head which it is found desirable to maintain. The area of the
cross-section required to carry the quantity q with velocity v is
a=-3- After the slope angle has been selected, for the material in
which the channel is to be constructed, the corresponding values
may be taken out of the table from their respective columns and
multiplied by the square root of a. The result thus obtained gives
the desired dimensions. If, for example, we desire to carry loo
cu. ft. of water per second in a canal at a velocity of 2 1/2 ft. per
second at which velocity small pebbles are unaffected, and with a
side slope of 1.5 to i, which is suitable for loose earth, has been
decided upon, the required area of cross-section will be 100/2.5
=40 sq. ft. The square root of 40 is 6.33. The required dimensions-
of canal as taken from the table are
Depth d=.689 x 6.33=4.36 ft.
Bottom width b=.4i8 x 6.33=2.65 ft.
Top width 6=2.485 X 6.33=15.73 ft. and
The wetted perimeter p=2.904 x 6.33=18.38 ft
Computation of the area from the above dimensions gives 40 sq. ft
Hence the work has been checked.
42. The Back Water Curve. — One of the problems which be-
comes very important in many water power installations is the
effect on the elevations of the stream produced by the erection of
a dam or other obstruction therein. The back water curve can best
be determined by the use of the simple formula of flow, equa-
tion (13).
Flow of Water in Pipes, 5p
From this, as shown in equation (15)
From this equation can be derived
(35) h. = 2^=a^xi
With ^^ constant, h, : h', ::^ : JBl, therefore
(36) h/.^ h»P'<^' ^ h»>'r
That is to say, with the quantity of water and length of section
constant, if the coefficient remains constant the head due to any
obstruction will vary in accordance with equation (36).
Where the water is greatly deepened in proportion to its orig-
inal depth the value of c will not remain constant but will vary.
Where such is the case and where q*l is constant, under which
condition
The difficulties in the determination of the value of c are, of
course, obvious, but it is believed that the back water curve can
be closely calculated by this simple formula in which the new
value of c is the only factor to be estimated, and where the other
elements of the problem can be determined by actual measure-
ments. In using this formula the original value of c under exist-
ing condition of flow can be determined by calculation based on
actual observation of flow under different conditions of water and
tjie conditions of the channel under the new regimen can be
closely estimated. New values of c can be very closely estimated
on the basis of the values known to exist under other similar cir-
cumstances. This method will permit of a more practical solution
of the problem than by the use of formulas based on entirely the-
oretical consideration of conditions which can never be approxi-
mated in practice.
43. Flow of Water in Pipes. — Mathematical expressions for the
flow of water in pipes may be derived from either of the funda-
mental hydraulic formulas
v = ci/ra or V = c^/^ba
Starting with the former equation, in the case of a pipe flowing
6o Hydraulics.
full the hydraulic radius p=-^- where d is the diameter of the pipe
and for s we may substitute --i We then have
(38) '=*'A^*
In a pipe of unit length and unit diameter without friction the
flow would be expressed by the formula
— v»
V = i/2gli or h = ^
To modify this for friction a friction factor f is introduced and the
equation then reads:
The friction varies directly as the length and is assumed to vary
inversely as the diameter. Hence, for any pipe of length 1 and
diameter d the complete equation is :
Placing (38) and (39) equal it will be found that
16.04
so that the equations can be made equivalent by the proper modi-
fications of friction factors. An extensively used formula for the
determination of c in equation (38) is that of Darcy. It reads :
For new pipe a = .00007726 and fi = .00009647.
For old pipe a = .0001543 and fl = .00001291.
These coefficients were determined from experiments on small
pipes and therefore in the case of large pipes with high velocities
the velocities computed by this formula are too small.
Various modifications of the Chezy formula, having the general
form
(41) v = cr°8»
have been proposed or derived from experiments. Lampes and
Flamant's are the best known of this type. Lampes reads
(42) v = 77.68 d0.6M gO.US
and Flamant's
(43) v = cd* 8*
in which c:=76.28 for old cast iron pipe and 86.3 for new pipe.
Flow of Water in Pipes.
6i
63
Hydraulics*
The value of c in the formula v^^cV^s may vary from 75 to 15c
for large cast iron pipe. For riveted steel pipe the coefficient varies
but little with velocity and diameter and at ordinary velocities
ranges from 100 to 115, A- L, Adams gives values of c for wood
stave pipe ranging from 100 to 170. Experiments on the Ogden
pipe line showed average values of about 120. ^
An examination of the various formulas proposed for calculating'
the flow of water in pipes will show a very wide range of results
For example, for calculating the head lost in a four-foot new cast
iron pipe, some of the principal formulas offered and the graphical
solution of the same are shown by Fig, 25, From these results it
will be seen that the data from which the formulas were derived
are evidently obtained under widely varying conditions and that
in the relation of such formulas for use on important work, they
must be chosen after a careful consideration of all the elements of
the problem, and that it is usually much better, when possible, to
utilize the original data and obsenation along similar lines when
such can be obtained, and derive the formula to be used instead of
accepting one whose basis may be obscure or unknown.
In construction %vhere pipes are short and comparatively unim-
portant, a formula may be selected which seems to agree with the
Flow of Water in Pipes.
63;
9.Ct «J0
VBLoeirv iM rccT pir sccono
Fig. 27.
1.0 *.o
vcLoeiTv IN rccT wtn second
Fig. 28.
I
Hydraulics,
elements of the problem. The formulas offered by Tutton seem
to agree well with the actual results of expferiments and several
diagrams based thereon are shown in the following pages* In two
of these diagrams (Figs, 26 and 27) the limiting values are shown
and the results obtained from any pipe of the character represented
therein should lie between these limits depending on its condition.
44- The Flow of Water Through Orifices.— It is found that
water flowing through an orifice in the side of a vessel acquires,
a velocity practically equal to that which would be acquired by ^
falling body in passing through a space equal to the head above
the center of the opening, i, e.j
(44) v= i/2iir= 8.025/E
in which
v=veIocity of spouting jet*
g=acceleration of gravity=32,a-
h^=head on opening.
The discharge through the opening would therefore be (45) q=^*
va^^aV^gh or practically (46) q^caV^gh where c is a coefficient
varying with the size and shape of the orifice and with various
other factors.
A more accurate determination of the theory of flow through a^
given orifice is derived as follows: ^|
If a thin opening is considered at a depth y be-
low the surface the discharge through the ele-^
mentary section Idy would be
(47) dq = Idjy 2^
Integrating this equation between the limit
h^ and h^ we obtain the following;
(49)
t = IKht*— h|*)i/2g or practically
m being the coefflcient of practical modification due to condition
of the orifice.
45. Flow Over Weirs. — In a weir h|=o. Hence equation (49)
becomes
(bQ) q=^ m(|)ll/5ih*
in which h is the head on the crest of the weir. That is, the ver-
tical distance from the water level above to the crest of Uie weir.
4
Flow Over Weirs.
65
^- For practical use the coefficieiit m together with the constpnts
^E- and 2g are combined as follows:
^H e = m |;/2g =: M ^2g afid equation (50) beooEnea
■ (51) q = c Iht
^m The value of m and consequently of c varies with the shape of
Hhe weir and with other factors and must be determined experi*
Hnentally. This has been done with weirs of many forms, both by
^Eajiin in France and by Rafter and Williams at the Cornell hydrau-
lic laboratory. The results of these experimental determinations
Hpe given by Figs, 30 to 34, inclusive. These figures are reduced
^^irectly from the diagrams of Mr Rafter in the Report of the
Board of Engineers of Deep Waterways, 1900.
In practice many weir formulas are in use, based on various ex-
^periments and observations. The formula of Francis', equation-
^f(S2). is probably the best known in this country. It is best adapted
lo long, sharp crested weirs without end contractions.
q = BM Ih*
Fig, 30.— Wetr Catfficlenta for Weirs of Various Shapes.
Fiow Over Weirs,
67
Fijr. 35.— Weir Ooeffidentt for We! n of Tanons 91iap««»
•66
Hydraulics.
Heod
Flf r jl' IF itr'
on CntsT of Weir in Tecr
i3
^5^._^-44^^ q:
__ .^._^^.. J^^
- ^
- - 1
|3^f^l|t|gi^riTp-if|j^| *P| I'H \\\ ]'] \ j |
-3 ,
^M,dzz -^ ^~~ii i^ r- ;::
tefj^ feUwi iN^^I mI-1 \-\ l-U-R-H
zz:
W«f - ' ,^^::f-i ^11
IJEEhEEEE^EEEEE^^iEEEEEEE
1 *^ .1^ ^^^,--i_z.i-,^3H
i^W^^ffl
E!s±?
lai -"z--''"z-i = = --z ^"H
H ' IbHtttmiTf 1
:: -
^30 z ^_z---:
-It
"5^*h+j i + W'HMihHH''^L-tr(''W^
ntr^^^y-'lthi-.i^rrzyz-^
E^rEEEEEEEEEEEEEEEEEEE:
zziz=zzziz3is;PBBJJlJ3 = C;
!?||! = ?Ee55e!EeEEEE:EEEEE
'
f [Ifljlm^
EE;iEipipEE;iE::^::EE^EE
^,.
?s-=i==ii=ii=EEH!!
0»' :""-E""Ei====±-"-
■ 1 ■ -^ ir-i
..,
i«9---pl-^~— ----1— — — :^^-:::
— t
*7.zz-:_-Lij^44: - Ji_.i3aB
J3W.Z--I i = i = — = ---^5^:^:
|?!?:|||? = = *?*:?5:" = = = i
^aMp^^^nu^
^i
^s^» -z----'i?^!iiii-i=izzi:
r^^liJJjinlllllll4t^
M M n r[m"H
Jon Crast of Weir in Fo«r
^.
Fig. 31, — Weir CopfReienla for Welis of Various shapea.
Flow Ov<fr Weira.
67
Head on Great df Weir in fiset
g^fl y> 4fl
Hood on Creor of Weir rn Fe«r
Pi|E. .^,--Weir OoefRc!eTi*i for Weire of Vatinni 3hap«e*
70
Hydraulics,
fir- 38— Weir CoelBcients for Wein of Vailoua Shai>M.
Flow Over Weirs.
71
Head on Cresf 0/ Wetr in F««t,
Cneat of W«r m fc^
fig. 34.— Weir CoemclentJ, xor Weirs ot Vaj"loufl Sllai^es^
I-
lb oceompqny Report an 5|K
1899
US.0QARO or Engineers on deep waterwavs
WATER SUPPLY DIVISION
Diagram showing Ofacborqe over v/elrs wffh
irrcqular Crests. os per Boiirv's Experirr^t r?l8 .
in compariSQn svith Dischorqe a& per Ff5knciS'&
Formula fiif a stiorp crested woir
"/;
r' r'ff ■ ■gli?''^"ra -^
^ -— ^fe — vis — rt — KB — fk >Ar-Tn! — rit — rst — cAi — iJo— ■
Dl^hang* in Cubic f «ei- per s
SBCfuna of AKpvnmeflM Mm^
1 >»^ f"^-^*^
^^
130 ITO
fr Hoirr f«e 173
135
on5Bov»rw*(r,«9foloni^ffrpnaFbot,(flQJjic Fcef par 5(scona^Appin;sqma^
wHQttr
t«e
173
03
130
f/O
9%w«e>**«Hh
T ■
ao
a A
*«
a^
' "^olT"
■a
I4t
Lift
r»>
t.tt
lEO
1 »&
^m
4aa
as*
3/0
A9«
3^
3H.
ijd
T>0
ftflA
TtO
TtO
T«C
«rt
I9S
II »
IO>«
H*9
leoo
teoe
94t
03
IS«B
iy4a
■■30
iroo
ir jc
19. »
a»
VQ»
e»OA
ie»
Has
irso
hDO
M49
t5.«e
eats
M«o
e»iQ
2l9(»
>.AJi
JAM
Vl »1
a* 7*
Uil3
3daa
^£4^
h »rb — wi^ — licj u'a ■ le^o n'o — sse 190 — sm "»r5 sja — »p aJa sJg — Wt
Dt 0f Cf"«6+
n a ^tr-iiirttr Jit
74
Hydraulics.
A number of different tormulas for the flow over weirs are given
on Fig. 35 and the flow as calculated by these formulas is showi>
on the diagram. L in these formulas represents the length of the
weir crest which in the dimension above is represented by 1.
Figure 36 shows graphically the results of the application of the
value of c as given on Figs. 30 to 34 as compared with Francis
formula.
In small weirs the effect of end contraction and of the velocity
of approach becomes important and corrections to the formulas
must be applied in order to allow for those influences.
If n==the number of end contractions and the effect of each is to
reduce the effective length of the weir by one-tenth the head on the
weir, equation (51) will become
'>'
(63) q = c(l.
The effect of the velocity of approach, for a given quantity, is tc
reduce the head on the weir by the velocity head. This reductioD
is given by the formula:
(64)
in which v'=velocity of approach and h'==velocity head.
TABLE VII.
Coefficient of discharge C for use with Hamilton Smith, Jr.'s formula (56) for
flow of water over sharp crested weirs having full contraction,
I = length of weir.
Effective
h6«d=h
.66
i(?)
0
2.6
3
4
5
7
10
15
19
.1
.632
.639
.646
.650
.052
.053
.653
.654
.655
.655
.656
.16
.619
.625
.634
.637
.0:^
.K39
.640
.040
.641
.642
.642
.2
.611
.618
.<>26
.629
.6:10
.631
.631
.632
.633
.634
.634
.26
.605
.612
.621
.623
.624
.625
.62t>
.627
.628
.628
.629
.:^
.601
.608
.(il()
.618
.619
.621
.621
.623
.624
.624
.625
.4
.595
.601
.609
.612
.613
.014
.615
.617
.618
.619
.620
.5
.5<.K)
.596
.605
.607
.608
.610
.611
.613
.615
.616
.617
6
.587
..V.)3
.601
.604
.(J05
.607
.608
.611
.613
.«14
.615
7
.58.')
.590
.598
.601
.603
.604
.tM)6
.609
.012
.613 .614
8
.'>95
.598
.600
.602
.604
.607
.611
.612
.618
9
.592
.596
.598
.600
.603
.606
.60i»
.611
.612
1 0
.5JH)
.593
.5^5
.598
.601
.(504
.60S
.610
.611
1 1
.587
.591
.593
.596
.599
.603
.606
.(K)9
.610
1 2
.585
.589
.591
.5^4
.5M7
.601
.605
.608
.610
1 H
.5S2
.580
.58(5
.584
.5*<2
.589
.587
.585
.692
.5fX)
.589
.596
.594
.592
.599
.598
.5*»6
.604
.002
.601
.607
.606
.605
.609
1 4
.609
1 5
.606
1 (>
.580
.582
.587
.591
.595
.600
.604
.607
1.7
2.0
.594
.699
.603
.607
::::::i::::::
::::::i.;:...
••••
Literature. 75
To allow for the influence of velocity of approach h' must be
added to h and equation (53; becomes
m q = c(l~n^)(h4-hM'
Experimental results at the hydraulic laboratory of the Uni-
versity of Wisconsin show- that for small sharp crested weirs, with
end contraction, the formula (56) of Hamilton Smith, Jr., is prac-
tically correct :
(56) q = c 1 1^2^ Ihf
In this formula
c?=coefficient of discharge (to be taken from Table VII),
h=observed head on crest (H) plus correction due to velocity
of approach.
Variations in the forms of the crest of weirs and in the arrange-
ment of sides and bottom of the channel of approach cause con-
siderable variation in their discharging capacity. It is therefore
apparent that unless the conditions closely agree with those on
which experimental data is available that the error of calculation
may be considerable.
LITERATURE.
BEFEBXNOES ON GENERAL HYDRAULICS.
1. Francis, Jas. B. Lowell Hydraulic Experiments. New York. D. Van-
Nostrand. 1883.
t Panning, J. T. Hydraulic and Water Supply Engineering. New York.
D. Van Nostrand & Ck). 1886.
3. Smith, Hamilton, Jr. The Flow of Water Through Orifices, Dver Weirs,
and through Open Conduits and Pipes. New York. Wiley A
Sons. 1886.
3a. Church, Irving P. A treatise on Hydraulics. New York, Wiley ft Sons.
4. Welsbadi, P. J. Hydraulics and Hydraulic Motors. Translated by A,
Jay Dubois. New York, Wiley ft Sons. 1891.
5. Carpenter, L. G. Measurement and Division of Water. Bulletin No. 27.
Colo. Agric. Expt. Sta.. Ft. Collins, Colo. 1894.
€. Boyey, Henry T. A Treatise on Hydraulics. New York. Wiley ft Sons.
1895.
7. Merriman. Mansfield. Treatise on Hydraulics. New York. Wiley 6
Sons. 1903.
*• Hydrographic Manual, Water Supply and Irrigation Paper No. 94. U. S.
G. S. 1904.
^- Hoskins, L. M. Hydraulics. New York, Henry Holt ft Co. 1907.
BEFEBENCES ON FLOW OF WATER IN CANALS.
^^ Hill, A. Flow of Water in Rivers and Canals. Van. Nost Bng. Mag.
Vol. 8, p. 118. 1870.
Hydraulics.
11* Ganpiniet, E. Unlfomi Motloa la CansLls and Rivera. Vau. NosL Eng.
Mag* Vo!. 2, p. 211. 1870.
12. Searles, W> H< Slope of Water Surface in tlie Brie Canal* Trans. Am.
Soc. a E., Vol. C, pp. 290-296, 1S77
13. Ellis, Tlieo, G. Flow ol Water, Eng, News, Nov. 26, 1881, Vol. 8,
478-9.
14. Cunnlnghaio, Allan. General DlBcnssion of Flow In Canals* Proo. In
Clr. Eng, 18S2-E3, pp. 1-95.
IG. Fteley, A. and Stearns, F. P. Flow of Water In Conduits. Trans.
Soc. C. E, Vol. 12 (1883), p. 114.
16. Mmn, P. J. Irrigation Canals and Otbar Irrigation Works and Flow
Water In Irrigation Canals. Denver, Colo. 1892.
17, Adamai, A. L. Diagram for Calculating Velocities, Grades and Mean
Radii for Flumes and Ditches. Eng. News, Feb. 13, 1892. p. 157.
18* GanguUlet, E. and Kutter, W. R. A General Formula for the Uniform
Flow of Water In Rivers and Other Channels. Trans, by Ru
[ dolph Herring and John Trautwine. New York, Wiley & Sons.
1893.
19. Bou&sinesq, H. The Gradual V&rlatloas in th© Flow of Water la Chan-
nels of Large Section. Comptes Rendus. May 31, 1897.
20. Bouflfilnesq, J. Expertmental Verification of the Theory of Gradually
I Varied Flow in Open Channels. Comptes Rend us. June 14.
1897.
2L The New Formula of Bazln. Genie Civil, March 5, 1S9S,
22. A New Formula by Bazin for Computing Flow of Water in Open Chan^
nels. Eng. News, July 14, 1893*
23. Bazln's New Formula for Flow in Open Channels. Eng. News, 1898, Vo
2, p. 26.
24. A Study of a New Formula for Calculating the Discharge of Open Chan-
nels. Ann ales des Fonts et Chaussees. 2 Trimegtre, 1898.
25. Determination of Flow in Rivers and Canals. Zeltsclir. d Oesterr. Ing. u
Arch. Ver., Vol 50. pp, 533^34. 1898.
26. Swan, Chas. H. and Horton, Theo. M, Hydraulic Diagrams for the Dis
charge of Con du its and Canals, New York, Eng. News Pub
Co. 1899.
27. Croathwaite, Ponsby Moore. Two Graphic Methods Applied to HydraulicI
Calculations. EngineeHng. Loudon. July 15, lS98t 1
38, Concerning the Conception of a Hydraulic Moment of Conduit Cross Sec^
tlon. ZeitscJir, fur Arch, u Ing. Vol. 4G, 1900, Heft-Ausgabe.
Col, 402-417.
29, Siedek, Richard. Studies of a New Formula for Estimating the VeloclTy
of Water In Brooks and Small Channels. Zeltschr, d Oeaterr.
Ing. und Arch. Ver, Vol. 55, pp. 98-106. 1903. J
BErEBKNCES ON FLOW OF WATEB THROUGH Fn*ES,
30. Francis, Jas. B. Flow Through Pipes, Trans, Am, Soc C. E, Vol, 2,
p. 45. 1872,
31. Danach, a G. Flow of Water In Pipes under Pressure. Trans. Ahl So<
C. E. Vol. 7, p. 114. 1878.
32. TVehage, H, Fnction Resistance in Pipes. Dingler's Polytechnlsrhei
Journal. 1884, p. 89.
I
Literature. 77
33. Steams» F. P. Flow of Water Throat a 48^ Pipe. Trans. Am 8oc C.
R, Vol 14, p. 1. 1886.
34. Mair, J. G. Flow Through Pipes at Different Temperatures. Proc. Inst
C. E. Vol. 84, p. 424. 1886.
35. Duane, James. Effect of Tuberculatlon on Delivery of a 48^^ Water Main.
Tnuus. Am. Soc. C. B. 1893, p. 26.
36. Tuttle, Geo. W. Economic Velocity of Transmission of Wlater Through
Pipes. Eng. Rec. Sept 7, 1895.
37. Coffin, Freeman C. The Friction in Several Pumping Mains. Eng. News,
Feb. 20, 1896.
38. Hawks, A. McL. Flowage Test of 14"^ Riveted Steel Main at New Wes^
minster, B. C. Eng. News, July 30, 1896.
3S. Flow of Water in Wrought and Cast Iron Pipe. Am. Soc. Mech. Eng.
Dec. 1897.
40. Herschel, Clemens. 116 Experiments on the Carrying Capacity of Large
Riveted Metal Conduits. New York. John Wiley & Sons. 1897.
4t Gould, E. Sherman. The Flow of Water in Pipes. Am. Mach. Mar. 8,
1898.
42. Hawks, A. McL. Friction Coefficient for Riveted Steel Pipes. Proc. Am.
Soc. C. E. Aug. 1899.
4S. Palton, C. H. Flow of Water in Pipes. Jour. Ass'n Eng. Soc. Oct. 1899.
4i Marx, C. D., Wing, Chas. B., and Hosklns, L. M. Experiments on the
Flow of Water in the Six Foot Steel and Wood Pipe Line of
the Pioneer Electric Power Company. Proc Am. Soc C. E.
Feb., 1900; April, 1900; May, 1900.
45. Gregory, John H. Diagram Giving Discharge of Pipes by Kutter's For-
mula. Eng. Rec. Nov. 3, 1900.
46. Pbnnulas for Flow In Pipe. Eng. News, 1901. Vol. II, pp. 98, 118, 332.
476.
47. Noble^ T. A. Flow of Water in Wood Pipes. Trans. Am. Soc C B. Vol.
49, 1902.
^S- Sapb, A. V. and Schoder. E. W. Experimental Study of the Resistance of
the Flow of Water in Pipes. Proc. Am. Soc. C. B. Maj, 1903;
Oct, 1908.
BETEBENCES ON FLOW OF WATEB OVEB WEIBS.
49. Pteky, A. and Steams, F. P. Flow of Water over Weirs. Trans. Am.
Soc C. B. Vol. 12, p. 1. 1883.
50. Francis, J. R Experiments on Submerged Weirs. Trans. Am. Soc C.
B. Vol. 13, p. 303. 1884.
51 Henchel, Clemens. Problem of the Submerged Weir. Trans. Am. Soc
a B. Vol. 14, p. 189. 1885.
52. hrestlgations on the Flow over Submerged Weirs. Zeltschr. des Ver.
Deutsch. Ing. 1886, p. 47.
W. Hind, R. H. Flow over Submerged Dams. Proc. Inst C. B. VoL 86, p.
307. 1886.
W. Kaberstroh, Chas. B. Epxerlments on the Flow of Water Through Large
Gates and over a Wide Crest Jour. Ass'n Bng. Soc Jan., 1890,
p. 1.
5
f8
Hydraulics.
S5.
66.
67*
53.
eo.
6t
ea.
$5.
66.
67
6S.
€9.
70.
71.
72.
73,
74.
75.
76.
77.
The Floir of Water orer Dams and Spillways, Bug. Rea Jun« f , 1900.
Flow of Water over Sliarp Greeted Weirs, Annales des Ponta et Chaua^
sees. Jan, 1, 18&0; Nov., 1S91: Feb., 1894. Also Proc. Eng. Club
of Philadelphia, Jan., IBM; July. 1S02; OcL, 1892; Apr., 1893.
Flow over a Weir of Curved Proflle. Keltschr. d Oestarr, Ing. n AicIl
Ver. June 2, 1906.
Flymi, A, D. and Dyer, C. W* D. The ClppcletU Trapezoidal Weir.
Trans. Am. Soc C. B. July, 1894,
Warenaklold, N. Flow of Water over Rounded Crest Eng. Newi, J;
ai. 1895* Vol. 83, p. 75.
PrUzel, J. P. and Herachel, Clemena, Flow over Wide Horizontal Top
Welrt, Eag. News, 1892. Vol 11, pp, 290, 440, 446: 1895, Vol. 1,
p. 75.
John son, T. T. and Cooley, B. S. New Experimental Data for Flow ot©? a
Broad Crest Dam. Jour, W, Soc Engrs. Jan., 1896*
Wide Cr^t Weirs, Bazln'e Formula. Eng. News^ 1890. Vol. I, p. 16^
Vol, ir, p. 577: 1896, Vol, I, p. 26.
E:cperinient3 on Flow OTor Dams, Eng. News, 1900, P< 207*
Hafter, Geo. W. The Flow of Water over Dama, Proc Am* Soa C- IL
Mar,, 1900.
Heyno H. Study of Hydraulic Coemcienta, 2eltschr. d Oesterr In^. n
Arch. Ver Dec. 6 1900.
Dery, Victor A, E. D, Experiments on the Measurement of Water otw
Weira Proa Inst, G. E, Vol. 114, p. 333, 1893.
K^
^
BEFZBEKCES Olf BACK WATI3 AKP IN THEFEBIKOI.
d
Wood, De Volson, Back Water la Streams as Produced by Dams. Trans,
Am. Soc. C, E, Vol. 2, pp. 255-26L 1873,
Hutton, W. H, Back Water Caused hy Contractions, Transu Am* Soc. C*
m Vol. 11, pp. 212-240. 1882.
Olllmore, Q, A. Ohsrt ruction to River Discharge by Bridge Plera, Van.
Host, Eng. Mag, Vol. 2$, p. 441. 1882. J
Back Water from Dams. Eng, Rec, July 9, 1892, ^
Ferrlday, Robert Measurements of Back Water* Eng. Newa, 1896, VoL
n, p. 28.
Frescolm, S. W* Back Water Caused by Bridge Piers and otber Obf^tniG'
tlons. Jour Eng. Soc, Lehigh Univ. Feb., 1899.
The Estimation of Damages to Power Plants from Back Water. Eag.
Rec April 26, 1902.
Harria, E, G., Taylor, W. D.. Ladshaw, T. B. Back Water from Dams.
The E^ect on Meadow Lands, Eng, NewSf 1902* YoL II«
142 and 311
Tables for Computation of Swell on Open Water Courses* Zeltachr.
Ardi. und Ing. Vol. 49, Cola. 268-274* 1903.
Fllegoer, A. A New Method of Computing the Back Water Curva
SchwelzerlBChe Bauaeltting. Aug. 22. 1903.
Tolmaa, BreiUIav. The Computation of Back Water Curves. Oesterr,
Wocbensohn f d Oeffent Baudienst July 1, 8, 1905.
ms.
I
CHAPTER IV.
WATER POWER,
THE STUDY OF THE POWER OF A STREAM AS AFFECTED BY FLOW.
46. Source of Water Power. — ^Water power depends primarily
on the flow of the stream that is being considered for power pur-
poseSy and on the head that can be developed and utilized at the
site proposed for the power plant. Both head and flow are essen-
tial for the development of water power, but both are variable
quantities which are seldom constant for two consecutive days at
any point in any stream. The variations in head and flow radically
affect the power that can be generated by a plant installed fdr
power purposes. These variations also greatly affect the power
that can be economically developed from a stream at any locality.
The accurate determination of both head and flow therefore be-
comes very important in considering water power installations and
hence should receive the careful consideration of the engineer. The
neglect of a proper consideration of either or both of these factors
has frequently been fatal to the most complete success of water
power projects.
47. Factors of Stream Flow. — ^The quantity of water flowing in a
stream at any time, which is more briefly termed "stream flow"
or "nm-off," depends primarily upon the rainfall. It is, however,
mfluenced by many other elements and conditions. It depends not
only upon the total quantity of the yearly rainfall on the drainage
area, but also on the intensity and distribution of the rainfall
throughout the year. In addition to these factors the geological
structure of the drainage area, the topographical features, the sur-
face area of the catchment basin, the temperature, the barometric
condition, all influence and modify the run-off. Sufficient data is
not available for a full understanding of this subject, but enough
» available so that the general principles involved can be intelli-
gently discussed knd the problems considered in such a way as to
?ivc a fairly satisfactory basis for practical work. A knowledge
0^ the importance of the factors above mentioned and the extent to
which they modify, influence or control stream flow, is essential
Be-
Water Power.
to a broad knowledg^e of water power engineering. These factor?
are discussed in more detail in chapters VI, VII and VIIL
48, Broad Knowledge of Stream Flow Necessary. — The flow of
a stream is constantly changing and any single measurement of
that flow will not furnish sufficient data on which to base an in-
telligent estimate of the extent of its possible or even probable
economical power development* A knowledge of the economical
possibilities of such development must be based upon a much
broader knowledge of the variations that take place in the flow of
the stream. In order to fully appreciate the power value of a
stream, the character and extent of its daily fluctuations must be
known or estimated. Averages for the year, monthly averages, and
estimates of average power have been ordinarily taken as a basis
for water power estimates, but they are more or less misleading,
unsatisfactory and uncertain for the reason that such averages in-
clude extremes, the maximum of which are often unavailable for
water power purposes without more extensive pondage than is
usually practicable. These maximum and minimum flows which
affect the power of a stream not only through the quantity flowing
but also through the head as well, as will be hereafter discussed*
arc of the utmost importance for a broad consideration of water
power. So also is a knowled^ife of the various stages of flow and
the length of time that each will prevaiL Such knowledge demands
daily observations or estimates of daily flow which can be repre-
sented in graphical form by the hydrograph,
49, The Hydrograph, — ^The hydrograph, constructed for the study
of stream flow and its influence on water power, may be drawn by
representing the daily flow in cubic feet per second at the point
of observation by the ordinates of the diagram and the element of
tame by the abscissas, (See Fig. 37.) The result is a graphic
diagram which shows the character and extent of the daily fluctua
tions in the flow of a stream at the point of observation during thi
period for which the hydrograph has been prepared,
A single observation of the flow of a stream represents a totally
inadequate and unsatisfactory criterion for water power consid-
eration. By reference to Fig, 37 it will be seen that, if the dis-
charge of the Wisconsin River at Necedah had been measured only
on August $t 1904, the conclusion would have been reached that
the discharge of the river was about 2,100 cubic feet per second.
If the measurement had been taken only on August 15, 1904, the
flow would have been determined at about 5,850 cubic feet per
second, or almost three times as great as on the first date, Thfl
The Hydrograph.
8i
'0N033S H3d laaj otano
I
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2
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'aiiN suvntiB B3d ONoaas Hid xaaj siana m aauviaiio
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""-BNoaas Sad laaa "aiana n\ aaavHOiia.
89
Water Powtr<
difference between the dates might be even greater, and no slng!^
measurement nor any series of measurements for a single week or
month would ^ve a fair criterion from which the normal flow of
the river could be judged.
The hydrograph of the daily flow of a river for a single year
gives a knowledge of the variation in flow for that year only
under the peculiar conditions of the rainfall, the evaporation, and
the other physical factors that modify the same and that obtain
for that particular year. Such infonnationj while important, is noi
altogether sufficient for the purpose of a thorough understanding
of the availability of the stream flow for power purposes. Observa-
tions show that stream flow varies greatly from year to yeafp and
while, with a careful study of the influences of the various factors
on stream flow, together with a knowledge of the past variations
in such factors, the hydrograph for a single year may give a fairly
clear knowledge of the variations to be expected in other years
where conditions differ considerably, still it is desirable that the
observations be extended for as long a period as possible. Such
long time observations may remove the estimates of flow entirely
irom the domains of speculation and place them on the solid ground
of observed facts. Hydrographs of a river that cover the full range
of conditions of rainfall, temperature, etc., which are liable to pre-
vail on its drainage area, give a very complete knowledge of the
flow of the stream for the purpose of the consideration of water
power.
It is rare, however, that observations of stream flow for a lon^
term of years are available at the immediate site of a proposed
power plant. Such observations are ordinarily made only at loca-
tions where power has been developed and where water power oi
similar interests have been centered for a long period of time, Oc
casionally, however, the future value of potential powers is rccog*
nized and appreciated^ and local observations are maintained for <
series of years by interested parties, having a sufficient knowledge
of the subject to recognize the value and importance of such in-
formation. The variation of flow for some considerable time pre-
vious to construction is thus available upon which to base the desigra. .
In considering new installations, one of four conditions obtains -
First: Hydrographs are available at the immediate site proposed
Second ; Hydrographs are available at some other point on tN^*
river above or below the proposed installation.
The Use of Local Hydrographs. 83
Third: Hydrog^phs are not available on the river in question
but are available on other rivers where essentially similar condi-
tions of rainfall and stream flow prevail.
Fourth: No hydrographs, either on the river in question or on
other rivers of a similar character and in the immediate vicinity,
are available.
50. The Use of Local Hydrographs. — ^When hydrographs, con-
structed from observations taken at the immediate site of the pro-
posed water power installation, are obtainable, for a considerable
number of years, the most satisfactory character of information is
available for the consideration of a water power project. Under
such conditions the engineer is not obliged to consider the rela-
tion of rainfall to run-off or to speculate as to the relative value of
the stream in question compared with other adjacent streams, or
as to tl)e effects of the physical conditions of drainage area, evap-
oration, temperature and other factors on stream flow. The actual
daily flow of the stream from day to day, perhaps through all
ranges of rainfall, temperature, evaporation and other physical con-
ditions, is known and the principal points which must be consid-
ered are : First, the head available ; Second, the effects of the varia-
tions of flow on the variations in head; and Third, the extent to
which the flow can be economically developed or utilized. Gen-
erally, however, even where local hydrographs are available, they
arc not sufficiently extended to cover all the variations in river flow
which must be anticipated, and it is ordinarily desirable to com-
pare the available data with the flow at other points on the stream
in question or with other streams in the immediate vicinity.
51. Use of Comparative Hydrog^phs. — Hydrographs taken at
other points on the same river, or on other adjacent rivers where
conditions are reasonably similar, are of great value in considering
the local stream flow, — ^provided all modifying conditions are under-
stood and carefully considered. Hydrographs are ordinarily pre-
pared to show the cubic feet per second of actual flow at the
point at which observations are made. If the observations (and
the hydrographs based thereon) made at some other point on a
stream, or on some other streams, are to be used for the considera-
tion of the flow at a point where a water power plant is to be
installed or considered, the relation of the flows at the several
points must be determined.
I As a basis for such comparison of stream flow, it may be as-
Water Power.
Wis*
Use of Comparative Hydrographs. 85
stream, or at points on different streams under similar circum-
stances, is essentially the same. This is not strictly true, or per-
haps it may be more truly said that the apparent similarity of condi-
tions is only approximate and hence differences in results must
necessarily follow. For a satisfactory consideration of the subject
of comparative hydrographs, the variations from this assumption,
as discussed in another chapter, must be understood and appre-
ciated. For practical purposes, however, the assumption is often
essentially correct and forms a basis for an intelligent considera-
tion of stream flow where local hydrographs are not available. Fig.
37 is a hydrograph constructed from observations made on the
Wisconsin River at Necedah, Wisconsin, by the U. S. Geological
Survey for the water year, 1904, and shows the daily rate of dis-
charge of the Wisconsin River at that point for the year named.
The area of the Wisconsin River (see Fig. 38) above Necedah is
5,800 square miles. If, therefore, we draw a horizontal line from
the point representing 5,800 cubic feet per second on the discharge
scale (see Fig. 37), the line so drawn will represent a discharge at
Necedah of one cubic foot per second per square mile of drainage
area, and a similar line drawn from the 11,600 cubic foot point on
the vertical scale will represent a discharge of two cubic feet
per second per square mile, and so on. These lines may be fairly
regarded not only as indicating the flow per unit of area of the
river at Necedah, but also the relative flow per unit of area of the
Wisconsin River at points not greatly distant therefrom. At Kil-
l>oum, (see Fig. 38) located on the same river about forty miles
below Necedah, the flow may be assumed to be similar and pro-
portionate to the flow at Necedah. Above Kilboum the drainage
2rea is 7,900 square miles, and with similar flow the discharge
would be proportionately greater. The fact must be recognized,
^d acknowledged, that the hydrograph is strictly applicable only
to the point at which^ it is taken, and that certain errors will arise
in considering its application to other points, yet observations and
comparisons show that, while such errors exist, they are not nearly
so important as the errors which arise from the consideration of
averages, either annually or monthly.
Consider, therefore, on this basis the Necedah hydrograph as
^hown in Fig. 37. On this diagram a flow of one cubic foot per
second per square mile at Necedah, representing an actual flow of
5»8oo cubic feet per second at that point, would, by proportion,
present a flow of 7,900 cubic feet per second at Kilbourn and,
i
^H
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Reliability of Comparative Hydrographs.
8r
with a suitable change in scale, the diagram may be redrawn to rep-
resent the flow at Kilboum as shown in Fig. 39. This same method
can be applied to any point on the same river or to comparative
points on different rivers.
S3* Reliability of Comparative Hydrographs. — It must be clearly
understood that comparisons as above described hold good only
as the conditions are essentially similar at the various points com-
pared.
Stream flow at the best is very irregular and varies greatly from
year to year. The actual departure from the truth can best be
imderstood and appreciated from an actual comparison of flows
on adjacent drainage areas where observations have actually been
made for a term of years. From such an investigation, which can
be made as extended as desirable, the true weight to be given to the
comparative hydrograph can best be judged. It is not believed
that the actual variations from the truth, as shown by carefully
selected comparative hydrographs, will be any greater than the flow
variations which actually take place from a drainage area from year
to year under the varying conditions of rainfall and climate. This
method, therefore, is believed to be a scientific and systematic one
for the consideration and discussion of probable variations in stream
flow at any given point, if its limitations and the modifying in-
fluences known to exist on different drainage areas and under
liferent geographical, geological and meteorological conditions are
known and appreciated-
53, When no Hydrographs are Available. — In a new country
where no observations are available either on the drainage area
under consideration or on other areas adjacent thereto, the study
of comparative hydrographs is impossible and a different method
ol consideration must be used. If no data are available, time must
be taken to acquire a reasonable amount of local information which
should include not less than one year s observation. In addition
to such observation a study as thorough as practicable should be
made of the geology, topography, and other physical conditions
that prevail on the water shed. Rainfall data is commonly avail-
able for a much greater range of time than the observations of
stream flow. The relations of rainfall to run-off are hereafter dis-
cussed and approximate fixed relations are shown to exist between
them. From such relations, and from a single year s observations,
conclusions may be drawn as to the probable variations from the
observed flow which will occur during the years where the rainfall
I
Water Power.
t
II
3
i
2
s
P3
ixm lyvntis u3d dmqois «1iI 131J sians m ssuv^hdsiq
The Hydrograph as a Power Curve, 89
varies greatly from that of the year during which observations are
available. Such conclusions are necessarily unsatisfactory, or at
least much less satisfactory than conclusions based on actual
stream flow. The consideration of the best information available
on any project is the basis on which the engineer should always
rest his conclusions, and all relations which will throw light on the
actual conditions should be g^ven careful attention. If a water
power plant must be immediately constructed upon a stream con-
cerning which little or no information is available, then the risk is
proportionately greater, and safety is obtained only by building
in such a conservative manner that success will be assured for the
plant installed and on plans that will permit of future extensions
should the conditions that afterward develop warrant an extension
of the same.
54. The Hydrograph as a Power Curve. — ^The hydrograph, by a
simple change in the vertical scale similar to that already consid-
ered, may also be made to show graphically the variations in the
power of the stream. If, for example, at Kilbourn, a constant fall of
seventeen feet be assumed, then a flow of one cubic foot per second
per square mile represents a total flow of 7,900 cubic feet per second,
and this flow, under 17 foot head, will give a theoretical hydraulic
horse power as follows :
H.P. = :?520X17.^ 15281
Now if a hydrograph be constructed on such a scale that the line of
flow of one cubic foot per second per square mile will also repre-
sent 15,261 horse power, the result will be a power hydrograph
(sec Fig. 40), which represents the continuous (24 hours per day)
theoretical power of the river under the conditions named.
On account of losses in the development of power the full theoret-
ical power of a stream cannot be developed, and hence the actual
power that can be realized is always less than the theoretical power
of the stream. If it is desired to consider the actual power of the
stream on the basis of developing the same with turbines of 80
per cent efliciency, the line representing the flow of one cubic foot
per second per square mile will represent the actual horse power
to an amount determined as follows :
A rxT> _7900X17X .80 7900X17 -,,,^
^^•■^- 878 = 11 = ^^^
A hydrograph platted so that the line of one cubic foot per
square mile will represent this amount, will represent the actual
90
Water Power
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The Hydrograph as a Power Curve.
91
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92 Water Power.
horse power of the river at Kilbourn with the wheels working with
the efficiency and under the head named. Such a hydrograph is
shown by Fig. 41, referred to by the left-hand scale (A). Powcr^
however, is not always used continuously for twenty-four hours.
If pondage is available the night flow may be stored and utilized
during the day. If the flow of twelve hours at night is impounded
and used during the day under the seventeen foot head, the power
will be double that shown on scale A, and can be represented by
another change in scale as shown by Fig. 41, referred to scale B.
If the flow for the fourteen hours of night is stored and utilized in
the ten hours of day, then the hydrograph can be made by another
change in scale to represent the ten hours power as shown by
Fig. 42.
The total horse power hours which are available from a stream
for each day may be represented (either theoretically or actually)
by multiplying the scale of continuous power by 24. The actual
horse power available at Kilbourn under the conditions named is
represented by scale C in Fig. 41. It will be noted that by pointing
off one place in the figures of scale C, Fig. 41, the hydrograph will
represent the same condition as shown in Fig. 4a.
CHAPTER V,
WATER POWER (Continued.)
THE STUDY OF THE POWER OF A STREAM AS AFFECTED BY HEAD.
55. Variations in Head. — In the previous chapter the graphical
representation of stream flow has been considered. A method for
the expression of the power resulting from the fluctuations of
stream flow and under a constant head has also been shown. Ex-
perience shows, however, that such a condition seldom if ever
occurs. In some cases where the available head is a very large
element of the possible power, the fluctuations may be so small
as to be of little or no importance. In many other cases where the
available heads are considerable, the importance of the fluctuation
in head is comparatively small, under which condition the diagrams
already discussed are essentially correct and are satisfactory for
the consideration of the varying power of the stream. In power
developments under the low heads available in many rivers, the
fluctuation in head is almost or quite as influential on the con-
tinuous power that may be economically developed from a stream
wthe minimum flow of the stream itself.
The hydraulic gradient of a stream varies with the quantity of
Wer flowing. At times of low water the fall available in almost
every portion of its course is greater than is necessary to assure
^he flow between given points and frequent rapids result (see R.
^ %• 43) which are commonly the basis for water power develop-
rieed rrow.
M«dium Wiatttr
Loiv Wafmr
•tr«oni Bad.
Fig. 43. — ^Hydraulic Gradients of a Stream Under VarlOYiB Conditions
of Flow.
• 0
94
Water Power.
ments. As the flow increases, however, a higher gradient anc
greater stream section is necessary in order to pass the greater
quantity of water, and the rapids and small falls gradually become
obscured (as shown by the medium water lines, Fig. 43) or dis-
appear entirely under the larger flows (as shown by the higher
water linei Fig. 43) • Water power dams concentrate the fall of the
Ftg. 44. — Hydraulic Gradients of the Same Stream After the ConBtnietloii
Dam and Under Various Conditions of Flow.
tlon of™
J
river that is unnecessary to produce flow during conditions of lo'
and moderate water (as shown in Fig, 44), and when the gradient
of the water surface and the cross section of the stream are tn-
^ creased to accommodate the larger flow, the fall at such dams is
frequently greatly reduced (as shown by the medium water line In
Fig. 44) or, during high water, the fall is largely or completely de-
stroyed (as shown by the high water lines in the Figtire), or at
least is so reduced as to be of little or no avail under practical water
power conditions. M
The cross section of the river bed, its physical character ana
longitudinal slope, are the factors which determine the hydraulic
gradient of a stream under different flows* They are so variable
in character and their detail condition is so difiicult of determina-
tion that sufficient know^ledge is seldom available, except possibly
in the case of some artificial channels, to determine, with reason-
able accuracy, the change of the surface gradient and cross section
of the water under various conditions of flow. Where a power pi
is to be installed, it is important to ascertain the relation of floi
to head in order that the available power may be accurately detei
mined. Where a river is in such condition as to make the &i
termination of a discharge rating curve possible, either by din
river measurement at the point in question or by a comparison wi
the flow over weirs at some other point, such determination shoul
be carefully made, as such knowledge is of the utmost importain
in considering the problem of continuous power.
The Rating Curve,
95
S6. The Rating or Discharge Curve, — The rating curve, which
will be discussed in some detail in a later chapter, is a hydrograph
that represents the relation of the elevation of the v;^ater surface in a
channel to the quantity of water passing a given cross section. The
form of this curve varies with the various conditions of the cross
section both at the immediate point and for a considerable distance
above and below the location considered and can usually be de-
termined only by detail observations. The rating curve is a uni-
form curve only for channels in which no radical change in form of
cross section occurs with the increase of fiow. (See A Fig. 45.) If,
on account of o%^erflow conditions, or sudden enlargements of the
cross section, that cross section varies radically in form at a given
height, then at this elevation a radical change in the slope of the
rating curve is likely to occur. (See B and C Fig, 45,)
m
Ftg, 45. — Tte Influence of the Stream Cross Section on the Rating Curve.
Any change in the bed of the stream may, and frequently does,
modify to a considerable extent the rating curve, which must be
expected to vary under such conditions to an extent that depends
on the variations that take place in the cross section and elevation
of the stream bed. Such variations, however, are not, as a rule, of
great magnitude and consequently will not usually affect the head
materially at a given point.
k-^
96
Water Power*
In Fig, 46, which shows the rating curve of the Wisconsin Rin
at Necedah, Wis., as determined at different times during the years
1903 and 1904, an extreme change of head of about six inches will
be noted for ordinary flows. When tlie change in head is of s
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Discharge in Ciu Ft. Per Second.
Fig. 46. — Eating CurTes^ Wisconsin River at Necedah, Wla*, Showing Ch;
in Head Due to Changes In Cross Section.
u^
a&fM
ficient importance to warrant the expense, the river channel may b^
so dredged out as to restore the original head when the reduction
in head is occasioned by the filling of the section* ^
57. The Tail Water Curve. — It will be readily seen that while the
rating curve sliows the relation between stream flow and river
height prior to the construction of a dam, it will still represent the
condition of flow below the dam after construction is completed.
The water flowing over the dam will create a disturbed condition
immediately below. If the velocity of the flow is partially checked ,
or entirely destroyed, a heading-up of the water may result beloi^fl
the dam suflicicnt to give the velocity required to produce the iow^
in the river below, but it will soon reach a normal condition similar^
to that which existed previous to the construction of the dam*
58* The Head Water Curve, — In Chapter III is shown (see Fi|
35 and 36) the discharge curves over weirs of various forms and lh(
formulas representing them are also quite fully discussed, Froi
The Graphic Representation of Head.
97
these formulas or diagrams a discharge curve can be readily cal-
culated, with reasonable exactness, for a dam with a certain form
and length of crest. Such a curve will show the height of the head
waters above the dam and under any assumed conditions of flow.
From the rating curve of the river at the point considered, and the
discharge curve of the weir proposed, the relative positions of head
and tail waters under varying conditions of discharge can be readily
and accurately determined, and if a weir is to be built to a certain
fixed height, it will be seen that the head under any given conditions
of flow may be thus determined.
59. Graphic Representation of Head. — Fig. 47 shows the rating
curve of the Wisconsin River (see lower curve marked "Tail Water
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Tig. 47.--Showing Head at the Kilboum Dam Under Various Conditions of
Flow.
Water Power,
I Curve") at Kilboum. On this diagram has also been platted scv-
■ eral discharge curves^ two being for a weir of 300 feet in lengtb
I and two for a weir of 350 feet in length* Both weir curves in the
I upper set are based on the assumption that the entire flow of water —
I is passing over the weir. The crest of the dam is shown as raise^|
■ to gauge 19, and the distance between the rating curve, which now
m represents the height of the tail water, and the weir discharge
■ curves, which represent the height of the head water (with two dif-
■ ferent lengths of weir) under different conditions of flow, wilt show
I the heads that obtain at all times under these assumptions.
I The entire discharge of the stream, however, will not pass over
I the dam except when the plant is entirely shut down, which wouhl
I seldom be the case. The essential information which is desired
I therefore is the available head when the plant is in active operation.
■ At the Kilbourn plant the discharge of the turbines to be installed
■ under full head will be 7,000 cubic feet per second, hence, with the
I plant in full operation, this quantity of water will be passing
I through the wheels. Therefore in determining the relation between
I head water and tail water it must be considered that with a flow of
I 7»ooo cubic feet per second, the water surface above the dam will
I be at the elevation of its crest, no flow occurring over the spillway,
■ and that only the flows greater than this amount will pass over
I the dam. Another curve for each weir has therefore been added
I to the diagram in which the zero of the weir curves is platted
I from the point where the line representing the height of the dam
I (elevation 19) intersects the line representing a discharge of 7,000
I cubic feet per second. From this diagram (Fig. 47) it will be seen
I that other heads, shown in Table VIII, will obtain under variou
I conditions of flow.
I It will readily be seen that the line representing the height
■ the dam is not essential and that the curves may be platted relative
I to each other, leaving the height of the dam out of the question
entirely and indeterminate. A curve constructed on this basis but
otherwise drawn in the same manner as in Fig. 47, is shown in Fi^_
48. In Fig. 48, wherever the weir or head water curves pass abovfl
the tail water curve, it shows that an increase in the head will re-
Lsult under the corresponding condition of flow and wherever they
pass below such curve, it shows that a decrease in the head will
result under the corresponding condition of flow, the amount of
which is clearly shown by the scale of the diagram- Consequently,
:
y
>int
J
The Graphic Representation of Head.
99
of, no discharge, the head available under any other condition can
be immediately determined from the diagram.
From this diagram the changes in head (as shown in table IX)
can be determined and these, with a 17 foot dam, will give the total
TABLE VIII.
Oauge heightM and heada available at Kilboum Dam under varioue conditions
of flow, teith a length of ttpillway ofSOO and SSOfeet
Hkad Water
Tail
Water.
Head with
Flow in cabic feei
per second.
300
ft. dam.
a^o
ft. dam.
300
ft. dam.
350
ft. dam.
7000
10
23.9
25.2
27
28.5
30.2
31.5
32.7
19
22.3
24.6
26.2
27.7
29.3
30.4
31.6
2
6.1
8
10.3
12.2
13.6
14.7
15.6
17
17.8
17.2
16.7
16.5
16.6
16.8
17.1
17
14000
17 2
21000
16.6
28000
15.9
35000
15.5
42000
16.7
tfOOO
15.7
56000
15.8
heads available under various conditions of flow as shown in the
last two columns. These heads will be seen to correspond with the
heads given in table VIII.
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•II8MAI6C fr WlfCOMIN RIVCR AT KILIOORN —IN CUIIC FT. PCR 8CC.
FIc- 48. — Showing Change in Head at Kilboum Dam Under Various Condi-
tions of Flow.
6:J24;j?
lOO
Water Power.
TABLE IX.
Vhangev in heafi at Kilbourn D^m trifh lengths of crest ^/ SDO and S50 feet owrf
under isarious conditionM of flow vnth result in ff total available head with 17 ft.
dam.
CflAXtifift IN
HiiAD WITH
TotAL Head with
Flow in cubic feet
per eecoQd.
300
(t. dam.
350
ft. dam.
300
ft. dam.
350
ft. dam. ,
7000 ,
0
+ ,8
+ .2
— .3
— .5
— ,4
— ,2
+ .1
0
+ .2
— A
— l.l
—1.6
—1.3
—1-3
—1.2
17
17.8
17.2
16.7
16.6
16.6
16,8
17.1
17
14000
17.2
210t)0
16.6
mjoo
15*9
350UO, ..* ,
16 6
42000 **.***.
15.7 i
49000......
15,7 '
66000 -
15.8
I
60. Effects of Design of Dam on Head. — It should be noted in
both of the last diagrams that the height of the water above the
dam is readily controlled by a change in the form and length of
the weir; that a contraction in the weir length produces a corre*
sponding rise in the head waters as the flow increaseSp while the
lengthening of the weir will reduce the height of the head water
under all conditions of flow. The physical conditions relative to
overflow above the dam will control the point to which the head
waters may be permitted to rise and will modify the length and the
construction of the dam. Where the overflow must be limited, the
waters^ during flood times, must he controlled either by a suffi-
cient length of spillway or by a temporary or permanent reduction
in the height of the dam such as the removal of flash boards, the
opening of gates, or by some form of movable dam, ■
- Having determined the head available at all conditions of river
flow, the hydrograph, as previously shown, may be modified to show
the actual power of the river under the varying conditions of flow-
The vertical scalei in this case, instead of being uniform must be
variable as the head varies. Fig. 49 shows graphically the variation
in the continuous theoretical power of the river taking into con-
sideration the variation in head which wtll actually occur* Com-
pare this hydrograph with Fig. 40 in which no variation in head
IS considered. ^|
61. Effect of Head on the Power of the Plant — ^It is important^
at this point to take into consideration the effect of head and fiow^
on the actual power of the plant. In most rivers^ under flood coj
EfiEects of Design of Dam on Head.
lOI
nVSHlS JO U3M0d SSHOH 1V9IX3U03HX snonNUJOo
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M ^ n w —
3im 3iivntia usrf ONoaas uad laaj aiana ni
aaHVMasio
xoa
Water Power,
tions, the power theoretically available is largely increased, forJH
while the head may diminish, the flow becomes so much greater
that the effect of head on the theoretical power is more than off-
set thereby. Practically; however, the conditions of head under
which a given water wheel will operate satisfactorily (L e. at afl
flxed speed) are limited, and, while the theoretical power of the
river may radically increase, the power of the plant installed under
such conditions will often seriously decrease, and under extreme
conditions may cease entirely. The discharging capacity of any
opening is directly proportional to the square root of the head, andl
the water wheel, or water wheels, simply offers a particular fornlfl
of opening, or openings, and operates essentially under this general
law» With a fixed efficiency, therefore, the power which may be
dereloped by a water wheel is in direct proportion to its discharging
capacity and to the available head. Hence, the power of the wheel
decreases as the product of these two factors, and therefore the
power available under conditions of high flow and small head are
much less than where the head is large and the total flow of the
river is less. The only way, therefore, to take advantage of the
large increase in theoretical power during the high water condi-
tions is to install a surplus of power for the condition of average
water. This may sometimes be done to advantage, but its extent
soon reaches a practical limitation on account of the expense. ItH
often becomes desirable to take care of such extraordinary condition
by the use of supplemental or auxiliary power. Such power can^
usually also be applied during conditions of low water flow whe
the power is limited by the other extreme of insufficient water undc
maximum head.
In considering the effect of head on the power of a plants it is
necessary to understand that water wheels are almost invariably
selected to run at a certain definite speed for a given power plant
and cannot be used satisfactorily unless this speed can be main-
tained. Also that any wheel will give its best efRciency at a fixed
speed only under limited changes in head. If the head change
L radically, the efficiency changes as well and this fact become
more serious imder a reduction in head. As the head is reduced/
the discharging capacity of the wheel and its efficiency is also^
rapidly reduced so that the power of the wheel decreases moii
rapidly than the reduction in the diseharj^^in^ capacity would
indicate. When the reduction of head reaches a certain point thi
wheel is able to simply maintain its speed without developinf
I
can
: IS
bly
ant
in-
cei^B
?4
ed,
Iso^
ulfl
thm
Of
1
Relations of Power, Head and Flow. 103
power, and when the head falls below that point, the speed can no
longer be maintained. It is therefore plain that when the head of
a stream varies greatly, it becomes an important and difficult matter
to select wheels which will operate satisfactorily under such varia-
tions, and, when the variations become too great, it may be prac-
tically or financially impossible to do so. This subject is discussed
at length in a later chapter, but is called to the attention of the
engineer as an important matter in connection with the study of
head.
6a. Gcaphkal InvisstigatiMi of die Rdations of Power, Head and
Flow. — ^The relation of head and flow to the horse power of any
stream on which a dam has been constructed, may be graphically
investigated and determined by a diagram similar to Fig. 50. On
this diagram are platted hyperbolic lines marked "horse power
curves" which show the relation of horse power to head and flow
within the probable limits of the conditions at Three Rivers, Mich.
These Knes are drawn to represent the actual horse power of a
stream under limited variations in head and flow and on the basis
of a plant eflBLciency of 75 per cent. These heads, which actually
obtain at the Three Rivers dam, were observed under three condi-
tions of flow, and these observations were platted on the diagram
at c e e and a curve was drawn through them. From the intersec-
tion of this curve with the horse power curves, the actual power
of the river available tinder the actual variations of head and flow,
is determined. These measurements were taken with all of the
water passing over the dam.
Let us assume that it is desired to investigate the eflFect of an
installation of wheels, using 600 cubic feet per second, under a
nine foot head. Under these conditions part of the water will pass
thim^ the turbines instead of over the crest of the dam, the
available head will therefore be somewhat reduced, and the power
curve of the river, under these new conditions, is shown on the
diagram by the curve f f f. This curve was platted from the curve
c c e by computing the amount the head on the crest of the
dam would be lowered at different stages of the river by diverting
throogh the wheels the quantity of water which they will pass under
the reduced head. The actual power of the river at different heads
and nnder these conditions is shown by the intersection of the line
fff with the horse power curve, and the actual power of the pro-
posed plant under various conditions of flow is obtained by pro-
104
Water Power.
I
8.5 S.O 9.5 ID.Q IQ5
TOTAL FALL FROM ABOVE DAM TD MOUTH Qr TAlk RACE
Fig, 60.— Graphical Study of Head
'Ejecting the point of intersection of the discharge line with the
line f f f on the turbine discharge line d d.
Thus, with a flow of 6oo cubic feet per second^ the power of the
plant would be about 470 horse power, while, with a flow of
2 J 00 feet per second, the power of the plant would decrease to about
420 horse power. At discharges below 600 cubic feet per second,
the head would drop rapidly unless a portion of the installation was
shut down*
63, Graphical Study of Power at Kilboum. — A more detailed
I
•
Relations of Power, Head and Flow.
105
S3»lkaH|Tl «ZS^^» INVliI iO UiMDd 1V3I13U01H1
T I
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oisoia S31V3 nv
s g
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Water Power.
study of head in connection with the conditions at Kilbourn, Wis-
consin, is illustrated by Figures 51 and 52. In Figure 51 the theo-
retical horse power of any stream resulting from any variation be-
tween the head and flow is shown by the hyperbolic curves drawn
from the upper to the right hand side of the diagram. Figure 47*
already considered, shows the relation of the head and tail water at
Kilbourn, where a dam with a crest 350 feet in length is projected.
The curve on Figure 51 marked '* Height of crest of dam above
tail water** was obtained by subtracting the height of tail water
at the various river stages, as given by the rating curve of the
river, from the height to which the dam is to be constructed and
platting the same in their correct position on the diagram. The
dam here considered is 17 feet in height above average water or
with its crest at elevation 19 on the gauge. The curve on the right
marked "Fall over dam, — all gates closed*', is constructed in the
same manner by laying off as abscissas the actual head as deter-
mined from Fig, 47 under various conditions of flow when the
whole discharge of the river is passing over the dam. The ab-
scissas, therefore, between these two curves show the head on
the crest of the dam when the whole discharge of the river is
passing over the dam. For any given river discharge (as for in^V
stance 16,000 cubic feet per second) the total fall can be obtained
tin this case 18.8) and the theoretical horse power of the river (in
this case 34,000 horse powder) can be determined by finding the
intersection of the line for 16,000 cubic feet per second with the
curv^e marked "Fall over dam, — all gates closed*', and determining
the relation of this point to the power curves. This relation is
more clearly indicated by the first scale to the right.
64. Power of the Kilboum Wheels Under Variations in Flow* —
When the gates to the turbines are open a less quantity of water
will flow over the dam and the head on the crest w^ill therefore be
diminished. The amount of w^ater which will pass through the pro-
posed installation under various heads, is shown by the curve
marked "Discharge 24-57" turbines/* The intersection of this cun-e*
with the discharge lines, at all points to the left of the curve marked
''Height of crest of dam above tail water** indicates that such flows
will pass through the wheels at the head indicated by the point of
intersection. The practical limit of the turbine capacity is the
discharge indicated by the point of intersection of the turbine
discharge curve with the '^Height of crest of dam above tail water".
It will be noted that this intersection shows a maximum discharge
J
Effects of Low Water Flow, 107
of 7fiCO cubic feet per second under a head of 17 feet. A further
increase in the discharge of the river up to 8,700 cubic feet per sec-
ond, causes an increase in the head, which is found by following
upward the curve marked "Head 24 turbines" to the point m where
a maximum head is indicated. The discharge from the turbines
under this condition increases but slightly and is indicated by the
vertical projection of the point of greatest head (m) on the turbine
discharge line (at n) which is so slightly above the 7,000 cubic feet
line as to be hardly distinguishable on the diagram.
The power of the plant depends upon the head and the discharge
through the wheels, hence the theoretical power which might be
developed by the 24 turbines with a flow of 8,700 cubic feet per
second would be about 13,800 horse power, which can be deter-
mined by calculation or is shown by the relation of the point n to
the power curves. The actual value of these various points is more
clearly shown on the second scale to the right, marked "Theoretical
power oi plant 24-5/' turbines". A further increase in the dis-
charge decreases the head until for the 24 turbines a minimum is
reached at a discharge of 42,500 cubic feet per second. Under this
condition of head the discharge through the wheels has also been
somewhat reduced, and the corresponding horse power is reduced
to 11,300 as shown by the intersection of the discharge curve and
the line indicating the head existing under these conditions.
65. Effects of Low Water Flow. — In the case of low water when
the flow is not sufficient to maintain the flow over the dam, if the
turbines are run at full capacity, the water level behind the dam
will drop until a point of equilibrium is attained where the head is
just sufficient to force the entire discharge through the turbines.
As the water level is lowered below the crest,^ the power of the plant
rapidly diminishes owing to the great decrease in the head for a
small decrease in the flow. When the head decreases beyond a
certain point the power of the plant may be increased by closing
some of the gates of the turbines until the discharge through the
turbines is less than the discharge of the river, v/hen the head will
increase by the backing up of the water behind the dam.
Thus it will be seen by the diagram that, with only 6,000 cubic feet
per second flowing in the river, if all of the turbines are operated
the head will drop to about 12.7 feet, and the power of the plant
under this head and flow would be about 8,660 horse power. If,
under these conditions, one unit of six turbines, amounting to one-
fourth of the plant, is shut down, the water will rise until the head
toa
Water Power.
is increased to about i8 feet. Under these conditions about
cubic feet per second of this water will waste over the dam, and th
power developed by the remaining portion of the plant will be io,6jo
horse power, or, about 2^000 horse power more with one unit shut
do%vn and with the resulting head than with all units in operation
and the consequent lower head. The above discussion simply illus-
trates the point that it is rarely desirable to draw down the head
of an operating plant, at least to any great extent, for the sake of
operating a greater number of wheels, unless this is done for the
purpose of impounding the night flow for use during the day or at
times of maximum load. Even in this case too great a redaction ^
in the head is undesirable and uneconomicaL ^M
66. Effects of Number of Wheels on Head and Power, — Fig, 52"
is an enlarged section of that part of Fig, 51 shown by the dotted
lines. This diagram shows how the head on the wheels may be
maintained by shutting off some of the wheels in case the flow be-
comes so small as to entirely pass the wheels and thus reduce the
head, as described above. It will be noted that with a total instal-
lation of 48 wheels, by closing the gates of two wheels at a time,
the variation in the head would be only a fraction of a foot until as
many as 24 wheels ahe closed. Hence it will be seen that when th
power has been decreased by a rduction of head, the wheels shoul
be closed off until the same power can be secured by the less nura-^
ber of wheels operating with the highest head that is available with
the given discharge of the river. As the lower flows of the river
are reached great fluctuation in the head will occur with the opera*
tion of the turbine gates. This diagram shows the actual delivered
power of the plant and is based on a plant efBciency of 75 per cent
The po%ver obtained for a given discharge is therefore less than
shown by Fig, 51.
In order to secure more accurate results a small correction f(
the variations in efficiency under the variations in head may some
times be desirable. In the problem under consideration this is
unnecessary on account of the small variation which takes place.
Howevej-, when the variations in head are considerable, this correc-^j
tion is essential if a close estimate of power at different heads i^H
desired. Figure 53 is a power hydrograph similar to those already"
discussed but with such changes in the scale as to show the con-
tinuous power that could have been developed by these four groups
of turbines at Kilbournj Wisconsin, during the year 1904, under
I
Ih 1
Effects of Number of Wheels on Head and Power 109
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Head In Feet
Note— H. P. Ourrefl *re based on 7S^ efficiencj
Fig. 52. — ^Relation of Number of Wheels to Power and Head.
^hc variations in head which would actually have occurred with the
dan it is proposed to construct.
From the previous discussion of the conditions at Kilboum it
^ seen that with a dam with fixed crest the variations in head,
due to variations in flow, are comparatively small. Consequently
the power of the wheel to be installed will not decrease with an in-
crease in flow to as great an extent as usually occurs in water
power plants. If a system of flash boards or an adjustable crest is
found desirable in order to prevent overflow at times of flood, the
power of the plant when these are lowered will be still further
reduced.
* The hydrog^ph may be utilized for more detailed analysis of
water power questions and will be further discussed in a future
chapter.
no
Water Power,
s
o
m
^
31tlN BtiVntii Hid DflUaiS IHd 133i 311113 Ht 39lfVHlfi1C
J
CHAPTER VL
RAINFALL.
67. Importance of Rainfall Study. — The influence of rainfall on
ihe flow of streams is so direct that those unfamiliar with the sub-
ject are apt to assume that the relation may be represented by
some simple expression and that, therefore, if the rainfall for a
period of years be known, the corresponding stream flow may be
directly and readily calculated therefrom. With only a brief famil-
iarity with the subject it is evident that no such simple relation ex-
ists. The relationship is, in fact, complicated by a multiplicity of
other physical conditions which have an important if not an equal
influence.
Observations of stream flow are quite limited both in time and
geographical extent while the observations of rainfall have extended
over a long period of time and the points of observation are geo-
graphically widely distributed. If, therefore, it is possible to trace
such relationship between the flow of streams and the rainfall
and other physical conditions on the drainage areas as will enable
the engineer to calculate the flow even approximately, such relation-
ships become of great value to the water-power engineer, on ac-
count of the lack of other more definite information. It is there-
fore important that the engineer inform himself as fully as pos-
sible on the relations that exist between rainfall and stream flow
and the modifications of those relations by other physical factors.
By such means the information regarding rainfall, already recorded
for long terms of years, may be applied to the problem of stream
flow in which the engineer is more directly concerned. For this
reason the subject of rainfall is here discussed in as much detail
a£ the space will permit.
68. Distribution of Rainfall. — A continuous circulation of water
is in progress on the earth's surface. The evaporation from the
water and moist earth surfaces rises into the atmosphere in the
fir t?ff' 1^' 1^' KV lie* 117' 113' itr \ir
lor JDi' lor MJT
^0
jlr uV tif* iil^ ir m lojr laf ioT lir wF
"4
Rainfall.
lisa
111*
1117
llil
r •'
^SL^^lI^iHiMM
1900
isTote Petite tiE
|ti tn tt^^it TO nKc^i> to 4iE
aovr* 4*
fig. 55.— Distribution of Total Annual Ralnfitl In Wfseonmln
Fte fit,— DfBtHbutlon of Total Ajmna! Rainfall In Wisconsin.
ii6
RainfalL
form of vapor, partially visible as clouds, mist and fog, and is"
afterwards precipitated as rain and dew* The dtstribution of rain-
fall on the earth's surface is by no means uniform. An examina-
tion of Fig. 54, which is a map showing the average distribution of
the annual rainfall in the United States, will show how greatly the
average annual rainfall differs in various parts of the United States.
The local variation in the average annual rainfall in the United
States is from a minimum of no rainfall, during some years in the
desert regions, to an occasional maximum of more than one hun*
dred inches in the extreme northwest. From this map it will be
noted that from the Mississippi westward the lines of equal rain-
fall are approximately north and south and parallel with the moun-
tain ranges. In the Southern states, east of Texas, they are ap-
proximately parallel with the Gulf of Mexico, and on both the At-
lantic and Pacific coasts they are approximately parallel with the
coast lines. At various points in the United States other influences
come into play and greatly modify the genera! distribution as above
outlined. In a general way the rainfall may be said to be in*
fiuenced by the topography of the continent and, to a considerable
extent, by its altitude. In general, the rainfall decreases as the
elevation above sea level increases, although in some cases the op-
posite effect holds. This general law seems to be substantiated by
reference to the annual rainfall map. In passing along the parallel
of 40* as we ascend from the Mississippi River to the western
mountains the annual rainfall decreases from about 35 inches an*
nually to 10 inches or less. On the other hand, a reference to our
Western coast will show that some of the heaviest rainfalls that
occur are due to precipitation caused by the moist winds from the
Pacific striking the higher mountain ranges. This is a local condi-
tion, however, and is quite different in its character from the gen*
eral law above stated. The mountain ranges along the Pacific
coast which intercept the moisture from the Pacific and cause the
heavy rainfalls in the higher mountain areas are also the direct
cause of the small rainfall in the arid regions lying east of these
mountains,
6g. The Painfall Must be Studied in DetaiL — ^The map of average
annual rainfall is of value only for a general view of the subject.
For special purposes a detail study of the local variations from the
average conditions is necessary. Great variations take place in the
annual rainfall of every locality. Sometimes the annual rainfall
will be for a series of years considerably below the average, and
DistnbuLign of Weekly Rainfall io Wisconsio. 117
HAY 13 TO MAY 2d
MAY ao TO MAY 27
^UHC 3 TO JUNE 10
JUNC 17 TO JUNE a4
rMOHta IN DCPTH
OTO.^' ^nVO-fiO" j»OTOta' TO'TOr ir&OVtfl
Fig. 57.— DIstrlbntfon of Weeltly Rainfall tn Wlsconstn*
ii8
Raiofali.
Fl£. &8.— RainraU Conditions In the United Statefl at S A. M.. Julf Uit, mi
Ft£. G9.— Eatufali Condltioiui In the United States at S A. M.« Jaly 17tli, 110'^^
Local Variations in Annual Rainfall. 1 19
then for a number of years the average may be considerably ex-
ceeded. No general law seems to hold, however, in regard to this
distribution and the variation seems to occur either without law or
by reason of laws so complicated as to defy determination. The
variations in the distribution of the annual rainfall in the State of
Wisconsin for eleven years are shown by Figs. 55 and 56. From
these maps can be clearly seen how greatly the distribution of rain-
fall thronghout the state differs in different years from the average
annual rainfall as shown on the last map of the series. It should
also be noted that in the same manner these annual rainfall maps
are the results of the summation of an irregular distribution of
numerous rainstorms, the irregfularities of which can perhaps be
more clearly shown by the maps on Fig. 57 which show the weekly
distribution of rainfall in Wisconsin for six consecutive weeks in
May and June, 1907. All such maps are but the result or sum-
mation of individual rainstorms which occur during the period
considered Individual rainstorms never occur twice over exactly
the same geographical extent of territory nor with equal intensity
at any points within the territory covered. They are not only
irregular in their distribution but progressive in both their dis-
tribution and intensity, changing from hour to hour during their
occurrence. The extent of a somewhat general rainstorm in pro-
gress at 8: 00 A. M. (Washington time) over the Northwest on July
i6th, 1907, is shown by Fig. 58. On the area over which this storm
extended, the actual precipitation varied widely and the extent of
the storm rapidly changed from hour to hour. At 8 : 00 A. M. on
July 17th the general rainfall had ceased and the storm had be-
come localized as shown by Fig. 59. The varying character and
extent of the rainfall as illustrated by those two maps show the
extremes of one storm which affected the Northwest, and illustrates,
in a general way, the irregularity and lack of uniformity in rainfall
occurrence and distribution.
70. Local Variation in Annual Rainfall. — By reference to Fig. 60,
the variations which have occurred in the annual rainfall at various
localities in the United States will be seen, and from this data the
^2ck of uniformity in the annual rainfall will be more fully appre-
ciated. By an examination of the records of a sufficient number
^f years the limiting conditions may be determined and an ap-
proximate determination of the relation between the extremely dry
*ncl extremely wet periods made.
X20
RainEall.
Si ^
b' iu
ID
fD
40
10
igl
3
3
Ko Atlantic,
Hew Hiiven, Codii«
So Atlantfc,
St. LftwrfTio^
Detroit, Micli.
CiuamnatJ, O* ^M
F-Afltem (Tulf, Wimti^m Gulf, Upp^r M1«Bls»lppl, l4»v&r MiinlBsf pp^
Moiirgo[ueT7« Al^ San Atit02}lo, Tex. Uen ^Hglnes^, l«u tiiUe itoekt Ark.
mmmmmmMM
Red Rlvw.
Mrri>r«headf Minn.
Wo Padflo.
40
ID
— a, E^E,^ —
a ^ a J ^^ n
0
[jiiii^ }a\ ;jt 1 nir:i:i>t!^ii'^f^:tT-jitiitn 1 ? n j u iiiiu-un ■ l. n 1 1 ^
I
rnlumVjla,
Pad Ac*
Colorado, Great BaiiJii,
FhoOQijc^ Arts. Wltmemuoca, N«f ^
60. — Variation In Annual Rainfall at Various Folate to tbe ITnlted Statat,
Local Variations in Annual Rainfall.
121
Figure 6i i* a diagram showing the fluctuations that have occurred
in the annual rainfall at Madison, Wisconsin, from 1869 to 1905.
The variation at Madison has been from a maximum of about
52 inches in 1881 to a minimum oi about 13 inches in 1895 which
represents a greater range (4 to i) than ordinarily obtains. As a
general rule the maximum may be stated to be about double the
minimum annual rainfall.
I
i i i i
riUCTUATION or ANNUAL RAINFALL AT MADISON, WIS.
Fig. 61
71. Local Variations in Periodical Distribution of Annual Rain-
fall— ^The amount of the annual rainfall is only one of the elements
that influence the run-oflF. The time of occurrence or the periodical
distribution of the rainfall is even of greater importance. The
general character of the periodic distribution of the annual rain-
iall is similar each year in each locality, for the maximum and
minimum monthly rainfalls occur in each locality at fairly definite
periods. As the cycle of the seasons changes, conditions favorable
or unfavorable to precipitation obtain, and, while these differ very
largely from year to year and are subject to such wide variations
as to render the character somewhat obscure, unless a number of
reasons are considered, yet the same general character ordinarily
prevails.
Figure 62 shows the extreme and the average variation of the
monthly rainfall at Madison. The monthly rainfall in the various
"months differs widely in amount and is by no means proportional
to the total annual rainfall for the year. It is especially observable
that during the year of maximum rainfall, viz: for 1881, the rain-
fall for April was almost as low as for the April of the year 1895
^hen the total annual rainfall was at a minimum. It is also observ-
RainfaU*
VrLUCTUATiaK or MOHTHLY RAINrAlt AT MADtSOU, W19.
Fig. 62 ■
able that the rainfall for August ^ 1881, was less than the rainfall for
August of 1895. Figtirc 63 shows the typical average monthly dfe-
tribution of precipitation at various points within the United States,
and the general law to which even the variations mentioned par-
tially conform. The character of the monthly distribution varies
widely at different locations, but will be seen to have a similar
character wherever similar conditions prevail. Thus the New Eng-
land States present a similarity in the distribution of the monthly
rainfall. A similarity in the montJily distribution is also fourid
throug^hout the lake region and the Ohio Valley. The monthly dts*
tribution throughout the Great Plains is also similar, and a marked
similarity exists at points along the Pacific coast.
72* Accuracy of Rainfall Maps and Records. — ^It must be under-
stood that the rainfall maps, showing lines or belts of equal rain-
fall, are only approximately correct, and that it would be impossible
to show by such lines small differences in annual rainfall of less
^
Monthly Distribution of Rainfall,
lypes ef Monthly Dlstribiitkii of Predpilatioa in tk tJoited States*
133
124 ^^^^^^ RainfalL ^^^^^^^^^^^H
til an two or three inches. As a matter of fact, the rainfall actually
differs considerably within comparatively small limits, but within ^
such limits the average remains fairly constant for the year or sea-w
son. Frequently, however, the rainfall variations even within
narrow limits differ widely. Many questions of importance in con-
nection with the consideration of rainfall are still open to debate
and are frequently answered in a diametrically opposite manner hfM
data secured from different localities. "
73< Rainfall and Altitude. — ^The relation of the rainfall to al*
titude has been a subject of frequent discussion and perhaps the
tnajority of data secured tends to show that there is a material
■decrease in the fall of rain as the altitude increases, and this both
within a broad area and with great changes of altitude and within
a limited area and where the differences in altitude are coippara-
tively small. Mn Rafter, in the Hydrology of New York, points
out tlie fact that in the State of New York the rainfall records
show both increase and diminution of precipitation with increase of
altitude. Tlie Hudson River catchment area shows a higher precipi-
tation at the mouth of the river than it does at its source in die
Adirondack mountains^ while the Genesee River shows the op*
posit e : that is, a higher precipitation at its source than at its mouth.
In this case the influence of altitude, if such influence can be said
IQ obtain on such limited areas, is overshadowed by other predomin-
ating influences. In this connection Fig. 64 is of interest- This
diagram shows the variation in the annual and monthly rainfall
at three stations within the City of Chicago, Curv« No. i shows
the rainfall at the Auditorium Tower, at an elevation of 233 feet
above the level of the city. Curve No. 2 shows the rainfall at the
Chicago Opera House Building, at an elevation of 132 feet Curve
No* 3 shows the rainfall at the Major Block, elevation 93 feet* The
relative monthly rainfall at these three stations varies greatly, and,
while the annual variations at these three points, — all of which are
within a square mile in the business center of Chicago,^ — differ
considerably from each other, still the difference is insignificant in
-comparison with the monthly variation. While the influence of alti-
tude may possibly be seen in the annual results and possibly in
the monthly results as shown at stations one and three, the monthly
results at station two show no such effect, or, at least, the effect Is^m
greatly obscured by other inflLiences» ^
74- Value of Extended Rainfall Records, — ^One of the points that
becomes important in the consideration of rainfall records is thej
J
Value of Extended Rainfall Records.
JAI. PCI. MAR. APR. MAY JORC JULY A06. iCPT. OCT. ROV. OCO.
125
AHRRAL
I I 3
SO
to
10
Fig. 61— Monthly and Annaal Precipitation of Three Exposures in Chicago,
111. 1. Auditoriam Tower, Elevation 238 feet 2. Chicago Opera House
Building, Elevation 182 feet 3. Major Block, Elevation 93 feet.*
length of time required to make such records safe as a basis for
future estimates. This subject is well considered in a paper by
Alexander A. Binnie, member of The Institute of Civil Engineers,
published in the Proceedings, Vol. 109, pages 89 to 172. Mr.
Binnie's conclusions are that:
"Dependence can be placed on any good record of 25 years' dura-
tion to give a mean rainfall correctly within 2 per cent of the truth."
Mr. Rafter, after reviewing this paper, concluded, that :
"For records from 20 to 35 years in length the error may be
expected to vary from 3.25 per cent down to 2 per cent, and that
for shorter periods of 5 to 10 and 10 to 15 years the probable ex-
treme deviation from the mean would be 15 per cent to 4.75 per
cent respectively."
Mr. Henry from his examination of this question in reference to
various localities has drawn the following conclusion:
For a ten year period the following variations from normal have
occurred :
KewBedford + 16percent
Cmcinnati +20 "
BtLonis +17 "
Fort Leavenworth +16 "
amFrandsco +9 "
— 11 i)er cent
— 17 "
— 13 '•
— 18 "
— 10 "
^Beprodnced from original slide published by Qeo]?raphical Society of Chicapro^
X26
Rainfall.
For a 23-ycar period Mr. Henry found that the extreme variation
was 10 per cent both at St, Louis and New Bedford, and reached
the conclusion that at least 35 to 40 years' variations are required
to obtain a result that will not depart more than -j- or — ^5 per cent
from true normal. The average variation of the 35-year period Mr.
Henry found to be + or — 5 per cent and for a total 40-year period
-|- or — 3 per cent
75. Accuracy in Rainfall Observation.^ — It must also be under-
stood that on account of the marked variations which actually occur
in rainfall within limited areas and by reason of limited difference
of elevation, the observation of actual rainfall is not without its
difficulties. In order to secure great accuracy great care must be
exercised in the placing of rain gauges so that they may receive
and record the rain received in an accurate manner. Subject, as
they are, to considerable variations, it would seem unwise to use
great refinement in the calculations of rainfall, and in recording
rainfall one decimal place is probably all that is warranted and
two places is the ultimate limit of possible accuracy, fl
76, District Rainfall, — In determining the average rainfall on zf
drainage area an extended series of observations over the entire
district considered become essential and conclusions drawn from
more limited observations are subject to considerable inaccuracies.
Rainfall stations, distributed as uniformly as possible over the
drainage area, should be selected, and the average result of the ob-
servations of these stations should be used as the basis of calcula-
tion. Possibly a still more accurate method of considering this
subject would be the selection of rainfall observations on each
particular branch of the stream considered* The value to be given
to each set of observations used should be in proportion to the ter-
ritory drained by the tributaries. ■
77* Study of Rainfall as Affecting Run-off- — In considering the
rainfall on a district in relation to the run-off of streams, it is
desirable to study the rainfall records on the basis of what is
termed "water year"* The water year for most of the area of the
United States, instead of coinciding with the calendar year may
be best divided into periods beginning, approximately, with De-
cember and ending, approximately, with the foHowiog November.
The first six months of this period, December to May inclusive,
ts termed the "storage" period, June, July and August constitute
ihe *'gTowing" period i September, October and November^ the **re-
plenishing** period. For the purpose of discussing rainfall in
Mean Monthly Rainfall.
127
i »!
S3
Kort!n*m ArTnntfc,
61. — ^Hean Montlily EoinfalJ at ¥arioua Points fii tb« United Statea.
ii8
RainfalL
* > lit
ao
to
i
i
^
1
dl
Ifl
^^sJ
ro
^^^kr»«^
^.*s
TucsoQ, Aria.
WlUQcoitiectt^ Her,
Tig. 66.— Mean Monthly Rainfall at Varfaus Points In the United States.
Rainfall oo the Drainage Area of the Wtsconsio River. 129
l^gap^^^iiyHJ
— lU O ^ Hi
TOTAL
AMfTUAL. H
3T0RA8C
PERIOD
EROWINC
PERIOO *
iRCPLCillHlMI
Ipcrioq.
FIf. 67. — Hatufall on the Drainage Area of the Wlsconafn River.
r\
130 Rainfall. ^^H
relation to run-off it is desirable to divide the annual rainfall in
accordance with these periods. Figures 65 and 66 show the average
monthly rainfall at various points in the United States, tlie average
rainfall for each of the periods above mentioned and an additional
diagram for each location showing" the summation of the total rain-
fall for each period of the water yean
Here again attention is called to the fact that for most purposes
of the engineer the extreme conditions and the varying conditions
from year to year are of much greater importance than the average
conditions as shown on these diagrams. Figure 67 shows the annual
and periodic rainfall on the valley of the Wisconsin River at three
different points, the relative location of which will be seen by ref-
erence to the map on page 84. Tlie upper diagram shows the rain-
fall on the drainage area above Merrill, the center diagram the rain-
fall above Necedah, and the lower diagram, the rainfall above Kil*
bourn. In these three diagrams it is important to note the variation
in the rainfall condition above the different points on the water-
shed. For example, considering the entire area above Kilbourn and
above Necedah, it will be noted that the annual rainfall for 1895
was the lowest within the period shown, while for the area above
Merrill the rainfall for 1892 was the lowest for the period dis-
cussed. This diagram will illustrate the fact, which is manifest on
the investigation of most large streams, namely, that frequently
the intensity of the rainfall upon part of the drainage area is radi-
cally different from that on other parts, and that, consequently, the
various quantities of rain falling on a large watershed tend to
halance each other and keep the total more constant than observa-
tion at any one point would seem to indicate, so that the minimum
rainfall at any one point on the area is not necessarily coincidentj
with the minimum rainfall that may occur at any other point o!
on the stream as a whole. From this it is evident that in an area
of any magnitude it is necessary to consider the rainfall at a large
number of stations well distributed over the area.
LITERATURE.
OETTEEAL gtm.TECrr OF ItAI^fFALL*
n •
1
4
1. U. S. Weather Bureau. Annual Reports and Monthly Weather Re?!cT*-
S, Meteorologfache Zeltschrlft.
S. ZeltHchrift des Oaterreicbeti QesellacliaJt ffir Meteorologie,
4. Symon*s Meteorological Magazine.
B. Annuclue ds la Soclete Meteor ogique de Prance, Paris.
Literature,
131
6. Th© Royal Meteorological Society of Great Britain. Quarterly JournaL
7. Hawksley, Thomas. Laws ol Rainfall and Its UtilJzation* Proc Inst
C. E. Vol 31p pp. 63-55. 1871.
8. BIniile. Alei. R, Tables of Mean Annual RaJnfail in Various Parts of tb«
World Proc Inst C. K VoL 39. pp. 27-31- 1874.
S, Sehott, C. A. Tables and Results of tlie Preclpltatioa of Rain and Snow
in the U, 8. Smithsonian Contribution to Knowledge, No. 223,
1874,
10 Charts and Tables Showing Geological Distribution of Rainfall In the
U, S, TJ, S. Signal Service Professional Paper No. 9. 1S83.
11. Rainfall Observatlotia at Philadelphia, Reports Phil a. Water Bureau,
1S90-93. Eng, Record, 1891, p. 346, 1892. p, 360.
12. Blnnle, Alex. R. Mean or Average Rainfall and the Fluctuattoua to
which It is Subject Proc. Inst C, E, Vol, 119 (1893), pp,
J72'1S9.
13. Waldo, Frank, Modern Meteorology, New York, Scribner*s Sons. 1893,
14- Davis. W, M. Elementary Meteorology, Boston. Ginn Sc Co., 1891
15. Harrington, M, W, Rainfall and Snow of the United States. Bulletin
C, U. S. Weather Bureau, 1S94,
IG, RnsseU, Thomas. Meteorology, New York, MacMiUan Ca. 1895.
17. Henry, A* J, Rainfall of the United States. Bulletin D„ U. S. Weather
Bureau. 1897.
18. Ttimeaure & Russell. Public Water Supplies, Chapter 4. New York,
Wiley & Sons. 1901.
19. Hann, Jnlltia. Handbook of Climatology, New York* M^cMiHan Co.
1903.
20. Handbook der Ingenleur Wissenschaften, Part 3, der Wasserbau; sec 1,
Gewasserknnde. Leipzig. E. Engelmann, 1904.
21. Hann, Julius, Lehrbuch der Meteerologie. Leipzig. 1906w
EXCi:SfiIVlB BAII7FALL,
22. Francis, Jas. B. Distribution of Rainfall during a Great Storm In New
England In 1S69. Trans. Am. Soc, C, E, Vol. 77, p. 224.
23. The New England Rain Storm of Feb. 10-14, 1886, Eng. News, 1886, VoL
15, p. 216,
24- Hoxle» R, L, Excess Ive Rainfalls Considered with Special Reference to
Their Appearance in Populeua Districts. Trana. Am. Soc a H,
p. 70, June, 1S9L
25. Talbot, Arthur N, Rates of Maximum Etalnfall. Technograph, Univ. of
Illinois. 1891-1892.
26. Duryea. Edwin, Jr. Table of Excessive Precipitation of Rain at Chi-
cago, Illinois, from 1889 to 1S97, Indusive, Jour. W. Soc of
Engrs. Feb,, 1899.
CAUSES 07 BAHTTAIX.
27. Henry, D. F. Rainfall with Different Winds. Rept Chf, Engr. U. 8, A.
1867, p. 598,
28. Blanford, H. F. How Rain Is Formed. Smithsonian Report 1SS9, pt
1, P. 2S7.
132 Rainfall.
29 BeJschow, Frantz A. The Causes of Rain and the Structure of the At-
mosphere. Trans. Am. Soc. C. E. Vol. 23, p. 303. 1890.
30. DaylB, W. M. The Causes of Rainfall. Journal of N. E. W. Wks. ABs'n.
1901.
31. Curtis, a. E. The Effect of Wind Currents on the Rainfall. Signal Serv-
ice Notes No. 16.
THE EFFECT OF ALTITUDE ON RAINFALL.
32. Homersham, S. C. Variations of the Rainfall with the EleTation. Proc.
Inst C. E.. Vol. 7. pp. 276. 282 & 284. 1848.
MEASUBEMENT OF RAINFALL.
33. Clutterbuck, J. C. Dalton's Rain-gage. Proc Inst C. E., Vol. 9, p. 157.
1850.
34. Fitzgerald, Desmond. Does the Wind Cause the Diminished Amount of
Rain Collected in EHevated Rain Gages? Jour. As bo. of Ens. Soc.
1884.
35. Weston, E. B. The Practical Value of Self-recording Rain-gages. Bng.
News, 1889, VoL 21, p. 399.
36. Self-Registering Rain-gages and Their Use for Recording Ezcessiye Rain-
falls. EUg. Rec. 1891, Vol. 23, p. 74.
37. Duryea, Edwin, Jr. E^ffect of Wind Currents on Rainfall and <m the
Gage Record. Signal Serrice Notes Na 16.
CHAPTER VIL
THE DISPOSAL OF THE RAINFALL.
78. Factors of Disposal — ^The portion of the rainfall in which
the water power engineer is most directly interested is that which
runs off in the surface flow or flow of streams. In order to form
some idea of the amount of this run-off and the factors that control
it, it is necessary, however, to investigate and consider the various
ways in which the rainfall is distributed, for the ways in which the
distribution occurs are mutually inter-dependent and of necessity
modify and control each other. The rainfall disposal depends on a
large number of factors or conditions among the most important
of which may be named :
(1) The amount of the rainfall.
(2) The rate of rainfall.
(3) The condition of the surface on which the rainfall takes
place.
(4) The condition of the underlying geological strata. /
(5) The atmospheric temperature.
(6) The direction and velocity of the wind.
(7) The nature and extent of vegetation.
f8) The surface topography.
(9) The evaporation.
It will be noted that some of the factors mentioned above tres-
pass more or less on others and are not clearly separable.
79- The Rate or Intensity of Rainfall. — It will readily be recog-
"'zed that with very heavy or intense rainfall a larger percentage
^^ the water will run directly into the streams and a smaller per-
centage will be taken up by the strata than would be the case were
t^e rainfall very light. In very light rainfalls there is no run-off,
the water being either taken directly into the strata or re-evaporated
from the surface.
134 Disposal of the RainialL ^^^^^^^^
So. Condition of Receiving Surfaces and Geological Strata.--
Next in importance in modifying the disposal of rainfall is the
condition of the surface on which the rain falls and of the under-
lying geological strata. If the geological strata are poms in na-
ture and comparatively free from water they will readily receive
and transmit the rainfall if the surface is in proper condition to re-
ceive it. The condition of the surface itself modifies the reception
of the rainfall in a very marked mannen With high surface slopes
the rainfall may be large, even with somewhat porous strata, and
yet very little water will be taken up by the strata. With low
slopes and porus strata a large amount of water will be received
directly by the surface and passed into the ground water and deep
waters of underlying geological strata.
The temperature has an important influence on the condition of
the strata^ and consequently the disposal of the rainfalL Strata
otherwise porous but with saturated and frozen surface will r^
ceive and retain practically no water and the consequence is that
under these conditions even a low rainfall may produce a consider-
able run-off that under other temperature conditions would not
occur.
8r, Effects of Wind — The wind has a marked effect on evapora-
tion and consequently on the quantity of rainfall that passes away
in the atmosphere* The average velocity of the wind will vary iti
<]iffcrent parts of the United States from three to seventeen miles
per hour and, other things being equal, will increase evaporation as
such average velocity increases.
82. Effects of Vegetation,^ — The nature and extent of the vege-
tation on a surface has a marked effect on the disposal of the rain-
talk Experiments at the Wisconsin Agricultural Experimental
Station show that barley, oats and corn require 15,2, 19,6 and 26.4
inches of rainfall, respectively, to produce a crop. This includes
the transpiration and evaporation from the cultivated surface a^
well as the actual quantity used by vegetation. The amount act^
ually retained as a part of the vegetable growth is^ of course, very
smalL The water simply serves to convey the soluble foods of th^
soil to the various fibres of tlie plant. The actual amount of
water used in irrigation is not a fair criterion of the amount
needed for the development of plant life as in most cases crop^
arc over-irrigated. The actual depth and the rainfall and irri-
gation water used on crops vary from as low as 12 inches ia
sometimes as high as 16 feet, frequently running into quantities
J
Effects of Vegetation.
135
luch in excess of any ordinary rainfall in moist climates where
f irrigation is found to be unnecessary,
In the Report of the Kansas State Board of Agriculture for De-
cember 51, 18S9, Mn W. Tvveeddale, C E., gives the following ta*
ble containing the results of investigations by M, E- Risler, a Swiss
observer, upon the daily consumption of water by different kinds
of crops :
TABLE, X
Daily Coftnumption of Water hp CrfipB,
Crops.
Lucem grass, .
Me^idQW grass*
Oats
Xndiaa Coin . .
Clover* .......
Vineyard
Wb^b ..**...
Rye...
Potatoes, ,.*. .
Uak trees
Fir Trees . , . .
Ikches or Watxe,
Minimmij, Maximum.
0/J34
0.267
0,122
0.287
0J4il
0.103
o.no
1,570
0.140
0.03,5
0.031
0-106
0,110
0,091
0.038
0.055
0.03LJ
0,038
0.()2i)
0.04S
Mr. Tweeddale finds that this table agrees with careful experi-
ments made in France and elsewhere, and calculates from it that
from seed time to harvest cereals will take up 15 inches of water
and grass may absorb as much as 37 inches.
This table shows also one of the important reasons why a de-
crease of stream flow follows the destruction of forests and their
replacement by meadows and cultivated fields. It is quite evident
also that if the watersheds were covered by grasses or cereals there
would be comparatively little water left for the flow of streams.
From this it will be seen that the character of the vegetation on a
watershed exerts a considerable influence on the ultimate distribu-
tion of the rainfall.
The presence or absence of forests has also, as shown by a series
of observations in Germany, a marked effect on evaporation. Prof,
M, W- Harrington (see Bulletin No* 7, U, S. Dept. of Agriculture,
p, 97) has compiled the accompanying diagram (Fig. 68), w^hich
illustrates clearly the effect of forests upon the monthly evapora-
tion- The upper curve represents the evaporation from water sur-
136
Disposal of the RainfalL
faces in the open country, while the lower ctirve shows the evap-
oration from water surfaces in the woods. The shaded area thus
lUust rates the saving due to the cover and protection of forests.
83, Percolation, — On pervious and unsaturated strata a portion
of the rainfall sinks below the surface until it reaches a saturated
4
Fig. es.— Reduction in ESvaporatlon Due U> tlie Presence or Forests.
or a relatively impervious stratum. The water then follows the
of the stratum until it reaches an outlet along some stream or
pears in the form of springs, frequently in an entirely dtflFerent'
drainage area or possibly below the level of the sea itself. It is
this ground water that gives rise to the dry weather flow of
streams, and frequently is the only source from which stream flow
is maintained during the dry seasons of the year. The same sources
frequently maintain the winter flow at times when the rainfall is
stored on the watershed in the form of snow and ice.
Percolation is an important factor in the storage of water and
in the construction of raceways and canals and needs most careful
attention when such works are under contemplation.
A large amount of valuable data concerning the losses due both
to evaporation and seepage has been collected by Mr, E. Kuichling
in connection with the study of the water supply for the New
York Barge Canal and is reproduced in the Appendix.
A small portion of the ground water is taken up by the roots <dU
plants and frequently feeds vegetation during dry periods. Water
drawn from the soil for such purposes, after fulfilling its functions
in vegetation, is transpired from the vegetable surfaces into the
atmosphere. Streams fed from areas where large deposits of fine
grained but porous material are developed, are usually more
constant in flow and less subject to fluctuations either from
flood or drought. The flows of the deeper strata usually pass far
from the watershed on which the rainfall occurs and modify to a
limited extent the stream flow in other valleys frequently far from
the original rainfall source.
Evaporation. 137
S4. Evaporation. — Evaporation takes place from moist surfaces
and from the water surfaces of swamps, lakes, streams and the
oceans, whenever such surfaces are in contact with unsaturated
atmosphere. The absorption of the rainfall by the strata effectively
limits the amount of evaporation from a given area by reducing
the area of contact of wet surface with the atmosphere, thus con-
fining the evaporation largely to free water surfaces. Fig. 69
shows a map of the approximate annual evaporation which takes
place from water surfaces at various points within the United
States. It will be noted that this map shows, in the greater por-
tion of the United States, evaporations equal to or greater than
the annual rainfall at such localities. The total annual evaporation,
IS shown in the map, is based, however, on free water surfaces
only, and evaporation from ground surfaces only takes place from
xcasional moist surfaces which occur after rains and when the
humidity is high. The total amount of water evaporated, there-
fore, is very much less than that which the map would seem to in-
dicate This map and the table of monthly evaporation in the
appendix are taken from data given in the Monthly Weather
Review of September, 1888. The Weather Review observations
are not based on absolute evaporation tests but are deduced from
readings of dry and wet bulb thermometers as observed at various
Signal Service Stations in 1887 and 1888. These deductions are
supplemented by observations at several stations by means of the
Piche evaprometer. While evaporation, like rainfall, varies from
year to year in accordance with the variation in the controlling
factors, yet in lieu of more extended observations this map and
table indicate relative conditions at the various stations and ap-
proximately the evaporation from free water surfaces. The com-
parative monthly evaporation at sixteen stations distributed
throughout the United States is shown graphically by Fig. 70. At a
number of Eastern points, namely, Boston, Rochester and Nevi
York, evaporation observations have been made for a number oJ
years and from the data thus collected a knowledge of the local
variations that cxrcur in evaporation at these points can be obtained
Evaporation is greatly promoted by atmospheric currents which
nave perhaps the most marked effect of any single influence. The
temperature of the water and the humidity of the atmosphere also
"^^c a marked effect. Mr. Desmond Fitzgerald in a paper on
^^poration (see Trans. Am. Soc. C. E., Vol. XV, page 581) offers
*"« following formula for evaporation :
ifg* itr i-atf* igy_ itr_„ itr nr lu- ny nr ipg* Jpt*
sr ftSf* ir ar ta^ «• «^ rf* rs* nr rr tr ir «F
1
»•
M4rAyt'1^^^^ \M
? I _—J-isiriv^ 1 \ \\rj^ \ X^'-^j^-^ i" t2vO\>C/
45"
;;HrT^ \v^^
r>t>nS^i''H* ^ h v.L--'^*^^ \ \ JV>. if?.-^^ \ k
;:=$rT5,, . VV'T^
S^ViWl'iK \]
4**
^^EaAj
^!.^i^
JW— T^
^
&V-
4V
^NdLW-MJT^^^^i^^^r^^S^ *\
W V ■ - Tf*! J
i^SeM13J
ir
fe^^J^li.^^'^^^-feL^S^^ \ \
IT
1 f 23.---I ^.V7fs^^*«fYV* '' Wfc^t^ L---'---^''^ \
f H\A^X^ £-^^k\''\ \
»r
ir
tut
;i S r ^ H-fS^*' V i i^V^^ri \
V / t n^S?L y 1 - hI ^1 L— -4
jL \/ ^\ \ \\M/ A:£^-^-^c^ r
K\ Ift -+4-^4R^T>r'*^^ HI "^^ 1 \ ANNUAL
tr 1
l^^^^qT^^ U— 4""'^^*? W ^''^' *'''^^- STATE S
^ 5 ;^4iC-iJ^ 1 1 ll^?^ ^ ]J^ ^ a »,^r„„ ,(„«.,»„.(»
ET
^
L4Llli--^-IIP
'Y'^
L-i-4-4-T
\ tv^^,— T— ^ \
If
"ia* -w- t*' tl* aft* 13* 81* 70^" Tf* "IP f
^_
,
1^
1
140
Dispo£ial of the RaiDtall.
Sr
m^
mMmmmmmmmmmMmMmMumi
M.
No. AtlAntf«>
Hew HftTtifi, C'OQO,
So. AtTantlc*
St. LftWT^POP,
DeuoLt, MIcIl
HoDteOHiery, Ala. ral^tlns, Tex.
Upper Ml^sIsflSppU Low^r Mtwla»lpp!g
Dq» Moiae^ la, LitUe R<>ck, Ark.
o
R
&4
I
Tt>p«k^. KAflS. Helena, Monc
Red iJiviTt Ko. rttc<!i<.\
Hoorehead, Minn Olympic, Waitu
Co1urnhl&, nKriAfl^ Colorado,
Spokane, Wanh. f>ft<:ram«ikto, Oal, Yunm. ^rli.
©feat 1
Wi tine mil cca, H*v.
Fig,
lii.— Monthly Evaporation From Free Water Surfaces at Various Potnbi
in the Untted States.
I
k.
i
I
Evaporation. Z41
E=(V-v)C+^)
60
In this formula V equals the maximum force of vapor in inches
of mercury corresponding to the temperature of the water; v, the
force of the vapor present in the air; W, velocity of the wind in
miles per hour; and E the evaporation in inches of depth per hour.
The value of v depends on certain relations between the tempera-
ture of the air and the water. From a careful examination of the
formula it will be seen that evaporation as represented thereby does
not depend largely on temperature.
Table XI is taken from a paper on "Rainfall, Flow of Stream, and
Storage" by Mr. Desmond Fitzgerald (Trans. Am. Soc. C. E., Vol.
XXVII, No. 3), and shows the monthly evaporation from water
surface at Boston, Massachusetts, for sixteen years. The table is
partially made up from a diagram of mean monthly evaporation but
only when the observation practically agreed with the same.
85. Evaporation Relations. — Professor Cleveland Abbe gives the
following relations of evaporation, as established by Professor
Thomas Tate :
(a) Other things being the same, the rate of evaporation is
nearly proportional to the difference of the temperature indicated
^y the wet-bulb and dry-bulb thermometers.
(b) Other things being the same, the augmentation of evapora-
tion due to air in motion is nearly proportional to the velocity of
the wind.
(c) Other things being the same, the evaporation is nearly in-
versely proportional to the pressure of the atmosphere.
(d) The rate of evaporation of moisture from damp, porous sub-
stances of the same material is proportional to the extent of the
surface presented to the air, without regard to the relative thickness
<5^ the substances."
(0 The rate of evaporation from different substances mainly
depends upon the roughness of, or inequalities on, their surfaces,
the evaporation going on most rapidly from the roughest or. most
uneven surfaces ; in fact, the best radiators are the best evaporizers
^^ nioisture.
(0 The evaporation from equal surfaces composed of the same
material is the same, or very nearly the same, in a quiescent at-
"'osphere, whatever may be the inclination of the surfaces ; thus a
143
Disposal of the Rainfall.
I!
I
I
<
to
I
C3
I
8
S
's
p
II » *
o I- Om -f io ^ S c^ ^ s^ iQ
* * * # ♦ *
■^^ kO O 30 'S* -^ -*■ W 71" OQ 05 ^
Cv c: i>» o -H c^ o ?5 o lO C4 ^n
o o i-* oi *r ■+ tO M -**• ^ ^5 lo
s
s
s
§
s
fet: 5
■3
a
M
I
I.
Evaporative Relations.
14?
horizontal plate with its damp face upward evaporates as much as
one with its damp face downward*
(g) The rate of evaporation from a damp surface (namely, a
horizontal surface facing upward) is very much affected by the
elevation at which the surface is placed above the ground-
(h) The rate of evaporation is affected by the radiation of sur-
rounding bodies.
(i) The diffusion of vapor from a damp surface through a
variable column of air varies (approximately) in the inverse ratio
of the depth of the column, the temperature being constant,
(j) The amount of vapor diffused varies directly as the tension
of the vapor at a given tempera tare, and inversely as the depth of
the column of air through which the vapor has to pass*
(k) The time in which a given volume of dry air becomes satu-
rated with vapor, or sattirated within a given percentage, is nearly
independent of the temperature if the source of vapor is constant.
(i) The times in which different volumes of dry air becone
saturated with watery vapor, or sattirated within a given per cent^
are nearly proportional to the volumes.
(m) The vapor already formed diffuses itself in the atmosphere
much more rapidly than it is formed from the surface of the water.
(This assumes, of course, that there are no convection currents of
air to affect the evaporation or the diffusion,)
86. Practical Consideration of Losses. — From the previous dis-
cussion it will be readily realized that it wOuld be impossible to dif*
ferentiate all of the methods of the disposal of rainfall upon a drain-
age area. Evaporation differs widely from different classes of vege-
tation and from different classes of land surfaces; also on account
of the slope and exposure. No two square miles upon a drainage
area offer the same conditions as affecting evaporation which differs
very widely with such conditions. Evaporation and seepage from
any surface varies with the temperature, with the moisture in the
air, and with the \^elocity of the wind. Tt is therefore impossible
to compute, with any degree of accuracy, evaporation over an ex-
tended surface of a watershed or drainage area, or to ascertain
with any degree of accuracy the probable losses that will take place
in the same area.
For water power purposes, the rainfall can, therefore, be divided
into two quantities in which the water power engineer is interested:
First : The run-off on which the power developed directly depends.
144
Disposal of the RainfalL
and, Second : The losses, by whatever means they occur, which are
not available for such purposes* Evaporation is usually but not
always the source of greatest loss on a drainage area and commonly
other sources of loss are insignificant when compared with it It is
therefore a common practice to deduct the run-off from the rainfall
on a given drainage area and to classify the difference as evapora-
tion, including under this term all losses of this same general
character, whether through seepage, evaporation or otherwise. _
LITERATURE.
1. Vtrmeule, C, C. Report on Water Supply. G€oL Sunrey of New Jener^
Vol. IIL 1S94.
2. Yermeule, G. C. Report on Forests. Geol, Surrey of New Jersey, 1S99.
3. Turneaur© and Rusaell, Public Water StippUes, Chap* V, New Yorfe,
Wiley & Sons, 1901,
4* Rafter, George. Hydrology of tlie State of New York, pp. 46-197, Al-
bany, R Y. New York State Education DepL Bui. SB, 1905.
FEECOLATIOK.
5< Law€S, J, B, The amount and Composition of the Rain and Draia
Waters Collected at RoUiamsted. Jour, Royal Agrlc. Soc
England, Vol. 17; p, 241, 1881; Vol, IS, p. 1, 1882.
€. Fortier, Samuel, Preliminary Report on Seepage Water, and The Un^
derflow of Rivers. Bulletin No. 38, Agric Bxpt Statlos, Lops.
Utah, 1895.
7, Seepage or Return Waters from Irrigation, Bulletin Na S3. Colo*
Agrlc Expt Sta., Fort Collins. Colorado. 1896,
S. Fortler, Samuel. Seepage Water of Northern Utah. Water Supply as A
Irrigation Paper No, ?, 1S97*
9. The Lost of Water from Eeservoirg by Seepage and Evaporation. Bill'
letin No. 45, Colo, Agrlc. ESxpt Sta., Fort ColUns, Colorado.
May, 1898,
10. Loss from Canals from Filtration or Seepage. Bulletin No. 4S. Colo.
Agric, Expt Sta., Fort CoIUhb, Colorado, 1898.
11* Kulcbllng, EmlL Loss of Water from Various Canals by Seepage. (See
paper on Water Supply for New York State CaaaJSp Report of
State Engineer oa Barge Canal, 1901).
12. Wilson, H, M. Irrigation Engineering. New York, Wiley 4 Sons. 1901
13. Wilson, H- M, Irrigation In India, Water Supply and trrigallon Paper
No. 87. 1903.
14. Mead, D. W, Report on Water Power of the Rock River, Chicmgo. Pub.
by the author. 1904.
15. GreaTei^ Charles.
1875-76.
ETAPORATIOIC^
Oa Evaporation and on Percolation.
Vol. 46, p. 13.
Proc Inst
Literature. 145
16. Fitzgerald, Desmond. Evaporation. Trans. Am. Soc. C. E., Vol. 15, p.
581. Sept» 1886.
17. Loss of Water from Reservoini by Seepage and Evaporation, BuUetin
No. 45, Colo. Agric. Bxpt Sta., Fort Collins, Colo. May, 1898.
18. Depth of £?vaporation in the United States. Monthly Weather Review.
September, 1888.
19. Depth of Evaporation in the United States, Engineering News, Decem-
ber 30th, 1888; January 5th, 1889.
20. Harrison, J. T. On the Subterranean Water in the Chalk Formation of
the Upper Thames and its Relation to the Supply of London.
Proc. Inst C. E. 1890-91. Vol. 105, p. 2.
2L Femow, B. B. Relation of Evaporation to Forests. Bulletin No. 7, For-
estry Div., U. S. Dept A2Tic and Engineering News, 1893, Vol.
80, p. 239.
21 Kimball, H. H. ESvaporation Observations in the United States. Read
b^ore the Twelfth National Irrigation Congress, 1904; E«ngi-
neering News, April 6, 1905.
USB OF WATVB IN AGBICULTUBK.
The Publicatioiui of the United States Experiment Stations on Irriga-
tion and of the Experiment Stations of the various States contain much
information on this subject The following are of especial importance:
:i Hill, W. H. Report of State EAagineer to Legislature of California. 2
Vols. Sacramento, 1880.
24. Carpenter, L. G. Duty of Water. Bui. 22, Agric. Elxpt Sta., Fort Col-
lins, Colorado. 1893.
25. Fortier, Samuel. Water for Irrigation. Bui. 26, Utah Agric. Expt Sta.,
Logan, Utah. 1893.
20. Report of Irrigation Investigations, U. S. Dept Agriculture, Irrigation
Inquiry. Bui. 86 for the year 1899.
27. King, F. H. Irrigation and Drainage. New York. MacMillan Co., 1902.
The amount of Water Used by Plants, pp. 16-46. Duty of Water,
pp. 196-221.
2S Head, Elwood. Irrigation Institutions, Chap. VII, The Duty of Water.
New York. MacMillan Co. 1903.
29. Wilson, H. M. Irrigation Engineering, Chap. V., Quantity of Water Re-
quired. New York. Wiley k Sons. 1903.
CHAPTER VIIL
RUN-OFF,
87. Run-Off, — That portion of the rainfall that is not absorbed
by the strata, utilized by vegetation or lost by evaporation, finds
its way into streams as surface flow or run-off. The demands of
the first named factors are always first supplied and the run-off is
therefore the overflow or excess not needed to supply the other
demands on the rainfalL The run-off, therefore, while a direct func-
tion of the rainfall, is not found to increase in direct proportioTi
thereto, except perhaps in seasons such as early spring when from
seasonal conditions the demands of vegetation, percolation and
evaporation are not active and all or most all of the rainfall flows
away on the surface. The remainder of the year the run-off may
be said to increase with the rainfall but usually at a much less
rapid rate and in many cases the rainfall is entirely absorbed by
the strata or vegetation, and does not influence or affect the run-off.
In this case the run-off is supplied from the ground water, stored
from previous rainfalls, and is entirely or largely independent of
the immediate rainfall conditions.
An examination of the observed run-off of streams, and the rain-
fall on their respective drainage areas, for annual, monthly and sea-
sonal periods, will show that there is a relation more or less direct
between the rainfall and run-off (see Fig, 71, ct seq,). The relations
are shown by various diagrams and mean curves from which many
departures will be noted. The departure of individual observations
from the mean curve expressing these relations shows the relative
importance and influence of other factors in affecting such relations-
The relations of the numerous factors which are known to influence
the results are quite complex and are not well established and mudt
more meteorological information in much greater detail and a care-
ful consideration and study of the same will be necessary bcforfl
such relations can be even approximately established.
^ io •« <v» eq
143
Run-Off-
88* Influence of Various Factors, — Tlie influence of various
factors of disposal was discussed in the last chapter. Evaporatioo
is known to vary with temperaturCj the direction and velocity of
the winds, barometric pressure, and various other meteorological
influences, and yet no clearly defined relation has yet been shown
to exist between these factors, by means of which their actual in-
fluence on the run-off can be approximately calculated. Mr. C C
Vermeulc (see Vol, III, GeoL Survey of New Jersey) considers
that annual evaporation depends largely on the mean annual tem-
perature and offers a formula for the calculation of the same^ which,
in many cases, gives results which seem to agree closely with the
facts and data collected from a number of Eastern drainage areas.
Mr. Vermeule s formula for the relation between annual evaporation
and precipitation on the Passaic River, and some other Eastern
drainage areas where conditions are simitar, is;
£^15,50+0.16 R
in which
E^The annual evaporation (including all lasses on drainage ana
except from run -off)
and R^the annual rainfalL
For general application to all streams he suggests the formula
E=(i5.5o-|-o,i6 R) (0.05 T— 148)
in which T^ mean annual temperature.
Mr, Vermetite also offers a formula for the evaporation for each
month and discusses at length the influence of ground storage on
the flow of streams* Mr, Geo, W. Rafter (see Water Supply and
Irrigation Paper No. 80) has made a careful analysis of available
data which indicates that no such intimate relation can be found to
exist. In general, the information available does not seem to show
that other factors have a sufficiently definite relation to nin-off ofj
to each other to make such relation clearly manifest and y^t such
factors are known to have an unmistakable and constant influence,
This fact is quite clearly demonstrated by a number of diagrams
prepared by Mr. Rafter, which are here reproduced.
Figure 72 shows graphically the relation between precipitation^
evaporation, run-off and temperature on the Lake Cochituatc basin
for thirty- three years. In this diagram the years are arranged !«
accordance with the precipitation. In a general way the evapora-
tion and run-oflF for these years may be said to vary with the pre-
1
flucnce
K::i:;:»:;ii;::::;HH::
!s::::::::i::::::::;::::
JH
Xi
a
iai ii ii i i i iiiiiii ii ■ i
■* ■■«■■■ ■•■■»■■■■ r- ■■
■■'■'■««■■■■■■>■■*«■■■■
■■ ■! ■.«■■ ■■■■■>■■■ ■■'«'«
iill
!■■■
ill
■ ■■1
zz
l.iiiiH =
^■■■fl
■■■■■I
■ ■■
::"
««
k«i
■■■1
:::::
:s
sssss
k
!»:»»: ::!sb»::s:8:::8:»h::»:
H
■■■•
:::
■■■
[»:
■ ■■i,q
■ ■■fl
KtP
■ ■■
ills
PIT'
4?^
w
::
il
■ ■ 1
■ ■ 1
«■' 1
■• 1
h:::;:::;;::!:;:
::»;;: :::i::i:::!'::
?i itniiiiiiit lUHiiiii ••■■•••••I
»::»8lM«s:::::»H»::
-ii!! !!!! if !■!!!-
iiiiiiiiiiiiiiiiiiii
■ ■• ■ ■!■!■!!•■ !!!!!li»li !
Years arranged in order of dryness,
FIf. 7S.^RelatIon Between Precipitation. Eiraporatlon, Run-off and Temperir
ture oa Lake Cochituate Basin.
0
ISO
Run-Off,
cipitation. Evaporation, wliicb, it must be remembered, here itP
tludes all losses except that due to run-off, increases in g^neraJ
as the rainfall on the area increases and decreases with the rainfall.
For limited periods, however, this general law does not hold.
Other factors affect the relatiuus and cause material departures
from the general law. This is particularly marked in the years 1891
and 1872. For these two years The rainfall was almost identical in
nmount- The evaporation for \he same years, however, differed
materially, being about 16 in*^hes less in Wji than in 1S72* As
a consequence the run-ofl lo^ the year 1891 was about l$% inches
greater than in 187;^.
In order to demonstrate the mutual relation between evaporation
tnd temperature the d^ta illustrated in the previous figure has been
SO
^0 -
^:
3^
2Q
to
HM^^iMt
¥fan
t On Us ta ^ •
10 to^^q%C«^«w*«<-«»|ii»>AOitoe4»iiSr4Yn>
Wig, 73.— Relatfon Ectweea Evaporation auo Temperature on Lake Cocbltust*
Basin.
Years being arranged according to amount of eyaporatlon.
k
Influence of Various Factors*
151
Fipf. 74,— Relations between Preelpl-
Nation, Run-0£f, Evaporadon and
Temperaturtj on Sudbury Hifcr
Biain.
Yean arranged acscording^ lo regnlar
orcleFi dryne^JB and de^rea^iiig evapo*
ration regpDCU?elyt
i
jtr ur K5* nsr nr tir nr m* nr ui' nar tor
ps^^
^
15+
Run-Oi*
«0
so
40
00
20
ro
44^
%4^
S4€f^
10
jia
'»
ttt^tt
to
s&
' ■ H-i-HH+1 rH
^ -^ ■ _ I
g - - ■
4#** — -» _ _-
= — ^^ , ~ ^_-i_^
^ _
42<s ___^=_;__II
4^0 r_-
40O —^ ^^-
;jpo
IIIIIIIIIIH
rta^lllllillllllll
r£>uia||§sl3i§rE2
Pig. 75.— Relations Between Predpttation, Rtin^ff. EvaporaUon and Tempertr
ture on Upper Hudson River.
Years arranged according to regular order and decreasing etaporatloa,
rearranged by Mr, Rafter, and in Fig^ure 73 the relation for the
years has been arranged in the order of their evaporation, and com-
pared with the mean temperature for the year. This figtire serves
to show that while temperature may, and unquestionably does,
influence evaporation, yet the mean annual temperature has no
controlling effect on the annual evaporation. It will be noted that
for the year 1878, when the mean temperature was a maximum, the
evaporation was considerably below the average for this drainafT
^
Relations of Annual Rainfall and Run-Off.
155
area. Similar relations for the Sudbury River basin are shown in
Fig. 74 and for the Upper Hudson River basin in Fig. 75.
89. Relations of Annual Rainfall and Run-Off. — Figure 76 is a
mean run-off map of the United States and should be compared
with the map of average rainfall. The run-off as shown by this map
is expressed in inches on the drainage area and similarly to the com-
mon expression for the amount of rainfall. The value of this map
is comparative only. In this case, as in the cases of rainfall and
evaporation, the mean conditions are subject to wide variations.
A detailed study of local conditions is always necessary in order
to fully understand and appreciate the influence of extreme condi-
tions and of local factors.
The relation between the annual rainfall and run-off on various
drainage areas is shown in Figures 71 to 75, inclusive, as previously
described. The mean relations between these two factors on four
selected drainage areas are, however, more clearly shown by the
graphical diagrams Figs, yjy 78 and 79. From these diagrams a
Fig. 77.
Pig. 78.
ISO
RuD-Qfi.
fiieaa relation can be traced for each area from «inc3u bcnrem,
tlsere are considtnblt depaniires in indrridial jcns. Tbe saidj,
therefore^ of this subject on this basis will deiDonssxxlc l3ie aen
relation and tbe departure therefrom which imisr be rij>r» ird <■
the area considered and other areas where physical ciwfilimis aic
similar.
* *y^_ M<* A** X" AM *• «fll tf^ tt »»
I
1 1 r-r-r-TL4-]-
Fig. 79
Table XTl.^Mu$kingum River, 1888-1S95, inrluftire,
(Oifchnwnt mn^^^bjn aqnaxm mOm§,1
]M.
1
1889.
MIL
Period.
Rain.
Kan-
off.
5.17
1.77
3.39
Erspo'i Bahi-
ntioni IftlL
Rob.
off.
Etbpo-
ntioB.
5£"
^
ss
iT.ie
14.31
11.14
11.99
12.64
7.75
13. «
12.12
10.24
6.02
.96
7.80
10.88
8.28
xr.n
13L88
15.91
M.flr
8.81
8LI8
9L«
Orowlnif
ILN
BtpleniMhlnff
9lS
Y«*r ...«.
42.01
10.33
32.28 86.88
8.22
27.66
S8.tr
88.81
880
im.
18tt.
1898L
Storain*
16. T8
13.80
7.08
12.42
1.77
1.87
4.30
11.79
6.71
20.39
16.64
4.81
9.06
8.65
.67
1L83
18.89
4.14
25.04
8.81
ft. 01
14.18
LIS
.86
ma
Growing ^
B«pl«niiihfn|f ..............
7.»
Year
87.38
16.60
21.80
41.74
13.86
28.86
a.88
ULSO
811I
1894.
jtm.
SiulUPO
16.98
4.56
9.02
T.63
.66
.41
8.80
&90
8.61
18.01
" 8.U
7.66
4.04
.49
.87
18.81
OrowlofT .... ...................•.>«.•.••..•...••>
Ntf
y#ar
80.61
8.70
n.oi
89. 84
,4.80
tLtt
Ji^
The Water Year. 157
gK>. The Water Year. — ^The relation of annual rainfall and annual
n-oflF is more or less obscured by variations in the periodic dis-
bution of the annual rainfall. A study of the relation of the
riodic rainfall and the periodic run-off is therefore necessary.
For a comprehensive understanding of the relation of rainfall to
in-off it is more convenient to refer to the water year instead of
le calendar year. The water year is the annual division of time
lat represents the full annual cycle of change in hydrological
)nditions. It does not, as a rule, conform very closely to the calen-
ar year, neither is the water year constant for each annual period
I its beginning or end, but varies as meteorological conditions
ary.
As previously stated, in the greater portion of the United States,
he water year naturally divides itself into periods, beginning, ap-
proximately, with December, and ending, approximately, with the
oUowing November. The period from December to and including
Way is termed the "Storage" period ; June, July and August con-
Jtitute the "Growing" period, and September, October and Novem-
ber are termed the "Replenishing" period. Not only the year but
Jiese periods as well vary each year, and are not necessarily
limited by our artificial division of calendar months and years.
During the storage period, the snows of winter and the rains of
spring saturate the ground, and a large amount of water is held in
storage in lakes, swamps, and forests, and in pervious soils, sands
and gravels. The portions of this stored water tributary to a drain-
age area but not necessarily within the boundaries thereof, and at
elevations above the level of the stream, are, when conditions de-
mand, available to supply the stream flow, and are also available
for the purpose of sustaining plant life. Such waters will feed a
stream to an extent depending on their character and magnitude,
regardless of the amount of the immediate rainfall, and will cause a
stream to flow for several months, even without rain, if the per-
vious deposits and other storage resources are well developed
upon the area. These relations vary widtly with each individual
area, and in areas not well provided with such deposits the streams
^ften run dry through the warm days of summer.
Whenever the surface of the stream falls below the ground water
gradient the ground water is affected and begins to supply the
»tream flow. This sometimes occurs early in May, and seldom
ater than the beginning of June. During June, July and August
he rainfall is rarely sufficient to take care of the evaporation and
15S
Run-Off,
growth of vegetation without something of a draft on tl
water, and the stream flow during this period is usually entirely
dependent on the ground water, except during exceptionaUy heavy
rainstorms. By the end of the growing period about August 31st
the ground water is often so reduced as to be capable of storing
several inches of rainfall. During the replenishing and storage
periods of winter and spring the ground begins to receive its store
of water, and. with favorable rainfalls^ the ground becomes fully
saturated by the end of April or May.
Table Xlll.—Hudmn Himr^ 1S8S^1901, inctimve.
^
lase.
ll».
wm.
F^rbd.
Batxi-
Bim*
Ratn-
fmlL
Run*
Ktupcv
Rahi>
tea
Bun-
oil.
twtw^
ORnHnt. >,,...».
IT.OA
1.CG
19*
a. SO
9.H
ILIO
15.05
10,81
ILOt
4.SS
an
aoft
10. 7B
r.40
£4.15
U.10
1Sl»
2. IS
CBl
lOffi
Tbwf »„««,-—<...
4a«i
1^.04
».»
«ie.9e
Ei.n
£!.»
(!fio,afr
BS.M
tift
1ML
leiOL
upa
Steimff* ,_.>.,.^-,..w._.
SO. OB
laid
L9Q
i.10
ll,it
e,i8
i4.a&
lV.lt
f.ao
an-
aia
ia«a
lajfT
a 98
i&ao
fiii
an
4.9
1£L9
B^|ft^tll)lllAg i,m,,m,, .....>
IK
Tau... _.
4^m
soice
mm
mer
sa 08
fD.T^
4£.ia
ti.fiii
m.n
3JM.
18»v
urn.
Btenffs ._.
n.8T
lais
a. It
1&.7V
msr
10. »
a«s
4.11
a 01
T.O0
ttii
IDES
12,7?
laa
ass
4.08
aa
T It
Seple^iJfiliiQjf ,.^.^»«..:....^
an
Yaw..... ._.,-..
IL07
IS. ST
^.eo
W.S7
IT. 4ft
IS. SI
iSvH
latt
21. W
imft
mei
i»a
matmg9 .„.
19.77
10. M
14.60
f.7»
aao
6. IT
8.01
T.14
2&80
12, li
laa
4.11
mfs
a«e
12.48
7.40
aai
i«.ifi
lis
aiT
an
Tmr .................
U.ffI
»L1«
SO.tt
4A.bi
n.iiB
si.w
K.79
IfiiH
las
liOO.
UDU
.™„.
£1.1S
i».'n
i£.n
18.11
aso
a»
lil.
0.1S
It. SI
its
a
Ett
llff
att
Year......
Ilk 11
ftX«f
14.74
u,m
11. tt
mn
i
' .A.fiproxXaiit&
Relations of Periodic Rainfall to Run-Off.
Table Xiy.—ConnectictU River, 187S-1886, inclusive.
IS9
187&
1878.-
1874.a
Period.
Ralxi-
telL
Ron--
off.
Erapo-
ration.
Bain-
fall.
Run-
faU.
ETapo-
ratioii.
Bain-
faU.
Ron.
off.
ETapo-^
ration.
fitorsffd
14.98
18.96
lS.tf
1&80
6.S8
6.64
1.68
12.67
8.78
18.16
10.11
U.04
21.80
an
5.28
a64
7.40
a88
sacs
14.87
7.76
aaoi
a68'
ai5
aoi
Orowioff ....... .........r-«
7.m
a61
Ymr
48.80
8B.8S
2a07
4a 81
88.78
ia66
45.21
8L81
ia40
Pvriod
U75.
1876.0
i8n.;
Stonoe
17. n
14. »
11.85
8.80
8.60
8.01
io.:5
7.76
28.60
lau
law
24.74
asft
a28
(
-a24
0.16
a 89
laoo
14.00
iao8
laoB
aoi
6.87
a4i
Orowinc .....,..'
11.0»
• 7.81
Year
4a 42
88.87
80. 6S
46.66
80.87
16.81
4aK
8a 86
84.81
Pvrioo.
Mm
1878.
i8sa
8tof«»« i
tl.88
laao
10.56
18.tt
8.4ft
ao6
a86
10.14
7.60
28.19
16.07
9.48
21.40
a 02
a 08
1.70
iai5
a 56
ia»
11.88
11.66
14.78
a46
aos
a6i
Qtowlnc
O.ST
Bvplenishinv .^
age
Y«tr
46.08
24.68
21.S0
48.74
27.84
21.40
41.60
ia85
21. 8i
l>«iod.
Uffl.
1882.
188a
»or«ge
ItoplOTitelring
»L88
U.80
11. 8B
ULOB
S.98
&88
4.81
8.87
7.90
»ao.fio
»lL4ft
»a80
iai4
a86
a 17
a86
aio
4. 88
^laes
Ma 80
»a20
a78
a6i
1.87
4.1»
ia9»
• 4.88
Year
4&51
IS. 84
tl.l7
8a 46
17.66
80L79
&66
ia6i
19.94
P«rk>d.
1884.
188a
Storace
21.42
12.14
a 51
20.20
a 79
a 61
1.22
a 86
aoo
ia66
14. 8t
U.76
ia68
a80
a6i
496
11.68
ai5
Year
42.07
».60
ia47
45.16
8a 44
SaT8
«2lot included in mean.
^Ralnfkll compnted, approodnuite.
91. Relation of Periodic Rainfall to Run-OfF. — For streams where
the observations of flow have been made for a number of years,
comparisons can readily be made of the relation of annual and
periodic rainfall and run-off. Such investigations should be made
by the water power engineer when considering a river relative to
its availability for water power purposes. An analysis of such
data for the Muskingum, Hudson, and Connecticut Rivers as made
by Mr. Rafter, is shown in Tables XII, XIII and XIV (for ad-
i6o
Run-Off.
ditional tabular data see Appendix) » Graphical representations of
the periodic relations of the rainfall and run-off on the Upper
Hudson River basin are shown in Fig. 80, and the same relations
ior the Sudbury River basin are shown in Fig. 81,
10 U 2Q 29:
Preclfiit^tfon in McAfu
IQ IS 20
PffClpttatfon in Inciiti
S0\
a:
h \ \ \ \ I \
A/ff^ period ^
\VTV\V\
^=-----=
10 is JO
PrwcSoltatkkn tn tnchtt
25
Fig. 80.— Rainfall and Run-Off of Upper Hud eon River for Each Ptrlod df Ito^
Water Year.
[l>Dni W, a uut L P&psr Na, m "Relatloii of Balarftll 10 Iliui4>ft' ]
Relations of Periodic Rainfall and Run-0£E.
i6z
ts m 2$
Pnclptiatlon tit fadits
to 15 20 25 SO
26
lo\ lOr^
C
*rov
¥h
w
p
er
101
f
5 E
-
E
E
-
-
^
^
:-
^ z
£
^E
1?
=:
f
—
=
-
-
2 —
^1 P 5 ^
0 $
10 ' ' ';5' ' ' 'id' ' ' '26' ' '
PnelpitatlontnlnQliu
10 16 20 25
50
I g g
^ 8l-7Rainfall and Run-Off of Sudbury River for Bach Period of Oie
Water Year.
IFivm W. a And I. P&per No. 80 *'ReIaUoii of B*infaU to RuB-Off.**]
i62 Run-Oflt
92. Monthly Relation of Rainfall and Run-OfF. — ^The relations of
rainfall to run-off from month to month on a given drainage area
are not usually as direct and definite as the annual and periodic re-
lations. The mean and extreme relations can, however, often be
established within somewhat wider limits, and such relations will
permit of the formation of at least a general idea of the probable
limits of the monthly run-off, under other rainfall conditions. The
wide range of the possible error of such estimates will be shown
by the divergence of independent observations from the normal.
To establish accurately the maximum and minimum limits, it is
probable that observations, at least as extended as those needed
for accurate rainfall estimates, will be needed.
The observed relations between the monthly rainfall and the
monthly run-off in various drainage areas are shown by Figs. 82, 83,
84 and 85.
On Fig. 82 are shown the relations of monthly rainfall and run-oflf
for several Northern river basins, and on Fig. 83 are shown the
same relations for several Southern river basins. An examination
of these diagrams will show the marked effect of seasonal tempera-
tures and conditions upon the quantity of run-off. The high per-
centage of run-off in the spring should be noted ; also how the per-
centages of run-off in these rivers drop with the advance of the
season and rise again in the fall.
On Fig. 84 are given the monthly relations of rainfall and run-off •
for thirty years on three small river basins in the immediate
vicinity of Philadelphia. These drainage areas, being small, are
more readily and directly affected by rainfall, hence the relations
are much more marked and uniform than those that exist on larger
rivers. The marked variation from normal due to the influence of
other varying conditions on the drainage area, especially during the
summer months, should be noted.
Figure 85 shows a set of monthly diagrams prepared by Emil
Kuichling, C. E., for his discussion of the relation of rainfall to
run-off in certain rivers in the Eastern part of the United States.
On these diagrams the figures not enclosed are numbers of ob-
servations from drainage basins Nos. i to 8 inclusive, of the fol-
lowing list. The figures enclosed in circles are the numbers of
observations from drainage basins Nos. i to 28, inclusive.
I
o
c
3
I
o
Relations of
Monthly Rainfall and Run-OfiF.
^^* ■
JAUUAJtY
^/■^ ■
JULY ~1
V
^
r
^
?"
;^yr^:
^
/;
r
^
■^
/.
^>
^
.^
-a
-
^
^'
^
''*»•
1
^
Q
d
a
i^
■>'
*
K
163
^/A.
fEinUARY
^'/
\ —
AUCUIT 1
#
r^;
■^
9
■^\
r%-
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>
f^
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^
-"^
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<^
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^'
* J
a
J
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P-^
L^
.a.
•
J
1 — 1
SEPTCMBCR ]
s
a;
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& 1*
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aVA.-I ,"!"V
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St:
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DO
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y
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k"
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MAY
L P <
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1
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f^-
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y
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y
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oeccMirn 1
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Horizontal Ordinatee — Rainfall in Inches.
^ Wisconsin River at Neoedah.
D Chippewa River at Eau Claire.
A Grand River at Grand Rapids.
V Grand River at Lansing.
X Thunder Bay River.
* Rock River at Rock ton.
Fig. 82. — ^Monthly Rainfall and Run-off — ^Northern Rivera.
164
Run-Off.
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Horizoatal Ordinates— EainfaLl in Inchea.
* Talladega Creek, Watenebed Area 156 Square Milea,
VUpadacheo River, ** " 440 "
• Alcovy Eiver '* " 228 ** **
Fig. fi^.^-Monthly Rainfall and Run-Off-— Southern Rivera.
Relations of Monthly Rainfall and Run-Off-
I6S
1 •.. Ji
MUAIY
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2 3 4 5 G 7 Q 9 10 II 13 13 14
RAINFALL IN INCHES
OBSERVATIONS
J(*TOHlCKQN CREEK
A^NCSHAMINY
^3~ OFCRIiiOMEN
OI234&6789I0II rZI3l4
RAINFALL IN INCHES
WATERSHgp AREA
102,2 SQUARE MILES
la©, 3
1C2,0 ■ *
Ffg. 84* — Relation between Koinfal! and Run-Off un Tohickon^ Neshftminj, aod
Perkiomea Creeks near PbilBdelphiaT PennHylv&nia.
1 66 Run-Off.
V
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J
Relation of Monthly Rainfall and Run-Off. 167
Watersheds from which Observations were platted on Diagram 86,
No.
Name of Basin.
Area in Sq.
Miles.
No. of
Years
Reoard.
338.0
80
152.0
13
139.3
13
102.2
14
75.2
25
43.1
12
27.7
18
19.0
83
40.0
2
51.6
2
69.0
2
63.0
80.8
104.0
144.0
153.0
187.0
191.0
256.Q
618.0
2
563.0
822.0
17
879.0
1070.0
1306.0
1889.0
4600.0
12
5828.0
1
2
3
4
6
5
7
8
9
0
1
2
3
4
5
6
7
18
19
20
21
22
23
24
25
26
27
28
Croton River, N. Y
Perkiomen Creek, Pa
Neshaminy Creek, Pa
Tohickon Creek, Pa
Sudbary River, Mass
HemJock Lake, N. Y
Mystic Lake, Mass
Cochitoate Lake, Mass
Cayadutta Creek, N. Y
Saquoit Creek, N. Y
Oneida Creek, N. Y
Nine-Mile Creek, N. Y
Garoga Creek. N. Y
E. Branch Fish Creek, N. Y
Oriskany Creek, N. Y
Mohawk River. N. Y., at Ridge Mills
W.Branch Fish Creek, N. Y
Salmon Ri ver, N. Y
East Canada Creek , N* Y
West Canada Creek, N. Y
Schroon River, N. Y
Passaic River, N. J
Raritan River, N. J
Genesee River, N. Y
Mohawk River, N. Y., at Little Falls
Black River, N.Y •
Hudson River N. Y., at Mechanic ville, N. Y
Muskingum River, Ohio
A continuous graphical record for ten years, showing the rela-
tions of rainfall to run-off on the Illinois River basin, based on ob-
servations of stream flow made at Peoria, 111., is shown by Fig. 71.
93* Maximum Stream Flow. — In the construction of spillways,
dams, and reservoirs, and the study of their effect on the overflow
of embankments, levees, and lands, the question of maximum run-
off becomes important.
Many formulas have been suggested by engineers for determin-
ing flood flows, each of which is based on more or less extended
observations, and are applicable only when used under conditions
similar to those on which they are founded. Very few of these
formulas take into account the great number of conditions that
"modify the results. For this reason most of such formulas are of
little use except for the purpose of rough approximation. None of
these should be used without a knowledge of the conditions under
i68
Run-OfiE.
*
4
1 ^
4 f 1 3
5 i 1 S 'S
■a 5 B |i . .y> S
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r
Max. rate oE Di^chat^e in Co. FL per Sec. per Sq. Mile^ (q)
Stream Flo^
which they are applicable. Such calculations sliould, wherever pos-
sible, be based on the known ratio of actual maximum and mini*
mum flows on the drainage areas, or on drainage areas adjacent and
similar thereto, and the use of a factor of safety as great as the
importance of the local condition will warrant. Such data serves
as the best and most conservative guide for all calculations of this
class,
A record of the maximum and minimum flows of various Ameri-
can and foreign streams from the report of Mr, Kuichling, to which
reference has already been made, is contained in the Appendix.
Figure 86 shows a graphical representation of the actual rate of
maximum flood discharge of these rivers and on this diagram is
given the formulas, both graphically and analytically, for ordinary
and occasional maximum floods as proposed by Mr Kuichling. It
is evident that Mr. Kuichling has endeavored to represent the
maximum flood conditions that may occur on any riven In many
localities, the results given are much larger than the actual condi-
tions of flow will warrant.
In some cases the overflow of lands and property by floods,
caused by back water or otherwise, may be prevented by the con-
struction of levees and the installation of pumping plants for drain-
age ptjrposes. Under such conditions both the extreme height pf
the flood and the length of its occurrence become important and
can be determined only by gatige observation. A graphical study
of such data affords the best means for its consideration- Figure 87
shows hydrographs of the high water conditions on the Fraser
River at Mission Bridge. British Columbia. This stream is fed by
the melting snows of the foot-hills, and the floods occur at essen-
tially the same time each year within certain limits, as a rule reach-
ing a maximum during May, June or July. Th& difTerences that
occur from year to year are shown by the different hydrographs
which represent, however, gauge heights in feet and not discharges.
The highest record is that of the flood of June 5, 1894, of which,
however, no hydrograph was obtained.
94, Estimate of Stream Flow. — For the purpose of estimating
water power no safe deduction can be made from average run-off
conditions, although a knowledge of such conditions is desirable.
The information that is needed for the consideration of water power
h a clear knowledge of the maximum and minimum conditions,
the variations w^hich occur between these limits and a knowledge
of the length of time during which each stage is likely to occur
n>
M- rf^
Estimate of Stream Flow. 171
hroughout the year or throughout a period of years. As pointed
►ut in the previous section, the extreme conditions are important in
onsidering the height of flood as influenced by spillways and
ther obstructions in the river. The extreme and average low water
onditions commonly control or limit the extent of the plant which
hould be installed.
By the illustrations already shown it is fully demonstrated
hat the run-oflF of any stream, either for the year, period or month,
annot be approximately expressed either as an average amount or
s a fixed percentage of the rainfall. An expression showing the
elation between rainfall and run-off necessarily assumes quite a
omplex form, from which large variations must be expected.
Vhere average amounts of run-oflF are considered, care must be
sed to base the deduction on correct principles. In considering the
ariation in the monthly flow of a stream, the flows of such stream
hould be considered in the order of their monthly discharge
ather than in their chronological order. For example: in Table
iV, the mean monthly flows, of various streams, in cubic feet per
>econd per square mile of drainage area are given. These flows
ire arranged in the chronological order of the months. The aver-
age monthly discharges of the streams are calculated therefrom,
and are shown in the last column. An examination of this table will
show that the minimum monthly flow of a stream docs not always
occur during the same month for each year. For the consideration
of these streams for water power purposes, the better arrangement
of the recorded flow is not in the sequence of the months, but by the
monthly periods arranged in the relative order of the quantities of
flow.
In Table XVI this data has been rearranged. In this arrange-
ment the least flow for any month in a given year is placed in the
first line and the flows for other months are arranged progres-
sively from minimum to maximum. The average for each month
will, by this arrangement, give a much better criterion of the
Average water power to be expected from each drainage area dur-
ing each year than the average monthly flow as determined in
Table XV.
172
Run-Off,
TABLE XV.
Mean MoniM^ F7aw9 of Various Eastern Streams Arranged in ChronotSffM
Order. (In Cubw Feet per Second per Sq^tare Mile.)
Kennebec River at Watervilie, Me.
Drainage Area 4380 eq miles.
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I
Merrimac Blver at Lawrence, Mass.
Drainaf^e Area 4553 Bq. mi.
4
Estimate of Stream Flow.
173
TABLE XV.— Continued.
Potomac River at Point of Rocks, Md.
9654 sq. mi.
Year.
*D8
■w
M»
M)i
M?i3
xia
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W
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Juaaaiy . . ♦*♦»*.*♦,**,*,,
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From Table XVI it will be seen that the average minimum
-monthly flow of the Hudson River at Mechanicville, N. Y., is .52
cubic foot per second per square mile, the smallest monthly mini-
mum for any year during the period of the observations being .31
and the largest monthly minimum for any year being .81. On the
Potomac River, with a somewhat greater total annual rainfall, the
average minimum monthly flow is .21, the smallest monthly mini-
mum for the year being .12, and the largest monthly minimum for
any year being .37. These figures, it must be remembered, are aver-
ages for each month, and the actual minimum flow during the period
is a much less quantity. These records show that the minimum flow
01 a stream cannot be based on the mean annual rainfall. This same
TABLE XVL
^ean Monthly Flow of Various Eastern Streams Arranged in Order of their
Magnitude. ( In Cubic Feet per Second per Square Mile.)
Kennebec River at Waterville, Me.
4410 sq. mi. 4380 sq mi.
Year.
Jl*l]mnfn ,,. p.
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Run-Off,
TABLE XVL— Continued.
Hudson Eiyer at Mechanicvillej N. Y*
Drainfige Aren 4500 eq. mL
T*ar.
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.47
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.57
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.40
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.48
.44
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:S
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.44
,74
,81
.81
.64
.30
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.57
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1.44
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.87
M
.44
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,75
.88
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1.64
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5. til
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Polotnac River at Pomt of Rocks, Md,
0654 «q. mi.
m
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fact is more fully demonstrated by the tables on maximum and min-
imum run-off given in the Appendix. From the data in the Appen-
dix it will be noted that the recorded minimum of some of the
Southern streams is between ,5 and .6 cubic feet per second per
square mile, while numerous other streams will vary from .2 to 4;
nevertheless a large oortion of the streams shown have minin
flows of ,1 and less.
CHAPTER TX,
RUN-OFF (Continued).
95. Relation of Run^Off to Topographical Conditions. — The rel-
ative run-oflf from a drainage area depends largely on its topo-
^apliical condition. This is due to the fact that climatic condition
depends on the elevation and slope of the drainage area, and also
to the fact that the rapid removal of the water from steep slopes
assures less activity in the other factors of rainfall disposal and
consequently a greater run-off, Mr, F, H, Newell in a paper before
the Engineering Club of Philadelphia (see Proceedings Engineer-
ing Oub of Philadelphia, vol. 12, page 144, 1895) presents a dia*
gram (see Fig. 88) which shows in a broad way. the influence of
such conditions. In describing this diagram Mr. Newell says:
"The diagonal line represents the limit or the condition when
all of the rain falling upon the surface, as upon a steep roof, runs
off; the horizontal base, the conditions when none of the water
«|30
M
3£
E
u
t
IS
0
/
/
t
y
/
/
'A
/
/
/
/
/
V
^
/
/
/
y
Z\
y
y
/L
^
^ — 1
10 15 20 23 HO 35 40
DtPTM or MEAN ANNUAL RAll^FALU in tNCHCS
Fig. S3
45
sa
176
Run-Off.
flows away. Between these are the two curv^ed lines, the lower rep-
resenting tbe assumed condition prevailing in a catchment basb of
broad valleys and gentle slopes, from which as a consequence there
is relatively little flow, and the upper curve, an average condition
of mountain topography, from which large quantities of water are
discharged* For example, with a rainfall of 40 inches on an un-
dulating catcl ment basin, about 15 inches is discharged by the
stream, while from steep slopes 30 inches runs off. With le^s
mean annual rainfall the relative run-off is far less, as for example,
with 20 inches, about 7 inches of run-off is found in steep catchment
basins, and abont 3 inches on the rolling plains and broad valleys
of less rugged topography* Following these curves down, it would/
appear that as the average yearly rainfall decreases the ruti-off'
diminishes rapidly, so that with from 10 to 15 inches no run-off
may be expected on many areas, and from 2 to 4 inches from the
mountains. There is an apparent exception to this, in that with
very small annual rainfall the precipitation often occurs in what isj
known as cloudbursts » large quantities of water falling at a sur-l
prisingly great rate. Under these conditions the proportion of run-l
off to rainfall increases, as the water does not have time to sat- J
urate the ground/'
'These curves should not be regarded as exact expressions, but
as indicating general relationships and as showing graphically de*
ductions based upon long series of observations of quantities noi
determined with exactness. Computations of this relation made
in various parts of the country have, when platted graphically,
fallen near or between these curves, according to the character of j
the country from which the water was discharged. On the figure]
are shown three average determinations, numbered i, 2 and 3, rep- [
resenting respectively the relation of run-off to rainfall, for the]
Connecticut, Potomac and Savannah Rivers. The horizontal !mes
indicate determinations made for western streams coming from |
areas of small precipitation. The exact amount of rainfall is not
known, as the observations are not representative of the conditions 1
prevailing upon the mountains, and therefore the horizontal line has I
been used instead of a dot, as indicating the probable range erf
rainfall, as. for example, being from to to 15, or from 15 to 20 1
inches. The height of these short lines above the base indicate*!
the average annual nm-off of the basin, a quantity which has beeaj
determined with considerable accuracy according ta the methnij
just described,"
t^m
Effects oTGeological Conditions on the Kun-i
Figure 88 is presented on account of the general principles
illustrated thereby and should be used for such purpose only.
While the limits given by Mn Newell are sufhciently broad to
include many of the conditions in the United States, they are too
broad to g-ive a sufficiently definite relation for most local conditions
and too narrow to include all conditions which may occur in the
United States. The latter fact is perhaps best illustrated by Figi
8g, reproduced from a paper by Messrs, J* B* Lippincott and S. G-
Bennett on "The Relation of Rainfall to Run-Off in California",
published in the Engineering News, voL 47, page 467. This fignre
shows the annual and mean run-off from various California drain-
age areas based on several years* observations. The diagram shows
both the Newell curves, illustrated in Fig. 88, and three mean curves
for California conditions, also several mean and numerous annual
rtin-off obser%^ations which can be studied in detail in the article
above referred to. The general curve for large drainage areas is
for areas of 100 square miles or oven
'
?a m >a vi *o 4% ao
AMNUJIL KAINPALI, IN INCHES
ifl IB 70 7h
Fip:, 89
96, Effects of Geological Condition on the Run-Off, — The geo-
lofical condition of a drainage area has a marked effect on the
run-off. The determination of the exact geological conditions of
my drainage area, which control or modify the resulting run-off,
is difficult or even impossible and can seldam be done with suf-
ficient accuracy so that the results may be even approximated with-
out actual observ^ations on the drainage areas. The effects of these
conditions, however, are important and they are here pointed ooit
178
Run-Off,
so that such effects may be realized and the fact appreciated
the run-off of streams otherwise similarly located may be matenall/
different on account of difference in these conditions. A ^ood ex-
ample of the geological infiuence on run-off may be seen by compar-
ing the stream flow of any of the Northern Wisconsin streams with
that of the Rock River in the Southern portion of the state. Most
of the Northern Wisconsin streams flow, in part, over pervious^
beds of sand-stone and a considerable amount of the water fallinf
on their drainage areas is undoubtedly lost through absorption by
the underlying strata. These losses undoubtedly affect the flow of
the stream to a considerable extent. These streams, however, have
no large under- flow through loose material which can absorb and
transmit any considerable portion of the rainfall that would other-
wise appear as surface run-off. The Rock River, on the other hand,
follows for a considerable portion of its course through Wisconsin,
its pre-glacia! drainage valley which is filled to a depth of 300 feci
or more with drift material consisting largely of sands and gravels
through which a large amount of water doubtlessly escapesi Tlie
TABLE XVII.
Comparative Mean Monthtt/ Run- Off of the Whemrna Biver at Nf'(^&iah Wti^
cons in, and the Rock River at Rock f on, IfVnou, in Cuhi<; Feet
Per Second Ffr Square MUe.
1903
gd
jS
^
C
A
S
<
4)
<
«2
0
>
6
it
WUconsin river,
Hocic river. . « * . ^ . ^ . ,
.45
A4
2.04
I A3
2,50
L19
1.56
.91
1.15
<63
.91
.86
-:
^
1904.
Wisconsin river*
Rrick river
[^
111
ilm
2.21
1.7^3
2.63
.8K
1,96^
.39
1.02
.20
,fi6
.24
,90
.3^
2.34
.50
M
.30
li
10OII« _J
Wipconfiin river
Rock river*. .-..,.
"M
^'M
2.10
2.72
1.63
1.91
MO
4,02
L.06
1.50
.61
1.05
.41
1.28
.39
M
.40
i
100«, _|
Wieconain river.
Rock river* ■ - ■ ■
i'.m
iM
i'm
3.90
I AM
.58
1.96
.37
I.IS
.38
.90
.S9I
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1.17
i
J
4
M
:i
Effects of Area on the Run-Off. 179
deposits of this old river bed have been quite extensively explored
for water supply purposes and yield very large quantities of water
for domestic and manufacturing supplies. Most of the under-flow,
however, undoubtedly passes away to an unknown outlet as tht
modern river leaves the old valley near Rockford, 111.
A comparison between mean monthly flows of the Wisconsin and
Rock Rivers, as shown in Table XVII, will give an idea of the effect
of these different conditions as shown by the run-off of these two
rivers.
97. The Influence of Storage on the Distribution of Run-Off. —
Favorable pondage conditions on a watershed have an important
effect on the distribution of the run-off, and this effect is readily
discernible in the records of flow from such areas.
Figure 90 is a hydrograph of the discharge of the various rivers
draining the Great Lakes for the years 1882 to 1902. A general
similarity is seen in the annual variations in these hydrographs and
yet there is a considerable variation from the maximum to the
minimum discharge in accordance with the rainfall and other condi-
tions prevalent on the watershed. In every case, however, the
minimum of the year is found to occur at about the same time, and
the time of maximum height is also fairly constant. The ratios
between maximum and minimum flow are very much less than those
that obtain on other watersheds where the pondage area is much
less.
In the St. Lawrence River the maximum mean monthly discharge
is about 320,000 second feet, and the minimum is about 185,000
second feet, the maximum being not quite double the minimum. In
the discharge of the Niagara River the maximum mean monthly
discharge is about 260,000 cubic feet, and the minimum aboui
75.000, the fluctuation being still more moderate.
The mean monthly discharge of the St. Marys River shows a
niaximum of about 110,000 second feet, and a minimum of about
50,000. The ratio here is somewhat higher, because, in this case,
Lake Superior and its drainage area being the source of supply,
the relation of pondage to drainage area is less than in the com-
Wned lakes, and the effect is seen in the variation in the discharge
of this river.
98. Effects of Area on the Run-Off. — The size of the drainage
area of any stream has a marked effect on the distribution of the
nin-off. The hydrographs of small areas show the effects of
heavy rains by an immediate and marked increase in the flow*
I So
Run-Off.
D
B
■
s
"in
i
i
X3
t
HA
The Study of a Stream from its Hydrographs. i8i
liis is well shown by a comparison of the. hydrographs of Per-
iomen Creek and the Kennebec River (Fig. 96), and of the
lood and Spokane Rivers (Fig. 99). On small streams where per-
ious deposits are largely developed, the rainfall is rapidly absorbed
nd does not so radically affect the run-off. Large streams do not
jel the immediate effect of rainfall, on account of the time required
>r the run-off to reach the main stream. The flow of large streams
; also modified by the fact that uniform conditions of rainfall
sldom obtain on the entire area. On large drainage areas, condi-
ons of rainfall may prevail on one or more of the tributaries only^
rhile on other portions of the drainage area the conditions may
e quite different. Such conditions may frequently be reversed,
^ith the result that the larger the stream the less becomes the
Ktremes of flow and the greater the uniformity of flow.
gg. The Study of a Stream From Its Hydrographs. — ^The influ-
nces of various factors on the run-off, as above discussed, can be
[early seen from an analysis of the stream flow data, but they can
est be appreciated by noting their effect on the hydrograph. The
ydrograph of the actual flow of a stream is the best means of
tudying its manifold variations, but to fully comprehend the wide
imit of such variations, hydrographs must be available for a
ong term of years. When the hydrographs are sufficiently ex-
tended to cover all of the usual variations in rainfall and other
meteorological conditions, they afford a comprehensive view of
the entire subject of the run-off of the stream.
Figures 91 and 92 show hydrographs of the Passaic River for
seventeen years. From these hydrographs the actual variations in
flow as they have occurred on this drainage area during this period
can be seen. The average monthly rainfall on the drainage area has
also been shown on these diagrams and the effects of such rainfall
on the run-off should be noted. It is important to note especially
the marked effect of a limited rainfall during the months of the
storage period, when the ground has previously become saturated,
^^ compared with the effects of the same or greater rainfalls during
^he growing period, when the ground water has been partially ex-
hausted by the demands of vegetation and the draft of the low
^ater flow.
h these diagrams, and those following, the flows are shown
in cubic feet per second per square mile, in order that their
value for comparative purposes may be increased. The absolute
discharge of a river in cubic feet per second gives no comparative
iSi
Run-Off.
i
4
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Figures n«Ar top of eftcb (fla|7nm show total nionililj mlnf^l.
Fig. 92— Dally flow of Passaic Blver, Little Falls, N. J.
184
Run-OE
measure of discharge values, but when the corresponding area is
also shown, the diagram becomes more or less applicable for com-
parative purposes to other areas. Hence, for general or com pan-
tive discussion, the discharge per unit of area should be the basi^
of consideration.
100. Comp^-ative Run- Off and Comparative Hydro graphs.— In
studying and comparing all run-off data and the liydrographs basd
thereon it is important to note that a uniformity of conditions pri>
duces a uniformity of results. Such data is not only of value in
the study of the river from which it is obtained, but also furnisher
information regarding other streams that exist under the same or
similar conditions, both physical and meteorological*
Table XVI T I, which shows the monthly run-off for a term of year>
of certain Michigan streams, gives a comparison of the flow of
streams under such conditions, as expressed by their comparative
monthly run-off. The relative geographical locations of these
streams are shown in figure 93. The run-off from each drainage
area is given in cubic feet per second per square mile, so that ttie
results are strictly comparable, the question of size of area feeing
eliminated. A general resemblance can be traced between most of
these streams. The Manistee and Au Sable Rivers, in the Northern
portion of the state, have sand and other pervious deposits largely
developed on their drainage areas, and show, in consequence,
greater uniformity of flow amj a greater mean flow than that of
the other streams.
Comparative hydrographs of some of these streams for the yea^
1904 are shown in Fig. 94. The vertical scale for each of the '
hydrographs shown on the diagram is the same, and represents the
discharge in cubic feet per second per square mile. The relative,
flows of the different streams are thus easily compared. On tlies«
diagrams has also been shown the average rainfall which occurro
on each drainage area for each month. A study of the rainfai
record in connection with the flow lines of the h yd rograph, wil
show that the difference in flow is not entirely attributable to tb
prevailing rainfall conditions on the drainage area» but that otli6
physical influences have a material effect. These hydroirraph
were originally prepared in order to form a basis for an estiniatt
of the probable horse power on the White River, on which fi£* j
gauge readings had been taken- On the right of the diagram i?
shown a horse power scale from which the probable po^ver of the
White River, with a given fall and drainage area, and on the basis
Comparative Hydrographs*
i8S
Fig, 93.— Mmp showing location of variouB MicLigac dminage
U
^
i86
Run-0£f,
Fig. d4. — Ckmiparative Hydrography of VarlouB Mlchlsaa ElTers for Uie l«
1904.
Comparative Hydro^raph*.
187
«V0IA4 MUM IMflaM i3»fli ItUfii
I
i
a
en
I
I
i
i
9
La
S3
d
■a
I
iO ^ W €U - O
A
iS8
Run-Off.
TABLE XVfIL
Discharge in cubic feet per second per square mile of drainage area of various
Michigan rtwer*
1001
Marcli ..,.,,
April
May
June
July.
August
HepDettiber. .
OcUiber
November , .
December . . .
I
1902
JaTiimry .......
February
March —
Apnl ----., —
May
Juue
July .
August
September
Ociober
November . *.»»
Decern ber .*,.,.
Yearly mean.
19U3
January ..*...,
February * , * . . ,
March «..^
April .,,,
May , , .
June -* — ** *
July..
August ...
September « . . . .
October........
November
December
Yearly mean.
1904
January
February ,,..
March .......
April * . . ,
May , , -
June ..*....-
1.49
1.18
.63
.74
.51
1.31
.70
.41
.32
.40
.29
Llil
.91
.78
.74
,40
.46
.21
.48
.77
.34
-59
.44
.65
1.67
1.16
.62
.44
.4d!
.79
.68
.43
.as
,71
.38
,64
3.48
1.17
Grand river
■^^
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bb
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^1
^
2
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3Q'Cffl.
3.25
i.au
.6t)
.h9
.92
.38
.39
.47
.42
.66
M
.40:
1 41
1.03
1.16
.70
1.57
.53
.5
.79
.95
.96
1.53
2. 20
2.13
2-04
.68
.53
.45
.52
l.Oti;
l.}5
.64
.62
1.05
2.90
1.00
..52
2,73
1.06
.48
.34
.78
.68
.44
.61
.35
.66
.65
.43
1.26
1.02
1.09
.88
1 78
.57
.50
.84
.66
.62
.83
1.36
2.69
2.45
.52
.4^>
.53
.79
1,04
.62
.43
.33
1.00
.48
1.07
3.05
3.22
.6it
.33
.64
.63
.57
.61
.62
.50
.60
,57
.64
.46
.46
.68
.55
.55
.56
.62
.54
.52
.61
.63
.64
.56
.93
1.20
1.84
1 m
.76
.69
' .62
.69
.92
.81
,6S'
.72
.82
.98
3.44
2.08
1.
.73
Q *
Es(^*j be
« * C -J
s s^ £ '^^
L29
.76
.53
.45
,38
.54
.71
.70
.69
,62
1.32
.90
.98
.U2
1.10
.60
.58
.84
.79
1.00
.86
1.13
1.62
2.06
1.76
.41
.66
1.40
1.4R
3.07
2.24
.68
.46
.45
.40
.37
.50
.38
.38
.30
.33
.67
i.oa
1 34
.77
.04
.47
.46
.67
.57
,54
.68
.67
1.58
1.38
.91
1.22
1.40
1.40
1.S5
1.28
1.41
1.
1.18
1.29
S.36
2,00
1.42
.71
.71
.76
.96
.93
1.94.
IM
1.49
1 06
.^^
Comparative Hydrographs*
189
TABLE XVTTL— Continued,
Grand river
a
dS ?* £
5-2
o
o
N
1- 5
OJ *» n
aj * §
-a '^ ■^
xTP5
0
o
>3> Id
> lit
y
3 P S
« ^ ^
:sS3
luly..,.
Augoat
September
October.,,, .,
Xovetnber
December ,
Yearly m^an .
Mean for Last 5 01
6 months .^.. . .
19(^
January ...^.*» *..,
Febniary **.,,*.
March*
April , , ,
May
June . . , , .
Mean for 6 mos. . .
.34
.m
.36
.35
.35
,41
,63
,67
1,94
1,47
1.4«
2 7e
1 49
.25
,24
,21
,3se
.24
.2H
w8
.25
.66
.55
.61
.71
.55
56
1,06
.67
.33
.47
*47
.40
.47
.45
,33
.45
.42
.39
,41
1,22
.90
1J8
.85
1,11
.77
l.iy
.82
1.09
.76
1,08
1.37
1.3t>
KS3
1,14
.91
1,20
1,31
1.31
1,97
1.52
1.19
1.81
1.07
1.51
1^4
i.2;i
.98
X.ol
i.n
.40
.66
.68
.93
.94
,74
1 34
1.51
1.55
1,55
1.47
1 84
1.54
of the com para tiv^e flows of various Michigan rivers, could be es-
timated. In Fig. 95 these hydrographs have been re-drawn, the
daily flours being platted in the order of their magnitude. This
form of diagram represents the best basis for the comparative
study of stream flow for power purposes where storage is not
considered, and where the continuous power of the passing stream
is to be investigated.
A careful study of Figs, 94 and 95 will show that the run-off is
similar in streams situated under similar geographical, topograph-
ical, and geological conditions, and having equal, or similar, rain-
falls on the drainage area. The departure of the various streams
fiere considered, from the average of all, gives a very clear idea of
ifie errors which may be expected in estimating the flow of any par-
Ijcular stream from the hydrographs of other adjacent streams, or
from the flow of streams more remote, and which are located under
different physical conditions,
10 r. Comparative Hydrographs From Different Hydrological
Divisions of the United States, — The hydrographs off streams differ
widely in character, both in accordance with their geographical
location and the diverse physical character of their drainage areas.
Their geographical location afifects their climatic, geological and
19^
Run-Off.
1303
^^i*M*^M»mJK.
Sldl^
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14 '
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Aloovy River, GovlngtOD, Ga,: Drainage Area, 22i Sq, ML
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Coosa River. Riverside, Ata.: Drainage Area, 70G5 Sq. Ml. ^
r^^^i^:?^:-W>>UwA^J
ieo4
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Creek, Nottingham. Ala.: Drainage Area, 16C Sq, MI.
Fig. 96.— Hydrographa of AOantic and Eastern Gulf Drainage.
I?
CQ
K
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8
Licking Blver, Pleasant Valley, O., Drainage Area G90 Sq. Ml.
ti^^Mi^'^n^
m^A '/s^s^M'/m y/miMmi^s^,^^z^^r/^'jm w/5f.9s»iS^mKTsm>. fjmw/A ^m^. '^/a /^^i, ^7^^^AWk*w^.
Seneca River, Baldwinsvllle, N. Y,. Drainage Area, 3103 Stj. AIL
l«
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id
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Grand River, Grand RapUs, Mich,, Drainage Area, 4900 Sq. Ml. a
m
—
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Ftg. %1, — H^drugraphs of Ohio Yalley and St Lawrence Drainage,
^
%^
RtiD-Off.
WiscoBMUi Itlver. Necedat. Wi«., Drainage Area, 5Si'
T
li»3'
-tSD4
i - ■ 4 ■ ! i
m
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Meraiuec Klver^ £urek&. Mo., Drainage Area, 3497 BQ. ML S
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T ^'
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Otter Creek, MQuataiii Park, Okla., DnUiiage Arii
03
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ail!
Tal
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Wyo.,
DralnaE'e Area.
llf
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YeUowatoiie River, Livingston, Mont,, Drainage Area, 3680 Sq. Mi |
^^
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^™
^"
m^
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^^
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Niobmm River, ValentlDe, Neb., Drainage Area, 60t0 Sq- Ml.
1904
^^
iffl:
Rlo Grande River, l^lmtos. N. M., Drnlnage Area, 7695 Sq- MI. fl
3;
1903
lao
^^B
^^
8alt River, McrlXnvell, Arlt,. Drainage Area, 6260 Sq. ML
ing tg.—Hydrosi'&pl^a ot Mississippi Y&lley^ and Quit Drainage.
Comparative Hydrographs.
193
«
a
u
w
<
3
<
1
-5
i
3r
u
0
-1 u.
3-
0. 5 3
< 2 T
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.
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fjim
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m^mimm^/m:wAyA'.wAmcf.
v^
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tfjs sd
Spokane River, Spokane, Wash., Drainage Area, 4005 Sq. MI.
I88d
IB88
Hood RSver. Tucker* Ore., Drainage Area, 350 Sq. Ml.
%yy^y//////A'WAm^ymyy/^.m'jyjm^
m^A:4mYM
M'/AW^yM
€^yAVj^/:yyAyyAy//AWA'y/M^Ay/yAyyA^yA//yAy/A'jm^
Kalawa River* Forks, Wash., Drainage Area, 213 Sq. Ml.
C3
J
Ktrn River
, Bakersfield,
Cal..
Drainage Area,
2345 Sq
. Ml,
4
1
In
^903
1904
~
J
2
Yi
J
m
^
^
t
^
_
db
^
=
—
—
San Gabriel River. Azuaa, Cal, Drainage Area, 232 Sq. Mi-
Bear River. Collinston, Utah. Drainage Area, HftOO Sq. MI.
T
rAss^MzitX
1804
^22
P
'.4^/ywA'y.
Walk<f*r River. Colevllle* Cal.* Dra!nngo Area. 300 Sq. M!.
Fig. 99.^Hydrographs of Western Drainage.
194
Run-Off.
topographical conditiotiSj and results in a material difference inH
the distribution and quantity of run-off* f
Hydrographs from the various hydrological djvistons of the
United States are shown by Figs. 96 to gg, inclusive. For each
drainage area hydrographs for two years are shown in order to
eliminate, partially at least, the effect of any peculiar conditions
which might have obtained during a single year, and to show that^
the hydrographs are characteristic, ^
103. General Conclusions,^ — A complete discussion of run-off is
impossible in the space available in this volume. Attention has
been called to the general laws upon which the amount of run-off
depends, and to the similarity in flow that obtains on watersheds
which are physically similar, also to the variations in run-off that
occur on different watersheds due to differences in physical condi-
tions, A
Each stream presents peculiarities of Us own, and in investigating'™
stream flow the data available is seldom the same and is always
fotund to be much too limited for a complete understanding. Only
general suggestions can be offered for the study and investigation
of these subjects. Attention has been directed, as clearly as pos-
sible, to the errors which are likely to arise in the investigation of
water power conditions by comparative study. From a knowledge
of such errors the engineer will realize the limiting values of iiis
conclusions, and hence should so shape his design as to effect a^
safe a construction as the condition will permit, and also a construc-
tion which will bear out fairly well his conclusions at the time of its
inception* It is evident that no exact conclusions are possible in
these matters, and that an element of uncertainty is always pres*
ent. A knowledge of the extent of these uncertainties and the
probable limits of exact knowledge are as important to the engineer
as his ability to draw correct conclusions from data which is known
to be correct.
LITERATURE.
BESULTS or STSEAIC FLOW MEABUTSBWDT^TS.
1. Annual Reporta of the Water Bureau of Philadelphia, Contain eon^|
plete data relating: to the Perkiomen, Tohlckon and Neabamlny*
Z, Monthly Data Relating to tlie Sudbury; Cochituate, and Mystic, ReporU I
ef the Boston Water Board, and of the Metropolitan Water |
Board, Boston,
Publications of the U, S. Geological Survey contain data for the ye
Indicated below:
literature.
195
3.
ism.
4.
1SS9.
5.
1890.
6,
1S9L
T,
18B2.
S.
1S93.
B.
1804.
to.
1894-
IL
1S95,
12.
1895.
13,
1896,
14.
1896.
15, 1S97.
le.
1897-
17.
1898-
18,
1S98,
19.
1899.
20,
1899.
21-
1900.
22.
1900.
23,
1901.
24.
1902.
ZS.
1903.
26.
1904.
27.
1905.
TeoUi Annual Report. Part 1.
meventh Annual Report. Part II.
Twelfth Annual Report Part II.
Tblrteentli Annual Report Part IIL
Fourteen th Annual Report, Part 11.
BuUeUn No, 131-
Sixteenth Annual Rer:>rt Part IL
Bulletin No. 131.
Seventeenth Annual Report Part II*
Bulletin No. 140.
Eighteenth Annual Report Part IV,
Water Supply and Irrigation Paper, No. 11*
Nineteenth Annu^ Report Part IV.
Water Supply and Irrigation Papers, Nob. 15 and 16,
Twentieth Annual Report, Part IV.
Water Supply and Irrigation Papers, NoB. 27 an^ 23.
Twenty-first Annual Report. Part IV.
Water Supply and Irrigation Papers, Nos. 35 to 39, Inclusive.
Twenty- second Annual Report. Fart IV.
Water Supply and Irrigation Papers, Nos. 47 to 52, inclusive.
Water Supply and Irrigation Papers, Nob, G5, 68 and 75,
Water Supply and Irrigation Papers, Noi. SI to 85. inclusive.
Water Supply and Irrigation Papers, Nos. 97 to 100. inclusive.
Water Supply and Irrigation Papers, Nos. 124 to 135, inclusive.
Water Supply and Irrigation Papers, Nos. 165 to 178, Inclusive.
EIXATIOXS OF BAIXFALL A>'D STREAM FLOW.
28, Fteley, A, The Flow of the Sudbury River, Mass, Trans. Am, Soc, C. E.
Vol. 10, p. 225, 1881.
29. LaweOp J. B, On tb© Amount and Composition of Rnin and Drainage
Waters, collected at Rothamated, Jour, Royal Agric. Soc. Eng.
Vol. 17. p. 241, 1881, and Vol. IS, p. 1, 1882.
Si Coghlan, T. A. Discharge of Streams in Relation to Rainfall, New South
Wales. Proc. Inst C. E., Vol. 75, p. 176, 1884.
3L Groes, J* J. R. Plow of the West Branch of the Croton River, Trans.
Am. Soc. C. E., Vol, S. p* 76. May, 1884.
32. Bracliett, Dexter, Rainfall Reoelved and Collected on the Water-shed?
of Sudbury River and Cochituate and Mystic Lakes. Jour. Asso.
Eng. Soc, Vol, 5. p. 395, 1S86.
33- McElroy, Samuel, The Croton Valley Storage. Jour. Asso. Eng. Soc.
1890.
Si* Pitigerald, Desmond, Rainfall. The Amount Available for Water Sup-
ply, Jour. New Eng. W. Wks. Assn. 1891
^S. Fliigerald, Desmond. Yield of the Sudbury River Watershed in the
Freshet of February 10-13, 18S6, Trans. Am. Soc. C, E., Vol
25, p. 253, 1S91.
^' Talbot A. N. The Determination of the Amount of Storm Water, Proc
III. Soc. Eng. ^ Surveyors. 1892,
196
Run-Off.
37,
ss.
39.
42.
43.
44.
45,
46.
47.
48.
49.
60.
5t
12.
53,
5S«
56.
f*7.
59.
Fitzgerald. Desmond. Flow of Streams and Storage in Massachosetb
Trans. Am. Soc. C* E., Vol. 27, p» 253. 1892.
Fitzgerald, Desmond, Rainfall, Flow of Streams, and Storage. Tnua
Am, Soc. C. B., Vol 27, p. 304> 1892,
Babb, C, C, Hydrography of tbe Pc omac Basin. Trans, Am, So<v C _
E„ Vol. 21, p. 21, 1S92. I
Babb. C, C. Rainfall and Flow of Streams. Trans. Am. Soc C, EL. VM.1
SS, p. 323, 1393, I
Meadt D. W. The Hydrogeology of the Upper Mississippi Valley, and oil
Some of tbe Adjoining Territory. Jour. Ass*n Eng. Soc,» VoM
13, p. a29. 1894, 1
Ruport on Water Supply of New Jersey, Geol, Survey of N. J„ Vol, %'
1894.
Starling, Wm. Measurements of Stream Flow Discharge of the Missis-
sippi River. Trans, Am. Soc. C. E., Vol. 34, pp. 347-192, 1895.
HcLeod, C. H, Stream Measurements. The Discharge of St. Lawrence
River, Trans. Can. Soc, C. EJ, June, 1896.
Data Relating to the Upper MlBsisstppl. Report, Chief of Elnglneera, 0^
S. A.. 189G, p. 1343.
Wegmann, Edward. The Water Supply of the City of New York- Dati
Relating to the Croton. Wiley & Sons. 1896.
Johnson, T. T. Data Pertaining to Rain f nil and Stream Flow, Jonr.
Wes. Soe. Eng., Vol, 1, p. 297. June, 1896,
Chaniler, Geo, Capacities Required for Culrerts and Flood Openlnp^
Proc. Inst C. R. Vol. 134, p. 313. 1898.
Pftrmalee, W. C. The Rainfall and Run-oiT in Relation to Sewage Prob-
lems. Jour. Asao. Eng. Soc, Vol. 20. p. 304, Mch., 1398.
Seddon. J. A. A Mathematical Analysis of the Influence of Reservoirs
upon Stream Flow, Trans. Am. Soa C. E., Vol, 40, p. 401. 189S.
Sherman. C. W. Run-off of the Sudbury River Drainage Area, 1S7S-1899.
inclusive. Eng, News, 1901.
Clark, E. W, Storm Flow from City Areas, and Their Calculation. Eng
News, Vol, 48. p. 386, Nov. Gth. 1902.
Pence. W. D. Waterways for Culverts. Proc. Purdue Soc, C, E., 1903.
Weber, W. O. Rainfall and Run-off of New England Atlantic Coafit aH(3
Southwestern Colorado Streams, with Dlscusalon. Jour, Asbo.
Eng. Soc Nov., 1903,
Abbott. H. ti. Disposition of Rainfall in the BasJn of the Chagrei
Monthly Weather Review. Feb., 1904.
Mead, D, W. Report on the Water Power of the Rock River. Chicago
1904. Published by the Author.
FUKJnS.
The Flood in the Chemung River Report State Engineer, N. T., ISH
p. 387,
The Floods of February Gth, 1S96. GeoL Survey of N. J. 1896. p. S
Morrill, Parle. Floods of the Mississippi River. Bui. E., U. S. Dept 0^
Agric. 1897.
n
Literature. 197
60. Starling, Wm. The Floods of the Mississippi River. Eng. News, VoL
37. p. 242. Apr. 22nd, 1897.
61. Starling. Wm. The Mississippi Flood of 1897. Eng News, VoL 38, p. 2^
July 1st, 1897.
62. McGee, W. J. The Lessons of Galveston. Nat. Geo. Mag. Oct, 1900.
63. Study of the Southern River Floods of May and June, 1901. Eng. News,
Vol. 48, p. 102. Aug. 7th, 1902.
64. Brown, Im W. The Increased Elevation of Floods in the Lower Missis
sdppi River. Jour. Asso. Eng. Soc., Vol. 26, p. 345, 1901.
65. Holister, G. B. and Leighton, M. O. The Passaic Flood of 1902. Water
Supply and Irrigation Paper No. 88, U. S. G. S.
66. Leighton, M. O. The Passaic Flood of 1903. Water Supply and Irriga-
tion Paper No. 92, U. S. G. S.
67. Murphy, B. C. Destructive Floods in the United States in 1903. Water
Supply and Irrigation Paper No. 96, U. S. G. S.
68. Frankenfleld, H. C. The Floods of the Spring of 1903 in the Mississippi
Watershed. Bui. M., U. S. Dept of Agric. 1903.
69. Flood Damages to Bridges at Paterson, N. J. Eng. News, Vol. 50, p. 877,
Oct 29th. 1903.
70. Kansas City Flood of 1903. Bng. News, Vol. 50, p. 233, Sept 17th. 1903.
71. Engineering Aspect of the Kansas City Floods. Eng. Rec, Vol. 48, p.
300, Sept 12th, 1903.
72. Murphy, E. C. Destructive Floods in the United States in 1904. Water
Supply and Irrigation Paper No. 147, U. S. G. S.
F0BE8T8 IN RELATION TO BAINFALL AND STREAM FLOW.
73. Swain, Geo. F. The Influence of Forests Upon hte Rainfall and Upon the
Flow of Streams. Jour. New Eng. W. Wks. Ass'n.
74. Rafter, Geo. W. Data of Stream Flow in Relation to Forests. Ass'n
C. E., Cornell Univ., Vol. 7, p. 22, 1899.
75. Thompson, D. D. Influence of Forests on Water Courses. Scientiflc
American Sup. No. 807.
76. Vermeule, C. C. New Jersey Forests and Their Relation to Water Sup-
ply. Abstract of Paper Before Meeting of The American For-
estry Ass'n. New Jersey, June 25th, 1900; Eng. News, July 26th,
1900; Eng. Record, VoL 42, p. 8, July 7th, 1900.
"7. Bremner. Water Ways for Culverts and Bridges. Jour. West Soc Bngrs.,.
VoL 11, p. 137. April, 1906.
CHAPTER X,
STREAM FLOAV. '
103. Flow m Open Channels. — The discussion of the flow of v\*ater
in o]jcn channels in Chapter II! inchides only such channels as
have uniform cross sections, ahgnment, and gradient and a bed of
uniform character throughout the length considered* Such cotidi-
tions are closely approximated in artificial channels in which the
quantity of water flowing is under control. In such channels, and
with a steady flow, — that is with the same quantity of water passing
every cross section in the same time, — it is shown that:
(1)
w
c vts and ihsX
A§ =
In natural water courses no two cross sections are the same but
may differ in area, a, and wetted perimeter, p ; and tlie fall, h, in any
length, I, usually differs considerably from reach to reach. The
quantity, q, of water flowing in any such stream is also constantly
changing. There every condition of uniform flow is lacking and
can only be approximated for selected reaches of such streams andj
during periods when stream flow is fairly steady*
104. Changes in Value of Factors with Changes in Flow, — Frofflj
an examination of equation {2) it is evident that in any channel a* j
the quantity of water flowing, q, changes, there must be a co^^^j
sponding change in some or all of the factors on the other side of thej
equation.
For steady flow in a uniform channel, s remains constant and all]
■changes are confined to the values of a, c and r. The laws
change in the values of c are given by Kutter's and Bazin's formu*!
las, but are best illustrated and understood by reference to Fig* A j
which is a graphic expression of the formula of Bazin.
In variable flow a change in all of the factors usually accomp^*!
nies a change in the value of q, each factor changing in accordance,
with the physical conditions of the channel.
The changes in the value of c, in an irregular channelp do not 1
ways seem to follow Bazin^s law* In some cases c is even found 1
Flow in Open Channels.
199
•decrease as r increases. The law of simultaneous increase in c and
r presupposes a channel of uniform character and condition. If an
increase in the hydraulic radius, r, in any channel is accompanied by
a radical change in the character of its bed the law will not hold.
It is evident that under such conditions the values of c for different
values of r are not fairly comparative. No more uniform law of
change can be expected under such conditions than would occur in
the comparison of the relation of c and r for entirely different chan-
nel sections.
In Fig. 100 are shown the observed values of c and r for certain
reaches of the Wisconsin River above Kilbourn, Wis. It will be
26
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VALUES or "^C.
Fig. 100. — ^Relations of Ck>efflcient to Hydraulic Radius in Certain Reaches
of the Wisconsin Riirer.
200
Stream Flow.
noted that the value for reacnes A, D and E follow in general the
law as established by Bazin. These are fairly uniform. On the
other hand the values of c and r for reaches b and c seem to follow
an entirely different law, a condition due to irregularities in the
cross section of the reach.
Where the values of a, p and r vary radically from section to sec-
tion and differ materially from the values in the sections considered
and on which calculations are based, the value of c will be found ta
differ radically from that which the character of the bed and the en-
tire section would indicate. Absurd values of c are a clear indica-
tion that the sections selected are not representative. The calcu-
lated value of c is modified by all unknown or unconsidered factors
of the reach. The influences of irregularities in bed or section, the
presence of unconsidered bends or changes in the gradient, and alf
other irregularities in the channels, modify the values of c.
Z05. Effects of Variable Flow on the Hydraulic Gradient— lo
order to understand the effect of variable flow on the surface gradi-
ent of a stream, and in order to realize how conclusions drawn from
the laws of uniform flow must be modified to meet conditions found
in natural streams, it is necessary to consider the cause of variable
flow in a stream, the variation in channel conditions, and both the
effect of flow on such conditions and the effect of such conditions on
the flow of a stream.
Bepnoot/criON of ffcco/fo of U.S.L.S. Gauge Ah.S foa MAt /7, /6SSL
JIT
e • 10 n 'V » 14
D.u„i.^.T^»^i^d,p.m f^.A£f^,». ^67fk^lh^ m^i^sf ^,k^.
Fig. 101.— Variations in Gauge Height of the St. Clair River.
Effects of a rising or a Falling Stream on Gradient, 30i
The surface of a stream is constantly fluctuating, not osily on ac-
count of the variation in flow, but also on account of wind, baro-
metric pressure and changes in the hydraulic gradient. Such
changes occur from hour to hour, and even from minute to min-
ute* Larger rivers, fed directly by great lakes, are 'more sus-
ceptible to these changes on account of the broad lake area, giving
wind and barometric pressure greater opportunity to act. Every
stream is, however, more or less susceptible to these changes, and
gauge readings taken daily, therefore, show only in an approximate
way the true height of the surface of the river at the point of ob-
ser\'ation* This is well shown by Fig, loi, which is reproduced
from the autographic record of a gauge at the head of the St. Claire
River.
io6. Effects of a Rising or a FaUing Stream on Gradient. — In a
channel of uniform section, the bed of the channel AB (see diagram
A, Fig. 102) having a uniform slope^ all cross sections, such as Aa
and Bb, will be alike and the wetted perimeters and the hydraulic
radii will be identical for all sections. The fall, bx, will be uniform
in all equal lengths, 1, of the channel, and such uniform co!nditions
will be maintained for all regular discharges after regular flow is
once established.
In such channels, during changes in the stages of flow, the hy*
draulic gradient or slope will change until uniform flo>w is estab-
lished. In all cases illustrated in Figs. 102 and 103, the line ab rep-
resents the hydraulic gradient which will obtain if uniform flow is
maintained in the channel and if there be no change in the channel
section or other conditions. The actual water surface, caused by
variable flow, is in each case shown by the line a'b. In each case, the
fall, bx, would be necessary to produce uniform flow from A to B
and to assure the flow of the normal quantity of water passing the
section Bb as in diagram A, In diagram B and C, Fig. 102, the con-
ditions of variable flow in a uniform channel are graphically repre-
sented. The actual flow is greater or less than the normal quantity*
according as the gradient is increased or diminished.
In diagram B, the conditions with a rising stream are shown.
Under these conditions the quantity of water passing the section
Aa is greater than the quantity passing the section Bb, by the quan-
tity of water necessary to fill up the channel of the stream to a new
and uniform surface gradient. The head needed to produce the flow
past the section, Aa, is represented by the height, xx'. The total
fall between A and B is therefore greater than that required for the
It
20%
Stream Flow.
Fig. It^. — Effects of Variable Flow on the Hydraulic Gradient of a Streaa.
Effects of Channel Conamon^STGradienl.
uniform flow as represented by the head bx'. This produces not
only a greater flow at Aa, but also a flow greater than would be nor-
mal at section Bb.
In diagram C, Fig. 102, the conditions of a falling stream are rep-
resented. In this case, the head at section Bb at the moment of
observation would, if the flow was uniform, produce a normal flow
which would require the fall, bx, to maintain it With a falling
stream, the section AB is emptying and the quantity of water pass-
ing the section Aa is less than the quantity of water passing the^
section Bb, which in turn is also less than the normal flow for the
existing head. A less fall is therefore required to produce the flow
passing Bb, which, with the lower slope and the same cross section,
is less in quantity than would be the case under conditions of uni-
form flow. This fall is represented by the height, bx', which is less
than the height bx, required for, uniform flow by the height xx':
consequently the slope of the river is a'b.
From the above considerations it will be seen (see diagram D,
Fig. 102) that a given gauge height, Bb, may not always represent
the same flow, for the discharge, Q, is a function not only of the
cross section, a, but also of the slope, s. A single gauge height may
therefore represent a considerable range of flows depending on the
hydraulic gradient which may pass through the point with a uni-
form, a rising or a falling stream. It is obvious that the flows rep-
resented by the hydraulic gradient, a' be', abc and a'^bc", while pro-
ducing the same gauge height at Bb, nevertheless represent three
di fife rent conditions of flow.
In the establishment of the relations between gauge heights and
floWf it is therefore important that the observed flow corresponding
to a given gauge reading be taken during a period of essentially uni-
form flow, for, from the above considerations, it will be seen that
any determination or observation made %vith a rising or a falling
stream must necessarily be more or less in error. It will also follow
that, after a rating curve and rating table have been established,
the gauge height taken during changes in the conditions of flow will
be more or less in error, althonjgh such errors will equalize to a con-
siderable extent and will, in the main, prove unimportant,
107, Effects of Channel Condition on Gradient— The flow of
water in a natural channel is far from being uniform and it is im-
portant for the engineer to realize this lack of uniformity and the
effect of such conditions upon the flow of the stream. In any chan-
nel of uniform gradient, as AB in diagram E (Fig, 102), if at the
204
Stream Flow.
Pig. 103. — Effects of Channel Grade and of Obstruction on the Hydraulic
Gradient of a Stream.
section Bb the coefficient c is decreased on account of increased
roughness in the bed of the stream, or if the area of the channel, a,
is contracted, a change in the hydraulic gradient will follow. The
normal gradient with uniform flow would take the position ab, but
on account of the change in conditions at Bb, the depth must in-
crease to keep q a constant ; a must increase to offset the decrease in
c or c must increase to offset the decrease in a if q remains constant.
The surface must therefore rise to the point x and a new hydraulic
Effect of Change in Grade.
I
205
gradient will be established and maintained until other changes in
the channel condition again modify the same. Between the new and
old gradients, a transition curve will be established extending both
above and below the point at which the change in condition takes
place to some point, y, frequently a long distance upstream.
The opposite condition is shown by diagram F, Fig. 102. In this
diagram the effect of an increase in the coefficient, c, of the bed or
in the area, a, of the stream is represented. If c increases, a less
section will be required below that point and again the surface Is
lowered ; or if the width of the stream increases, the depth will
diminish in order that ca may remain constant.
Variable Bow is also caused by a sudden enlargement in the
river section or by a discharge of the stream into a larger stream or
into a lake or pond. Such conditions are shown by diagrams G
and H, Fig< 102. The character of the transition curve in such
cases will depend on ^ the height of the surface of the water into
which the stream is discharged. If the water surface of the lake
is above b, the curve will be concave upward (see diagram G) and
if the surface is below b, the curvature will be dofn^'nward (see dia-
gram H).
108, Effect of Change in Grade and of Obstmctions. — Variable
flow may also be caused .by changes in the slope of the stream bed
as shown by diagrams A and B, Fig* 103. The area of the stream
must increase as the bed slope is decreased, or must decrease as
the slope of the bed is increased in order to fulfill the conditions of
equation (2),
It is evident that uniform slope may be maintained even with
changed conditions if the changes that occur give rise to equal and
opposite effects* For example, uniform slope may be maintained
if the area of section a is reduced and the coefficient c is increased
to such an extent that tlie product ac remains constant at each sec-
tion of the channel.
Variable flow is also caused by the passage of the stream over
weirs or dams and the effect on the gradient will vary as shown by
diagram C and D, Fig. 103. Variations may also be caused by a
change in the bed (see diagram E, Fig 103), or by local contrac-
tions, submerged weirs or other obstructions as shown by dia-
gram F, Fig. ro3.
In all of the above described cases it is obvious that if the slope
of the stream is measured on any of these transition curves, a false
idea of slope will obtain and a false relation will be established for
^^^ 206 ^^^^V Stream Flow. ^^|
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GAUCE HEIGHTS AT KILQOURH. ■
Fig, 104.— Relatloni of Guage Heights at Vaj-louB StaUous on the Wiscon-fl
J
k. 1
Effect of Change m
the condition of stream flow. It is therefore essential in any meas-
urement of a stream or in the 'establishment of any gauging station
that the location for such observations be carefully selected on a
reach of the stream where conditions of essentially uniform flow
prevail and that all observations be taken during stages where the
flow of the stream is practically constant- If gauges are established
at various points along the course of a river and are read simultan-
eously, and if the flow is uniform and no falls, rapids or tributaries
intervene, the same diflFerences in elevation should always obtain
with the same stage of water,
A system of gauges as described above was recently established
at Kilbourn on the Wisconsin River in order to determine the river
slopes near that place, A large number of practically simultaneous
readings were taken in order to determine the relations between the
gauge heights at the various points compared with the Kilbourn
gauge.
Fig. 104 shows the results of the gauge readings at the various
stations compared with the gauge readings at Kilbourn. It will
be noted from the diagram that the slope of the river was far from
uniform at different times during these readings, and, in a number
of cases, the same gauge reading at Kilbourn was accompanied by
readings at other gauges that differed from each other by more
than a foot. For example, compare the gauge readings at Kilbourn
with the readings at gauge No, 5. With a gauge reading of 17 ft*
at Kilbourn, the normal gauge reading at No* 5 should be 23 feet,
and with a normal flow, the fall between gauge No, 5 and the Kil-
bourn gauge would be 5 ft* From the diagram it will be seen that
during a certain stage of flow in the river the gauge reading at
gauge No. S» with a 17 foot reading at Kilbourn, was about 22^ ft.
Under these conditions the fall between gauge No. 5 and the Kil-
bourn gauge was only 4^ ft. The slope being reduced, the quantity
of water actually passing the Kilbourn gauge under these condi-
tions was less than the normal flow for the 17 ft. gauge height.
On two other occasions where the gauge reading at Kilbourn was
approximately 17 feet, the actual gauge reading at gauge No. 5 was
about 24 feet. During these conditions the actual fall in the river
between gauge No. 5 and the Kilbourn gauge was 5 feet, or one
foot more than normal. Hence the quantity of water flowing by the
Kilbourn gauge at this time was more than the normal quantity
indicated by the Kilbourn gauge.
Readings of other gauges compared with the Kilbourn readings
308
Stream Flow.
will show that at certain times the flow
was normal and at other times the river
I must have been rising or falling and thata
T consequently the gauge at Kilbourn at the
time of such reading, was not accurately
representing the quantity of water flow*
ing by the Kilbourn section. The above
example taken of the variation in slope
between the Kilbourn gauge and gauge
No. 5 indicated practically the maximiini
abnormal conditions. The actual varia*
tion in flow at Kilbourn during these con-
ditions was not determined and is not
definitely known,
109. Relation of Gauge Heights to
Flow. — The area of anj crot.s section
equals the product of the height of tbe
section into some function of its width:
(3)
a = h X f (w)
In a rectangular cross section f=i, (see A, Fig, 105). In a tn-
angular section, f=.5 (see B, Fig, 105), In all cases of regular sec-
tion f can be mathematically expressed, and for irregular sections
(see C, Fig, 105) the relation may be obtained by measurement
If the height of the surface is referred to a gauge height, H, the
zero of the gauge may or may not correspond with the bottom of
the channel. If H=the gauge height, then h— -H+e, in which e h
the distance from the bottom of the channel to the bottom of the
gauge. Substituting, therefore, the value of h in equation {3) ^t
becomes :
(4) » = (H -f e) X fCw) = Hf(w) + eftw),
And substituting this value in equation (2) it becomes;
(5) Q = Hf(w)ev^ra +er(w)cv^ri"
With this equation p and with the flow in a fixed and uniform cban- ,
nelp if the relation can be established between r, s, c, e, w and f 1
each gauge height, H, the correspondmg value of Q can be deter-j
mined. As these relations are mathematically expressed for wni-j
form flow by the above equation, they can also be rcprcsente
graphically by a curve which will show the relation between Q anil
H for all conditions of uniform flow that obtain iti the given chan
Relation of Gauge Height to Flow.
209
ncl. Such a curve is called a discharge or rating curve. This equa-
tion (5) can be readily solved when f is a regular variable and when
c, r and s can be determined. Where the function, f, is an irregular
variable, no mathematical solution is practicable but the relations
may be determined experimentally and can be expressed by a rating
table or graphically by a rating curve. Such a rating table and curve
can be constructed for every fixed channel or section of a stream
for condition of uniform flow, no matter how irregular the section
or how the values of the function of the section may vary for differ-
ent gauge heights.
Discharge in Cubic Feet per Second.
Pig. 106. — ^Rating Curve for Wisconsin River at KHbaum, Wis.
Fig. 106 shows a rating curve established for the Wisconsin River
^tKilbourn, Wis. The small circles show the flow relative to gauge
height at the time the observations were made. They Wfere care-
Wly made in a fairly satisfactory section and fall fairly well on a
smooth curve drawn from this data to represent the relation of
gauge height to flow at similar or intervening heights.
The character of the rating curve for regular and irregular sec-
tions is shown by Fig. 45, page 95. Whenever the section remains
3IO
Stream Flow.
similar for different gauge heights, the rating cun^e will be a smooth
curve, but when irregularities occur in the section, the curve be-
comes broken more or less according to the extent of the irregu-
larity<
It has already been pointed out that any change in the cross sec-
lion of the stream after a rating curve has been established will
necessitate the establishment of a new cur^^e. The variation in rat-
ing curves under variation in channel conditions is shown in Fig, 46,
page 0.
m^
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r^^fi^f JfT jfo^jpfin
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IOTh — Variations
i 4
Cross-section of
Omnha, Neb.*
Missouri
near
The actual change in channel conditions that affects the relationM
of head and flow is well illustrated by Fig, X07 which shows the T
changes that actually took place in the cross secticm of the Missouri
River near Omaha ^ Nebraska,
no. Variations in Velocity in the Cross-section of a Stream.— '
The velocity of flow of a stream varies greatly at different points in-
any cross section. In any channel the friction of the sides and bed^j
reduces the velocity of that portion of the stream in contact and .
adjacent to them. If the bed at different points of the cross-section' I
is not uniform, as is always the case in the beds of natural streams, [
the retarding effects on different portions of the stream varies, andl
a consequent variation in velocity results. The distribution of ihft I
velocities in the cross section of the St. Clair River is shown in Fif*j
108, both by lines of equal velocity and by figures giving the ve-"
locity as actually measured. In this figure the effect of the frictiotKj
•Todd. Bull 158 U. S, Geol Surv,
Variation in Velocity in the Cross-Section of a Stream. 211
Secfion
Fig. 108.
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srr
Fig. 110.— Vertical Velocity Curves, Section Dry Dock.
:2I2
Stream Flow*
L
r^"^-^.^ of the bed and banks is clearly shown.
/ '^^^ The friction between the stream sur-,
/ \ face and the atmosphere is th
I \ shown by the fact that the maximmi
\ velocity is not at the surface btit is 3
^ short distance below the surfacej
The surface velocity may be modified
radically by the direction and velocittl
of the wind,
\ ;^^^^^^HH|^HHK Fig. 109 shows the transversej
' ""^^ ctirvx of mean velocities in this m
tion. The distribution of velocitifl
* in each vertical section is shown iirl
Fig, 1 10* The velocities here showitj
^^^^ 2ire relative only as compared witliJ
i "^ — -.^ each vertical. The %^elocity at tlie
j \ .bottom of each curve is that shown
I ^ by figures in Fig^. 108.
/ V i^ ^^^^ distribution of velocities mJ
oRoiNAftY itfATCft \^ ^^y scction is not the same under afll
conditions of flow but differs mater-
ially with the stage of the river, Tln^
y^ 'W^M is illustrated by Fig, 1 1 1 in which H
'---:'"' shown three sections of the same
B stream illustrating conditions of low.
medinni and high water* Above eacli
f^s^ section is shown a correspondiTig
/ N transverse curve of mean velocities
I \ of flow* The change in the distdbu-
/ ^^/ "^ M *^*^" ^^ velocities as the stream ifl'
! LOW WATCR \& creases should be noted.
-. - -jp^^ -J'^¥$ The distribution of velocity is al^
/' '^' .'^ a flfec ted by bends in the stream above
y _^MStL the point of observation which tends
^'^^^^ to throw the current of the stream
^ toward the concave side, and to cause
^' ■ a transverse slope in the section <^^
the stream at the curv^e. Such a condition {see Fig. 112) creates
cross currents and eddies and produces conditions of variable flow.
From Fig. 108 it will he seen that in any vertical line in a given
section, the velocities will vary with the condition of the bed, and
Variation in Velocity in the Cross-Section of a Stream. 213.
Fig. 112.
CALM
WMD D0Wlt8TWEAM WWD UP tTREAM ICE COVERED
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PER CENT OF MEAN VELOCITY
Fig. 118.— Ideal Vertical Velocity Curves.
100
50
60 70 eO 9t3 100 no J 20 130 140
PCR CKNT OP MEAN VELOCITY
Fig. 114.— Mean Vertical Velocity Curves.
^m 314 Stream Flow. V
^H the influence of air current or ice at the surface. These conditions
^B liave an influence on the velocities in each section considered. Van-
^H attons in the vertical velocities can be better studied by means of the
^M vertical velocity curve, which can be obtained by means of velocity
^m observations taken in a vertical line from the surface to the bed of
^B the stream. Ideal curves under various conditions are illustrated by
^1 Fig. 113. Figs. 114, 115 and 116 are reproduced from the report of
^m the State Engineer of New York for the year 1902. These diagrams
^1 show comparisons between the mean vertical velocities of streams
^B having different classes of beds. From these illustrations it will be
^M noted that there is a general similarity between the varioos velociiy
^m curves which aids materially in the measurement of stream flow. It
^K will he noted, for example, that the mean velocity, in any vertical
^M velocity curve from an open channel, lies near the point of .6 total
^H depth but that with varying conditions this position may vary from
^B 55 P^^ cent to about 75 per cent, of the depth- The velocity at .6
^m depth is found to average nearly 100 per cent of the mean velocity, d|
H t>ut may actually vary from 95 per cent, to 105 per cent, of the mean 1
■
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PtU CENT OP M£AN VELOCITY
Fig, UB.— Mean Vertical Velocity CurveB.
Effects of Ice-Covering on the Distribution of Velocites. 215
0
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ME AH OF IS CURVES 'VARIOUS STREAMS.
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PCR CENT OF MEAN VELOCITY
120 140
Fig. 116. — Mean Vertical Velocity Curves.
velocity. The velocity at the surface is subject to the external influ-
ence of atmospheric currents and is not so constant in its relation to
^hemean velocity. The surface velocity will average about no per
cent of the mean velocity of the vertical curve, but is found to vary
^th the variations in conditions from 105 per cent to 130 per cent
^^ such velocity.
ni. Effects of Ice-Covering on the Distribution of Velocities. —
The effect of the formation of an ice sheet over a stream is to ma-
terially increase the surface friction and results in a rearrangement
^ velocities in the cross section. As the ice sheets form in winter,
the conditions will vary from that of an open stream to that of a
closed channel. The velocities are gradually affected as the ice be-
gins to form, until the entire surface is affected where the stream
)ecomes entirely covered. As the ice sheet thickens more of the
ross section of the stream is occupied by the ice sheet, and greater
fiction results. Fig. 117 shows two vertical velocity curves, one for
n open and one for an ice-covered channel. These may be regarded
^ Stream Flow.
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PER CENT or MEAN VELOCITY
117. — ^Comparative Mean Vertical Velocity CurveB for Open and
Covered Section.
rpical of open and closed conditions between which the acti
;ities will vary with the conditions of the ice,
le change in the distribution of velocities results in an ent
ge in the relation between gauge height and flow so that t
g curve for an open section will not apply to the river um
on di tions.
therefore the stream flow is to be accurately determined duri
condition, it becomes necessary to establish the new relati
een gauge height and flow.
i before noted, such relations vary somewhat with the con
of the ice sheet but may be regarded as fairly constant wl
ection is fairly clear and deep. The relations between the f
curves for this open channel and for ice conditions as dct
d by the United States Geological Survey for the Wall
r at Neupaltz, N, Y, is shown in Fig, Ii8.
tble XXI, from an article by F. A. TilHnghast (see Engim
C^ews, May nth, 1905), shows the relations of maxifnum
1
Effects of Ice-Covertng on Velocities,
217
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EMSCKAAaC IK CUMG FEET rER flfCONO.
Fig. lis.— Rating Curve for Wallkill River at Newpaltz. N, Y.
mean velocities in the verticals. It should be noted that there are
two points of mean velocity under ice conditions that average ir
per cent and 71 per cent, of the total depth below the Surface, The
point of maximum velocity is at an average depth of 36 per cent, of
the total depth of the stream and averages T19 per cent, of the mean
velocity.
TABLE XXI.
Pxymxiion of jlfcan a-nd Maximum Veloeitiea in a Vertical Plane Under lee.
Stream and Place
Depth from
Under Sur-
face of Ice
Feet
Num-
ber of
carves
Depth of
Mean
Velocity
Depth
of
Maii-
tniim
Veloc-
ity
Coeffi-
cient
to re-
duce
Mfl3t.
to
Mean
Wallkill at Netjpalt^c. N. Y. , . . (a)
WallkiH at Neupaliz, K. Y, . . .(b
Reopnf at Kinj^tton, N. Y, . . . . . (a)
Empua at Emp^ton, N. Y. . . . , . ( b
Kondoutat Roeeudale, N. Y, , .(«
Rondoat at Roaendale, N. Y. , .(b)
C^nuvecticut at Orford, N. H. , . (c)
Mean .......,•,,«
4 to 12
4tcil9
2.3to7.4
5to8
4toa
5toT
2.5 to 7, 7
20
2S
16
8
6
8
18
0.12
0.13
0.08
0.11
0.08
0,13
0.11
O.U
0.71
0.74
0.68
0.73
0.08
0.21
0.69
0.71
0.3F
0.38
0.36
0.37
0.35
0.35
0.35
0.36
0.86
0-88
0.80
0,86
0.82
0.85
0,86
0 84
Kotes: a. By F. H. Tiliinghast.
b. By W. W. Schlechl,
c* By a A. Holdeii.
13
CHAPTER XL
THE MEASUREMENT OF STREAM FLOW.
112, Necessity for Stream Flow Measurements. — In order \n
ascertain the value of a stream for water power purposes, it is neces-
sary to determine the amount and variations in its continuous flow
either by comparison with the flow of other streams or by the direct
observation of the flow of the stream itself. As has already been
showuj the latter method is by far the most satisfactory as the de-
termination of the actual flow of the stream eliminates all errors of
comparison, and the necessity for any allowances or modifications
on account of differences in geological^ geographical, topographical
or meteorological conditions on the drainage area.
The Hydrographic Division of the United States Geological Sui^
vey has undertaken the gauging of a large number of streams in ih^
United States and has established numerous gauging stations 3t
which observations have been made for a number of years. This
data J references to which are given in the list of literature appended
to Chapter IX, is of great vahie for comparative purposes. It iS_
seldom, however, that, when a stream is to be investigated for waia
power purposes, flow data, at the particular point under consider*
ation^ is available* One of the first duties of the engineer, ther«j
fore, usually consists in making measurements of the stream flo
and establishing stations at which the daily flow can be observe
and recorded.
The methods in use by the United States Geological Survey ii^
the result of much study and investigation and probably represen
the most practical methods for making such observ^ations with a i
degree of accuracy. Many of the methods and suggestions in th
chapter are based on the methods and conclusions of the Surs'cy I
modified by the experience and practice of the writer,*
fail
* Thase methods are described In detail in Water Supply and IrrlgaU
Papers No 94, entitled^ "Hydrographic Manual of the United States G^ld
cal Survey/' and No» 95, entitled **Accuracy of Stream Measurements."
also "River Biaeharge" by J. C. Hoyt and N. C* Grover, — John Wiley
Sona, 1907,
Methods for the Determination of Flow. 219
1x3. Methods for the Estimate or Determination of Flow in
pen Channels. — ^There are three general methods of estimating or
itermining the flow of water in streams with open channels.
First— By the measurement of the cross section and slope and the
Jculation of flow by Chezy's formula, together with Kutter's or
azin's formulas for estimating the values of the coefficient.
Second — By means of weirs or dams of such form that the coeffi-
ent of discharge is known, and
Third — By the measurement of the cross section area and the
slocity of current passing through the same.
The method which should be selected for any particular location
spends on the physical conditions of the problem, the degree of
:curacy required, the expense which may be permissible and the
ingth of time during which the record is to be continued.
114. Estimates from Cross-section and Slope. — Chezy's formula,
V = c Vts
Dgether with the formulas of Kutter and Bazin, for the determin-
tion of the flow of streams, has already been discussed in Chapters
II and X. Much information is now available in regard to the
'alue of the coefficient c, but this value varies greatly in different
treams, in accordance with the conditions of the beds, and in the
ame stream under various conditions of flow. The results obtained
rom the application of these formulas are therefore necessarily very
ipproximate. The method, however, is of considerable value in es-
imating the flood discharge of streams and in obtaining an approxi-
nate knowledge of flow under other conditions where other methods
ire not available or are difficult of application.
In using this method two or more cross sections of the stream
ihould be measured on reaches of the river where the cross section
ind other conditions are fairly uniform and can be readily deter-
nincd and at a time when the flow is steady. It is also important
hat the stream in which the flow is to be estimated shall be compar-
ble in cross-section, depth, and other conditions, on which the
alue of the coefficient c depends, with other streams on which the
alue of c has been determined.
115. Weir Measurement — Where dams are so located that they
m be utilized for weir measurements, and are so constructed that
ich measurements are reasonably accurate, or where suitable weirs
n be constructed from which such measurements can be made,
ch dams and weirs afford the best practicable method for measure-
220
The Measurement of Stream Flow.
ments of the flow of a stream, la order to assure accurate results in
weir measurements, the following conditions must be fulfilled:
First — The dam or weir must have sufficient height so that back-
water will not interfere with the free fall over the same; otherwise
the dam will be available for purposes of measurement only during
stages when no such interference exists.
Second — The dam or weir body, must be so constructed that no
leak of appreciable size will occur during the time when it is utilized
for measuring purposes.
Third — The abutments of the dam or sides of the weir must be so
constructed as to confine the flow over the dam at all stages: other-
wise the weir will be useless for measurements during flood condi-
tions.
Fourth — the crest of the weir must be level and must be kept free
from obstructions caused by floating logs or ice.
Fifth — The crest of the dam or weir must he of a type for which
coeflficients for use in the ordinary weir formula have been deter-
mined- (See Chapter IIL)
Sixth — If the dam has an adjustable crest» great care must be used
to prevent leakage along such crest and to keep a complete and
detailed record of the condition of the crest during the time of the
observations.
Seventh — If water is diverted around the dam, which is usually
the case when a dam is built for power purposes or for navigatior),
the diverted water must be measured or estimated and added to the
amount passing over the dam* Such diverted water can sometimes
be measured by a weir or current meter. When such water is use*i
in water wheels, an accurate record of the gate opening of the
wheels can he kept, from which the amount of water used in thf
wheels can be estimated if the wheel's discharge has been calibra^eij
or if the wheel is of some well known type,* The conditions for the
accurate determination of weir discharge should be such as not to
involve the use of low heads of less than 6'' over broad crested dams.
Measurements by means of a weir or dam have the general acKati'
tage of continuity of record during the periods of ice and flood and
the disadvantage of uncertainty of the coefficient to be used in the
weir formula, of complication by the diversion of water around the
dam^ and the interference of flow by the occasional lodgement of
material, or of injury to the crest.
• See Water Supply and Irrigation Paper No. 180. — Turbine Wmter WN
Tests and Power TablaBr— by R. E. Horton.
The Use of the Current Meten
221
Hurement of Flow by the Determination of Velocity. —
of a stream, or the quantity of water flowing past a
I of the stream in a given timej is the product of two
le area of the cross section ; and second, the mean
' through said section,
tlie cross-section of the stream were uniform the
the flow would be a simple matter, A surface float,
given stations, or a current meter placed at any
s-section, would then indicate the average velocity.
If however, never obtain* It is therefore necessary
mean velocity of flow in the section which is a
jtt matter,
of measuring the velocity of a stream are in use:
le of a current meter, and second, by the use of
these methods has advantages peculiar to itself,
knosvn and appreciated in order that intelligent
nay be made*
of the Current Meter.— The current meter (Fig.
^t:nent designed to revolve freely with the current so
lining the number of its revolutions the velocity of
1C€ Electric Current Meter with Buzzer.
322
The Measurement of Stream Flow,
Section A- A
Flf, 12(J
Section of small Price Electric Currenl Meter, ShowlBi
details,*
the current will be known. A well made current meter carefuH|
maintained and frequently rated is reasonably accurate when prop
erly used under conditions to which it can be applied. As the fno
tion of operation is rarely constant ^ the relation of current velocitie
to number of revolutions is not always strictly proportional and iti
necessary to determine the relation between the revolutions of \hi
meter and the corresponding velocity of water. This is accomplisliea
by rating the meter, which is usually done by passing it throisg
still water at known velocities and noting the results* It is assume
that the same relation wifl exist between the revolutions of
■meter and its longitudinal velocity through still water and bet we
its revolution and the velocity of flowing water when this meter!
held in a similar position in a stream. The meter should be ratd
under conditions as nearly similar as possible to those under whic
it was, or is to be, used. The meter when being rated is usually ;
•From W. S. & T. Paper No. 94 Hydrograplilc Manual, by E. C. Mu
J, C. Hoyt and G. B. HoUtiter
k
Current Meter Observations.
223
Fig. 121.— Current Met&r Rating Station at D«flTer, CoL*
ched to some movable device (see Fig. 121) such as a carriage or
sat which is propelled by hand or machinery at a known rate over
fixfd distance* Observations of the revolutions of the meter at
irious rates of speed are noted and the relation is then established
ctween the velocity of the meter and the revolutions of the meter
fhcel. This data may be platted upon cross-section paper or so
ganged in tabular form that the corresponding velocity may be
Piediately ascertained when the revolutions of the meter are
Hown, (See Fig. 122.) Experiments have shown that with veloci-
l&less than one-half of a foot per second little or no dependence
■ be placed upon the meter observations and that for velocities
TOW one foot per second, the meter usually tinder registers. Where
iich low velocities obtain, float measurements are believed to be
tore accurate*
18, Current Meter Observations and Computation. — On account
great variation in velocity at different points in the cross-sec-
im Hydrographlc Manual.
■ 224
The Measurement of Stream Flaw-
1
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usua
usua
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usee
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VELI
Fig. 122.-
, the flow through ai
flow through other
, in order to systems
as well as for ease ir
parts, both horizont
city of each of said
ion of the stream s!
ical sections, chosen
Lily five feet or mo
illy somewhat less ai
illy much greater tha
zontal and vertical
'ibution of velocity
cy required in the d
[ in the deter minatio
ter the number of «
e accurate will be th
tClTY.'
--Curi
ny ur
simil
iticat
1 calc
ally a
parts
totild
for
re ai
I the
n in
divisi
in th
etern
n of
iuch
e wo
1 (
IM FE
-ent U
>it of
ar ar
[y su]
Iilatic
nd v<
. Ki
first
the p
)art 1
varia
horiz
on d<
e crc
linati
the V
sub-c
rk.
ET pi
leter ]
area
eas.
rvey
in, to
^rtica
i a b;
be c
urpoj
but t
tions
ontal
?penc
>ss-sc
on of
elocit
ivisic
r i ■ Id 1
.R SECOND
iatlng Curve.
may vary more or \k
On this account it
the velocities in a ci
divide the cross-sect
lly, and determine th
isis for the work, th
>btaincd by soundin
ie of water observal
he horizontal divisi
in the vertical veloc
velocities. The size
s on the irregtilarit
ction as well as on
flow. The greater
ies in the unit areas
ms of the cross-sec
1 %
ESS fr
is dc3
rofis-s
ion a
le act
le cro
g. 1
tion,
tons
ities
:ofb
yaf
the
the c
and
tion»
J
m
sir
res
ua
s*
111
art
ixi
an
atl
tW
ae
af
th
til
i
I
Current Meter Computations.
225
The meter readings may be made in one of four ways :
First — By determining the velocity at frequent, definite intervals
depth and then ascertaining the point and amount of average velo-
ty in each vertical section.
Second — By what is known as the integration method, which
nsists in lowering and raising the meter with uniform motion
Dm the surface to the bottom of the vertical section and noting the
^erage velocity determined by this method.
Third — By making a point measurement at the depth correspond-
g to the thread of mean velocity as determined in the first method.
Fourth — By determining the velocity at some other point of
)scrvation and deducing the mean velocity from the known rela-
on of the point measured to the point of mean velocity. The last
vo methods can be safely used where the vertical velocity curve
as been determined with sufficient accuracy, and are fairly approxi-
late at other sections where the conditions are not of an unusual
ature.
0
i
fie* rrom MUai point
in feflt
Q ^
2
1
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S-^
'— — '
"-- •"
— —
—
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% 123. — Cross-section of Saline River at Guaging Station near Salina,
Kans.
"Fig. 123 shows the cross section of the Saline River near Salina,
Kan., on September 30th, 1903, while the discharge measurements
•ccorded in Table XXII were being made. The soundings were
^ken at each 5 feet of width from the initial point and the velocity
vas observed at 0.6 depths below the surface in each of these verti-
als.
The discharge through each 5-foot strip might be computed sep-
rately, but the computations are shortened by finding the discharge
irough each double strip at a time."
♦ From Water Supply and Irrigation Paper No. 94, — Hydrographlc Manual
B. C. Murphy, J. C. Hoyt and G. B. Hollister. See page 46 et seq.
226
The Measuremeot of Stream Flow.
= me&n depth for double strip;
^ =s mean velocity for datible itrip;
Letd'
ft, bt c are three conHecutive depths, L feet ^part^
V^ V^ V^ are observed velocities in the
L = the width of a single strip;
Q' 1=: the diecharge through double etrip.
"The mean depth and the mean velocity for the double strip olj
width lo feet are found from the formula :
a>
m
d^„ =
a + 4b + c
6
The discharge through the double strip is ,
(3) Q' = d'„ V'„ 2L
= (-
+ 4b + e.
a
-) (
V^ + 4V, + \\
Formulas (i) and (2) are based on the assumption that the!
stream bed is a series of parabolic arcs, also that the horizontal v^|
locity curves are parabolic arcs, both of which assumptions arc]
approximately true at good current-meter stations.
In computing the discharge and the mean depth through a]
single strip near the stream bank or a pier the mean velocity is |
found from the formulas ;
W
(6)
V^ =
d =
a' -fa
where cither Vo or Va and a' or a may be **0*'.
Velocity is computed to two places of decimals, mean depthtl
area, and discharge to one place of decimals for streams of Drdinaryl
size ; for small streams with hard, smooth botton, where depth caflj
be measured to hundredths foot, the mean depth and area should I
computed to two places of decimals and the discharge to one pbc^"
These observations can be taken in shallow streams by wading
or from a cable car (see Fig. 124), boat or bridge as the circun^
stances and conditiottis permit. A rope or cable, marked into sufe
able divisions and stretched across the stream, offers the best mean
of locating the horizontal points at which observations in the vcri
cal planes are to be made.
119. Float Measurements. — Where a single or only au occasioni
measurement of the flow of a stream is to be made, the use of floatl
CurreDt Meter Measurements.
327
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ziS
The Measurement of Stream FloWi
Is believed to be preferablei as tinder such conditions the caHbrati
of the current meter and the exercise of necessary skill in its use are
not apt to receive proper attention. Under such circumstances,
therefore, float measurements are believed to be more accurate*
In the use of floats the writer usually selects round soft wood one
to two inches in diameter and in various lengths, varying by about
&^. These are weighted at the lower end, usually by attaching pieces
of lead pipe so that they will float with only about one to three
inches of the rod exposed. To the exposed end is usually attached
small red or white streamers so that they may be readily seen and
yet not be seriously affected by wind*
A point for the gauging is selected where the stream Is fairly
straight and uniform in section, and ropes, wires, or cables are
Fig. 124.^Cable Station, Car Guage, etc.
stretched tightly across the stream, parallel to each other and 25, 5o|
or 100 feet apart, as the location and velocity of the stream seen
to demand. The ropes or wires should be tagged at intervals of J
10 or 25 feet, as the conditions seem to warrant, beginning at zcroc
the straight bank.
In starting the work a float is selected that will reach as near th
bottom as possible without torching and should be about ,9 deptll
The float is started 5 to lo feet above the upper line and so place
that it will pass as nearly as possible under one of the tags,
point at which it actually passes under the line is noted and
corded, also the point and time at which it passes the lower Hnc* 1|
the float shmild touch the bottom or a snag in its passage, the ne
shorter length should be used until the float passes both lines frcel^
Floats should be run at frequent intervals across the stream usuaQ
at each of the tagged stations.
ream GauglngT
Extensive experiments were made by Francis at Lowell, Mass.,
tn 1852 to determine the accuracy of rod float measurements.*
He found that discharge measurements based on the determina-
tion of velocities by floats were nearly always large as compared
with measurements by a standard weir. This was due to the fact
that the rod, on account of not reaching the bottom, was not
aflfected by the low velocity near the stream bed and hence indi-
cated too great a velocity. He found that the effect could be cor-
rected by multiplying the discharge as obtained by the floats by a
coeflficient as follows:
(0) Q = CQi in which
Q = actual discharge
Qt — discharge as determined by floats.
C = coefficient = 1 — 0,116 (V^D"— 0.1) and
_ . distance of bottom of float from bottom of Btream
D = rat JO — ; — -r — ^-
depth ot stream.
It will be obser\'ed that this coefficient C is always less than
unity except where D is less than 0,01 which condition could not
be possible in any natural stream.
The Francis experiments were made in a channel of rectangular
cross section and floats of uniform length were used* In a natural
stream the depth will vary at diflferent points in the cross section
and floats of different lengths must be used. In such cases D will
vary widely for the various floats used and to apply the correction,
the velocity as determined by each float should be reduced by its
particular consatnt, C
Experiments made at the Cornell Hydraulic Laboratory in 1900
by Kuichling, WilHams, Murphy and Boright confirmed Francis'
conclusion that rod float measurements are too large, only two out
of thirty being smaller than measurements made by a standard
weir. No attempt was made, however, to verify Francis' formula
for the correction of such observations.*
In calculating the discharge from these measurements the ave-
rage cross-section» in square feet, of each division is calculated and
multiplied by the average velocity for the same in feet per second
and the product will represent the discharge in cubic feet per second
of the section represented by that float and the sum of the sections
of all the floats will give the total discharge of the stream.
• See *Txiw^tl Hydraulic Experiments" by James B, Francis, pp. 146-20S.
*See W. S, & L Paper No, 05» Accuracy of Stream Me els u rem en ts. p- 64.
K^ 230
The Meftiurcment o£ Stream Flow. 1
0 10 » do 40 DH 60 ;d 6D 90 100 lli 1
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Area of one square
equivalent to 2i cu. ft.
per second*
Area within discharge
curve equals 341,6 »q.
Diecharige:
2} X 34L6 = 354.1
OIL ft. per. aec^
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;. 13&* — Oraphic Determination of Stream Flow From Measu
i
remanti^
J
The Applicatiocn of Stream Gaugings. 231
is frequently desirable to calculate the discharge graphically,
h niay be done as shown by Fig. 125. This is done by plotting
wo sections at the tag lines over each other and drawing in an
age section between them. It is frequently desirable to draw
e floats in their true length and average position so that it may
;en at onv'e how well the section was covered by the floats,
ider each float is laid off the velocity as determined by the
!, to a seltcted scale, and a mean velocity curve is drawn
lagh these points. By multiplying the ordinate of the velocity
e by the ordii^atesl of the mean section, a quantity is obtained
le discharge cmve which, when fully constructed, gives a dis-
ge polygon, the area of which represents at the correct scale
discharge in cubic toet per second of the stream.
0. The Application %A Stream Gaugings. — A single measure-
t of stream flow is of comparatively little value as a basis for es-
ting the continuous chaiacter of the flow of the stream, as will
5tn by examination of any of the hydrographs previously shown,
flow of a stream, while it niay appear to the casual observer uni-
1, is actually subject to many and violent fluctuations and the
may vary several hundred per cent, from minimum to maxi-
n within a few days.
has already been pointed out that in order to study the flow of a
am intelligently it is necessary to know the variations in flow
: take place from day to day for a long term of years during
ch the effect of the extreme of all of the factors controlling
am flow may have made themselves manifest.
Tic actual measurement of the flow of a stream by current meter
ioats is usually accomplished with considerable difficulty, and it
lid be practically impossible to repeat such measurements daily
the length of time for which records are desired. It has
tady been pointed out that under many conditions it is possible
:stablish a discharge or rating curve which will show the relation
he height of the water surface to the flow through orifices over
rs or through channels of various forms. In the establishment of
h relation it is assumed that the raising of the water surface to a
tn height is always accompanied by the same flow of water
)ugh the section. In order to assure accuracy in the observa-
s based on such a rating curve, sections must be selected where
conditions assumed are correct. Such stations should be se-
fd, where possible, on a fairly long uniform reach of the stream
232 The Measurement of Stream Flow*
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Literature. 233
and the influences of the back water from large rivers or
gaugings of the stream have been made under a considerable
conditions and a rating curve is established therefrom, it is
ssary thereafter to measure the daily flow but only to note
5 gauge height. It has been determined by many observa-
nt under constant conditions a fixed relationship exists be-
auge height and the discharge of a stream, subject to the
le to variable flow as described in Chapter X. If the section
sr conditions of the stream flow remain unchanged, the rat-
re will remain constant and hence the daily gauge height
uickly read and recorded and will give at once, by reference
ating curve or table, the quantity of water flowing in the
it all times.
the soundings and levels made to determine the cross sec-
area curve can be constructed showing the variation of
:h gauge height. The float or current meter observations
the necessary data for the construction of a curve of mean
s. The product of the area and mean velocity, as shown
i two curves, for any given gauge height, must equal the
:e and must equal the reading of the discharge curve for
e gauge height. The construction of these curves, and a
ation of their properties, furnishes a check on the construc-
the discharge curve and aids materially in correcting any
t irregularities therein.*
26 shows the discharge, mean velocity and area curves for
)mac River at Point of Rocks, Md.
LITERATURE.
8TBEAM GAUGING. .
igarten, M. Pulsations of Velocity in River Current. Annales des
Fonts et Chaussees. 1847.
idy of the Law of Flows in Rivers, Oscillations of Velocity, Obser-
vations of Vertical and Transverse Velocity Curves. Annales
des Fonts et Chaussees. 1847.
, Jas. R. Flow of the West Branch of the Croton River, N. Y.
Trans. Am. Soc. C. B. vol 3, pp. 76-90. 1874.
Theo. O. Flow of Water in Open Channels. Trans. Am. Soc. C. B.
vol. 6, pp. 250-258. 1877.
River Discbarge," — Hoyt and Grover.
14
^34
The Measurement of Stream Flow.
5. Wood, de Yolaen, Flow of Water In Rivers. Trans. Am. Soc. C. E. vol.
8, p. 173, 1879,
6. McMatb, R. E. River HydraiiHcs. Trans. Am, Soc, C. E, vol 9, pp. Ill
390. ISSO.
7. McMatb* R. E. The Mean Velocity of Streams Flowing In Natural CliaB-
nela. Trans. Am, Soc. C. E. vol. 11, pp. 186-211, 1882.
8. Current Meter Measurements on the Rhine. Allgeraeine Bauzeltung, Vol
47, pp. 53-80. 1SS2.
9. Unwtn, W. C. Current Meter Observations In the Thames. Proc lnH
a K Vol. 71, p. 33S. 1883.
10. Stearns, F. P, Why the Maximum Velocity is Below the Surface. Trans
Am. Soa C. E. Vol 12. p. 331. 18S3.
11. Cunningham^ Allan. Recent HydrauHc Experiments. Proc. Inst C. E
Vol. 71, p. 1. 1883.
12. Fteley, A. and Stearns , E. P. Description of Some Experiments on tN
Flow of Water. Trans. Am. Soc. C. E. Vol. 12, pp. M18. ml
13. Measurement of Water. Buh fi, Montana Agric. Expt Sta. 18SS.
14. Isakoski, R. Discharge of Rivers from tlie Drainage Areas. Zeitscbr*^
d Oesterr. Ing. u Arch. Ver. ISSfi, pp. 09*9S.
15. Seddon, J. A. Consideration of the Relation of Bed to the VariibM
Jour. Assn. Eng. Soc, Vol 5, p . 127. 18SG.
16. The Determination of Normal Cross-Sections of the Elbe. TauherL Zalt-
schrlft fur Bauwesen, pp. 5B1-5C2. 1886.
17. Green, J. S> Fourth Biennial Report State Eng. of Colo, 1$89.
IS. Bazln, M. Recent Experiments on the Flow of Waters over Weirs.
nales des Ponts et Chaussees, Oct. 1888; see also Proc. Ensj. <
of Phlla. Vol 7 p 2C0. 1890,
19. Flynn, P. J. Flow of Water in Irrigation Canals. San Francisco. Pubj
lished by the Author. 1892.
20. Oangulllet, E. and K utter, W. R. A General Formula for the Ualfon
Flow of Water in Rivers and Other Channels. Trans, by Herim
and Trautwine. New York. Wiley H Sons. IS 93.
21. Foss, W. E. New Formula for Calculating the Flow of Water in Pities ao^
Channels. Jour. Asso. Eng. Soc. Vol. 13, p. 295. 18S4.
22. Flynn and Dyer. The Cippoletti Trapezoidal Weir. Trans. Am. Soc C
Vol, 3^, p. 9, 1S94,
23. Carpenter, L. G. Measurement and Division of Water, Bui. 27, Colfl
Agrlc, Expt. Sta., Fort Collins. Colo. 1894.
24. Newell. F. H. Discharge Measurements of Streams. Proc. Eng. €l^^
Phila. Vol. 12. No. 2, p. 125. 1895.
25. Humphreys, D. C. Discharge Measurementfl. Jour, Assn. Eng. Socs. ?o(
IE, No. 5, p. 187. 1805.
26. Starling, Wm. The Discharge of the Mississippi. Trans. Am, Soc. C. 1
Nov, 189S.
27. Grunskj'v C. E. Method for Approximate Gauging of Rivers. Eng.
March 1, 1890
28. Keating, W. J. CoeJhclents in Hydraulic Formulas. Jour. Wea. Soc.
Vol. 1, p. 190. 1896.
29. Johnson, F. T. and Cooley. E. L. Experimental Data for Flow over Br
Crest Dam. Jour. Wes. Soc. Eng. Vol. 1, p. 30. 1S96.
Literature.
235
n.
n.
34.
35.
16.
tt
SI
4S.
17.
51.
A Study of Gauging Statistics. Annates dea Fonts et Cbauaseos. Part IIL
1897.
Jasmund, R, Variation In Valoclty In Croaa- Section of a Stream. Efr
peclally with Obstructions on the Surface and Ice. Zeitschr. fiir
Bauwesen. 1S9T, pp. 303, 465, 5SS. Centrallb. der Banverwaltung
p. 101.
Jobnson, Clarence T. Stream Gaugings. Proe. Purdue Soc. Civ. Eng.
1897.
Skinner, Jobn W, Description of the Method of Gauging the Discharge
Through the Outlet of Hemlock Lake, N. Y. Trans. Assn, Civ.
Enga* of Cornell University. 1898.
Blndemann, H* DitTerence Between Average Flow and Flow at Center of
Stream. Central blatt der Bauverwaltnng, p. 63S. 1S9S,
Llppincott, J, B. Low Water Measurements in the State of California dur-
ing the Summer of 1898. Eng. News. Jan, 12. 1899.
Average Velocity of Water fn Natural Streams. Zeitscbrirt. fflr Gewas-
ser, pp. 20^36. 1899,
Newell, F. H. Stream Measuring in the United States. Scl. Am. Sup.
Nov. 11, 1899.
Fuchfl, Paul. The Measurement of the Velocity of Flow of Streams. Go-
Bundbeits Ing. Nov. 30, 1899.
Sttwart, Clinton B. Discharge Meaaurements of the Niagara River at
Buffalo. N, Y. Jour, W. Soc. Engs. Dec. 1899.
tnveetigation of Relationship of Average Flow of a Stream with the Flow
at the Center, Zettschrlft fur Gewas&er, p. 212. 1900,
Manaer of Movement of water ia Streams. Zeltschr. fiir Bauwesen. Nos,
Vn to rX. Centralblatt der BauverwaUung, p. 611, 1900.
M^tliods of Stream Measurement Water Supply and Irrigation Paper
No. 56. I90L
Murphy, E. C, Accuracy of Stream MeasuremenL Water Supply and Irri-
gation Paper, No. 64. 1901.
Turneaure and Russell. Public Water Supplies. Chap. 12. New York.
Wiley & Sons. 190L
Tutlon, C, H. The Laws of River Flow. Jour. Assn. Kng, Soca. Jan.
ary, 1902.
The Natural Normal Sections of Streams, Zeltschr. d Oesterr. Ing. u Arch
Ver- Feb. 21, 1902.
Relation of Surface to Mean Velocities of Flow.— An investigation Con-
ducted by J. B. Lippincott and others in the West. Eng. News.
Vol, 1, p. 424, 1903.
Aanua] Report Chief Eng. U. S. A. 1900. Appendix I. L I. Survey of N.
and N. W, Lakes. Same 1902. Appendix B. E, E. and 1903 Ap-
pendix F. F. F.
Presaey, H. A. Methods of Measuring Velocity In River Channels. Sci. Am.
Sup. Sept, &, 1903.
Merrlman^ Mansfleld. Treatise on Hydraulics. New York, Wiley & Sons.
1903.
Belliiis, E. D. Hydraulics with Tabiea New York. D, Van Nostrand
Company, 1903.
236 The Measurement of Stream Flow.
62. Murphy, E. C, Hoyt, J. C. and Hollister, O. B. Hydrographlc Manual of
the U. S. G. S. Water Supply St Irrigation Paper No. 94. 1904.
53. Ho3rt, John C. Methods of Measuring the Flow of Streams. Bng. New&
Jan. 14. 1904.
54. Miller, C. H., Pratt, R. W., Rohinson, H. F. Methods of Determining
the Mean Velocity of Cross-Sections. Eng. News. Vol. 1, pp.
258-307. 1904.
55. Anderson, R. H. Some Flood Discharges and Values of "n" in Ratter's
Formula. Eng. News. Aug. 4, 1904.
56. Hoyt, John C. Methods of Estimating Stream Flow. Eng. News. Aug. 4,
1904.
57. Recent Russian Studies of Flow in Rivers. Eng. News. Sept 1, 1904.
58. Stout, O. V. P. Notes on Computation of Stream Measurements. En&
News. Vol. 2, pp. 521-547. 1904.
59. Mullins, J., and Span, F. N. Irrigation Manual. 1906.
60. Hermanek, Johann. The Mean Velocity in Natural and Artificial Chan-
nels. Zeitschr. d Oesterr. Ing. u Arch Ver. Apr. 21, 1905.
01. Murphy, E. C. A Method of Computing Flood Discharge and Cross-Section
Area of Streams. Eng. News. Apr. 6, 1905.
62. Barrows, H. K. Work of the Hydrographlc Branch of the United States
Ceol. Sur. in N. E. and a Discussion of the Methods used for Es-
timating Stream Flow. Jour. Assn. Eng. Socs. July, 1905.
63. Butcher, W. L. The Gaging of Streams hy Chemical Means. Eng. News.
Dec. 14, 1905.
C4. Hoyt, J. C. and Grover, N. C. River Discharge. New York. J. Wiley I
Sons. 1907.
CHAPTER Xn.
WATER WHEELS.
xai. Classification of Water Wheels. — ^Water wheels include
most of the important hydraulic motors that are adaptable to large
hydraulic developments. They may be divided into three classes,
viz:
First — Gravity wheels.
Second — Reaction wheels.
Third — Impulse wheels.
In gravity wheels the energy of the water is exerted by its weight
acting through a distance equal to the head.
In both reaction and impulse wheels the potential energy due to
the weight of the water under the available head is first converted
into kinetic energy. This kinetic energy does work in the reaction
wheel through the reactive pressure of the issuing streams upon
the movable buckets from which they issue.
In the impulse wheel the nozzles or guides are stationary and
the energy of the issuing streams is utilized by the impulsive force
which they exert in impinging against movable surfaces or buckets.
Figs. 127, 128 and 129, which illustrate the various types of
wheels included in the above classes, are adapted, with many mod-
'fications from Reuleaux's "Constructor." *
laa. Gravity Wheels. — Fig. 127 shows the various types of gjav-
^^y water wheels or those wheels that are driven by the weight of
^he water. At moderate velocity, these motors are practically
Operated by gravity only, although under some conditions the im-
pulse due to the velocity of the entering water may have an appreci-
^'>Ic effect. In Fig. 127, A is an undershot water wheel ; B is a
"alf-breast wheel (see also Figs. 3 and 4), and C is a high breast
^heel. D is an overshot wheel. In C and D the buckets should be
^0 designed as to retain the water until they reach the lowest point
*n the revolution of the wheel. E in this Figure illustrates Dup-
•"The Constructor." F. Reuleauz— tnuiB. by H. H. Suplee, Philadelphia,
'a., 1893.
338
Water Wheels.
af;
A
5?^?i^n;
i^
iM^^e^V^ir,
II
Fig. 127. — Diagram of Gravity Wheels.
^Reaction Wheels. 23jf 4
ngcr's side-fed wheel. F illustrates an endless chain of buckets
hich is essentially the same in principle as the overshot wheel. G
a similar arrangement using discs running with as small a clear-
icc as possible in a vertical tube. When the water acts only by
avity, the wheels represented by A to E, inclusive, are only prac-
:able when the wheel can be made as large or larger in diameter
an the fall of the water. Where small diameters must be used,,
c arrangements shown in F and G are available. Very small
heels acting under high pressures may be employed by making
5C of the so-called chamber wheels, illustrated in H, I and J.
123. Reaction Wheels. — The wheels illustrated by the diagrams
I Fig. 128 are of the second class or reaction wheels. Diagram A
lustrates Barker's Mill of the form known as the Scotch turbine
lustrated also by Fig. 8. This form of turbine is known in Ger-
lany as the Segner wheel. The water enters the vertical axis and
ischarges through the curve arms. B represents a screw turbine
^hich is entirely filled with water. C shows a Girard current tur-
bine which has a horizontal axis and is only partially submerged.
) is Cadiat's turbine with central delivery. It resembles the Four-
leyron turbine except that there are no guides to direct the flow
nto the buckets. E is Thompson's turbine with circumferential
iciivcry and horizontal axis. The discharge from this turbine is
ibout the axis at both sides.
In diagrams A, B, C, D and E the column of water is received as a
•vhole and enters the wheel undivided. The remainder of the forms
Huslrated in Fig. 128 show wheels in which the flow is divided into
I number of separate streams by guides interposed in the streams
Wore the water enters the wheel. Diagram F illustrates the Four-
ficyron turbine which acts with central delivery. The guide vanes
ire fixed and the discharge of the water is at the circumference of
^He wheel. The ordinary vertical form of the Fourneyron turbine is
fetrated in Fig. 128. Diagram G, also in Fig. 128, is a modification
^f the Fourneyron turbine in which the water is being delivered
^pvi-ard from below. This form is sometimes called the Nagel's tur-
bine. Diagram H is the Jonval or Henschel turbine. (See also
^?- '35') The guide vanes in this turbine are above the wheel
^hich is entirely filled by the water column. Diagram J is the
'rancis turbine in practically its original form. (See also Fig. 14.)
diagram I illustrates the present American form or modification of
le original Francis turbine. K is the Schiele turbine, a double
leel with circumferential delivery and axially directed discharge.
2^0
Water Wheels.
Sis* 128.— Diagrams of ReacUoa Wheell.
L
Itnpiilse Wheels, 2^1
In forms H, I, J and K, a draft tube may be used below the wheel to
utilize any portion of the fall which occurs below the level of the
bottom of the wheel.
In all reaction turbines, the water acts simultaneously through a
number of passagfes around the entire circumference of the wheel.
In the impulse or action turbine, the water may be applied to all of
the buckets simultaneously or to only a portion of the circumference
at a time,
134, Impulse Wheels, — The wheels illustrated in Fig. 129 are the
third class of wheels which are driven by the impulse due to the
weight of water acting through its velocity. Of these wheels, A is
the current wheel or common paddle wheel. The paddles are
straight and either radial or slightly inclined toward the current,
as in the illustration. (See also Figs, i and 2,)
Diagram B is Poncelet's wheeL (See also Fig, 5,) The buckets
run in a grooved channel and are so curved that the water drives
upward and then falls downward, thus giving a better contacL
Diagram C shows an externally driven tangent wheel. The buck-
ets are similar to- the Poncelet wheel but with a sharper curve
inward. The discharge of the water is inward, D is an internally
driven tangent wheel similar to the preceding but with an outward
discharge.
E is the so-called hurdy-gurdy or tangential wheel. The water
is delivered through a nozzle and the wheel is practically an ex-
ternally driven tangent wheel of larger diameter and with a smaller
number of buckets.
Diagrams F, G and H illustrate three types of impulse wheels
with inclined delivery. (See also Figs, 6, 7. 9 and 10.) Diagram F
shows a crude form of vertical wheel similar in form to the Indian
wheel, Fig, 6. It is used on rapid mountain streams and is probably
the original conception from which the turbine has been developed.
Diagram G is the Borda turbine and consists of a series of spiral
buckets in a barrel-shaped vessel Diagram H is a Danaide turbine
which has spiral buckets enclosed in a conical tube. This is an old
form of wheel formerly used in France.
125* Use oi Water Wheels. — Almost all water wheels in prac-
tical use are modifications of some of the above forms and by a
study of these forms a wheel may be classified and a clearer under-
standing obtained of the principles of its operation. Many of the
^orms of wheels shown in Figs, 127, 128 and 129 are practically db-
^lete or are used only in minor plants or for special conditions
24a
Water Wheels.
%.^
B
H
Fig. 129.— Diagrams of Impulse Wheels
Use of Water Wheels.
243
tat make them of only general interest in the study of water
power.
While gravity wheels are still occasionally used their application
is entirely to the smaller water power plants. In many cases the
turbines purchased for such installations are of cheaper make,
Poorly designed, constructed and selected, and often improperly set
itid, consequently, inefficient. In such cases, and where the ques-
ion of back water and the interference of ice is not important, the
ISO.— **OrerrBhot'* Water Wlie#L Manufactured by Fitz Water Wheel Co,
^vity wheel may be more efficient and quite satisfactory. Well
%ned and well constructed gravity wheels are said to give effi-
Dcies of 85 per cent, and above, (See Frontispiece and Fig.
). With such plants the engineer has usually little to do and
sequently they will not be further considered here. The types
[wheels now mc^t largely used for moderate and large water
rer developments are the reaction and impulse turbines.
Classification of Turbines. — All moder turbines consist of
vheel ID which buckets are attached and whicn is arranged to re-
yvrii in a fixed case having attached to it a nozzle, guide
244
Water Wheels.
series of guides. The guide passages or nozzles direct the waicr
at a suitable angle onto the buckets of the wheel. The revolving
wheel contains curved buckets or passages whose functions art to
receive the water, utilize its energy and discharge or waste it u
nearly devoid of energy as possible.
Turbines may be classified in various ways;
First. — In accordance with the action of the water on the same.
(A) Reaction or pressure turbines^ such as the Fourneyron, Jm-
valp Francis, etc< (See Fig. 128, G, H, I and J.)
(B) AcHon or impulse turbines, such as the Girard and tangen-
tial wheels* (Sec Fig. 129, diagrams D and E.)
(C) Limit turbines, which may act either by reaction or impulst
Second.^In accordance with the direction of flow in reference
to the wheeK
(A) Radial fiotv turbines. In these turbines the water flows
through the wheel in a radial direction, Tliese may be subdivided
into —
(a) Outward radial flozv turbincSf such as the Fourneyron and
Cadiat. ,(See Fig. 128, diagrams F and D,)
(b) Inward radial ftouf turbines, or wheels in which the water
flows inward in a radial direction such as the Francis and Schtlk
turbines. (See Fig. 128, J and K.)
(B) Axial flow turbines in which the general direction of the
water is parallel to the axis of the wheel such as the Jonval and
Girard wheels of similar design. (See Fig. 128, H»)
(C) Mixed flow turbines, or turbines in which the flow is
tially radial and partially axial as in turbines of the American
(See Fig. 128, diagram I; also Figs, 143 to 15S inclusive).
Third. — In accordance with the position of the wheel shaft
(A) VerHcal (See Figs. 132, 134, 135, 151, etc.).
fB) Horizontal (See Figs, 140, 152,)
Fourth, — In accordance with the arrangement of nozzles
guides,
(A) Complete ti4rbines with guides surrounding the entire whi
(B) Partial turbines with guides partially surrounding the wh<
in one or more groups.
The re-action turbine is a turbine with restricted discharge whii
acts through the reactive pressure of the water. Under some con*
ditions the energy of the water may be exerted, at least in pat
by its impact or momentum. The impulse turbine acts prindj
I
Condition of Operatioti. 245
^ly through the momentum of the moving mass of water although,
when the current reverses, some reactive pressure may be recog-
nized. The limit turbine may act entirely as a reaction or as an
impulse turbine according to the conditions under which it oper-
ates.
127. Condition of Operation. — These wheels operate under the fol-
lowing conditions :
REACTION OB PRESSURE TURBINES.
Guides complete.
Buckets with restricted outlets.
Buckets or wheel passages completely filled.
Energy most largely developed through reactive pressure.
Discharge usually below tail water or into a draft tube.
ACTION OR IMPULSE TURBINES.
Guides partial or complete.
Buckets with outlets free and unrestricted.
Wheel passage never filled.
Energy entirely due to velocity.
Discharge must be above tail water.
No draft tube possible, except with special arrangement which
will prevent contact of tail water with wheels.
UMIT TURBINES.
(A) Buckets so designed that the discharge is unrestricted when
above tail water.
Buckets in this case are just filled. Act without reactive effect.
Discharge above tail water.
(B) If tail water rises to buckets, the discharge is restricted and
reaction results.
In this case the full bucket admits reaction and discharge may be
Wow tail water.
19& Relative Advantage of Reaction and Impulse Turbines. —
jfihe reaction wheel is better adapted for low and moderate heads,
especially when the height of the tail water varies and where the
amplitude of such variation is a considerable percentage of the
fetal bead. Such a wheel, which is designed to operate with the
dockets filled, can be set low enough to utilize the entire head at
246
Water Wheels*
all tim^s and will operate efficiently, when fully submerged,
reaction wheel can therefore be set to utilize the full head at tin
of low tail water and when the quantity of flow is limited. ¥a
low head developments this is an important factor. The impiilK
turbine, on the other hand, must have a free discharge and mu
therefore be set far enoug^h above the tail water to be free from bad
water if it is to be operated at such times.
Another difference between the reaction and the impulse turbin
is the higher speed with which the former operates. This is olta
a distinct advantage, for direct connection with high speed
chinery, and with low and moderate heads. On the other han^
with high heads the slower speed of the impulse wheels is frequentljj
of great advantage, especially in the form of the tangential whff
when the diameter can be greatly increased and very high head
utilized with moderate revolutions. In such cases the height ■
the back water is usually but a small percentage of the total he
and the loss due to the higher position of the wheel is compaci
tively small.
The speed of a wheel foe efficient service is a function of the ratwlj
of the peripheral velocity of the wheel to the spouting velocity (
water under the working head. This ratio will vary from ,65 to .
in reaction turbines, according to the design of the wheel. In in
pulse' turbines this ratio varies from .40 to ,50.
129. Relative Turbine Efficiencies. — ^The impulse turbine has the^
further advantage of greater efficiency under part gate, — that is*
at less than its full capacity. When, as is usually the case, a wheel
must operate under a variable load it becomes necessary to rcduo
the discharge of the wheel in order to maintain a constant sp
with the reduced power required. (See Fig. 131). This is le
compHshed by a reduction in the gate opening which commonly
greatly aflfects the economy of operation.
The comparative efficiencies of various types of the turbines i
shown in Fig, 131. The maximum efficiency of turbines whc
operated at the most satisfactory speed and gate will be about th
same for every type, if the wheel is properly designed and coa
structed and the conditions of operation are suitable for the typ
used. This maximum efficiency may vary from 75 to 85 per cent
or even between wider limits, but, with suitable conditions^ shouJfi
not be less than 80 per cent. In order to make the curves on thq
diagram trnly comparative, the percentage of maximum efficient
Relative Turbine EflSciencies.
247
10
20
— - — \^-'^ :ss
^ ^ ^''=H ^5^ ^
J^ ^ Z ^'^
^'^ ^ -^ J^ ■
7 ^'^ f \y
^ / 4 ./ ■
ft zw -.fizw ■
^l ii ^twi
-€ ^/_ _±/2: _j
jp // f/lW ■
h 1 i. tt
t ' -IT •
-A t 4 21
-/ t J/- '
4- - -f
1- X ^ Zj
ti t J
. t ' '^^
x/ 77:
: JZl J2
30 40 SO 60 70
PER CCNT or MAXIMUM OISCHARGC
80
90
100
Fig. 131. — Comparative Efficiencies of Various Types of Turbines.
A of maximum discharge are plotted instead of the actual efli-
mcies and actual discharge.
The Foumeyron turbine usually shows very poor efficiencies at
rt gate as shown in Fig. 131. The curve for this turbine is
iwn from Francis* test of the Tremont (Fourneyron) turbine
5C Fig. 132, also Table LXI) and is substantiated by efficiency
rves shown by various tests by James Emerson.*
rhc Jonval turbines usually show better part gate efficiencies
m the Foumeyron but are not as efficient, under such conditions,
turbines of the inward flow or Francis type. The Jonval curve,
>wn in Fig. 131, is plotted from the test made in 1884 at the
See "HydrodTnamics" by James Emerson.
^49
Water Wheels.
L
Holyoke testing flume * of a 30-inch regular Chase- Jon val turbine, '
(See Table LXXVl),
The American-Francis turbine varies greatly in part gale effi-
ciency according to the details oi design and the relation of speed
and head under which it operates. The curve shown in Fig, IJU
representing this type, is from the test of a wheel manufactured by
J* & W* Jolly of Holyoke, Massachusetts, similar but not tlie sara
as that illustrated by the characteristic curve Fig, 249.
The impulse wheels when properly designed and operated s]ioi(
a higher part gate efficiency than any other type of wheel,
curve shown in Fig, 131 is from a test oi a 12" Doble tangentij
wheel in the laboratory of the University of Wisconsin.t
As already indicated, the design of the wheel has a great uj
fluence on its efficiency at part gate* Individual wheels or
of wheels of any type may therefore depart widely from the cur
above shown, which are intended only to show as fairly as possib
the usual results obtained from well made wheels of each type.
It should be noted also that efficiency is only one of the facto
influencing the choice of a wheel and that many other factors mil
be weighed and carefully considered before a type of wheel is 1
lected as the best for any particular set of conditions,
130, Turbine Development in the United States, — ^The dcvtio
ment of the turbine in the United States has been the outgrois
of some seventy years of practical experience. In the early setti
ment of the country the great hydraulic resources afforded faci^
ties for cheap power and numerous water powers were develop
under low and moderate heads. These developments created I
corresponding great demand for water wheels and stimulated il
vention and manufacturing in this line, "American inventors bail
devised many different forms of wheels which were patented, co
structed, tested and improved to meet the prevailing conditio
When a successful wheed was designed, it was duplicated in
original form and its proportions increased or diminished, to co
form to the desired capacity* As wheels of greater capacity or I
higher speed have been required, modifications have been mn^
and improved systems have resulted.
* See page 44 of 1S97 catalogue of Chase Ttirbine ManufactarliiS
Orangcv Mass.
tFrom "Feftt of a 12* Dohle Tanfrential Water Wheel," an Dnpubliflli
thesis hy H. J, Hunt and F. M. Johnson*
^^V Turbine Development in the United States. 2^9
The best American water wheel construction began with the
Boyden-Foumeyron and Geylin-Jonval turbines of improved
French desigi^, but modern American practice began to assume its
characteristic development with the construction of the Howd- Fran-
cis turbines, already described* Moderate changes in the form and
arrangement of buckets and other details gave rise to the earlier
forms of "Swain," "LefFel" and ''American" wheels each of which
consisted of an inward flow turbine modified from the earlier de-
signs of Hawd and of Francis as the experience of the inventor
seemed to warrant. In all of these cases the wheels discharged
inward and essentially in a radial direction and had to be built of
sufficient diameter to provide an ample space for receiving the dis-
charging waters. This necessitated slow speed wheels of com-
paratively low capacity (see Table I, page 13), In order to secure
higher speed, the diameters of the wheels were reduced thus re-
ducing the power. This reduction was, however, more than coun-
terbalanced, in the later wheels, by an increase in the width of
the bucket in an axial direction. It was found also that the cap-
acity of the wheels could also be materially increased, with only
small losses in efficiency, by decreasing the number of buckets-
Wheels were gradually reduced in diameter and the buckets in-
creased In breadth until, in many cases, they reached very nearly
to the center of the wheel This necessitated a downward dis-
charge in the turbine and resulted in the prolongation of the buck-
ets in an axial direction in many cases to almost double the width
of the gate. From this development has resulted the construction
of a series of wheels known as the "American turbines*' having
bigher speed and greater power than has been reached in Euro-
pean practice.
The entire line of development has, until within the last fifteen
years, been toward the increase of speed and power for low and
moderate head conditions. It is only within this period that a con-
si<3erable demand has been felt in this country for tuitiines having
other characteristics and adapted for higher heads.
■The American type of turbinei in its modern form is not designed
or suitable for high heads its origin being the result of entirely
different conditions. About 1890 came a demand for turbine wheels
under comparatively high heads which manufacturers of wheels of
the American type were therefore poorly equipped to meet The
^rst of such wheels supplied were therefore of European types,
n
2 50
Water Wheels.
which apparently better suited such conditions, Recogoizing,
however, the importance of meeting such demands^ the Amerian
manufacturer found that the wheels of essentially the origiiial
Francis type were well suited for this purpose. The narrow wheel
and nuraerous buckets of the earlier types rednced the discharge of
water, and, increasing the diameter, reduced the number of revo-
lutions. Such t^pes of wheels of high efficiency can now be
obtained from the leading manufacturers in the United States, aod,
while many manufacturers still prefer to furnish simply their stock
designs, which are only suited for the particular conditions for which
they were designed, still, other manufacturers are prepared to
furnish special wheels which are designed and built for the particu-
lar conditions under which they are to be used.
The systems of wheels offered by American manufacturers, which
can be readily and quickly duplicated at a much less expense than
would result from the design of special wheels for each particular
customer, has resulted in the ability of American manufacturers to
furnish water wheels of a fairly satisfactory grade and at a cost
which would have been possible in no other way. In the United
States the cost of labor has been comparatively high and special
work is particularly expensive, much more so than in Europe where
skilled mechanics receive a compensation for labor which is but
a small fraction of that of their American cO(m pet iters. Average
American practice, at the present time^ leaves undoubtedly mticHj
to be desired and considerable advance may be expected from the I
correction of designs, resulting from practical experience and by ti^t j
application of scientific analysis,
131. The American Foumeyron Turbine. — As noted in Chapterl
I, one of the first reacticai turbines developed in the United States J
was the Boyden wheel of the Fourneyron type.
In these wheels (see Fig. 132) the water entered from the Genter||
guided by fixed curve guides, g, (Fig. 133) and discharged outward
through the buckets^ B. The use of these wheels gradually spread
and they rapidly replaced many of the old overshot and breasl
wheels used up to that time, and soon became the foremost whe
in New England-
The manufacture of the Fourneyron turbine has, for commo
use, been discontinued on account of the competition of olhe
cheaper wheels which were fooind to be more efficient at pan gat(
k
252
Water Wheels.
and more generally satisfactory under ordinary conditions of sm-
ice.
The Fonrneyron turbine, when well designed and constructed, i^
a turbine of high full gate efficiency. This wheel is adapted for
high heads where a comparatively slow speed is desired, — and u
is now frequently used for high grade and special work where its
peculiarities seem best suited to such conditions. '
One of the modern applications of the Fourncyron turbint \^
that in the power plant of The Niagara Falls Water Power Com-
pany< Fig* 134 shows vertical and horzontal sections of one of the
double FournejTon units used by this company in their first plant
These wheels discharge 430 cubic feet per second and make 2^
revolutions per minute; at 75 per cent* efficiency each wheel wili
develc^ S^ooo horse power. The buckets of these wheels are di-
vided vertically into three sections or stories in order to increase
their part gate efficiencies. These wheels are of Swiss dtsign by
the firm of Faesch and Picard and were built by The L R Morris
Company of Philadelphia. (The wheels are vertical and connecte^t
by vertical shafts, each with one of the dynamos in the staiioii
above. The shaft is built of three-quarter inch steel, rolled into
tubes 38 inches in diameter. At intervals the shafts pass through
journal bearings, or guides, at which points the shafts are reduced
to II inches in diameter and are solid* The speed gates of these
wheels are plain cytindrical rims which throttle the discharges
on the outside of the wheels and which, with the co-operation of
the governor, keeps the speed constant within two per cent under
ordinary conditions of operation. Another wheel of this type is
that manufactured and installed at Trenton, Falls, N. Y„ by 1^"*^
same firm> (See Fig. 51 1»)
132, The American Jonval Turbine.— The Jonval turbine, orig-
inally of French design, was introduced into this country about
1850 and became one of the most important forms of turbine of
early American manufacture. In the tests of turbines at PhiU^
delphia in 1859-60 (see page 360) a Jonval turbine developed th^
highest efficiency and the type was adopted by the city for use iJ>
the Fairmount Pumping Station, Like the Fourneyron turbinc«
these wheels, while highly efficient at full gate, have largely hcco
superceded by other cheaper and more efhcient part gate types*-^
except for special condition s.
I
The American jonval Turbine.
253
134.— Doutle Fmirnejrron Turbfiie of The Niagara Fa\W ^aUt Tc^^^t
npaay. { Designed by Faesch & PIcard; built by L P. Mor ^>^A
^54
Water Wheels.
Fig- 135 shows the Geylin-Jonval turbine as manufactured bv-
the R. D, Wood Company of Philadelphia, W represents the mn-
ner, B the buckets which receive the water throug^h the guides, |,
The wheel shown has double inlets that are closed by the douWe
cylinder gates, GG, This
gate closes op against the
hood, C» by means of the
rod r. r, which connect
with the governor mech-
anism. The general de-
sign of the ordinary whctl
of this type is perhaps
best shown by Fig. 136.*
In this figure A is the
fixed or guide wheel and
B is the movable or tur-
bine runnen
In the later hydraulic
developments the use o(
this wheel has been con-
fined, largely at least,
to locations that require
special designs. Ooe
of the Later develop-
ments of the Jonval tur-
bine has been that for
The Niagara Falls Paper
Company, The first in-
stallation consisted of three upward discharge Jonval turbines of^
1,100 horse power each, under a head of 140 feet The installatioii
provided, however, for a total installation of six turbines. The ver-
tical shafts are 10 inches in diameter and 140 feet in length atid
weigh about 19 tons each. These shafts, in addition to the weighf
of the wheels, — which are 4' 8" in diameter, arc supported by marine
thrust bearings, under the beveled wheels, together with a step^
bearing under the turbine. When the turbine is in use, however; ^
the weight of the wheel and the shaft is balanced by the upward
pressure of the water which at two-thirds gate is designed to ex-
actly balance this weight. At fo^ill gate there is an unbalanced up*
Fig. 135.— Vertical Gey] In- Jonval Turbine
(Manufactured by R, D, Wood & Co.).
* Sa« page 7, 1877 catalogue, J. L. & S. B. Dlx» Qlen Falls, N. T
American Jonval Turbine.
^55
fpfessurc, and, at less than twothirds gate» an unbalanced
fcrard pressure; these pressures are, however, only the differ-
between the weights and the water pressure and are easily
for by the bearings above described.
These wheels have thirty open-
rl ings and operate at 260 revolu-
I tions per minute. The gates are
I provided with sleeves (cylinder
I gates) each weighing 2,800 pounds
i and slide outside the guide wheels
to the hood. These sleeves are
guided by four rods which extend
above the turbine casing about 10
feet to a yoke which is ctjunter-
balanccd. A sectional view of
one of these turbines is shown in
Fig, 137 and the general arrange-
ment of the plant is shown in Fig.
138.
A still more recent type of the
Jonval turbine is the double, hor-
izontal wheel built for The Niag-
ara Falls Hydraulic Power and
Manufacturing Company and in-
stalled in 1898, (See Figs. 139,
These wheels have a common, central intake and quarter-
draft tube which turns down to and is sealed in the tail
flow the floor. The speed control is effected by a register
irough which the water passes before it reaches the guide
!This is said to give a somewhat Io\ver emciency at part gate
pes a gate interposed between the guide tubes and rimrier
Economy of water at part gate is said to be no PJ^ i
tn this plant and reduced efficiency is, in fa.ct, an g
.^ , . J ^ -^c -a velocity in the
I it reduces the gate movement and retains <* i ^
ck, with a given change of load, and consequently recliiccn
.» -I f , , ^r^n This turbine U
atia action and aids the speed regulation.
tr 1-1 1 .- -^,,+#* under the normal
2,500 H, R at 250 revolutions per mmute, w
210 feet.*
.^JonvaJ TtirMne as Manu
lired by J. L. & S. B. DU,
>Tle EleetrJc&l World/* January 14. 1899.
256
Water Wheels.
I
Fig, 137. — Geylin-Jon%^a! Tarhine of Nia^ura Falls Paper Mill Co. Mintifs^
tiired by R. D. Wood & Co. (Frcim Eng, News, Apr. 6. 1S&4.)
133. The American Type of Reaction Turbine* — The Howd
Wheel (Fig. 13) from which the idea of the Francis inward flo^^'
wheel (Fig. 12) was derived, was invented in 1838 and acquired s
considerable market throughout New England, From these wheels
originated the American inward and downward or mixed flow Mr-
bines.
The early wheels of American manufacture were designed vc^v
much after the style of the Francis wheel with changes, more of
less radical, in the shape and details of the buckets. The de^iand
for wheels of greater power, and higher speed, has resuhed in *
gradual development of other and quite different forms*
The development of the turbine in the United States is wrll
illustrated by that of the *' American" turbine of Stout, Mills k
Temple, now The Dayton Globe Iron Works Co, This wheel wa&
i
L
J
American Jonval Turbine-
^h. 13S, -Plant of the Niagara Fali>
rkpi*r Co. 8howinf Installatiafi of
*fcmval Ttirbinep. (From Ca&eier'e
Magaxine* Nov.^ 1004,
designed in 1S59 and was called
I he American Tarbine. The
f;eneral form of the original tur-
bine wheel is shown in Fig, 14K
This was followed (1884) by
the design of what is known as
the **New American" turbine,
illustrated by Fig. 142, In this
wheel the buckets arc length-
ened downward and have a
partially downward as well as
inward discharge.
This wheel was foltowed in
1900 by the **Special New
American" illustrated in Fig.
143, having a great increase in
capacity and power.
The fourth and most recent
type (1903) is the "Improved
New American*' illustrated in
Fig. 144. The comparative
power and speed of these vari-
ous wheels is shown in the
tables on pages 258 and 259,
Table XXIII is misleading to
the extent that while the diam-
eter of each wheel is given as
4S" such diameters are not
strictly comparative. Part of
the additional capacity and
power of the * 'Special New
American" and of the **Im-
proved New American" is due
to the cutting back of the buck-
ets (see Figs, 141 to 144) which,
while it reduces the diameter
at the point of nneasurement,
gives a discharge which would
be fairly comparative with
wheels of the older type of per-
haps three or four inches larger
diameters. (See Sec, 140.)
4
I
i
258
Water Wheels.
TABLE XXin
Deveiopmmit of Mm«Hea«* Turbines,— C^padiy^ Spetsi and Fmi^er of a 4I1VA
Turbine und^r a IS^foot Head*
Year
brout^ht out,
in CM. ft.
Americftii «
Standard New American
New American .,*--**-<
Special New Amen can >.
Improved New American
1859
lgS4
1894
1900
1903
3271
5S64
9679
11061
Rev, per
(nin.
102
102
107
107
139
m
141J
i
Fiff. 139.— HorlEantal Geylin-JonTal Turtilne of Nta^ara Falla Hydraull^^
Power h ManufacltirjQg Ce. Sbowlng Guide Chutes.*
* Cuts 139 and 140 reproduced from Electrical World, Jan. 14, 1899. Ta^|
bluea manufactured hy R D. Wood & Co.
The American Type of ReactioD Turbine,
259
The development of turbines may also be illustrated by a compar-
ison of the size and speed of turbines of various series required to
develop essentially the same powen {See Table XXIV.)
|| TABLE XXrV
Intr€(i»e in Speed of **Am€TiGan" Turbines for Same Poumr (le-foot head).
New Amerii^n .„♦,....,
Special New American . , ,
Improved New Amerioin
Sisteof
wheel.
Horse
power.
48
25
79.1
81.5
87.5
R. P. M-
102
136
186
267
I
Fig. 140— Honzoutal GeyUn— Jonval Turbine .Showing Bucket Ring.*
Figs. 145 and 146 show a vertical and a horizontal half plan, half
section of a vertical Improved Kew American turbine, W is the
crown and hub of the wheel ; B^ the buckets ; G, G, are the wicket
•See foot note page 258.
36o
Water Wheels.
gates that control the admission of water to the wheels and which
are operated by means of the ring Gr, which is moved by an ecci^n-
trie and rod, r, connected with the governor throoigh the shaft, P.
The inner edges of the bucket are spaced some distance from the
shaft and the main discharge is inward and downward, though a
portion of the bucket will admit of a slightly outward discharge.
134. The Double Leffel Turbine,^ — Perhaps the greatest depar-
ture of American inventors from the lines of the original Francis
Fig, 142.— New American
Fig. 141,— American Turblae Rua-
nen*
TABLE XXy,
Ikvelopment of "I^Jfef Wheel— Capacity, F&vme' and Bp^d &f 404n4h
Wheel U-nder IG-foot Mmd>
i
Year
brought out.
StandBrd , » . , .
Sfwciftl , , * , w * . . . .
Samson
Cmproved Samson.
1860
187C
laeo
1897
DUcharge,
2547
3Q72
i
E«T. per
• Maiiiifactured by The Dayton Globe Inm Wi>rkB C«l
The Acncrican Type o£ Reacuoa Wheels, 263
flm. 147 and 148*— SeiJtJon and Plan of Sainaon Turbine,^
lufactQrBd ^r The James LelTol k Co.
j^
^02
Water Wheels.
^ mm
flgi. 145 and 146.— Se<!tIoti and Plan of rmprovedNew American Turb
♦Manufflcturea by The Dayton Globe Iron Works Co,
The American Type at Reacuoa Wheels, 363
Pigi. 147 and 148.— Section and Plan of Samson TurblneL*
lolftctnred by Tbe J&m«fl Lelfel A Co.
264
Water Wheels,
Figs. I49p 150 and 151, — Top View, Runner and OuUlda Ttew of Saaj^n '
bine.*
* Manufactured by Tbe James LefTel & COh
he Double Leffel Turbine*
«^ater iQward and discharge it downward, outward and inward with
the general purpose of distributing it over the cross-section of the
turbine tube. The gates, G, are of the wicket type and are con-
nected by rods with an eccentric circle which is operated through
the arm, A, and the gearing, Gr, by the governor shaft, P* The
gate gearing is well shown by reference to the section-plan^ Fig.
148, and the top view, Fig. 149.
The Samson turbine runner is illustrated in Fig, 150, and Fig.
151 shows an outside view of one of the vertical, turbine units.
^C 1&£.— Double Horizontal Leffel TurblEe of Tb« Niagara F&lls Hydraulic
Poww A Manulacturing Co. Manulactured hf Tk© Jamefi L^Sel A Ca.
^c development of this wheel is illustrated by Table XXV. This
^l>le Is fairly representative of the growth of this turbine as the
ujatnetcr is, in all cases, the maximum diameter of the wheeL (See
^<^. 140.)
"Hie adaptability of the earlier turbine designs to the later mod-
^^te head developments is well illustrated in the design of the
266
Water Wheels,
wheels for The Niagara Falls Hydraulic Power and Matiufacttmnff
Company, installed by The James Leffel Company about 1891
These turbines have the single naj-rower buckets, smaller discharge
and relatively slower speed of the earlier designs. The runners arc
double discharge, horizontal, seventy-four inches in diameter and 1
operate at a speed of 250 revolutions per minute under a head ot |
215 feetj and each wheel develops about 3,500 horse power.
Fig, 153.— Leffel Doubl© Runner of Tbe Niagara Falls Hydraulic Powtbt
Manufacturing Go. Manufaetured by Tbe James Leffel & Co.
Fig. 152 shows one of these units complete. Fig* 153 is a vicwj
of the runner. For a test of this wheel, made December 190J,
page 381,
135. Other American Wheels. — The development of moden
American wheels could, perhaps, have been equally well illustraie
by the growth of various other American turbines. The deveic
ment of all American wheels up to the present time has been
the line of increasing both the speed and the power of the whe
for low head, with a return to the earlier type for wheels to be ^
under the moderate heads-
Fig. 154 illustrates a runner of the well-known McConnick
tern, Mr. J. B. McCormtck, who had previously become famiU
1
Other American Wheels.
267
Tertaiii wheels of large capacity desi^^ned and patented by
£W and John Obenchain, re-dcsigiied and improved these
I, about J876, and secured high efficiencies together with
ltd power far beyond any other wheels of that period. Mc-
Cormick wheels in their
original or modified form
are now made by a large
number of American man-
uiacturers and these
wheels have had a marked
effect on the design of
almost 'all modern Ameri-
can water wheels. The
runner in the illustration
is the Hunt-McCormick
ru n n e r as m an u f ac t u red by
The Rodney Hunt Ma*
chine Company, but is
very similar to the Mc-
Cormick wheels of various
other manufacturers.
The Smith*McCormick
runner is manufactured by
The S. Morgan Smith
Company. This company
has also recently brought
out a new wheel called
the "Smith Turbine/'
of greater power and
higher speed, the runner
of which is illustrated by
Fig. 155. Fig. 156 repre-
sents the Victor runner or
**type A** runner of The
Piatt Iron Works Com-
pany, designed for low
heads,
Fig. 157 is the "type B"
runner, of the same Com-
1S6.— Smith aiinner of S. Morgan pany, designed for medi-
Smith Co. um heads. This runner
154. — Htiiit*Mt5Goniil€k Rnnner of The
Rodnef HuDt Machine Go.
i
V 263 ^IV Wilier
^m^^iH
^M again illustrates the tendency tc
) return to the earlier forras i>f|
^M runner for medium head wheels.
This
latter type has also been H
^m adopted by other manufacturers of turbines, as may be seen by rtl-|
^H erence to Fig, 158 which shows *
"'" Hunt runner manufactured for^
^^^^ moderate heads by The Rodney Hun' Machine Company. |
i^^B_ ^^^^^^^^h^
Fig. 159 is from a shop
^^^^_ ^^^^^^^^^^^
photograph of the Sbawic^
^^^^^B ^^Bm^T Y ^^^B
k
igan FaUs turbine raauu'
^^^^^B ^fW^^^^^L : ^
k
factured by the I, P. Mor^
^^^^^ ^^^'-'^■^^Q^fe^^.'
1
ri 5 Co m pa ny , Th is is on t
^^m ^^^^K_
i
of the largest turbines evci
constructed and develops
10,500 horse power under
a head of 140 feet Itiia
double mixed inflow type
^^m ^^^^^^^^L^
n
with spiral casing and i
double draft tube through j
1 ^^^^^E/'
A
which the water discharge ]
^m ^R,,iHW^"^
f
outward from the center
The diameter of the cas-
^^^ ^^^nl^w^
1
ing at the intake is IQi i
^^ Fig* 156* — Victor or '*Tjpe A" Runner cf
feet and the sectional
Tbe Piatt Iron Works Co,
area gradually dimimshci ,
around the wheel in pro-
portion to the amount of
water flowing at each
^^f^l
k
point The wheel com*
plete is 30 feet in beighi
and w*eighs 182 tons. The
^^^!^^^|£^N1K^^^^
■
runner, which isofbronic,
^
is shown in Fig. 160. A
Ei^iiflvjfei
^1
Figs. 161 and 162 sh0ifl
li^^^yK
two sections of a sinfl^^
turbine of the Francis il^|
\^^^^^^^^HH^
flow type built for tll^|
S n oqual mie- Falls plant (mH
^^Crr^^P^V^B X»
W
The Seattle & Tacom«
"^ A^ LV
Power Company by TteB
Piatt Iron Works Com 1
ng. 15T,— nigh Head or "lype B" 1
Runner
pany. The turbine has J
of The Piatt Iron Works Co.
L^
capacity of about 9.O0fl
Other American Wheels,
269
der 270-foot head st 300 R. P. M, The mnner is 66 inches
:ter and has a width of 9i inches through the buckets.*
elieved to be the largest capacity single discharge wheel
imctcd.
rther details see Figs. 183, 189 and 190.
arly Development of Impulse Wheels* — As already pointed
Chapter I, Fig;s. 6 and 7), water wheels of the impulse
e among the earlier forms used. In the practical construc-
^•ater wheels for commercial purposes in this country, the
reaction turbine was^ how-
ever, the earliest form of
development This was
because the reaction tur-
bine was best suited for
the low heads first devel-
oped. As civilization ad-
vanced from the more level
country into the moun-
tainous regions the condi-
tions were found to radi-
cally differ. In the form-
er location large quanti-
ties of water under low
heads were available; in
the latter, the streams
diminished in quantity
but the heads were enorm-
ously increased. These
IS demanded an entirely different type of wheels for power
and the demand was met by the construction of the tan-
rheel now so widely and successfully used in the high head
: the West
arliest scientific consideration of impluse wheds in this
was by Jearum Atkins who, apparently, anticipated the
f the wheels of the Girard type in Europe by" hi* design of
bcel io 1853.t (See Fig. 163.)
!. — Hunt Runner of The Rodney
Hunt Macbloe Co.
Ineineerinir Newfi/' March 29, 190e.
rjttigential Watex Wheek" by John Richards, Cai«ier^i Htgazinep
270
Water Wheels,
Other Americaa Wheels,
%Ji
In Atkins* first application for a patent (in 1853) he shows a
lear conception of the principles of the impulse wheel.
After describing the mechanical construction of his wheel, Mr.
mcins says: 'The important points to be observed in the con-
ruction of this wheel and appendages, are: First, that the gear-
; • * ♦ should be so arranged as to allow the wheel's veloc-
at the axis of the buckets to be equal to one-half the velocity
the water at the point of impact, ♦ * ♦
"As the power of water, * * * is measured by its velocityp
• it is obvious that in order that the moving water may
imiinicate its whole power to another moving body, the velocity
the former must be swallowed up in the latter* This object is
^
Fig. ICO,— Shaw tnlgan Fallis Turbine Runner,
.effected by the before-described mode of applying water to a wheel
[in the following manner, the velocity of the wheel, as before
|stat6df being one-half that of the water,
**Let tis suppose the velocity of the water to be twenty- four feet
[per second ; then the velocity of the wheel being twelve feet per
Uecondr the relative velocity of the water with respect to the wheel,
[cr the velocity with which it overtakes the wheel, will be twelve
I feel per second. Now it is proved theoretically, and also demon-
ed by cxpcrimentt that water will flow over the entire surface
mi-circular buckets of the wheel with the same velocity
di it first impinged against them, or twelve feet per sec-
len, as the water in passing over the face of the buckets
A
2 72
Water Wheels,
has described a semi-circlej and as its return motion on lea\in|
the wheel is in an opposite direction from that of the wheel, its
velocity with respect to the ■wheel being twelve feet per second,
and as the wheel has an absolute velocity of twelve feet per sec-
Fig, lei.— Section Snoqualmle Falls Reaction Turbine. The Flatt Iron Wflrttj
Company.
ondj it is obvious that the absolute velocity of the water with t^I
spect to a fixed point is entirely suspended at the moment of \n^\
ing the inner point of the buckets, its whole velocity, and const- j
quently its whole power, having been transmitted to the wheeL"
Early DevelofMnent of Impulse WheeL
373
^* ■'"■«* *^^*^
Ic 162. — &ection*Elldvatioii Snoqualmie FaHs Reaction Turblii« (The Ratt
Iron Works Co.)*
nil
^gTlfiS,— Plati of Atkina Wheel and Wheel Case (1853). From Cksslei'B
Magazine, Vol t. p. Hi,
274
Water Wheels.
a. Moore bucket, 1874.
& Bodd bucket, ISSa
<u Boble EUipeoidal bucket ^
1889.
b. Knight backets, 1870.
/» PeltOD bucket^ 1$80,
Fig. 164, — Buckets of TangcDtlal or Impulse Water WheelB. (Trans.
Inst Mining H7ng. 1MB.
Mr. Atkins* first application for a patent was rejected. After
long illness, from which he finally recovered, he agfain applied for
patent which was finally granted in 1875, Tlie Atkins* patents are*
simply of historical interest as his inventions have bad little eff<
on the practical development of the impulse wheel.
American Inipuist; Whetils*
n$
fj. Anierican Impulse Wheels, — ^The impiilse wheel found its
test practical development in California where the conditions for
jdevelopment of power made such a wheel necessary. The
f tang^ential wheel, used on the Pacific Coast, was quite simple
{instruction and the development of the backets, which began
I the simpler flat and curved forms, was very largely based on
ptperiniental method used for the development of the reaction
(Pelton Water Wheel CoJ
ijUO Foot Hea*!,
e in the East, Experiments were made at the University
Jifomia, by Mr. Ralph T. Brown, as early as 1883, and the
in, published by the department was the earliest literature on
fcntial wheels published in this country,
!th the early development of the tangential bucket are con-
the names of Knight, MoorCp Hesse, Pelton, Hu^, Dodd
>oble, and many other inventors, whose wheels have become
nown and widely used. The most extensive early develop-
i
276
Water Wheels.
ment of this wheel was by The Pelton Water Wheel Company
whose work has been so widely known and used as to make the
name '* Pelton Wheel" a common title for all wheels of the tangen-
tial type.
Some of the many forms of American buckets used are shown iir
Fig, 164 with the approximate
date of their invention or d^
sign.
The general arrangement of
a double 2Q0O H. P. unit, run^
ntng at 200 R P. M, under SOO
foot head is shown in Fig, 165,
This is one of three units in-
stalled by The Pelton VValcf
Wheel Company for The Tellu^
ride Transmission Plant of 0)1-
orado*
The wheels arc of cast $ltd
fitted with steel buckets^ held
in position by turned stcct
bolts. They arc connected by
a flexible coupling to a 1«200
H, P. generator
Fig. 166 shows the runncf oi
an impulse wheel made bytk
same company. This is 9 10
in diameter^ and is designed to
develop 5,000 H, P at 325 R-
P M under an effective licad
of 865 feet
Fig. 167 shows the runner of an impulse wheel manufactured by
the Ahner Doble Company. This runner was from the Doble Wa-
ter Wheel Exhibit at the St Louis Fair and developed 170 H* F-
at 170 R. P. M. under a head of 700 feet and generated direct cur- ^
rent for use on the intramural railway-
In addition to the tangential wheels already described, a fewj
manufacturers have developed wheels of the Girard type. Oii«*
such wheel, designed and built by The Piatt Iron Works Company,'
is illustrated in Figs, 168 to 171, inclusive. Fig. 168 is a section-
elevaUon showing tlie arrangement and design of the guides ami
Fig. 166.— Pf Hon Tanpential Water
Wheel Runner- Designed for 5000
H, P at 865 foot head and 225 R.
P- M. t Pelton Water Wheel Co.)
American Impulse Wheels.
277
fckets of the wheel. Fig, 169 shows a section through the wheel
ll on the line of the shaft. In these figures W represents the"
Itoer; BE the buckets; g, the inlet guides, and G, the gate by
peh all or a portion of the guide passages may be closed and the
ktr of the wheels reduced. The gate, G, is connected by the
ings, Gfj with the rod, tt which is connected through the rocker
Fig, 157. — Doble Runner. (ATiner-Dobl© Co.)
I wtth the governor mechanism. The wheel or runner of this
int is shown by Fig. 170, and a general view of the wheel is
wn by Fig, 171,
IS. Turbine Development in Europe. — Modem European tur-
practice has been the development of the last twenty years,
ppean manufacturers have approached the subject more on the
278
Water Whet:L*,
basis of theoretical analysis than has heen done in America. The
conditions of development have also been largely special and not
under such uniform conditions as in America. The result has been
the development of special designs for special locations and the
rapid accumulation of a considerable experience under a wide range
r
^Ig. IC8.— E3iid Section aDd Elevatton, Glrard Impulse Turbine wiUi ^^ (
Tut©- CPlatt Iron Works Ca.>
of conditions* While the radial flow turbines were the earlier typcj
developed, European practice has been largely centered on the a3q3l|
flow wheels of the Jonval type for complete turbines, and axil
flow and radial flow wheels of the Girard type for partial turbin
-under high heads.
Afnerican Impulse WheeK
279
The axial flow turbine while simple In constructicm and low in
cost is difficult to regulate and hence the demands of electrical de-
velopment for dose regulation has given rise to a variety of mod-
em designs which are summarized by Mr. J* W* Thurso essentially
follows:
W ^ffl "k^
[% Ua.^LoQgitudinal Section Glrard Impulse Turbine. (Piatt Iron W^&rksi
CorapaufJ
1st For low heads to 20 feet. Radiai inward flow, reaction tur-
oincs with vertical shafts and draft tubes*
2ncL For medium heads^ 20 to 300 feet. Radial inward flow reac-
tion turbines with horizontal shafts and concentric or spiral cases
tod draft tubes.
jrd. For high heads over 300 feet. Radial outward flow, full or
al action turbines (of the Girard type) with horizontal shafts,
i^
'See "Modern Turbine Practice'* by J. W. Thurso.
28o
Water Wheek.
often with draft tubes;
also, modified impulse
wheels of at taagcotiai
type.
The types of tar-
bincs for low and mod-
erate heads are mod-
ificattoos of the Fran*
CIS inward flow turbine
Earlier European
practice is perhaps wei:
represented by Fig
172 which represent*
one of eight turbine^
installed by Messrs
Escher, Wyss & Co
Fig, 170— Runner of Glraxd Turbine. Type C, for the City of Geneva.
High-Pressure Runner (Piatt Iron Works Co.) Switzerland These
wheels are of the Jon-
val type and operate
under heads some-
times as great as 12
feet but during higti
water the heads de-
crease to about five
and one-half feet
The turbines consist ot
three annular rings or
buckets and arc so de-
signed that the water
is admitted to as many
buckets as may be re-
quired for economics^
operation under the
very great differences
in the condition c»f
supply. The width of
the inner and intcrme'
PIf?, ITL^GeneraJ View of Girard Turbine with diate rings are cacH
Cover Raised, (Piatt Iron Works Co,) ieventeen and thfCC-
Turbine Development in Europe*
281
rs Inches^ and the outer ring is eleven inches, all meas-
radially. The outside diameter of the wheel is thirteen feet,
inches. The outer ring of guides is not provided with
IS for excluding the water from the buckets but the i n termed i-
inner rings can be entirely and independently closed. The
171— Oo© of the ierenteen 210 II. P. Jonval Turbines at the Geneva
Water Works. Built by Eacber, Wyea & Co.
few closing the intermediate and inner rings consist of a flat
in the form of a half ring, which lies on the top of the crown
vertical curtain which hangs from the end of the plate and
etes the closure of the other half of the bucket the openings
282
Water Wheclst
of which are on the side of the same^ the water entering theBu-
by a quarter- turn,
Tliese turbines are used to operate the pump that furnishes
water supply for the city of Geneva for domestic and maunfacin
ing purposes.
Fig. 173* The 1200 H. R Double Turbine at Chlvres near Geoem
Eacher^ Wysa Jc Co. (Cassier^s Magazinep October, ISW.)
Fig. 173 shows a pair of vertical turbines furnished by the sU
company for Chlvres near Geneva, Here the fall in siimmer is
feet and in winter 28 feet. The lower turbine will develop tj
Turbine Development in Europe. 283
. at 80 R, P. M. under the higher head, and under the lower
the turbine above works with the lower one.
ch turbine is cone shaped and divided into three compart-
s in order to maintain the efficiency of the wheels at the same
utions under the wide range in heads.
pid advancement is now being made in turbine design both in
:ountry and in Europe and the progress can best be known and
2ciated by reference to the current technical press.
I
CHAPTER XIIL
TURBINE DETAILS AND APPURTENANCES,
139* The Rimner — Its Material and Manufacture. — The rnnners
of most reaction turbines (see Figs. 136, 142 to 149, 151, 154 to 159,
161) consist of hubSi crowns and rings, to which the buckets are at-
lached. The wheels are sometimes cast solid, and sometimes built
up. In built-up wheels the buckets are first cast, or otherwise
formed, after which they are placed in a form or moulded, and tbe
crownSj hubs and rings are cast to them. Turbine water wheels
for low heads are usually made of cast iron or of cast iron with
steel buckets. Wheels for high heads are frequently made of cast
bronze or of cast steel. (See Figs, 158 and 159.)
Probably the majority of cast wheels manufactured at the pr«-
ent time are cast in one solid casting of buckets^ rings, hubs, and
crowns. The buckets are formed by carefully prepared cores and
in such manner as to leave them uniform in spacing and thickness,
and smoothly finished so as to admit of the passage of water lhn>u|
or between them without excessive friction. With wheels so
no material finishing or smoothing of the surfaces of the bucket
practicable, and the casting must come from the sand with a sal
factory surface. In wheels cast solid, great care is necessary
order to prevent serious shrinkage strains. This is partially ov'
come by the use of soft iron, which results, however, in increJ
wear of runners subject to the action of sand-bearing waters.
With buckets cast separately, a higher surface finish of
bucket is possible ; but when separate buckets are made and afti
wards united, the runner must be strongly banded in order to gi^
it the necessary strength. Buckets of sheet steel, forged or
to the desired shape, present a uniform and satisfactory surf;
and when punched at the edges before casting, form a solid
substantial wheeh
The runners of Girard impulse wheels (see Fig. 171) are
in the same manner as reaction runners.
The runners of tangential wheels are usually made with scpti
buckets and body, (See Figs. 167 and 168.) The bodies are
Diameter of Runner. 285
cording to the severity of the service, of cast iron, semi-steel,
rged steel, etc. The buckets, dependent on the conditions of
rvice, may be of cast iron, cast steel, gun metal, bronze, etc. The
ckets, in the best wheels, are cast, shaped and polished and care-
lly fitted to the wheel body. The bolt holes are then carefully
illed and reamed and the buckets are bolted in position by care-
lly turned and fitted bolts.
140. Diameter of tfie Runner. — ^The diameters of reaction runners
e measured at the inlet, and, when the buckets at the inlet are
rallel and of one size, the determination of the turbine diameter
a simple matter. (See Fig. 174, diagram A.) In order to give
2 runner greater speed and capacity, the buckets are sometimes
t back at a point opposite the bottom of the gate opening (see
igram B), and the diameter of the runner opposite to the gates is
iuced below that of the lower diameter. In such cases the edges
the buckets are sometimes made parallel with the shaft but are
ually inclined upward. In the latter case, the diameter of the
leel at its top may be considerably reduced over its diameter at
e offset. In such cases the cutting back of the runner may be one
more inches at the bottom line of the gate with an inch or more
clination to the top of the buckets, and the diameter of the wheel
D and D'", diagram B, may differ from two to six inches or even
ore.
With wheels so constructed, there is considerable difference in
ic practice of different manufacturers in measuring and listing the
ameter of the wheels made by them. In some cases, the inside
iameter, from ring to ring, D, diagram B, of the runner, is given
$ the list diameter. In other cases, the diameter is taken at the
iner angle of the offset as D'. In a number of cases the diameter is
leasured at about the center of the gateway, D", and in other cases,
IC diameter is measured at the upper and smaller diameter of the
inner, D'". This variable practice leads to a considerable differ-
ice in the nominal diameter of the various turbines as listed in
e catalogues, and frequently a runner listed as of a certain diame-
r by one manufacturer may be two to six inches larger than the
nner of another manufacturer which is listed as of the same di-
leter. This discrepancy in the method of measuring and listing
5 diameter of turbine runners accounts, in some degree, for the
parent greater capacity, higher speed or greater power of the
eels of one manufacturer over those of another.
^^^ 286 Turbine Details and Appurtenances. ^^H
^^^" The practice of some of the American manufacturers of turbines,
^M in measuring and listing the diameters of their wheels, is shown
^H in Table XXV, In this table, all runners which are not cut back
H and with edges parallel to tlie shaft, are classified as Style A, even
H where they differ widely froin the form shown in diagram A, Fi^.
■ 174.
H All runners with buckets cut back are classified as Style B, tnn
^^^^ where the bucket edges are parallel with the shaft.
^^^P The diameters of tangential runners are usually measured 1^
^^^^ tween the centers of buckets or on the diameter of the circle on
H which the center of the jet impinges on the buckets.
H TABLE XXV% 1
^M Praciiee of Various American Mannfaciurerii i>t MeamiHttg and Catalogi^^M
^B Ui€ Diameter of Turbitm Water Whe^lB, H
^^ M&niifactuTer.
Name of Banner.
Style,
Poinl d
^P Dayto0 Globe Iron Worke. . ,
Eodiaey Hiitit Machine Co. . .
The James Lefiel h Co« ......
1
\
' Piatt Iron Work i Co,
A merican ...^*i .. #ii>fi»»*t
A
A
B
B
B
A
A
A
B
H
B
A
H
B
B
B*
B
D
D
J/
W
D
D
D
0
D
D'
0
W
n^
D
Sew American. i
Especial New American. ....
Impros^ed New American^ . .
McCormick* .,...*«,*.*.*».
Hunt. . ... *
Standard Xrpffel. ,.,,,,. , , , .
Special Leffel ..............
Samnon .»... ,.,,,«..,.
Improved SamEon. ,.,,..«..
Type A ,
1^ 8 Morgnn 8mith C4>, , ,
Tvpes B and C* .••.*.
McGorniick'
^H TheTrumpManufncturingCo.
^f W el) man ^ Sea ver, Morgan Co.
t^mith ........ ...,♦♦.,,,,..
Standard Tnimp* ..........
Hiifh Speed Trninp* ..,,,...
JolJj'M cCormick »,,,.,..«.
I Fillet at angle. Dimneier mewflured just above.
'Diameter of HsJnt-MLCjnniclc rutuiere \\h measured al the crown which pi*
jects beyond the tips of the buckets and la essentially the same in diameiera^itp'
•Diameter of the Smith -McC^irmick rutinera in meastired at the crown uhici
projects beyond the tips of tbe bucket!^ and la essentially the ^aine in diatnaeri
at D',
« Diameter at D ie 20$ j^reater than at D".
* Bucket or of high spt^ runner has parallel edges but is cut back as ebowii^ii^
141. The Details of the Runner. — The reaction rtinner will %*at
in design with the conditions under which it is to operate and t)
1 experience and ideas of its designer. In American practice t
Details of the Runner.
287
lanufacturer usually constructs a series of runners of similar ho-
nogeneous design; that is to say, each wheel of the series has all
)f its dimensions proportional to that of every other wheel of the
icrics, and is of similar design in all of its parts.
On account of demands for considerable variations in speed or
power, or on account of improvements which have been found de-
sirable by reason of the demands of his trade, the manufacturer
often designs and constructs several series of wheels, each of which
is particularly adaptable to certain conditions which he has had to
meet. (See Tables XXII and XXIV.) In such cases each series
is best suited for the particular condition for which it was designed,
and is not necessarily obsolete or superseded by the later series.
Fig. 174.
The curves of the runner buckets (see Figs. 13, 14, 133, 134, 136,
J46-148, 175) must be such as to receive the jet of water from the
nozzle or guides without shock, permit it to pass along the surface
^f the buckets or through the passages in the runner with mini-
'^um friction, and discharge it as nearly devoid of velocity as prac-
ticable.
To accomplish this, the relative position and relation of the
^rves of guides and buckets must be carefully arranged. As the
jet of water is always directed forward in the direction of the revo-
lution of the wheel, the jet has an original velocity in that direc-
tion, and, since the bucket must be so shaped as to give a continued
contact, as the jet progresses and the wheel revolves, the portion of
the bucket farthest away from the guides must be curved back-
ward, and terminate at such an angle as shall permit the jet to
pass away from the wheel with free discharge. (See Figs. 175 and
128.)
288 Turbine Details and Appurtenances.
B
Fig. 175.— Curves oY Buckets and Guides in Turbine Wheels.
Vertical Turbine Bearings. 289
tion runners are made either right or left handed as de-
When looking at the top of the runner, if the wheel is de-
to move in the direction of the hands of a watch, it is called
handed wheel, and if it moves in the other direction, it is
left handed wheel. (See Fig. 176.)
buckets, hub, crown, and ring of the reaction runner must
ufficient strength to receive the impact or pressure of the
column of water under the working head, and to transmit
rgy to the shaft through which it is to be transmitted to the
ery to be operated.
avy ring is usually desirable, both to give strength and
to the outer edge of the buckets and also, under some cir-
cumstances, to give the effect of
a fly-wheel in order to materially
assist in maintaining uniform
speed. Floating blocks or other
material, in spite of the use of
trash racks, sometimes reach the
turbine, and when caught between
HAND LEFT HAND ^^it buckets and the case are apt
—"Hand" of Water Wheels, to cause serious injury to the
buckets,
runner is attached to a shaft passing through the hub, to
t should be closely fitted and strongly keyed to prevent its
ig loosened by vibration and the strain of operation. This
:ially necessary in vertical wheels, for if, under these con-
the wheel becomes loosened and drops from the shaft, it is
e practically destroyed. Impulse runners acting under high
ire subject to heavy shocks and must be especially sub-
i^ertical Turbine Bearings. — In all turbines where the dis-
is axial and only in one direction, there is a reaction in the
irection that tends to unbalance the wheel and to cause a
n the direction opposite to the discharge. The leakage into
:e back of the runner frequently produces a thrust in the
J direction which may be wholly or partially relieved by
s left in the runner, usually close to the axis. In large
I attempt is made to balance these various pressures with
rm of thrust bearing to sustain the difference in pressure
vill occur under different conditions of operation.
290
Turbine Detaila and Appurtenances*
In most single vertical turbines a simple step bearing is us«i
The bearing itself in American turbines usually consists d£ a lig-
num vitae block, turned to shape, and centered in a bearing block
which is held firmly and centrally in place by the cross trees. Tbe
bearing block is shown by T, and the cross trees by t, in Figs. 146,
147 and 185. The bearing on the shaft itself is usually a sphcrica!
sector, or some other symmetrical curve of similar form. In some
cases this bearing is cut directly in the shaft itself, (See Fig. 14?)
In others, a cast iron shoe is provided and attached to the shaft
(See M, Figs. 145 and 184.) Above the turbine a second bearing
is also provided (see T', Figs. 145 and 147) to keep the shaft \n
vertical alignment* This bearing in American wheels is usually
Pig. 177.^GeyUn (Pateat) Glass Suspension Bearing (It D, Wood t Oa).j
of the type shown in Fig, 182, except that it is adapted to its vcr- j
tical position.
In the Geylin-Jonval turbine, manufactured by R* D* Wood]
Company^ a patent glass suspension bearing is used, (Fig 177*) j
This bearing is attached above the wheel (see T, Fig. 135) andh^j
the advantage of being readily accessible. The turbine is here sus* j
pended on a circular disc composed of segments of glass, B. H-
Fig. 177, arranged with depressed divisions which form a conlifli*"]
ous space around each segment of which the disc is composed, a'- j
lowingt while the turbine is in motion, a perfect, free circitlalioul
of the lubricating matter with which the space is filled.* The bfar-J
ing is a true metallic ring, A^ firmly secured to the turbine sli*ftj
which revolves on these stationary glass segments.
In most European vertical turbines the step bearing is simply ^
guide, the main bearing being above the turbine and more fea^w;
accessible than in the American form.
•Catalogue of R. D. Wood i Cd., ISOl, p. lOT.
Vertical Turbine Bearings.
291
5. 178 and 179 represent vertical bearings of this kind. In
bearings C is a spherical sector so arranged as to take up any
error in the vertical alignment of the shaft. Fig. 178 is a
ball bearing; the hardened
steel balls, AA, revolve
between the special bear-
ing plate, B and Bi.
In Fig. 179 oil is pumped
underpressure through the
inlet, pipe OE, into the
space A. By its pressure
the bearing plate, B, is
raised from its companion
plate, B, and the oil es-
caping between the plates
lubricates them and over-
flows through the overflow-
pipe, 00.
In both Figs. 178 and
179 the height of the shaft
is adjusted by the nut, N,
which, after adjustment, is
fastened securely in such
position.
At the power plant of
The Niagara Falls Power
Company a thrust or hang-
ing bearing of this disc
type, somewhat similar to
Fig. 179, is used (See Fig.
180). In this bearing the
shaft is suspended to a
revolving disc carried on
a stationary disc. The
discs are of close-grained
charcoal iron of 25,000
pounds tensile strength
• 14" inside, 34'' outside diameter. The lower or fixed disk is
led to a third disk with a spherical (3' 4" radius) seat. This
178. — Vertical Suspension Ball Bear-
ing.*
eerkraftmaschinen von L. Quantz.
292
Turbine Details and Appurtenances.
is to provide for an automatic adjustment for slight deviations from
the vertical due to uneven wear of the discs and other causes.
The bearing surfaces between the discs are grooved to allow a
circulation and distribution of the oil over the surface.
Three methods of lubri-
cation,— forced, self, and
a combination system^
were experimented with
and the combination sys-
tem finally adopted In
the system of forced IuIk
Hcation, the oil enters the
fixed disc at two diamct*
rically opposite points and
is forced between the discs
under 400 pounds pres-
sure. Self-lubrication is
accomplished by oil sup-
plied at the inner circum-
ference of the disc and
on Pres- thrown outward by cen-
trifugal force.
The disc bearings arc
enclosed in a case provided with sight holes through which the
condition of the bearing as well as the temperature of the oi) can
be observed, A thermometer and an incandescent light are sus-
pended in the casing for this purpose. The oil is cooled by water
circulating pipes inside the casing.
The shaft is provided with a balancing piston (see Fig. 181)
supplied with water from a pipe entirely independent of the pen-
stock and under a head of 136 feet. This piston carries the greater
part of the load, less than 2 per cent of the load being left to be
carried by the oil- lubricated disc bearing described above. M
143. Horizontal Turbine Bearings. — In horizontal wheels vari-"
ous forms of bearing may be used according to the conditions and
circumstances of their operation. When practicable the bearitigs
should not be submerged and should otherwise be made as accessi-
ble as possible. In such cases the forms of bearings may be tlie
^ame as those used on other machines subject to similar strains-
' WflBserkfftfimaflehfnen von L. Quants.
Fig. 11^ —Vertical Suspension
sure Bearing.*
Horizontal Turbine Bearings.
293
many horizontal American wheels, where submerged bearings
c necessary, lignum vitae bearings are used similar in type to the
)pcr vertical bearing before mentioned (see T', Figs. 145 and 147) .
jch a bearing is shown in detail in Fig. 182. In this bearing the
laft, S, is sustained in position by the blocks, TT, which fit the
Thruj^
I !l!i!k-i *V--K
Secfion fhrough Boll Disk Oil Inlef
Section through Oil 5i9hf Ho!©.
Fig. 180.— Vertical Thrust or Hanging Bearing of the Ni-
agara Falls Power Co. (See Eng. Record, Nov. 28, 1903.)
esses of the cast iron bearing block, K, which in turn is attached
a cross tie in the case or to a pedestal, P. The blocks, TT, are
listed by means of the screws, BB, which, after adjustment
locked in position by the lock nuts, LL. Such submerged
rings are sometimes lubricated by water only, in which case op-
294
Turbine Details and Appurtenances.
ft
portnnity must be given for the free circuktion of the water In
other cases the boxes are made tight and flow into them along tht
shaft is prevented by stuffing boxes at each end of the main box^
the boxes being lubricated
by forced grease lubrica-
tion.
Bronze boxes of the types
used for other high grade
machines are sometimes
used for submerged bear-
ings. In such cases great
care ts necessary to pre-
vent the entrance of grit-j
bearing waters. Suchj
bearings are lubricated byj
forced oil or grease.
In forced lubricatioa itj
is desirable that both 1 1
force and return pipe be I
used so as to give visiblej
evidence that the lubri'^
cant is actually reactiing|
the beari ng* In some
cases bearings that woUd
be otherwise submerged
are made accessible at allj
times by metallic tub
(see Fig. 322) used
manholes.
Where the turbine is placed horizontally, gravity can no long
oflfset the thrust caused by the reaction of the turbine when th
discharge is in one direction, and the thrust must therefore be ove
come by the use of some form of thrust-bearing. Where other con
ditions permit, it is quite common practice to install two turbina
on a single horizontal shaft, having their discharges in opposite dH
rections, in which case the thrust of each turbine is overcome 1
the thrust of its companion (see Figs. 153, 160 and 316)* In manj
cases, however, the arrangement, size and capacity of the whcei
to be used are not such as will permit the use of twin turbines an^
thrust-bearing, and other means of taking up the thrust must 1
tjrovided.
Pig, 181, — Section of Turbine used m new
Power ilouse of The Niagara Fall^ Power
Oompapy, showing Balancing Hydrauliti
piston nsed to in&lnin Turbine and Shaft
(Eng. Record, Nov. 28, 1903,)
onzontal Turbine bearififfs.
295
144, Thmst^Bcaring in Snoqualmie Falls Turbine, — In the Sno-
<iualmie Falls Turbine, manufactured by The Piatt Iron Works
Company (see Figs. 161 and 162), the device for taking up the
thrust is thus described by the designing engineer, Mn A. Giesler:*
**Sing!e-wheel horizontal-shaft units are relatively infrequent in
turbine practice, especially in large sizes, where the thrust of a sin-
gle runner is large enough to require careful consideratian. The
thrust is made of two parts: (1) that due to the static pressure or
effective head of water at the various points of the runner surface ;
and (2) that due to the deflection of the water from a purely radial
/^]r\
FSf. l82.^HorlzontaI Lignum Vltae Bearing as Used In American Turbines.
path through the wheel. As concerns the first part, the front face
^f the wheel is pressed upon by a pressure varying from the supply
head at the outer circumference to the discharge pressure (vacuum)
^t the inner edge of the vanes* which latter extends over the whole
^^ntral area of the runner (and shaft extension). The rear face of
^^c runner is subjected to the pressure of water leaking through
'he radial air-gap between casing and runner, substantially equal to
^"^ supply head. This greatly over-balances the pressure on the
f^Ofit face, and the resultant thrust is to the right in Fig. 161 (to-
^^t*d the draft tube). The discharge ends of the vanes, being
^^^ed transversely, also have a pressure component directed to-
* See "Englnetrlng News'' of Marcb 29. 190e.
2^6
Turbine Details and Appurtenances*
ward the right. The velocity effect produces a thrust directed to*
ward the left, but this is very small and does not materially reduce
the pressure tlirust.
*'Ey far the larger part of the pressure thrust is eliminated by
venting the space back of the runner into the discharge space. Six
holes through the wheel near the shaft, indicated in Fig. 161, have
this function. The water leaking in through the air-gap is continu*
ously discharged through these vents into the draft*tube, and the
accumulation of any large static pressure back of the wheel
[hereby avoided.
"The average pressure on the front of the runner, however^ if
always lower, and the resultant thrust is therefore toward the draftJ
|i /7^'r: 4
Crp«* Section.
Lon^'itudinol SvcHon*
Fig. 1S3.— Thrust'Bearing Snoqualmle Wheels.
tube, though its amount varies considerably, being greatest for fu^
gate opening. This thrust is taken up by the balancing piston in
mediately back of the rear head of the wheel case, and the tiltimat^j
balance and adjustment of position is accomplished by the coU
thrust^bearing behind the balancing piston.
"The balancing piston is a forged enlargement of the shaft,
ished to a diameter of 17 inches, which works in a brass sleeve !
in a hub-like projection on the back of the wheel-hotising. The ifl
side of the sleeve has six circumferential grooves, each one inch wid
and one-quarter inch deep, as water packing. The chamber in fn
of the piston communicates by a pipe (containing a strainer) witkj
the supply casing of the water-wheel, and therefore reccivea tS
full pressure of the supply head. The chamber back of the piston'
— *- —
Thrust-Bearing in Snoqualmie Falls Turbine. 297
is drained to the draft-tube, so as to carry off any leakage past the
piston. The device thus produces a constant thrust on the piston.
directed toward the left. By throttling the pressure pipe this
thrust can be adjusted as desired.
"The thrust-bearing shown in Fig. 161 and in detail in Fig. 183
:onsists of a group of four collars on the shaft, working in a babbit-
ed thrust-block which is bolted to the back of the wheel-housing.
[Tie collars are formed on a steel sleeve which fits over the shaft
nd is bolted to the rear face of the balancing piston ; this makes
t possible, when the collars are worn out, to renew the bearing by
ismounting the thrust-block and placing a new sleeve. The
hrust-bearing is lubricated by oil immersion. An oil chamber is
ored in the block and communicates by numerous oil holes with
he bearing faces ; a constant flow of oil is maintained by means of
►il-supply and drain-pipes. Concentric with the oil chamber and
»utside of it a water chamber is cored in the block. Cooling water
3 supplied to this chamber by a pipe from the pressure side of the
urbine, and drains from the top of the bearing through a drain-pipe
0 the draft-tube. A U-pipe attached at one side of the bearing forms
:onnection between the water chambers of the upper and lower
lalves of the block. This detail avoids making the connection by a
lole through the joint face, which would allow leakage of water
nto the oil-space and into the bearing.
"The balancing piston is so proportioned and the pressure supply
)ipc is throttled to such a point as to give exact balance (i. e., with
:cro thrust in the thrust-bearing) at about half to five-eighths the
uU output of the wheel. At larger power there will be an unbal-
mced thrust to the right, and at smaller output to the left, which
ire taken by the thrust-bearings. The maximum thrust on the
:olIars is about 25,000 lbs. The collars are 2^^ inches high (2%
nches effective) by 1314 inches mean diameter, giving a total effec-
ivc bearing area on four collars of 418 sq. inches. The maximum
x)llar pressure is thus about 60 lbs. per sq. in."
145. The Chute Case. — ^The chute case (see Figs. 146, 147 and 184)
onsists of the fixed portion of the turbine to which are attached
he step and bearings of the wheel (T), the guide passages (g)
rhich direct the passage' of the water into the turbine bucket, and
le gates (G) which control the entrance of the water, and also
le case cover (C). The case cover keeps the wheel from contact
18
293
Turbine Details and Appurteoaoces.
with the water except as it passes through the guide and gates* To
the chnte case is usually attached the apparatus and mechanism for
manipulating or controlling the position and opening of the gate.
{A. P, Gn, etc) In vertical turbines a tube, d, is usually attached
to the lower ring, forming a casing in which the lower portion of
the turbine revolves an»l on which the bridge tree, t, holding tlic
step bearing is attached
When this lube is no long*
er than one diameter it is
u?sually called the turbine
tube; but when it is con-
siderably extended, it is
termed a draft tube.
The design of the tur-
bine tube depends largely
on the character ot the
wheel. Some wheels dis-
charge downward and in-
ward, some almost entire-
ly downward^ some down-
ward and outward, and in
some cases, the wheel dis-
charges in all three direc-
tions. For the best re-
sults the tube should be
so designed that the water
from the wheel shall
received by it with
radical change of velocii
and so that the remaininl
velocity will be gradually
reduced and the wat<
discharged at the low«
practicable velocity.
The chute case and its appurtenances should be so designed tin
the water will enter the bucket with the least possible shock or 1
sjstance at all stages of gate and with a gradual change in vclocit;
and will discharge from the buckets into the turbine tube with
little eddying as possible and be evenly distributed over the cr
section of the tube so as to utilize the suction action of an unbrok
column of water The case must also be designed of sufEtie
Fig. 184.
k
The Chute Case.
299
185. — Section Swain Turbine.
o sustain the weight of the turbine wheel and so that the
igs are accessible and can be readily replaced or adjusted,
gement of the case must also be such that the openings
he wheel and the case are as small as practicable and the
line of possible leakage
will be as indirect as pos-
sible so as to avoid leak-
age loss.
Most chute cases are
either cast or wrought
iron. Cast iron usually
lends itself to a more sat-
isfactory design for receiv-
ing and passing the water
without sudden enlarge-
ment and opportunities
for losses by sharp angles
and irregular passageways.
Wrought iron, while not
always lending itself read-
ily to designs which elim-
iuch losses, possesses much greater strength for a given
tiich is a g^eat advantage under some conditions.
rbine Gates. — ^Three forms of gates are in common use
lling the admission of water into reaction turbines. The
^te consists of a cylinder closely fitting the guide that
ition admits or restricts the flow of water into the buck-
184 is a section of a turbine of the McCormick type,
ired by the Wellman-Seaver-Morgan Company, having
this type, GO, between the guides and runners, which is
sed in the cut. The gate is operated by the gearing. Or.,
>es it into the dome, O, through connection with the gov-
't, P. This same type of gate is used over the discharge
agara-Fourneyron turbine (see GO, Fig. 134), over the
e Geylin-Jonval turbine, GG, Figs. 135 and 137, and be-
: guides and buckets of the Niagara turbine, shown in
Red form of the cylinder gate is that used by the Swain
lompany (see Fig. 185), which is lowered instead of being
) the dome as in Fig. 184.
300
Turbine Details and Appurienances,
A similar modification, called a sleeve gate by its desi^er. J, W.
Taylor, is shown in Fig, i86.
When partially closed the cylinder gate causes a sudden contrac*
tion in the vein of water which is again suddenly enlarged in enter-
ing the runner after opening the gate, (See Fig. 1 88.) These con-
ditions produce eddying which results in decreased efficiency at
part gate. (See Figs, 185 and 186.)
The wicket gate, when wdl
made, .is perhaps the most satisfac-
tory gate, especially for moderate
or high heads. It can be readily
balanced and should be made witl
perhaps a tendency to drift shut,
so that should the governor mech-
anism break or become disabkfl,
the gates will drift shut. These
gates are illustrated by GG,
Figs, 147 and 148, which illustraif
the wicket gate of the Samsor.
turbine of The James Leffel ^
Company, and Fig* 187 which
shows the wicket gate of the Well
man-Seaver- Morgan Gompaoy
In both cases the wickets are con-
nee ted by rods with the eccentric
circle and through an arm and
section with the gearing Gr,
Figs. 145 and 146 show the wick-
et gate of the Improved Nctf 1
American, and Figs. 161 and 1611
show the wicket gates of the Sno- j
qualm ie Falls turbine, nianufacl*j
ured by The Piatt Iron Wori
In both the New American ai*
Sleeve Snoqualmie wheels^ the gates a^
moved by a gate ring (see
Fig. 145). Figs. 189 and 190 sh
the details of the wicket gates and connection of the same to 1
gate ring of the Snoqualmie Falls Turbine.
The tendency to produce eddying is much rediiced in well
signed wicket gates, although the sudden enlargement of the rt-j
Fig.
186.— Section Taylor
Gate.
^^m
Turbine Gates.
301
vem at part g^ate undoubtedly reduces the efficiency of the
(See Fig. 191, A and B,)
register gate (see G, Fig> 192) consists of a cyhndcr case
pertures to correspond with the apertures in the guides, g,
so arranged that, when in proper position, the apertures rcg-
nd freely admit the water to the wheel, and is also so con-
id that when properly turned the gate cuts off the passage
ftely or partially as desired,
»iderable eddying is produced by the partially closed reg*
ite, with a consequent decrease in part gate efficiency, (Sec
Fig. 193.) The cylinder
gate is usually the cheapest
and most simple form of
gate» but the wicket gate,
if properly designed and
constructed seems to ad-
mit of the entrance of
water into the bucket with
least possible resistance
and eddying, and in the
most efficient manner.
This form of gate is the
most widely used in high-
grade turbine construc-
tion at the present time,
although the cylinder gate
is largely in use and has
given satisfactory results.
In some cases the pas-
sage of water is restricted
or throttled by the use of
irfly valve, either in the inlet or in the turbine tube. This
ts the inlet or discharge and regulates the head in a very
ent manner, but may be reasonably satisfactory where econ-
[ water is unnecessary.
npulse wheels the gates are usually so arranged that the
passages are opened one at a time instead of all opening par-
is in part gate conditions with the reaction wheel. This re-
a less loss in the cddyings caused by part gate. Fig. 194
the type of gate used by The Piatt Iron Works in their Gir-
L87. — Wicket Gate of the WeUmaii
Seaver Morgan Co.
3Q2
Turbine Details and Appurtenances.
ard turbines where the guide passages are arranged symmetricalH
in three groups about the wheel. In the tangential wheel, where
a single nozzle is used, the most efficient method found for redu-
cing the opening is with the needle as illustrated in Fig. 195. This
figure shows a cross section of Oie Doble needle nozzle, a form
which gives a high velocity coefficient under a very wide range oi
opening. The character of the stream froni a needle nozzle when
fi^reatly reduced is shown by Fig-
196 where the clear and solid
stream gives evidence of high effi-
ciency. If the flow of water
through the nozzle is regulated by
throttling the water with a valve
before it reaches the noziki
very low efificicncy results.
147. The Draft Tube.— The r
action wheel is of particular ad
vantage under low heads oa ad
count of the fact that it can mq
efficiently under water, and then
fore, under backwater condition
can be made to utilize the full hca
available. It is not nece^^aryj
however, to set the reaction whed
low enough so that it will be beM
water at all times for the principle
of the suction pipe can be utiliza
and the wdieel set at any reasoo'
able distance above the tail waici_
and connected thereto by a if*
tube which, if properly arrange^
will permit the utilization of the full head by action of the drafl
or suction puil exerted on the wheel by the water leaving tb
turbine through the tube from which all air has been exhausted
The water issuing from the turbine into a draft tiibct which at lb
starting is full of air, takes up the air in passing and soon estal?
lishes the vacuum necessary for the draft tube effects. The f«"C
tioo of the draft tube is not only to enable the turbine to utiliii
by suction that part of the fall from the wheel discharge to tbct*l
water level, but it should also gradually increase in diameter so J
Ftg. l&S.— Stiowing Cylinder Gate
Partially Open and E<3 dies Caused
by Sudden Contraction and En-
largement of Entering Vein of
Water.
Fig. 189.— Showing Relations of Gate Guides and Buckets in Snoqualmie
Falls Turbine (Piatt Iron Works Co.).
SsctJon A-B-
1g. 190. — Showing Rigging for the Operation of Wicket Gate in Snoqualmie
Fpll9 Turbine (Piatt Iron Works Co.).
3^4
Turbine Details and ADpurtenaoceSi
A. Gate wide open. B. Pan i:il gate.
Fig, 191. — Showing Couditton of Flow Through Open and Partiallj
Wicket Gatea.
^y
to gradually decrease ihe
velocity of the water after
it is discharged from the
turbine wheel, thus enab-
ling the turbine to utilijc
as much as possible of thi^
velocity head with whiclj
the water leaves the tup
bine. It should be not^
that a partial vacuum isl
established in the draft
tube and, therefore, tfce
draft tube must be stron
enough to stand the c^te I
rior pressure due to the I
vacuum so created. Inor-I
der to perform its functions j
in a mo re satisfactory man- 1
ncr, it must also be madc^
perfectly air tight
One of the great advantages in the use of the draft tube is the
possibility, by its use» of setting the wheel at such an elevation
ng.
192.— Register
Works
Gate
Co.).
(Piatt Iron
Turbine Gates.
305
tail water that the wheel and its parts can be properly
by draining the water from the wheel pit. Otherwise it
accessary to install gates in the tail race and pumps for
'Ut the pit in order to make the wheel accessible. The-
thc draft tube can be used of as g^eat length as the suc-
>f a pump, and this is probably true of draft tubes for
very small wheels. Practically, the
draft tube should seldom be as
long as 20 feet, especially for large
wheels, for its success in the util-
ization of the head depends on the
maintenance of an unbroken col-
umn of solid water, which is diffi-
cult to maintain in large tubes. As
the size of the wheel increases the
difficulties of maintaining a vac-
uum increase and the length of the
draft tube should correspondingly
decrease. It is practically impos-
sible to maintain a working head
with large turbines through long
draft tubes with the turbine set at
great distances above the water.
Long draft tubes should, as a rule,
be avoided and in all cases where
draft tubes are used, they should be
as straight and direct and as nearly
vertical as possible. It is the prin-
ciple of the draft tube that per-
mits horizontal shaft wheels to be
utilized, as otherwise, with this
chinery, only a small portion of the head could be used
j^e under normal conditions, for such wheels being often
ected to the machinery are, of necessity, placed above
ter. The draft tube is commonly of iron or steel, but in
re concrete construction is used the draft tube may be
ictly in the concrete of the station or wheel foundations,
ourneyron turbine Boyden used what he termed a difFu-
Fig. 197.) The main purpose of the diffuser, and of the
e as well, is to furnish a gradually enlarged passage
lich the velocity of the water as it leaves the wheel is
lowing Eddying Caused
1 Closure of Register
3o6
Turbine Details and Appurtenances.
B'lg* 194. — Gates and Guides of Qtrard Impulse Turblae. (Turbine Dwlp
ss Modified for Close Speed Reflation, G. A. Buvinger, Froc. Am. Soc
M. E., Vol. XXVI Ij
I
Fig. 19S. — Cross-section of Doble Needle NozEle.'
* From Bulletin No. 6« Abner Doble Co.
The Draft Tube,
307
Fig. 196. — ^Stream from Doble Needle Nozzle**
so gradually reduced as to
enable the velocity head to
be milized in the wheel,
thus saving head which
would otherwise be lost
It has already been noted
that impulse wheels of the
Pel ton and Girard types
cannot operate satisfactor-
ily submerged, and must
be set at such positions
that they will be above the
tail water at all times. In
many localities where the
variation in the surface of
tail waters is considerable,
ans a large relative loss in the head utilized and that this
wheel will therefore not be practicable except under high
197. — ^BoydeD D Iff user
1 Bulletfn No G« Abner Doble Co.
3o8 Turbine Details and Appurtenances.
head conditions and where the loss entailed by the rise and fall of
the tail water will be inconsiderable. An attempt has been made,
however, to so design a draft tube that a vacuum will be established
and maintained below the wheel, in such a manner, however, that
the water will not come in contact with the wheel. The vacuum is
so maintained as to hold the water at an established point just below
the wheel, thus permitting the wheel to utilize the full head except
for the small clearance between the wheel and the water surface in
the draft tube. This arrangement is shown in Figs. 168 and 171, as
applied by The Piatt Iron Works Company to a Girard turbine.
CHAPTER XIV
HYDRAULICS OF THE TURBINE.
148. Practical Hydraulics of the Turbine. — It is not the purpose
of this chapter to consider mathematically and at length the princi-
ples of hydraulic flow in relation to the curves of guides and buckets
and the effects of such curves on the power and efficiency of the tur-
bine. These relations are expressed by long and involved equations
of considerable interest to the engineer who is to design and con-
stract the turbine but of little practical value to the engineer who is
to select and install it in a water power plant. Few of the designers
of American wheels have given much attention to the involved
mathematics of hydraulic flow in the turbine and the designs of
most American wheels are based on the results of experiment and
broad practical, experience. The designs of Swiss and German
wheels are, to a much greater extent, based on mathematical
analysis. It is an open question whether the best work of either
American or foreign manufacture shows any marked superiority
in comparison with the other. The results actually attained in the
nianufacture of wheels in this country seem to show that the
American practice in wheel design will give equal and even more
uniformly satisfactory results than the European methods, — at
^east as carried out by foreign engineers under American condi-
tions.
Correct theory must be the basis of all successful work. The
theory of the experienced man may be unformulated and unex-
pressed, but correct design has always a correct theory as its basis
^vcn if unrecognized as such, and such a theory properly applied will
lead to correct results. On the other hand, formulated theory will
lead to correct results only as far as the theory is correct and takes
into account all controlling or modifying factors and is properly ap-
plied. A correct theory, carefully formulated and properly applied,
^nnot fail to be of g^eat service to the engineer in extending his
Experience to wider fields. Scientific study and mathematical an-
^ysis of the turbine, based on wide experience and careful experi-
ments, can but lead to the accomplishment of better results than
have yet been attained.
3IO
Hydraulics of the Turbine.
An understanding of certain laws of flow through turbines as con-
firmed
by both theory and practice is essential to a proper compre^
liension of the principles which should govern the selection and
installation of such wheels and these laws are considered
in this
chapter
149-
Nomenclature used in Chapter. — In the discussion
in this
chapter
the letters and symbols used have the following
signifi-
cancc:
a
= Area of gate orlfioe or ortScea
B
= Angle of defleniion of jet.
^m
= Supplement to anj^le of deflection = 180' — ci.
^M
— Diameter of wheel in inches.
H
= Energy in foot pounds per second.
^B
^ Force producing preesLire or motion.
^m
= Aeceierfltioa of grnvity*
^1
= Effective head at the wlieel.
^B
=i Numljer of revolutions per minute*
^M
= Number of revolutions per minute for hend hj.
^M
= Ratio of circumference lo diameter ^ 3;1416
^m
^ Home powers of turbine at any given head.
^M
— Horse power of turbine at head hj<
^M
= DiBcltar^e In cubic feet per Becond at any given head*
^M
= Discharge in cubic feet per second at head h^.
^B
= Interna) radius of wlvee!.
■
s= External radius of wheel.
k.
^ Space passed tti rough by force acting.*
^B
= Velocity of wheel at gate entrance*
^1
= Velocity of wheel at point of discharge.
H
= Theoretical spouting velocity due to head = r %n
^1
= Velocity of the periphery of the impeller, in feet per second.
^B
= Al^isolule velocity of water entering the wlieel.
^"
= Absolute velocity of water leaving tlie wh^^el.
J
W
=i Relative velocity of water entering ihe wheel.
1
^
= Relative velocity of water leaving the wbeeL
I
^^
= Average velocity.
■
B
= Total weight per second.
I
^
= Weiglit of unit of water = 62.5 lbs.
.,■
ss Batio peripheral velocity of wheel to epouting velocity of water ^r H
TURBINE CONSTANTS,
C
= Coe0cient of discbarge of gate orifice or orificea.
A
= Constant relation of turbine diameter and apeed*
K
= Cbnstant relation of turbine diatneter to discharg@u
Kt
= Constant relation of turbine diameter to powder.
K,
= Constant relation of peripheral velocity.
K4
— Doefilcient of relation of turbine speed and discharge.
^H
— Ooeflicient of relation of turbine power and speed* (Specific
q.Md.1
First Principles. 311
C50. First Principles. — In the utilization of water for power pur-
ses it is the first principle of design that the water should enter
r wheel tvithout shock and leave it without velocity. This should
interpreted to mean that the approaches of the water to the wheel
ist be such as to cause no loss by undue friction or by sudden con-
ctions or enlargements (inducing eddies and other sources of lost
^rgy)» 2ii^d that all shocks should be confined as far as possible to
t action on the wheel buckets leaving the full amount of energy,
d consequently the velocity, to be entirely converted to power
erein.
In gravity wheels, illustrated by the various overshot wheels for-
erly so extensively used for water power purposes, the water
ould enter the wheel at the lowest practicable velocity and should
: retained in the buckets until the buckets have made the greatest
)ssible descent from the nearest practicable approach to the eleva-
on of head-water, to the nearest practicable approach to the eleva-
3n of the tail water. Part of the velocity of approach to the wheel
ay be utilized by impact on the buckets but the entire energy re-
laining in the water as it falls or flows away from the wheel is lost,
id cannot be further utilized in the wheel.
The greater the reduction in velocity, the greater the proportion
f energy that can be utilized, but there comes a limit beyond which
is not practicable to go. This limit varies with different condi-
ons and may be the result of too great expense in the building of
ceways or in the construction of the machine itself. A point will
- reached where the friction expended in the large machine needed
reduce the velocity will consume more energy than would be lost
inducing a higher velocity. These losses must be equalized. In
actice it is found that about two or three feet per second are satis-
:tory velocities at which to reject or discharge the water used by
itors. These velocities represent heads of from .062 to .014 feet,
from three-quarters to slightly less than two inches. The veloc-
'of discharge must, however, be fixed for each individual case and
:er all conditions are fully understood and considered.
151. Impulse and Reaction. — A jet of water spouting freely from
y orifice will acquire a velocity (see Eq. 9, Chap. II).
(1) V = v/^
i will possess energy in foot pounds per second (see Eq. 10,
ap. II) as follows:
312
Hydraulics of the Turbine,
The energy of the jet leaving the orifice is the product of a fort«j
F, which acting on the weight of water^ qw, for one secotid gives ^
the velocity v.
The space passed through by the force in one second, in raisin
the velocity from 0 to v is (see Eq. 6, Chap. II)
(3)
8 = vat=y
and the work done in foot pounds is therefore
(4) E = FS = ^
From Equations 2 and 4 therefore
w
The force, F, is exerted, by reaction on the vessel of which the
orifice is a part and may produce motion in that vessel if it be fr«
to move, or it may produce motion in another body by impube
through the extinction of the momentum of the jet in impingiaf
against it
These equal and opposite forces are well shown:
1st. By the force required to sustain a hose nozzle against the
reaction of a fire stream, and
2nd, By the force of the jet, from the nozzle so sustained when
exerted against any object in its course.
These conditions are illustrated by Figs. 198 and 199,
The force, F, which may be exerted by a jet impinging against
a surface depends on the momentum of the moving stream of wa-
ter and is directly proportional to its velocity. It is also a function
Fig. Ids,
The Impulse Wheel.
3i3
the angle through which the jet is deflected. If friction be ig-
>red, the stream will be deflected without change in velocity, and
e force exerted against the surface in the original direction of the
t will be equal to the momentum of the original stream less
Fig. 201.
■9
Fig. 202.
Fig. 200.
the component, in the original direction, of the momentum of the
diverted jet. (See Fig. 200).
(7)
F =
If the jet impinges against a flat surface (see Fig. 201)
a = 90®, Cos a: = 0 and
(8) F=3^
g
If the jet is deflected i8o* by means of a semi-circular bucket
(see Fig. 202)
Cos 180® = — 1, and therefore
(9) F=22^
g
152. The Impulse WhccL — Impulse water wheels utilize the im-
pulsive force of a jet impinging against buckets attached to the
•ircumference of the wheel. The bucket must move under the
^pulse in order to transform the energy of impact into work and
he ratio of v', the Velocity of the periphery of wheel, to the velocity
of the jet is indicated by ^
(10)
y'
fl) = — and v' = ^ ▼
▼
19
3H
Hydraulics ot the Turbine.
I
In determining the force, F, exerted upon the moving bucket, the
relative instead of the actual velocity of the jet mtist be considered _
and it is readily seen that
value of the relative velocity v^'
will be as follows:
(11)
▼t= ▼— gj V ^(1 ^^)T
-^^ The relative weight of water]
that strikes a single bucket perl
second wilUalso be less on ac-
count of the movement of the
buckets, but as new buckets con-
stantly intercept the path of the
jet the total amount of water,
effective is equal to the total discharge of the jeL Hence frofi
equations (7 and U)
Fig. 203.
(12)
F ^ (1 - COB a) 3^ {1 - <p}
The work done upon the buckets per second is equal to the fo
F, times the distance <f> v through which it acts, i* e#
(IS)
E = F ^ V = (I ■
Qoea) (1 — <p) -^^ — ff ?
This is a maximum when Cl — 4') ^ is a maximum the soluti
of which gives ^ = .5
Substituting ^-.5 and i»=i8o*, in equation (13), there is
tained
That is, E equals the entire energy of the jet (see equation 2), an
hence the theoretical efficiency when ^»=^o.S is lOO per cent
Another criterion for maximum efficiency is that the absolati
velocity of the water in leaving the bucket must be zero.
When a ^180'', the absolute velocity with which the
leaves the bucket is evidently the velocity relative to the buck
minus the velocity of the bucket or
(15) v^ = (1 — ^) T ^ ^v s= V — 2f» V = 0
This gives
<p = 0.5
EfiFect of Angle of Discharge on EflBciency. 315
155. Effect of Angle of Discharge on Efficiency. — In an impulse
wheel it is not practicable to change the direction of the water
through 180** as it would then interfere with the succeeding bucket,
r must hence be less, than 180** and the absolute velocity of the
water in leaving the buckets cannot be zero. The loss from this
jonrce is small as a may differ considerably from 180* without
much effect on the bucket pressure and hence on the efficiency.
For example, — ^the ratio of actual pressure when a is less than
i8o* to maximum possible pressure with a .=180** is (see Fig. 203).
If/Jr:8^ a = 1720, and ^— ^|2i£. = .W6
showing only 0.5 per cent reduction. The effect on the efficiency
is in the same ratio.
Fig. 204 illustrates the flow of the water in entering and leaving
the bucket with all velocities pven relative to that of the bucket.
The jet leaves the bucket as shown with a relative velocity of (i — <^)
V. If this velocity is combined graphically with the velocity of
the bucket, ^v, the true absolute residual velocity v, of the water
will be obtained. The efficiency is evidently maximum when ^ has
a value which makes v^ a minimum. This condition can readily
be shown to maintain when the triangle is isoceles or when
(17) ^v = (l — ^)v
which gives
^ = 0.5
as obtained by two other methods and here shown to be indepen-
dent of the angle p.
The absolute path of the water in space is shown by ABCD Fig.
204, and the magnitude of this velocity is shown below in curve EF
where ordinates are absolute velocities along the tangent lines to
curve ABCD at the point directly above. These curves are based
on the assumption that ^==0.5 and the bucket is semi-circular in
cross section as shown.
The theoretical considerations thus far discussed are modified by
the frictional resistance which the bucket offers to the flow of wa-
ter over its surface and by the spreading of the original jet from
its semi-circular section to a wide thin layer in leaving the bucket.
3i6
Hydraulics of the Turbine-
Further loss no doubt takes place as a result of the fact that the
bucket is in its assumed position at right angles to the direction
of the jet only at one instant during its rotation. Upon entering
F(g- 204.
and leaving the jet it is inclined considerably to this direction and
doubtless operates less efficiently. These conditions result in ^
much greater drop in efficiency than the above analysis would
seem to indicate,
154. Ruction WheeL — ^Thc flow of water through the buckets of
a reaction wheel is less easily analyzed than in the case of the ini*
pulse wheeL The chief difference in the two types of wheels arises
Reaction Wheel,
317
om the fact that the reaction wheel is "filled" and hence the ve-
Kdty of the water relative to the buckets at any point does not
smain constant but varies inversely as the cross sectional area of
le passageway.
fThe path described by a particle of water in passing through the
Fig. 205.
ivhcel has been investigated by Francis,* by a method based upon
the assumption that "every particle of water contained in the
irhecl, situated at the same distance from the axis, moves in the
«ame direction relative to the radius and with the same velocity."
This assumption becomes more accurate as the number of buckets
increases.
Fig. 205 shows the path, resulting from the application of this
assumption, of the water through the "Tremont" Fourneyron wheel
and Fig. 206, through the center vent wheel at the Boott Cotton
Mills. The former indicates, since the jet of water is carried for-
ward in the direction of rotation, that the water resists the rota-
Plg. 206.
•See "Lowell Hydraulic Experiments," p. 39.
3iS
Hydraulics o£ the Turbine.
Fig. 207.
tion of the wheel until nearly to the circumference when it is sud*
denly deflected and leaves the wheel, as it should, in a direction
nearly normal to the wheel.
The jet of water in the Boott wheel (Fig, 206), on the other
handf shows a continual backward deflection of its path from the
point where it leaves the guideSt and
hence a continual delivery of tb
energy to the wheel This seems to
indicate a more logical conditioaand
a better shaped bucket than that of
the Fourneyron, It will be noted
that the actual path of the water in
this case is very similar to that in the
impulse wheel shown in Fig. 204.
For the economical operation of
the reaction wheel the following
principles must be observed;
1st. In order that the jet of water may enter the wheel without
shock the resultant of the velocity of the water as it leaves iht
guides and the velocity of the periphery of the runner must have
a direction parallel to the bucket blades at this point, and a mag*
nitude equal to that which will produce the required discharge
through the cross sectional area of the passageway.
2nd, The relative velocity of the bucket and of the water relative
to the bucket at the point of discharge must be such that the water
leaves the buckets with the minimum practicable absolute velociiy^j
3rd, Such residual velocity as may remain in the discharging wi
ter must be conserved and utilized as far as practicable by tb
proper arrangement of the draft tube.
4th. In all wheels it is also essential by proper design to re^iuO
losses from friction, eddying, etc., as greatly as possible.
The first requirement is illustrated in Fig. 207 where AD is oft
of the runner buckets of an outward flow wheeK The guides, AC
direct the water into the buckets with an absolute velocity, v**
velocity of the runner at point A, where the water enters, is u|
The two velocities combined graphically give a resultant » v^
must be tangent to the curve of the bucket and eqtial to
(18)
T^^ — where
q, = required diieharge throuj^h the pa^^agewftyi n&d
«, = area of cniaa section of the paseageway at point of etitmiice. K
Reaction WheeL
3^9
This reqtiirement does not enter into the desi^ of an impulse
wheel since the jet impinges against the edge of the wedge-shaped
partition in the bucket always in a direction tangent to the bucket
curve at that point regardless of the relative speeds of runner and
jet. Further, since the discharge is "free" and the buckets not
'^filled/' no sudden change of velocity occurs.
The effect of part gate conditions upon the first requirement de-
pends upon the type of speed gate and may best be studied from
Figs. i88, 191, 193 and 207. A change in either direction or mag-
nitude of v^ will change Vr unless the two effects tend to neutralize
which may happen in some instances. In all reaction wheels the
velocity of inflow, Vi, through the guides is increased by partly
closing the gate, while the velocity, ui, of the wheel remain un-
changed, v^ will therefore change, and a change in either its direc-
tion or magnitude will produce an impact or sudden enlargement
respectively as the water enters the runner, and therefore a loss,
unless the direction of the guides is changed to correspond.
The wicket gate, when carefully designed, has given rise to part
gate efficiencies more nearly approaching those of impulse wheels
than with gates of any other type (see Figs. 131 and 236),
Tlie second requirement, that of minimum residual velocity of
the water in leaving the buckets, is shown graphically in Fig, 207.
vm is the velocity of discharge of the water relative to the bucket
and is, of course, tangent to the curve of the bucket, u, is the
peripheral velocity of the runnen The resultant of two velocities
is the absolute velocity with which the water is discharged from the
wheel, and is shown in magnitude and direction by line v^. Now, at
part gate the quantity of water discharged is less than that at full
gate and hence vb must also be less since the cross section of the
passage must be filled. Ua remains unchanged and hence the resul-
tant Vj will be increased with a corresponding waste of energy and
loss in efficiency. This is an unavoidable loss in a wheel operating
under part load and makes it impossible to maintain full efficiency of
operation by any design whatever of the regulating gates. This
loss does not appear in the impulse wheel since the velocity with
which the water leaves the bucket is theoretically at least not in-
fluenced by the quantity.
The third requirement is pnrtially satisfied by gradually expand-
ing the draft tube from the wheel to the point of discharge. This
will recover only the component of the residual velocity in the axtat
320
Hydraulics of the Turbine,
direction, ITie larger component of the residual velocity however
tends to produce a rotation of the water column in the draft tube,
and is not recovered by any present design.
The fourth requirement is evident*
Fl^ 208-209.— Reaction ^Wlieel wttli Concrete Draft Tut)®.*
TOTAL AVAfLAflLt ENCftCT
"^«^^SE^
LC^ IM WHi:CL a'iS
imUSCO Vr WHCCL-Kd
VELOCITICS m DRAfT TUBE^
aciTy-QTT~Bi
QSB liH VeiuQCITV-aTl fclflfel
CHTRAWCE^ IMJCS
DRAT* TUBF
Fig, 210.— Graphical Relation of Velocity and Energy la tha Flow ThroQ]
a Beactlon Turbtne wlUi Draft Tube.
* Turbiaen and Turbinenanlagen, Viktor Gelpk^> page 61.
Energy Transformation, Reaction Turbine. 321
155. Graphical Relation of Energy and Velocity in Reaction Tur-
bine—The relations of the changes in velocity and in energy in the
passagne of water through a reaction turbine and its draft tube are
graphically shown in Fig. 21a
Fig. 208 shows the cross section of a radial inward flow reaction
turbine with a concrete draft tube. The cross sections of the draft
\ tubes at various points are shown in Fig. 209 from which it will
be seen that the draft tube of this turbine gradually changes form
and increases in cross section in order that the velocity of flow may
be gradually decreased from the point of discharge of the turbine
to the end of the draft tube.
The changes in absolute velocity in the passage of water into and
through the turbine and draft tube are shown by line V, V^, Vj, V4,
VjI the height of the ordinates at these points shows the approxi-
mate absolute velocities at such points in the flow. The absolute
velocity is a maximum at or near the point where the water enters
the runner and is decreased as greatly as possible at the point of
its discharge into the draft tube. By gradually increasing the area
^ of the draft tube, an additional reduction in velocity is obtained,
the water finally issuing with a velocity Vg. The maximum veloc-
ity, measured by the ordinate Vg, is, in reaction wheels, consider-
ably below the spouting velocity (v^2gh).
In its flow through the wheel, the velocity of the water relative
to the bucket increases and becomes a maximum at the outlet of
the wheel. This increase in relative velocity is shown by the line
; v., v..
The energy transformation which takes place during the change
in velocity is illustrated by the ooited line marked "Energy trans-
[ formation" which begins at a maximum of 100 per cent, at the en-
f trance of the wheel ; is decreased by friction, leakage, shocks, etc.,
I by about 16 per cent, under full gate conditions. The energy is
! transformed into useful work in the wheel by the reaction at the
[ point of discharge and utilizes about 80 per cent, of such energy,
the remaining 4 per cent, being rejected in the discharge from the
draft tube with a slight recovery of velocity energy as before de-
scribed.
156. Turbine Relations. — In all water wheels the quantity of dis-
^arge, the power, speed, efficiency and effective head on the wheel
^re closely related and vary in accordance with certain definite laws
modified by the design of the turbine and the conditions under
3Z2
Hydraulics of the Turbine,
which it is operated. The conditions of operation must be adapted
to the type of machinery used, or the machinery must be selected In
accordance with the conditions under which it must operate, in or-
der that the best results may be attained.
If a jet or stream of water, with a velocity, v, acts on the movinf
surface of a motor bucket, this bucket, if the friction of the wheel is
negligible, may acquire a velocity essentially equal to that of the
jet, i. e., to the theoretical velocity due to the head. In actual prac-
tice the velocity of the bucket will always be less by the amoum oi
velocity lost in overcoming the friction of the wheel. The velocity
of the wheel here considered mtist be measured at the center of ajh
plication of the forces, i. e„ at the point of application of the result-
ant of all the forces of all the filaments of water that act on the
wheeL Under conditions where the resultant velocity of water and
bucket are the same, it is evident that the water will produce no
pressure cm the bucket and the motor can deliver no power* As
soon as resistance occurs, the speed of the wheel is reduced. Under
reduced speed the momentum of the jet, or the reactive pressure of
the water, according to the circumstances of design, is converted
into power. This impact or pressure increases as the speed or ve*
locity of the bucket decreases until the maximum impact or pres-
sure results with the bucket at rest, in which case also no work is
done. At some speedy therefore, between these extremes the maxi-
Turbine Relations.
323
aV3H lOOi N33X(ilHX (l3QNn H2MD6 aSMOH
324 Hydraulics of the Turbine, ^^^H
mum amount of work, from a given motor, will be obtained. That
is to say, — at a certain fixed speed the maximum w^ork and the maxi-
mum efficiency of a given wheel will be obtained, and at any speed
below or above this speed, the po%ver and efficiency of the whd
will be reduced. These conditions vary considerably according 10
the type and design of the wheel considered and also according to
the gate opening at which the wheel may be operated.
The efficiency curves of a 48" Victor turbine, under a thirteen
foot head and under various conditions of gate, arc shown in Fig,
211. Fig- 212 shows the i^-power curve of the same wheel under
the same conditions of head and gates.
157* Relation of Turbine Speed to Diameter and Head.— Tlie
velocity of the periphery of the impeller or buckets of a wheel is
not necessarily and in fact is not usually the same as the velocity oi
the point of application of the resultant of the forces applied to tlie
wheel. This point may be at some considerable distance within the
wheel and at a point not easily determined. This point of applica-
tion of the resultant forces may vary in position with the gate open-
ing. The peripheral diameter is fixed and is therefore more conve-
nient for consideration than the point of application of the forces.
The peripheral diameter^ or the catalogued diameter, is therefore
used in the discussion of the general subject. Many w^hecls var}^ in
diameter at various points on the periphery (see Fig, 174), and thertJ
is no uniform practice among manufacturers in designating such fr
ameters so that the diameters used in the following discussion ami
the functions based thereon are in accordance with the practice oi
each maker and arc therefore not strictly comparative. In this dis-
cussion the laws discussed are equally true if based on any actual
diameter or any simple function of the same. The diameter chosen
simply influences the magfnitude of the derived function and not tk
character. The discussion holds therefore in each case regardless of
the method of measurement except for the purpose of comparison*
between wheels of various makers in which case similar diameters
must be used.
In reaction wheels^ the buckets extend from the periphery of the
wheel to a point quite near the axis of revolution (see Fig. ij8,
Diagram I). In such wheels the resultant of the forces applied falls
a considerable distance within the circumference of the wheel. In
such wheels the peripheral velocity may exceed the velocity of the
jet acting on the wheel. In impulse wheels (see Fig. 129, Diagram
E) the buckets are small in comparison to the wheel diameter and
i
Relation of Speed to Diameter and Head. 325
are located at the periphery ; hence, in this class of wheels, the re-
sultant of the forces applied lies at or near the periphery, and the
peripheral velocity will be less than that of the jet acting on the
wheel.
Taking the velocity of the periphery of the wheel as a function
of the velocity due to head, the relations may be expressed by the
formula:
(19) v' = *p}/2gh ^^^™ which
V' _ v^
(20) fp =
>^2gh
The velocity of the periphery of the impeller may be expressed
by the following formula :
/2i\ V D ir n _ 8.1416 D n
^^' ^ ~ 12 ± 60 "" 720
Combining equations (20) and (21) it follows that:
,^v 3.1416 Dn ^ . ^Dn
(22) ^= 720 X 8.025 /r = '^^^ VK
From this may also be written:
(2R) n = y ^^ = 1841.6 (p Vh'
^ ' .000543 D D
As equation (22) is general, it follows that when <p is constant:
Dn
(24) . —7^ = 1841.6 ^ = A is constant.
If h=i, this will reduce to:
(25) D nj = 1841.6 <?> = A
The catalogue speed, power and discharge of each series of
vheels, as given in the catalogues of manufacturers, are usually
>ased on the conditions of maximum efficiency and constant ^.
From the above considerations it follows that in any homogen-
ous series of wheels, that is in any series of wheels constructed on
niform lines and with dimensions proportional, the wheels of the
erics are designed to run at the same relative velocity, and there-
>re
326
Hydraulics of the Turbine*
That is to say: In any hmriogeneous series of turbines the pr^
diici of the ddameter of any wheel D, (md the number of revohiim^
n, divided by VjT ^ill be a constant A provided <^ rsmaim comiani.
In investigating the values of A and ^ for various makes of
wheels, as expressed by the data in the manufacturers* catalogues,
it is found that these values vary somewhat for different wheels o(
a series but are usually practically constant. It will be noted,
however, from the efficiency speed curve, shown in Fig, 211, and
the ^ power curve, shown in Fig, 212, that the speed, and ccmse-
quently the values of <^ and A , may vary somewhat without materi-
ally affecting the efficiency or power of the wheel*
It should also be noted from Figs. 211 and 212 that if it is dt
sired to secure the greatest efficiency and power at part gatet the
values of 0 and A for a given wheel must be reduced* Table
XXVI gives the values of A and it for various American wheels,
calculated from the catalogues of the manufacturers.
TABLE XXVI.
ShcwiTig Belation of Diameter and Speed of VariouM Amm<:^n Tu,H>inuworkvf^
under Qatalogtie Conditions.
D n V'
Vh
i
A = -?T=
V=-= .000543^
i
Manufactiurer.
Eeaetion Wheda.
X a Aloott & Son. ,
Alex&ndefi Brmdley d
Dunninjf
AmericftD Steel Dredge
Works-,..
•Camden Water Wheel
Workfl. ....,.,-....
Cbate Turbine Mfg, Co,
ChristUna Machine
Co..
Name of Wheel,
Alcott'a Standard
High Duty ,
AleoiVg Special High
Doty..
Syracuie Turbine..-.
Liitle Giant ,
United Stfttee Turbine
*Ch ase * J on val Tiir -
bine (regutar).^.
*Ch aae - J on val Tur-
bine (ipecial)
Balanced Gate Tut-
bine
Min. Ma^*
Min,
1210
1254
.658
1211
1253
.658
1203
1226
.664
1235
14§2
.071
1S72
1588
,745
1612
1907
.876
1840
2337
.099
1220
12d8
.663
•NoTK.— Wide Tarbtioo lo consUtiU due to the detfgfi beln|r
(•ertCA not exactly boma^Qeoui}.
.68! j
.633
M
i.su
■peoiil ftEir ?artoi» ilwd vbick
J
Relation of Speed to Diameter and Head.
327
TABLE XXVI— Continued
SeUxHon of Diameter and Speed of Variotu American Turbines working
under Catalogue Conditions.
v' D n
<p = l-=. 000543 -7==
V Vh
afacturer.
Name of Wheel.
Min. Max
Min.
Max.
^ Wheel— Coiu
dgway A Son
dgway A Son
!}lobe Iron
Co
LB. Dix.
) Turbine A
MUlCo
) Turbine A
Mill Co
t Machine Co
-ey Machine
Hani Ma-
Co
need; Sons Co.
efieldb Co..
Bros. Co.
Doable Perfection . . .
Standard
American Turbine...
fNew American Tur-
bine (high head
type)
Improved New Amer-
ican
Special New American
Improved Jonval Tur
bine
Flenniken Turbine..
McCormick'B Holyoke
Turbine
Hercules Turbine..
JIXL Turbine...
tXLCR Turbine.
McCormick Holyoke
Turbine
Hunt McCormick Tur-
bine.
New Pattern Hunt
Turbine
Standard Wheel, 1887
Pattern
Crocker Wheel —
Samson Water Wheel
Improved Samson. .
Standard
Special
Phoenix ''Little
Giant"
1186
1200
1218
1064
16:^2
1284
1474
1511
1196
1160
1198
1196
1169
1158
1163
1200
1208
1543
1578
1330
1380
1001
1250
1275
1295
1077
1738
1340
1617
1533
1296
1170
1209
1206
1278
1272
1415
1291
1292
1554
1632
1339
1434
1020
.644
.652
.662
.578
.886
.697
.800
.821
.650
.630
.652
.652
.630
.629
.632
.651
.657
.838
.856
.722
.750
.544
.679
.704
.585
.944
.727
.880
.704
.636
.657
.666
.694
.691
.768
.701
.702
.844
.886
.727
.779
.654
nie reoommendf a maximum and minimum speed. Constants glTen are for the arer.
baaed od full theoretical power of the water. Wheels are said to giwe from 75 per cent
Mit effldeDcy, depending on location.
3^8
Hydraulics of the Turbine.
TABLE XXVL^Continued.
Showing Eelution of Diameter and Speed of Various American Turbintt
tcorkmg under Catalogue Conditionsu,
g> —
= .000543 ^^
Mantifactarer.
Beuction Wittel—Con.
Nonish, Burn ham &
Qo,,.
Plait Iron Works Co,
Poole Engineering ^
Machine Co^
T. H- HiadojKfeCo.,.
8. Morgan Smith Co*
Trump Mfg. Co.,
Wellman^ iSeaverj
Morgan Co
ImpitlBe WheeU.
DeKemer Water
Wheel Co
Abner Dable Co
Pelton Water Wheel
Co.,
Plfltl Iron Worka Co,.
The Riadon Iron Wks
Name of Wlieel.
Victor Register Gate
Victor Standard CyJ-
iTider Gat«^ .«..*.
Poole- Leffel
RiFdon Standard * , ,
Riadon Turbine Tvpe
T, C. ,
Riadon Turbine Type
a C..*.-.
Smjth-McCorraick »
Smith
Standard Trump. - *
McCormick..
DeRetuer Water
Wheel .,.
Tangential Wheel . * .
Tangen ti II I Wheel.,
Victor High Press u re
Tangential Wheel ....
Min.
1213
1181
1380
1341
1213
12X3
1213
11 «0
1656
1320
1212
962
a41
912
915
917
Ma3£,
1233
mi
1410
1380
1420
1420
1420
1344
1679
1380
1260
1001
S4S
919
9
Mill.
,659
.ti41
.749
-72S
.659
.659
.(HI
.898
.716
.658
,522
.456
,495
.497
.49^
Mil.
.670
M
J65
.74&
.77t
,730
.911
.74ft
I
.S4^
.499
i
From equation (26) may be derived
^1^1 /h"
From this equation the economical speed or correct number of
revolutions n for any wheel of diameter D» at any head, vX, cao
be obtained if the revolutions n^ of any other wheel of the series
at head h^ and of diameter Dj is known-
Relations of 0 and Efficiency. 329
If in equation {2'j), D=Di, the equation reduces to
That is to say r The ecciiomical speed of any wheel will he in direct
proportion to the square root of the head uii\der which it acts.
If in the equation (28), n — 1, the equation reduces to
(39) n = nii/h
From which it follows that the revolutions of a wheel (n) for any
head, h, is equal to the evolutions nj for one foot head multiplied
by^hT
158. Graphical Expression of Speed Relations. — ^The relation
expressed by equations 18 to 2^^ inclusive, between the values of v,
<^, D, n, and h, are graphically shown by Fig. 213. The theoretical
relations between V and h, and <^ as expressed by equatio'n (19)
when ^=1, are represented by the upper curved line in the diagram
referred to ordinates and abcissas. The relation between ^, v and h,
where 4> has a fractional value or is less than 100 per cent., as is the
case for all wheels working under practical conditions, is shown by
reference to the curved lines below ; the fractional value of ^ as rep-
resented by each line is given thereon. The relations between v, D
and n are shown by the relations of the straight lines originating
near the lower right-hand corner of the diagram referred ta ordi-
nates and abcissas, and the mutual relations of all lines on the dia-
grams show the mutual relations between the various factors that
are here considered.
159. Relations of (^ and Efficiency. — In any turbine running
under different heads but otherwise under the same physical condi-
tions as to gate opening, setting, draft tubes, etc., the efficiency will
remain constant provided the ratio of the velocity of rotation to the
theoretical spouting velocity of the water under the given head
remains the same. This is to say, — the efficiency of a wheel will
remain cottistant under various conditions of head as long as the
value of <^ remains constant. This law is well demonstrated by ex-
periments made on a 12^^ Morgan-Smith wheel at the Hydraulic
Laboratory of the University of Wisconsin.* These experiments
were made under seven different heads varying from about 7.10 feet
to about 4.25 feet. The results of all these experiments have been
*"Te8t of a Twelye-Inch McOormick Turbine/' an unpublished thoBis by
O. W. IClddleton and J. C. Whelan.
20
330
Hydraulics of the Turbin*^,
ttiAe ii peer
I
REVOLUTlDltS PER MtNUTE
Fis 213. — Speed Relations of the Turbloeei.
Relations of 0 and Efficiency.
331
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 I.I
VALUES OF (t)
Fig. 214. — ^Efficiency— ^ Curve of a 12 "Smith-McCormick Turbine.
332
Hydraulics ol the Turbine*
platted in a single diagram (see Fig. 214) from which it will be
noted that all experiments are fairly cloee to the mean curve; that
the variation therefrom is probably due to experimental errors
(principally, it is believed, in the determmation of the relative
velocities) and that reduction in head shows no uniform decrease
in efficiency. The experiments referred to, which are soon to ht
published in a University bulletin, show that this law is true under
all conditions of gate as well as for the full gate conditions, illus-
trated in Fig, 214* Hence the conclusion may be drawn that the
efficiency of a wheel will remain essentially constant if <^ remains
constant at least under moderate changes in head.
160. Discharge of a Turbine at Fixed Gate Opening. — ^The dis-
charge of a turbine with fixed gate opening, but at various speeds,
is not always the same but varies within certain limits and as the
speed varies. In some cases the discharge of a wheel increases as
the speed increases. (See discharge of Tremont turbine, Fig* 215.}
Sometimes the discharge decreases as the speed increases (sec disr_
charge of Victor and McCormick turbines. Fig. 215), and some
times the discharge increases with the speed to a certain point ani
then decreases with a further increase in the speed (see discharges
Samson and New American wheels. Fig, 2I5<)
In reaction turbines the discharge takes place first through the
guide from which it passes into and through the buckets of the:
wheel The relations of these two sets of orifices change as thij
speed of the wheel changes and affects the total discharge. If i^4
ing such changes of speed, the ratio, i^= — , remains constant,*^
is found by experiment that the conditions remain similar to thos-^
of any short tube or orifice. The discharge of a turbine may then
fore be determined by the formula ;
(30) q = i^Vlgh
And it may be stated: In a given turbine with Hxed gate opi^
the discharge nnU be proportional to the square root of the
I. e., the dischaff^e ditnded by ■/JT is constant
The values of C and a vary with the opening of the gate orpt<
but for any one position are essentially constant.
Let the discharge of a wheel under fixed gate conditions andwitS
a given head, h,j be given by the formula;
(3i: q, = Ca/2gh7
k
Discharge of a Turbine at Fixed Gate Opening.
333
The discharge o£ any other head will be proportional to vT" and
therefore
(32)
hence
(33)
q =
qiVTT
or if hj = 1
(84) q = q,i/F
Therefore, it may be stated: In a given turbine with fixed gate
opening the discharge at any head h wiU be equal to the discharge at
one foot head multiplied by y/h.
That this law is essentially correct may be demonstrated by ex-
perimenL Fig. 216 shows the results from the series of tests on
the McCormick turbine, before mentioned, at full gate. Tljree sets
110
100
80
0
Sao
3
J
i
70
BO
SO
\
<
^
1
> \.
\
1
\
\
I
6
i
V
\
A- 4 8'' VICTOR CYLINDRICAL CATE
B-SS^'tURBINE LOWELL mass
!
I
U" ^^ llWIr
D- 4S''8AK
E-5|"M£(
ASON
;ORMICK W-l
l-MORBAN
2S
30 38 40 4S 5 0
0IBCHAII6E IN CUBIC FEET PER 8BC0N0 UNDER ONE FOOT HEAR
95
Fig. 215. — Full (3ate ^-Discharge Curves of Various Tarbinefl.
^m 334 Hydraulics of the Turbine* ■
^1 of experiments are platted with values of 4> equal to .35, ,65 and .90
^M and for heads from about 4.25 feet to 7.1 feet. Fig, 217 shows the
^M discharge of this turbine at various gate openings and under seven
^M different heads. For the purpose of this diagram the discharge*^
^m under each head have been reduced to the theoretical discharge at
^M one foot head by equation 34. It wHt be noted from both Fig, 2t6
^m and Fig. 217 that all experiments where i^ is the same lie close to
^1 the average line, and that the departures from this line are prob-
^M ably due to experimental errors. The results are sufficiently close,
^M however, to demonstrate that the discharge under practical condi-
^B tions essentially follows the law above expressed. j
y
1 4
a
y
i
1
i
f
/
/
«
h
/
<
1
i
/
/
h
i
I
/
/
/
f
u
/
/)
/
/
/
y
V
r
mL
fe>
1
/
A
r
)
1
/
A
y
%
J
Oa
'/
1
/
9^
r
I
.€^
^
^
1
0^^
^
'^
1
k
0
216
1 t 3 4 I i ? 1
DISGHAHCC IN CUBIC FZZT FCH SEtQNO
—The RelaUQQi of Head to Discharge of a 12 "Smitli M^Corml:
Turbine.
>^|
Discharge of a Turbine at Fixed Gate Opening.
335
i6i. Power of a Turbine. — ^The power which may be generated
by any wheel depends on the head a mailable, the quantity of water
which may be discharged through the wheel under the given head,
the relative speed at which it may be run, and the efficiency of
operation. Hence
(35)
p _ q w h e _ q he
560 "" 8.8
Combining equations (30) and (35) there results
(86 > p _ Caw l/2i h*e _ Cai/2g h^e
550
8.8
From equation (36) it is apparent that if C, e and a are constant
for any given turbine and fixed gate opening, and if the value of «f>
remains constant, the power of the turbine will be in direct propor-
tion to h*. consequently
1.1
07
i
s
%
\
( 1
*\l
^
fr*
^
\
^
V
^
>
53-
iJ
#
i"
a
t
\
t
^.
d
(
't i
v^
^
<l
#
«*\|
^^
■
Ns
*
;> '
•
K,
t».i
Lli
1
m
<
^*Y
1
L
Q 1.1
1
u"
tk 1
%
«
^r
[
>
^i
h
gM
Lt
(
1
•
■ 1
I
■
\a
M
(
Cfa
03
\
^
^
m
f
1 1
n
,
1
<
i
^
f
^'
ft
^
^
i
(
»
_1
' r
>
•
4
/
e,r
& 1
—
—
—
—
s
S\
i
iif-
3
g<i
u
iJ
^
LIl
__
1*1 1.0 a*i
FKT rai.NBOND UNOOI ONE FOVT HCAO
Tig. 217.— Helatlons of Velocity to Discharge for a 12* "Smith-McConnlbk"
Turbine at Various Gate OpeDlngs.
336
Hydraulics of the Turbine.
ir)
P P.
h» - hi
Equation (37) may be reduced to
P,hl
(88)
P =
hj
x^'rom which can be determined the power of a wheel at any given
head, provided its power at any other head is known.
In equation (38) if hi = i, there results
(39) P = Pih»
From which it may be stated : In a given turbine with a fixed gait
opening, the power that can be developed' at any head will be equal
to the power at one foot head multiplied by h^.
This law may also be demonstrated experimentally as will be
seen by reference to Fig. 218, in which is shown the theoretical
curve representing the relation between head and horse power of
the 12" McCormick turbine before mentioned. The turbine on
which these experiments were made was small and the heads were
Z 4
a
>
^
^
/
»
^
■
. ,_^
4^
^
<
y
m^ \
^
X
^
^
/
/
c
?r.
^
^
i^'
y
^
y^
\
/
/
y
y
^
y'
n
y
/
{<
[y
^
y
fl
t
/
/^
y
/
y
<<
r
/
vH
<;
y
/
y
C'
^
/
y/
^ — ^
u
^
/
r
/
r
ii
Q 1.0 a.o 9,0 ^
ACTUAL HORSE POWER OP WHEEL
Fig. 218.— Relations of a Power to Head tn a 12 "Smlth-McCormlck Turbine."
The Relation of Discharge to Diameter of a Turbine. 337
limited so that there is some variation from the theoretical curves
but the fact expressed by the general law is quite clearly shown.
162. The Relation of Discharge to the Diameter of a Turbine.
—In any homogeneous system of water wheels, the diameter, height
nd corresponding openings and passages are proportional and it
ollows that in such similar wheels similar areas are proportional to
ach other and to the squares of any lineal dimension. In such
vheels, therefore, the area a of the gate openings is proportional to
he square of the diameter of the wheel, and the equation may there-
ore be written :
(40) Oal/2i"= K D»
In this equation K is a constant to be determined by experiment.
Combining equations (40) and (30) there results
(41) q = KDVF
from which can be obtained, by transposition
(42)
D=4/ q
Equation (41) is not only theoretically but is also practically cor-
ect, as is shown by the data in Table XXVII, which is also graphi-
:ally represented in Fig. ^19. These data are taken from a paper
TABLE XXVII.
Discharge of thirteen water wheels of the same manufacture but of different di-
ameters, €u determined by actual tests, compared with value computed by the
formula:
q = K D* •? Id which h = 13, K = .0172
DISCHARGE.
No.
Diam-
eter in
inches.
Redaced
from actual
teste, Cu. ft.
per Sec.
Computed
(Mean
Curve) Cu.
ft. per Sec.
Variation
from Com-
puted Dis-
charge Cu.
ft. per Sec.
Per cent.
Variation
from Com-
puted Dis-
charge.
1
2...
3....
9
12
15
18
12
24
27
30
36
39
42
45
61
5.17
8.79
13.85
18.85
29.07
35.31
47.81
54.15
77.33
93.51
107.73
128.53
161.07
6.02
8.92
13.93
20.07
27.32
35.68
46.16
55.75
80.28
94.22
109.27
126.44
161.12
+ 0.16
-0.13
-0.08
-1.22
+ 1.76
-0.37
+ 2.65
-1.60
—2.95
—0.71
—1.54
+ 3.09
-0.05
+ 2.99
—1.46
-0.57
-6.08
+ 6.41
1 04
A
5....
6....
+5.87
—2 87
^■..
9....
lo "";•
-3.67
—0 75
ll : ;
— 1.41
12,
+ 3 10
13. . .
— o.o.s
338
Hydra uiics of ihe Turbine.
by A, W, Hunkin^, entitled "Notes on Water Power Equipment/'
in vol. 13, No, 4, of Jour. Asso. Eng. Soc, April, i894* In this tabic
are given the discharges of thirteen water wheels of various diam-
eters, the discharges of which were determined from actual tests.
DIQCHAIiar IN CUBIC FCCT Kfl SCCOND
55
1
S
S fi I
5 ;
3 C
0 « 4
3 0 C
^ 0 0 □ D
4
H
^
^s
vi
^
Sv^'^s^
°
^
°^
br-^
*'^a
?
Fig, 219. — Relations of Dlacharse to Dtameter in EeacUon TiLfblAt of tie
sama manufacture.
These results have been reduced to the common basis of the dis-
charge at 13 foot head. The computed discharges at 13 foot heati
on the basis of equation (41) are also given, as well as the percent-
age of variations of the actual from the theoretical discharges. The J
wheels were of the same make with inward and downward di*- m
charge. The departures or variations from the mean values, as d^
termined by calculation, are probably due both to imperfections l^
the construction of the wheel and to errors in making the tesEs.
They may be seen, however, to practically conform to the theoretT
cal deductions* The values of the coefficient K, as calculated froru ,
the tables contained in the catalogues of various manufacturers cf
American wheels, are given in Table XXVTII.
163, The Relation of Power to the Diameter of a Turbine.— Bf
substituting the value of q from equation (41) in equatioa
(SS) "-"'"'
there results
(4S) P =
i
aB
D»h*Ke
S.S
"(S)"-'
The Relation of Power to the Diameter of a Turbine. 339
TABLE XXVIII.
'mg Belatum of Diameter and Dieeharge of Varioiu American TurMnea
working under Catalogue Conditions,
_q
K =
D'l/F
M&nuiactuTer>
Name of Whe«l,
Min,
Max.
Meaetion Wh^el^
41eoUd 80a
odtr^ Bradley & Dunn
icmn Ste«l Dredge Wki.
en Water Wheel Works
Turbine Mfg. Co
iana 3Iachine Co. ... .
Bidgway & Son Co,. »
Eidgway 6l Son Co.. .
\n Globe Iron Worka O
fcS, B. Dix.
lue Turbine & BoUt*
[ Co ,
loe Turbine & Rolle
rco
}ke Machine Co. ....>.
>hrey Machine Co. . . .
ej Hunt Machine Co.
Jones ^ Sons Co.,
) Leffel (k Go.
on BroB. Co , .,
ih, Btimham A Co.
Iron Works Co*...
AlcoU'e Standard High Duty
AleoU'a Special High Duty .
*9yracuee Turbine - - .
^Little Giant...* «. ...i ....
United Slatea Turbine.
*Cba9e-Jonval Turbine ( reg-
ular).. p ,,.
•Chaee-Jonval Turbine
(apecial). .,.. .«. ..
Balanced Gate Turbine
Double PeriecUon
i?tandard ***,**
'American Turbine
New American (high head
^vpe)
Improved New A^leri(^an..
Speciitl New American
Improved Jonval Turbine..
Flenniken Turbine
MeCormickVfl Hoi yoke Tur-
bine. ,
Herculea Turbine
tlXL Turbine
fXLCR Turbine..*,
McCormick^B Holyoke Tur-
bine. ............... . * ,
* H u n t- McCorm iek Tn rb i n e .
New Pattern Hunt Turbine.
Standard Wheel, 1387 pat-
tern
Crocker Wheel
Samaon ,,,,.,
Improved Saoison.
Standard
Special ..*..., ...
iPboenix "Little Giant". ..
Victor Register Gate.
Victor Standard Cvlinder
Gate .'
.00B54
.00860
,0157
.0168
0053S
,00622
0205
.orMO
02U
.0229
0064*3
♦00913
OID&O
.01346
00902
.00052
,0116
.0142
006S6
.0005^
00543
.00801
00509
.00644
0233
.0263
0175
.ti205
00454
.00546
00052
.01^
0184
.0191
0162
.0176
00361
.0053&
00645
.00063
01877
.01929
01913
.02867
01297
.01643
OIS.'J
.OHI
0175
Min
0170
,0171
022
.022
O116I2
.00fi4a
,00ft37
.00966
00924
.0172
.00917
.00955.
.0107
.0186
.0222
.0327
340
Hydraulics of the Turbine-
TABLE XXVIIL— Continued,
Showing Bdaiion of Diameter and Discharge of Various American TvrMfut
toorking under Catalogue Condiiiona,
Name of Wheel.
K
aiannfactnrer.
Min.
Mu.
Beactitm Wiieels. — Cod,
PcK>le Kngineering and Ma-
chine Co ..,,,- ^ ^ «,. 4 ♦ . . .
Poole- Leffel .*•-,,,,.
*Risdon i^iandard Turbine* *
*Rifl(lon Type T. C Turbiae
♦Risdon Type D. C, Turbine
*Smith-McCormick
Smith ..>>..*
.00625
.00501
.00753
,0100
,0187
.0247
.0210
.01&&
.000185
,mxx*75
.00010
.0017
,000184
1
.OQ6S7
T H* Riadon & Co
.00398
S. Morgan Smith Go , . ^
.01S2
.0238
.0256
Trump Mfjf, Co.
MiJiTid*Lwl Tmirm^ ^ - . « ^
.021)3
Wei Im fin, Seaver^ Morgan Co.
Impulse Wheels*
D^Eeme^ Water Wheel Co. .
Abner Doble Co .,.*.,.
McCormick
♦DeRemer Water Wheel. , . ,
^Tangential Wheel
.om
.00017S
000 Hi
Pelton Water Wheel Co. . - - .
*Tangential Wheel . . ,
.000136
Piatt Iron Works i_:o
HiBdon Iron Works ...*■.,..,
Victor HiRh Pressure
*TanK«ntial Wheel , .
,00247
.000175
*Wlrte varlmiioD tn oniniitaiaia ^ue to the d^aij^ btlng epecfAt for T^rioos alc^ whestH (ferim
n>i pxar^tly hotrioifeu#<iu«i,
tTaiiJes in caTAJo^ue bofad on fuU theoretical power of the wi(«r. Wheela are said lo fl*ft &tHn
7£ per cent to 90 per cent ifffleieDv7i depend Inf? on location.
|Mun»c>a Bros. Co, rnnke Mver&Jtypea of "LUte Qiaol** turhJn«« c&tufaff t,borit wide tafi»ttDQ li
^ ^nstftjilfi.
Asf --^1 is constant for a given wheel, as lon^ as ^ is constant,
thj.s expression may be represented by a constant IQ which may
be derived independently for each make of wheel, or may be deter-
mined from the equation
r («)
With this
substitution
(43)
becomes
(45)
P =
= K,D«h*
IL Til at is to say: With zv It eels of homogeneous design, the pawif of
H any uheel under the given head is in direct proportion to the sqmre
H of its diameter. This law ts both theoretically and practically cor
H rect, as demonstrated by Table XXIX, and Fig. 220, taken from tlie
H pnper by Mr, H unking to which reference has previously been
Relation of Speed to Discharge of Turbine.
34^
TABLE XXIX
Rone Power of ihiriem water wkeeh of the mme manufactitre hut of diferent
diameiers, as determined 6y actiuil te^tif compared with values determined
by thjs formula:
P=K, D'
K, ^.00158
HORSE POWER
h = 13
Ha
teriu
inches.
FromTeatfl.
Computed.
VarUtioti
from Com-
puted H. P.
inH.P,
Variation
from Com-
pated H. P.
Percent.
1 .,.„..*.
2
9
12
15
18
21
24
27 ,
30
36
39
42
45
51
aio
10.41
16.49
22.89
S3. 71
41.53
66.67
63.69
97.45
109.98
133.09
15:1,82
190.28
6.00
10.67
16.67
24.00
32.67
42.67
54.07
66.68
96.a)
112,68
130.69
150.02
192.69
+ 0.10 ,
^-0.26
--0.18
-1.11
+ 1.04
—1.14
+ 2.60
—2.90
+ 1.45
-2.70
+ 2.40
+ 3.80
+8.59
+ 1.67
—2.44
4 1
—1.08
-4-62
5,,
+ 3.18
e.. .*,..--..
-2.67
7
+ 4.81
8
-4.48
9 ,.
+ 1.50
10..,.. ,.
—2.40
u .,
+ 1.84
12
+ 2,53
13
+ L86
t
n
3 C
HOMk. MWCn
isssiiiissi
o
*
2 °
\
^.
K
h
"^^
"W '^j'
X o
9 *■
*Vk^<
^
f^
^''0 *,
i
"•"--Is
^
£!^
vja
_^Flg. 2:0. — Relation of Power to Diameter in Reaction Turbines ot tbe same
■ manufacture.
H 3^2 Hydraulics of the Turbine, ^^^^H
H made. This table and figure illustrate the relation between the the-
H oretkal power, as determined by equation (45), and the actual horse
H power of thirteen wheels of the same manufacture but different
H diameters, as determined by actual tests.
H The values of the constant K^ for the most efficient relation of
H power to diameter in various American turbines, as calculated from
H the iables contained in the catalogues of various American manii-
H facturers of turbines, are given in Table XXX, The values of K,
H and other turbine constants will be found to vary widely in the
H various types of turbines, not only of different manufacturers bur
H of the same manufacturer. Tlie interpretation of this fact is not
H that one turbine is, in the abstract and according to the relatii^T
H value of the constants, more valuable than another, but that each
H turbine is best fitted for a particular range of conditions for whicb
H it was presumably designed,
■ TABLE XXX.
H Showing Bdation of Power and Diameter of Various American TurMn€$ Work
^M ing under Catalogue Conditions^
D» h*
1
^p Manufacturer.
Kame of Wheel.
K,
Min,
Mai.
K Reaction Wheela.
H T. C. Ale ott & Soil .*»,.
Alcott's Standard High Duty
Alcott's Special High Duty.
Syracu^^a Turbine<*«* •« ....
.0005S9
.00141
.000483
.oaiQO
,00190
.000590
.000932
.OCtOBOO
.00113
.00053S
.0004S4 !
.000422
.00212
,00158
.000447
.000506
.00167
.mm
.00155
.mm
,003St
.00:20:
,OO0M
.001150
,00150
,00088
.omB
,00GS8*
.0024*
.00187
.000652
.oooiie
00173 M
^ Alexatidefp Bradley & Dunn-
American Ste^l Dredge Wki,
Camden Water Wheel Worki
Cbaae Turbine Mfg. Ck». . . . . .
ChriitianH Machine Co. . . . . ,
Craig, Hidgway ^k Son Go
Craig, Ridgway & Son Co*. . .
Dayton Globe Iron Works Co.
J L AS B Dix *.
Little Gmnt.
United States Turbine
*Chase-Jonval Turbine (reg-
ular) ..,..-.,,,.^
*Che«e- Jo n va i Tu rbi ne
(ppeclal) .,....,..
Balanced Gate Turbine. * . , .
Double Perfection ..,.,,*,,.
Standard ,.., .. ..,, »
* American Turbine ....♦*.,
*New American ( high head
type), ,*,,,.,......,,,,..
Improved New American,,,
*Sp&cial New Amerii-an .....
Improved Jonvai Turbine*.
Flenniken Turbine • «■■■«• *
Dubuque Turbine Je Roller
Mill Co.... ..-, .^
Dubuque Turbine *& Roller'
Mili Go .1
McCormick*s Hoi yoke Tur-i
bine I • ^•,, ,i*.>>«*4<
m
The Relation of Power to the Diameter of a Turbine. 343
TABLE XXX.— Continued.
Showing Mdatitm of Power and Dianveter af Varwus American Turbinet Work*
ing under Catalogue Conditions,
K. =
D* h5
Manufacturer.
H&tne of Wheel.
I^eaction Wheel— Con,
Hoi yoke Machine Co.
Humphrey Machitie Co. . .
Rodney Btmt Macbioe Co. . .
E. D. Jonei A 0otii Co.
James Leifel & Co
Muti£on Btob, Co
Norrisb, Bumham &Co.
Piitt IfOD Worka Co
Foole Engineering and Ma-
chine Cix — *.,,,,
r H, RifidonitCo
S. Morgan Smith Co.
The Tranrip Mfg. Co
Wellmanj Seaver^ Morgan Co
ImpuUe WheeU
DeRemer Water Wheel Co
Abner Doble Co
Pehon Water Wheel Co. . .
Piatt Iron Worka Co *.
Riidon Iron Works Co. . . .
Hercales Turbine
tlXL Turbine »»*••»«.
tXLCR Turbine
McCormick Hoi yoke Tur-
bine^. , '.
*Hunl McCormick Turbine.
New Pattern Hunt Turbine
Standard Wheel, 1S87 Pat
tern ,.
Crocker Wheel
Improved Samion,
Standard ,-,>>..
HDCcial .<<*
tPboenii'*'*LiUle Giunt'* . * '
Victor Keeister Gate
Victor Standard Cylinder
Gate
PooIe-LeEfel
*Rl9don Standard Turbine.
•Rifidon Tvp© T. C Turbine
♦Risdon TVpe D. C. Turbine
Smith -McCormick *•*.,*<
Smith ..,,.,,,.
Standard Trump,
McCormick..
*DeRemer Water WheeL . .
♦Tangential Wheel , *
*Tan^ritial Wheel ,
Victor High Preeeure. ,.,,,»
•Tangential Wheel
K,
Mm, Max,
.00147
.000397
.000730
.00109
.00173
.00120
.00101
,00159
.00158
.00201
.00056
,000897
.000842
.000852
.00158
.00205
.000026
.000485
,000672
.000781
.00169
.00232
.00191
,00168
.000124
.0000065
,0000095
.000154
.0000128
.00159
.000620
.ooiaio
.00173
.00260
.00146
,00122
,00163
,00159
,00202
.Oft^S
.000920
.001560
,000885
,0017a
,00206
.000650
.000675
.000913
.00135
.00217
.00236
.00241
.00171
,000186
.0000107
.0000130
.000523
.0000165
*Wtde T»rliLtlo«i In tsofoaJtmnU dti« to the deslfrn beln^ ipeclml far TarJoua mizod wheels (aerie* not
rxmeG.1v hDmosviieoi.t*i.
tT&bl«!« bM«d on full theoretical power of the wAter, Wheals mre said ta kItb froDi 7D per eeiit
to m per cent «ffioieQcy, depend ja? od JocaUod.
tlf uaimii Bro«. CCk tn&ke KTerai iypm of "Util» Gluit" turbf see, OttUiLog: ftbore wide variation
in t
344
n
CM
UJ
01
m
r
n
CM
^
Hydraulics of the Turbinep
ID kn
TO CM —
S^HQNJ m 123KM iO tilXinVIG
Relation of Speed to Discharge of Turbine. 345
c power of a wheel varies directly with the value of Kj, this
t is a direct measure of comparative power and indicates
tive power that can be developed by various types of wheels
liameter and under a given head. The range of values for
3und in American practice is shown graphically in Fig. 221
he power of turbines of various diameter and types under
t head is given. The power of a wheel varies under differ-
ds as h', and therefore the power at any head can be de-
d directly by multiplying the readings of the graphical table
For example, from Fig. 221 it will be seen that various
E 40" American wheels, under one foot head, will give from
. H. P. and at 16 foot head they will therefore develop 64
le H. P. at one foot head or from 48 to 256 H. P. within
ange a choice must be made.
Rdatiocis of Speed to Discharge of Turbines.— As the speed
rheels of the same series must be proportional to Vh, the
1 may be written :
v/ = K. /F
[lich and from equations (19) and (21)
equations (42) and (47) may be derived
„_12x60K,l/K "^
e first term of the last expression is constant, there may be
^ 12X60 Ka VK
K. = .
hich equation (48) may be re-written.
head of one foot, b=si, equation (50) becomes
ion (50) may be rearranged to read :
Vh
21
^•=*»/*"^S
346
Hydraulics of the Turbine*
TABLE XXXL
Showing Relation of 5p^erf and IHmharge of Various Ammican T^^m
Working under Catalogite CondUion^
Mftnufactnrer.
Fame of WheeL
£.
Mid.
Ecaction Wheeh.
T. a AlcottA Son.
Alexander, Bradley A Dunn
ing..
American Steel Dredge Wrks.
Camden Water Whml Works
Chase Turbine M fg. Co . . > «
I
Cbnetiana Mscbine Co, . . « . .
CrtLig, Bidgway d Son Co.,. .
Gmig, Bid^way & Son Co
I)ty ton Globe Iron Works Go,
J. L. AS. B. Dii, ,..
Dabuque Turbine & Roller
MillOi...,.,
Dubuque Turbine A Roller
Mill Co.
Holyoke Machine Co.
Humphrey Macnine Co* .,
Rodney Htuit Machine Co.
E. D. Jones A Sons Co*
Jamee Leifel & C£iv>,...
Mnneon Bros. A Co. .. .
Norrieb^ Burn ham A Co.
Piatt Iron Works Co...,
Alcott'fl Standard High Duty
Aicott'a Special High Duly
* Syracuse Turbi ne
^Little (iiant i , .
United States Turbine* ****
*Chaae-Jonval Turbine (reg-
ular)
*Chage-JDnval Turbine
(special). .
Balanced Gate Turbine. * ,
Donble Perfection, ^ .
Htandard
* American Turbine ......
tNew American (high bead
type) *^.<.
Improved New American.*,
Special New American* . » ♦ .
Improved Jonval Turbine, .
F^enniken Turbine.
McCormick'fl Holyoke Tur-
bine * .- • -
HerctileB Turbine. . . . ^ . ^ ^
tlXL Turbine
JXLCK Turbine.
McCormick's Holyoke Tor*
bine
*Hunt McCormick Turbine
*New Pattern Hunt Turbine
Standard Wheel, 1^87 Pat-
tern .,
Cn)cker Wheel p
Samiiion Water Wheel****
Improved Sam peon,
Standard >* .**,
Special ♦ *
JtPhoenix *'Little Giant"
« f .. t « - > ^
Victor Eeiriater Gat-e
Victor Standard Cylinder
Gate * *
98. 8
154.5
89. S
17^.0
205. 2
140. 0
201.0
115.8
90.5
04.0
S3.0
75.4
265.0
170.5
84.0
122.0
162.0
14S,0
71.3
90.5
loSI.5
161 .4
132.4
126.0
161 .0
201.7
240.0
103.7
134/7
102.0
115.9
153.0
205.0
Mai.
mj
243.1
m>i
174.0
235.0
156.2
97.2
lOli
109.0
85.9
M*0
190.0
100 0
mo
17B.0
1M.(^
tl6,fl
ITfi.O
207,5
174,8
m.o
24 L3
JOT .ft
mi
132.1
1^.0
212.0
J
Relation of Speed to Power of Turbine.
347
TABLE XXXI.— Continued
howing Relation of Speed and Discharge of Various American Turbines
Working under Catalogue Conditions^
'* = "^i
Name of Wheel.
K4
Manufacturer.
Min.
Max.
Reaction Wheels,— Con.
*oole Engineering and Ma-
chine CJo •
Poole-Leffel
110.4
93.4
100.7
108.0
163.7
265.0
194.0
168.6
11.10
6.61
9.21
37.8
10.67
121.6
'. H. Risdon A Co
•Risdon Standard Turbine. .
*Risdon Type T. C. Turbine
♦Risdon Type D. C. Turbine
Smith-McCormick
117.2
w Monrain Smith Co t - -
137.3
158.0
185.0
Smith
266.0
*he Tmmu Mfflr. Co
Standard Trnmn
190.0
Wllman, Seaver, Morgan Co.
Impulse Wheels,
)eRemer Water Wheel Co. .
Lbner Ooble Co
McCormick ••
179.0
DeRemer Water Wheel
*Tanffential Wheel
13.20
9.20
^elton Water Wheel Co
Tangential Wheel
10.92
*latt Iron Works Co
Victor High Pressure
Tanirential Wheel
42.2
tii>don Iron Works
12.10
*Wide variation in constants due to the design being special for various sized wheels (series not
zsctlj homogeneous).
tCatakH?u« recommends a maximum and minimum speed. Constants given are for the arerage
peed.
(Tables in catalogue based on full theoretical power of the water. Wheels are said to give from
rs per cent to 90 per cent efficiency, depending on location.
^Munson Bros. Co. make several types of **Little Qiant** turbines causing above wide variation
in constants.
It is evident that K4 is constant for all turbines with constant K
and Kg ; also, for all turbines where q, the discharge, is equal at the
same speed, n, and under the same head, h, K^ must be constant for
different heads since n and q are proportional to V^- The values of
the constant K^ as calculated from the tables contained in the
catalogues of various American manufacturers are given in Table
XXXI.
164a. Relation of Speed to Power of Turbines. — From equation
(35) may be derived
(53)
q =
8.8 P
eh
348 Hydraulics of the Turbine,
From equation (48) may be derived
(54) K, i/K = 12 X ^ X i/h" ^ vT
Combining equations (53) and (54)
(66) K.V/K =^I2^n4/5
12 X GO^e h"
By transposing
(66)
K,Vk 12X60 /V = n i / L
As the first member of the equation is constant for any given
wheel, there may be written
(57) K, = ^^ ViJ J
and hence
(68) K. = I.' ^.
From equation (58) it will be noted that the value of K5 under a
given head is in direct proportion to the square of the velocity of
the wheel and to its power. Kg is termed the "specific speed" of the
wheel. A high value of Kg is an indication of high speed, and a
low value, of low speed.
The values of the constant Kg as calculated from the tables con-
tained in the catalogues of various manufacturers of American
wheels are given in Table XXXII.
Fig. 222 shows graphically the relation of power to speed under
one foot head, as expressed by the constant Kg within the range of
practice of American turbine builders.
The use of the diagram may be illustrated as follows : —
At 35 revolutions per minute various types of American wheels
will develop from i to 5.8 horse power. For the best efficiency,
that is for a constant value of <^, the number of revolutions ot a
wheel will vary as Vh, and the power will vary as h*. Thus foi
a 16 foot head these wheels will run four times as fast as for a on«
foot head or at 140 R. P. M., and will develop 64 times the power
that will be developed at a one foot head, or from 64 to 371 H. P^
between which limits the wheel must be chosen.
Suppose a wheel is desired to develop 500 H. P. at 150 R. P. M.
under 25 foot head. These conditions correspond to 4 H. P. at Jo
Relation of Speed to Power of Turbine.
349
3 4 s e r s I
MQflSC POWEH moeil DIK FOOT KCAD .
Jl
Fi£. 222.— Speed Curves of Various Standard American Wheels.
350
Hydraulics of the Turbine,
TABLE XXXII,
JShi^wing Relation Qf Speed and Pon>er o/' Various American Turbine*^
under Catalogue i and it ions.
K, = n*
b|
MAnufactnrer.
Name of Wheel,
K,
MitL Mw
Eeaction WhMU.
T. C Alcott &So]i^,,,,.>>..
Alexander, Bradley de Dunn
ing*,...
American Steel Dredge Wrke
Ganideji Water Wheel Works
Chase Turbine Mfg. Co
OhriHtiana Machine Cb... . * ,
Craig, Rid g way A Son Co.. , ,
Craig, Ridgway d Son Co.. . .
Dayton Globe Iron Worka Co.
J. L, &8.B.Dii.„.
Dubuque Turbine A Roller
Mill Co
Dubuque Turbine 6l Roller
MiirCo
Ho) yoke Machine Co** * *
Httmpbrey Machine Co.
Rodney Hunt Machine Co.
E. D. Jones A Song Co,
Janiea Leffel & Co-« . .. .
Miuieoii Bros. A Co
Norriab, Burnham & Co*
Piatt iron WortiB Co. . . .
Alcotfa Standard High Duty
Alcoli'i ^^peciat High Duty.
Syracuse Turbine. »
*Little Giant. ............
United States Turbine
*Chase-Jonval Turbine (reg-
ular) ,,,,,.....,.,..,..*.
•CbaFe-Jonval Turbine
(epecial ) ,•-....
Balanced Gate Turbine. ...
Double Perfection, i •••.,♦..
Standard
* American Turbine. .......
fNew American (high head
t)T>e)..-
Improved New American
Special New American . . .
Improved Jonval Turbine
Fleimiken Turbine,
McCormick's Holyoke Tur-
bine ....•.<,,..*..,
Herctilea Turbi ne * « « , < . * t * .
JIXL Turbine
tXLCR Turbine
McOormick*! Uolyoke Tur^
bine
*Hunt McCormick Turbine.
*New Pattern Hunt Turbine
•i^tandard Wheel » lti8T Pat-
tern , ,
Crocker W heel • . . • . « • . .
f^amson ^ .
Improved 8ameoQ
Standard..
tfpboenii' '^Littfe dfant"
Victor Regisier Gate
Victor Standard Cylinder
Gate \.,,
Victor High PreBSure* . . . *
941
2152
723
2880
3780
1680
S4riO
1220
840
77fi
623
520
6100
2490
1360
2S80
2030
572
1052
2310
2360
1624
1666
2360
H775
5013
948
17:^
843
li:w
2254
37.S3
129,10
1216
m
la
m
flf75
im
674
m:
isao
^9
m
1^
MO
31110
2W0
2180
26110
5400
lOfiS
1^^
IfiOO
im
2712
m
Relation of Speed to Power of Turbine. 351 ^^B
TABLE XXXII.— Coniintied. ^^B
Showing Edatvm of Speed arid Power of Various AmeHcan TurbintM t^orking ^^B
under Cataiogtte Conditions. ^^H
Manufacturer,
Kanie of Wheel.
I
Min.
Max. 1
Reaction Wheels.— Con.
^■tjol© EngioeeriDjr and Ma-
ehinaCo.*...
r> H- Risdon & Co. . , , -,
Poole^LeffeL «.«••>*.*
1170
2350
3520
4690
2640
6165
3307
23B0
12.34
4,00
7.84
3.24
1239 m
3680 m
5070 ^
7370
3013
6640
42d0
13.01
7.62
11.42
11.22
*Bi§don Standard Turbine. .
*Ri^on Type T. C Turbine
♦Risilon Type D. C. Turbine
Smith McCormick , ,
8* Mofv&n Smith Co. --.***..
Hie Tramp Mfg. Co
Well mail, Seaver, Morgan Co.
Impulse Whe^s.
DeReioer Water Wheel Co,.
Abnef Doble Co ........«..>.
Smith ,*B>4»«**»****.
Standard Truint* , ,
McCormick • • . - -
•DeRemer Water Wheel. . . .
*TttnizentiaJ Wlieel ...,.,...
Pelton Water AVheel Co
Risdon Iron Works ...,.,, .
*TanEential Wheel , . . , .
*Tanirential Wheel
•Wide TariatioQ in coiutaaU due u> the design belnR speclaL ior various iilxed wheeli 4 series not
tCat&loKui: recoiuiueDclB a maxim um and inlnimuin speed. Conitatita given am for ibe averagii
iTabJpft In c»tftJf?gne bfti#d m ftjll th'-oretic*! powtr of tli« water, WtieeU are said to glTe from
75 j»r qi*nt to MJ per cerat ert\t:lenc,v, tit| wilding on Jocaaon,
]^MuQ«on Broft, C^ make several typeb oF "LltUe Giant" turbines cauaEnjc aboni wide rartaUon
in coetsi&nta.
R, P, M. under one foot head, and would require a wheel having a
constant Kg = 3600.
165, Value of Turbine Constants. — The values of the constants
discussed in this chapter have been determined froni the cata-
logues of the manufacturers of American turbines and are the %'alues
which may be used for determining the manufacturer's standard re-
lations of the wheel for particular and fixed conditions where <^ is
constant, as, for example, the development of a certain power under
a fixed head and with a given speed. When the head varies at dif*
ferent times, the value of ^ also varies and the value of the other co-
efficients of the turbine, A, K, K3, K4, and K^, will also vary. In
order to discuss such conditions the laws of the variations of these
constants, tor any series of wheels, must be known. Tliese laws
352 Hydraulics of the Turbine.
can be ascertained from a complete test of any one wheel of the
series and the laws so determined will hold for the entire series if
the series is actually constructed on homogeneous lines. Owing to
imperfections in the processes of manufacture, there is actually
more or less variation between diflFerent wheels of a series. It is
therefore desirable, when the approximate size of the wheel needed
is known, to secure a test of a wheel of that particular size and
hand.
Of the constants discussed, <l> and A express the standard rela-
tion recommended by the manufacturer between diameter and speed
in the series of wheels he offers. See equations
(23) n = ^^^^^^and
(24)
D = A1^
The coefficient K is the constant of discharge and shows the
standard relation for various types of turbines between the quantity
of water discharged and the diameter of the wheeL See equations
(41) q = K DVF and
(^> ^=1/^^
Kl/h
Kj IS the constant of power and shows the standard relation b^
tween the diameter of the wheel and the power. See equation
(45) P = K,D«h*
K^ is the constant of discharge and shows the standard r?lation
between speed and discharge. See equation
(50) n = K^\/^
q
Kg is the constant expressing the standard relation of power and
speed for a particular series of wheels. See equation.
(58) ^ = ^- 1?
The catalogue tables of turbines from which the standard values
of the constants in the preceding tables have been calculated arc
presumably based on the actual tests of certain wheels of the series.
The actual results of a test of any individual wheel of the series is
likely to depart to an extent from the tabular val*ue. Differences
Literature. 353
en be found between wheels of different diameters, between
of the same diameter but of opposite hand, and even between
of the same size and hand which are supposed to be con-
l on identical lines.
5 differences in results are due to carelessness in construe-
to unusually good construction in the effort to secure special
where the conditions warrant special effort. Any change in
gn of a wheel for the purpose of reducing or increasing the
rt, and hence reducing or increasing its power, will give
differences in these coefficients which must be taken into
in any calculations made thereon. A careful study of these
nts as determined from the actual tests of any wheel, to-
vith a study of the design of the wheel itself, will form the
a complete and systematic knowledge of water wheel de-
LITERATURB.
ann, Gustav. Die graphische Theorie der Turbinen and Kreisel-
pumpen. Verhaldung des Vereiues zur Befdrderung dee Gewerb-
feisses In Preussen. 1884, pp. 307-379; 521-580.
;, C. Graphic Turbine Tables. Showing relation of head and dis-
charge for various sizes of turbines. Zeitschr. d ver Deutsch.
Ing. p. 980. 1890.
Kig, H. Allgemeine Theorie der Turbinen. Berlin. L. Simon,
1890.
rds, John. Turbines Compared with Water Wheels. Eng. News.
Vol. 1, p. 530. 1892.
ing, A. W. Notes on Water Power Equipment Jour. Asso. Eng.
Soc. Vol. 13, p. 197. 1894.
ner, G. Die Hydraulik und die hydraulischen Motoren. Jena. 1895.
er, G. R. Hydraulic Motors, Turbines and Pressure Engines. New
York. Van Nostrand. 1895.
B, R. G. Hydraulic Machinery. New York. Spon & Chamberlain.
1897.
s, Charles N. Centrifugal Pumps, Turbines and Water Motors.
Manchester. Eng., Technical Pub. Co. 1898.
William. Graphics of Water Wheels. Stevens Indicator. Vol. 16,
p. 30. 1899.
T. Ernst A. Grundrlss der Turbinen Theorie. Lelpsig, S. Hirzel.
1899.
r, Gustav. Vorlesungen iiber Theorie der Turbinen mit vorbereiten-
den untersuchungen aus der technischen hydrauhk. Lelpsig.
Arthur Felix. 1899. .
u, A. Traits des turo-machines. Paris. Ch. Dunod. 1900.
354
Hydraulics of the Turbine,
14. Henrotte* X Turblnes-liydrauUques, pompea et TentUateurs, centrlfogsa.
prlnceps tlieoriaaeai disposltlona pratiques et calcul des dlrnen-
Eton 3. Liege, I m primer I e Ll^geoUe. 1900.
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Nostrand. 1900.
16, Wood, DeVolaon. Turblnea, Theoretical and PraeticaL New York, Wilef
& Sons. 1901.
17. MuIIer, Wllhelm. Die Fraacls-Turblnen. Hanover, Janecke. 1901
15. Kessler, Jos. Berecbaung and Konstruktion der Turblneu. Lelpslg. I
M. Gebhardt. 1902.
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tech. Jour. p. 693> 1902.
20. Tburao, Jo ha Wolf. Modern Turblaa Practice aad the Development ol
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21. Rea, Alex. Turbines and the Effective Utilisation of Water-P^Jwef,
Mech. Engr. March 22, 1902.
22. Osterlin, Hermann. Unteraucbungen flljer den Energleverlust des Wis-
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23. ThurBO, Jobn Wolf. Effect of Draft Tube. Eng, N«wa, Vol. 1, P^ 21
1903.
24. de Qraffiguy, HenrL Les Turbo*motenrs et lea Machines Rotative fu\A
E. Bernard. 1904.
25. Dlekl. Ignaz, Die Berechnung der achaialen Actionsturbinen aaf «icli'
nerlschem Wege- Vienna. Splelhagen 4t Schurlch. 1904.
26* Danckwerta. Die Grundlagen der TurbJnenberechujig fur Pratlker tndl
Studierende dea Bauingenieurf aches. Wiesbaden. C- W» ^l^§
del. 1904.
27. Thurso, John Wolf. Modem Turbine Practice. New York* Van Kfl*|
trand, 1905.
28. Church, Irving P. Hydraulic Motora. New York. Wiley & Sons. 1^3-
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30* Grafp Otto. Theorle, Berechnung und Konitruktion der Turbinen tsni
dereu Eegulatoren; ein Lehrbuch fur schule und pfSJi*'
Munich. August Lachner. 1904 and 1906.
31. Wagenbach. Wllhelm. Neuere Turbinenanlagen. Berlin. 1905.
32. Gelpke, Viktor. Turbines und Turbinenanlagen. Berlin. JuUW
Springer. 1906.
33. Pfarr, A. Die Turbinen fiir Wasserkraftbetrleb. Berlin. Julio*
Springer. 1907.
34. Tangential Water Wheel Buckets. The Engr. May 1, 1904,
36. Klngsford. R. T. A Complete Theory of Impulse Water Wheels ta^ J^
Application to Their Design. Eng. News. July 21. 189S.
J
CHAPTER XV.
TURBINE TESTING.
166. The Importance of Testing Machinery.— A correct theory
based on mathematical analysis forms a valuable foundation for
machine design. In the construction of any machine, however,
theoretical lines can seldom be followed in all details, and, even if
this were possible, the truth of the theory must be demonstrated
by actual trial for there are usually many factors involved which
cannot be theoretically considered and yet affect practical results.
In any machine much depends upon the character of the workman-
ship, on the class gf material used, and on all the details of manu-
facture, installation and operation as well as on design. All of
these matters can hardly be included in a theoretical consideration
of the subject, and it therefore becomes necessary to determine
the actual results attained by a trial of the machinery under work-
ing conditions.
General observations or even a detailed examination of any
machine and its operation can rarely be made sufficiently com-
plete to g^ve any accurate knowledge of the quantity or quality of
the results which it can and does accomplish. It is only when the
actual effect of slight changes in design can be accurately deter-
mined by careful experiment that a machine can be impro^ ed and
practical or approximate perfection attained.
The ease with which such determination can be made is usually
a criterion of the rapidity with which the improvements in the de-
sign and construction of a particular machine take place. Where
such determinations are readily made, rapid advancement results,
but where they are costly and require a considerable expenditure
of time or money, the resulting delays and expenses usually so
limit such determinations that good results are attained but slowly.
The invention of the steam engine indicator and the Pu-^ny brake
placed in the hands of the engineer instruments by means of which
he could readily determine the action of steam within the engine
cylinder and the actual power developed therefrom. The knowl-
edge thus gained has been one of the most potent factors in the
rapid advancement of steam engineering.
356
Turbine Testing,
H ine
The physical results of radical modifications or changes in de-
sign are sometimes quite different from those anticipated by the
designer. Impro\^ement in any machine means a departure bom
the tried field of experience and the adoption of new and untried
devices or arrangements. Frequently a line of reasoning, while
apparently rational^ is found to be in error on account of unfore*
seen conditions or contingencies and the resulta anticipated are
not borne out in the actual practical results. Unless, therefore,
such results are carefully and accurately determined by exact
methods the actual value of changes in design may never be knows
or appreciated and designs may be adopted which, while apparently
giving a more desirable form of construction, actually accomplish
less than the form from which the design has departed,
157, The Testing of Water Wheels.— The value of the testing ol
water wheels was recognized by Smeaton who- tested various
models of water wheels about the middle of the Eighteenth Century,
Methods of turbine testing were also devised with the first develop-
ment of the turbine, which have been potent factors in the improve-
ment of the turbine. While the methods of testing have been
greatly improved since that time, they have not as yet reached a
state that can be considered reasonably satisfactory, and turbine
testing has not become so general as to assure the high grade of
design and workmanship in their manufacture as in other machin-
ery where testing is more easily and regularly practiced*
The principal causes of the backward condition of turbine test- .
ing lie in the difficulties and expense of making an accurate test ]
in place, and the expense and unsatisfactory results of testing tur-
bines in a testing flume where the head and capacity are so limited
as to confine satisfactory tests to heads of 17 feet or less and toj
wheels of a capacity of about 250 cubic feet per second, or less M
the full head of 17 feet is to be maintained. There is an urgent
demand for accurate and economical methods for the measurement
of the water used and of the power developed by water wheels in !
place, that can be readily and quickly applied without the almost |
prohibitive expense of the construction of expensive weirs and
other apparatus now used for such purposes. Apparently slight
variations in turbine construction produce radical changes in prac-
tical re?>ults. The high results achieved under test by a well-
designed and well-constructed wheel is no assurance that wheels
of the same make and of the same design, even though they be t(
the same size and even from the same pattern, will give sim'uar
Smeaton's Experiments.
357
This IS especially true when the contingencies of compe-
id the knowledge that a test of the wheel is impossible, or
highly improbable, offer a premium on careless construe-
cheap work.
*f examination of the work already done in this line, and
lethods now in vog^e, may afford suggestions for future
ments and development in this important work.
meaton's Experiments. — John Smeaton, the most experi-
id eminent engineer of his time, made a series of experi-
n the power and effect of water used by means of various
water wheels for mill purposes. Accounts of these experi-
ere published in the Transactions of The Royal Society of
England in 1759. Until that
time the relative values of the
different types of water
wheels of that day were very
poorly understood and ap-
preciated.
Smeaton's apparatus for
measurement of the power
of" overshot and undershot
wheels is shown by Figs. 223
and 224 taken from **The
Encyclopedia of Civil En-
gineering" by Edward
Cressy. Water was pumped
by means of the hand pumps
from the tail basin, X, to the
supply cistern, V, from which
it was admitted to the wheel
through an adjustable gate.
The power developed was
measured by the time re-
quired to raise a known
weight through a known
height by means of a cord
through a system of pulleys and attached to a small wind-
I or collar upon the wheel shaft. This drum revolved only
r slight longitudinal movement, it was made to engage a
le shaft.
se experiments Smeaton found a maximum efficiency of
Bmeaton's Apparatus for Testing
Water Wheels.
35S
Turbine Testing.
32 per cenL, and a minimum efficiency of 28 per cent, for undershot
wheels. He also observed that the most efficient relations between
the peripheral velocity of the wheel and velocity of tlie water were
attained when the former was from 50 per cent, to 60 per cent of
the latter, and that the force that could be exerted by a wheel to
f
Fig 224.— Section of Smeatoii'B Apparalna for Testing Water Wbeeli
advantage was from 50 per cent, to 70 per cent, of ilie force re-
quired to maintain it in stationary equilibrium.
For overshot wheels Smeaton found that the efficiency varied
between 52 and 76 per cent* From his experiments he concluded
that the overshot wheel should be as large as possible, allowinf.
however, a sufficient fall to admit the water onto the wheel witli^
velocity slightly greater than that of the circumference of the
wheel itself, and that the best velocity of the circumference of th<
wheel was about three and one-half feet per second. This spc<
he found applied both to the largest as well as to the smallest
water wheel.
From these experiments Smeaton concluded that the power of
water applied directly through the exertion of its weight by gia^
ity, as with the overshot wheel, was more effective than when its
power was applied through its acquired momentum* as in tht
i
The Early Testing of Turbine Water Wheels. 359
-undershot wheel, although his line of reasoning indicated other-
-wise. The later development of impulse wheels shows that his
reasoning was correct, and that the low efficiency of the impulse
'wheel was due to the method of applying the momentum of the
iwater rather than to any inherent defect in the impulse principle.
The experiments or tests of Smeaton, while crude and imperfect
and performed upon wheels which were merely models, afforded
a comparative measurement of the efficiency of the undershot, over-
shot and breast wheels then in use and had a marked effect on the
further selection of such wheels.
169. The Early Testing of Turbine Water Wheels.— The testing
of turbine wheels began many years ago in France before the turb-
ine became well known in the United States.*
Foumeyron began the study of the early forms of turbines as
early as 1823, and, in 1827, he introduced his well-known wheel
and also brought into notice a method of systematic testing of the
same by means of the Prony brake.
"La Society d' Encouragement pour V Industrie Nationale" is
credited by Thurston with the introduction of a general system for
the comparison of wheels and correct methods of determining the
efficiency.** Other engineers immediately accepted this method of
comparison of wheels. Morin, in 1838, reported the results of a
trial of a Fourneyron wheel as giving an efficiency of 69 per cent,
with only slight changes in values for a wide range of speed. With
another wheel he obtained 75 per cent, efficiency.!
Combes tested his reaction wheel and found that an efficiency
<rf about 50 per cent could be obtained.!
The first systematic test of turbines in the United States was
made by Mr. Elwood Morris of Philadelphia in 1843 ^rid reported
in the Journal of The Franklin Institute for December of that year.
The maximum efficiency reported was 75 per cent. This result
was reached when the value of <l> for the interior circumference of
the Foumeyron turbine was .45. In 1844 Mr. James B. Francis
determined the power and efficiency of a high breast water wheel
• See "The Systematic Testing of Water Wheels In the United States," by
H. H. Thurston, Trans. Am. Soc. Mech. Eng. vol. 8.
♦♦ See "Memolre sur les Turbines Hydrauliques," by H. Foumeyron, Brus-
sels, 1840.
t See "Experiences sur les Power Hydrauliques/' Paris, 1838.
t See 'Mechanics of Engineering," Weisbach. Translated by A. J. DuBois.
Hydraulics and Hydraulic Motors, vol. II, part I. p. 470.
36o
Turbine Testing,
I
I
in the City of Lowell, usin^ a Prony brake fitted with a dash-pot
to prevent irregular operatian.
In 1845 Mn Uriah A, Boy den made a trial of a turbine designed
by himself, using the Prony brake, and obtained an efficiency 0178
per cent, as the maximum. In 1846 a similar test of one of the
Boyden turbines was made at the Appleton Mills in Lowell, mi
an efficiency of 88 per cent, was reported. He continued the work
of the testing of water wheels for several years and tested manv
wheels of various types.* Mr. Francis introduced the system of
testing wheels which were to be used by purchasers of water from
the water power company which he represented. The chief pur-
pose of the tests was that the wheels might be used as meters in
determining the amount of water used by the various purchasers,
In i860 the City of Philadelphia undertook a comparative tniJ
of various turbines in order to determine their relative merits tor
used in the Fair mount Pumping Plant, The results o^f these tests
given in Table XXXIII are somewhat questionable but have i
comparative value.
TABLE XXXIIL
Water Wheel Ttsta at PhUaijkJphia in ISBQ,
Name of Wheel.
Kind of
Wheel.
Per
cent
of
Effect.
3 pet-
cent
added
for
frier n
Whete built.
Steveneon'e eecond wheel -
Geyelin'fl fiecontl wht^el ,,,..,...
Jonval . .
Jonval ..
Bpii^K,.
Jonval . .
Spiral...
Spiral , , .
Spiral...
Jonval , .
Scroll . . .
SCToli , . .
Jo rival . ,
Spiral . . .
Scroll . . .
Scroll . . .
Spiral . , .
Scroll...
Spiral..,
Scroll . . .
Jonval . .
,8777
.8210
*8197
.7672
.7691
.7669
,7457
.7335
,7169
,7123
.6799
.0726
.6412
.62€5
.6132
.5415
.5359
.4734
.9077
.8510
.8497
.7972
.7891
.7869
,7767
.7635
.74^9
.7423
.7099
.7026
.6712
.6624
,6605
.6432
,5715
.5659
.5034
PatcTson, X. J
Philadelphia. Fit.
Berovirie, Pa.
TroT N Y
Andre wg ^ K&lbaeh'e third wheel
( 'oHift'i, EifCfiiid wlieel ...........
Andrews 4b Kalbach'e eecond
wheel ,.,.,,.,..«,., .........
Bemville Pa.
Smithes, Parker^B fourth trial , . . .
Smith's, Parker's third trial
Kteven's l9,rst wheel. , » * * *
Readinir, P*.
Heading, Pa.
Patereon N J,
Blake -
East Peppered M»»^
Weit Lebanon. N H.
Tyler .......---. *
Geyelin*a first wheel ,.*........
Philadetphu, F^,
H«adiii«, Ph.
Guilford. N. Y,
Smiih*^, Parker's second wheel. .
Merchant's Goodwin
Maeon's SEtiUb .....»*
Buffalo, N T.
Andrew^s first wheel •«..
Bemville, P*.
Rich ♦ ..,,,.*,..* ^ »»........ .
Salmon River K. T
I*i til^T>tt#e ..iiiiT.»»«Tf'-
Anstiiii Texa^
Monroe ....#« >■■ ..
WoiresK^f, Man,
Collin's Erst, wheel *......*
Trov, N Y
The Testing of Turbines by James Emerson. 361
170. The Testing of Turbines by James Emerson, — One of the
en who did much valuable work of this character was Mr. James
merson who designed a new form of dynamometer of the trans-
itting kind. At the request of Mr. A. M. Swain, Mr. Emerson
^signed a Prony brake, embodying this dynamometer for the pur-
)se of testing a Swain turbine in a flume built from designs by
rands. The results obtained by Mr. Emerson from this test
ere so satisfactory that The Swain Turbine Company decided to
)en the flume for the purpose of a competitive test of all turbines
hich might be oflFered for this purpose. Announcement of this
St was dated June i6th, 1869. The pit was fourteen feet wide,
lirty feet long, and three feet deep, measured from the crest of the
eir. The best results of this competitive test, the accuracy of
hich has since been questioned by Mr. Emerson, were attained
ith the Swain and LeflFel wheels. The former ranged from 66.8
p to 78.9 per cent efficiency, and the latter from 61.9 to 79.9 per
ent efficiency. This competitive test was the beginning of a series
f such tests as well as of a general system of the public testing of
irbines. The testing flume was opened to all builders and users
f turbine wheels and such tests have been continued in the United
tates up to the present time.
The report of the results of this test attracted the attention of
fr. Stewart Chase, then agent of The Holyoke Water Power Com-
any, who, recognizing its very great importance, secured the
doption of a systematic testing of water wheels at Holyoke for
le benefit of the Company and wrote to Mr. Emerson as follows :
'The testing of turbines is the only way to perfection, and that
i a matter of great importance. Move your work to Holyoke and
se all the water that is necessary for the purpose, and welcome,
ee of charge."
Mr. Emerson, who had been conducting the testing of water
heels as a matter of private business at Lowell, at which place
t was obliged to pay for the water used, at once accepted the
beral oflFer thus tendered him and removed to Holyoke where he
mtinued the testing of water wheels until it was taken in hand
r The Holyoke Water Power Company.
The reports of Mr. Emerson's work were published and undoubt-
ly were the means of bringing a number of wheels up to a state
high efficiency. The reports were found to be full of valuable
22
362
Turbine Testing.
data, and, although not systematically arranged, formed an exten-
sive and valuable collection of figures. "*"
In 1879, The Holyoke Water Power Company, for the purpose of
determining the standing of wheels offered for use at that place,
I GATE
Fig. 225.
arranged for a coimparative or competitive turbine test at the flume
constructed by Mr. Emerson at Holyoke. The wheels were fd
under the direction of Mr. Emerson and a part of the tests were
♦ See James Emerson's "Hydro-Dynamics."
The Testing of Turbines by James Emerson.
363
ade or witnessed by Mr. Samuel Weber and Mr. T. G. Ellis.
heir report was accompanied by a graphical diagram (Fig. 225
id Table XXXIV) on which they commented as follows :
"By examining' the diagram and table, the peculiarities of the
veral wheels will be readily seen. It will be observed that the
>uston turbine, which has the highest percentage of effect at full
te, is really the least efficient at from half to three-quarters, and
)m half to full gate, of all those shown on the diagram, and is
ly superior to the Nonesuch at from three-quarters to full gate,
d that by a very trifling amount; so that the wheel which ap-
rently has the highest percentage is really the least desirable for
tnal use. The Thompson turbine, which has the lowest percentage
those shown at full gate, rises to the sixth place at from one-half
full gate, and to the fourth place at from one-half to three-quart-
5 gate. The Tyler turbine, which has the second highest per-
ntage at full gate, falls to the sixth place at from one-half to
ree-quarters gate. The Hercules turbine, which stands third
ly at full gate, takes the first rank at from half to full gate, or
ly of its subdivisions. The New American turbine, which stands
ly fifth in the percentage at full gate, is second only to the Her-
les at from one-half to full gate or either of its subdivisions, and,
deed, differs from the Hercules very slightly in its useful effect
rough the whole range shown.
"Taking the average useful effect of the wheels shown from one-
If to full gate as a measure of their efficiency, their relative value
in the order shown in the table."
TABLE XXXIV.
Showing Average Percentage at Part Gate,
Name.
Hto9i
Per cent.
H to Full
Per cent.
K to Full
Per cent.
rcules
r American
sees
Br
mpson ....
eiucb
iston
.737
.732
.708
.605
.680
.696
.619
.397
.805
.795
.786
.766
.744
.721
.712
.717
.771
.763
.747
.716
.712
.709
.666
.557
364
Turbine Testing,
The report of Mr. Emerson covered a much larger number or
wheels. The diagram accompanying Mr. Emerson's report* is re*
produced in Fig. 226.
I GATE
FDILJ
eiETCj
i^
Fig. 220.
171. The Holyokc Testing Flume, — The later work of systen
testing of American turbines has been carried on principally at !
Holyoke flume.
t 'The object aimed at by the Water-power Companies of Lowc
and Holyoke, in the establishment of testing flumes for turbin
* Emerson's "Hydro^Dynamlcs," page 300.
t*The Systematic Testing of Water Wheels/* by H. H. Thurston.
The Uolyoke Testing Flume. 365
the determination of the power and efficiency, the best speed,
d the quantity of water flowing at from whole, to, say, half gate,
exactly that the wheel may be used as a meter in the measure-
int of the water used by it. The quantity of water passing
x>ugh the wheel, at any given gate-opening, will always be prac-
ally the same at the same head, and the wheel having been
ted in the pit of the testing flume, and its best speeds and highest
ciency determined, and a record having been made of the quan-
j of water discharged by it at these best speeds and at all gates,
\ turbine is set in its place at the mill, speeded correctly for the
id there afforded, and a gauge affixed to its gate to indicate the
:ent of gate opening. The volume of water passing the wheel
various openings of gate having been determined at the testing
me, and tabulated, the engineer of the Water-power Co. has
ly to take a look at the gauge on the gate, at any time, or at regu-
times, and to compare its reading with the table of discharges,
ascertain what amount of water the wheel is taking and to de-
mine what is due the company for the operation of that wheel,
that time. The wheel is thus made the best possible meter for
t purposes of the vender of water."
The present Holyoke Testing Flume was completed in 1883.
le plan of this flume is shown in Figs. 227 and 228.
The testing flume consists of an iron penstock, A, about nine feet
diameter, through which the water flows from the head race
:o a chamber, B, from which it is admitted through two head
tes, G,G, into the chamber, C, and from thence through trash
cks into the wheel pit, D. Passing through the wheel to be
sted, it flows into the tail-race, E, where it is measured as it
»ws over a weir, at O. The object of the chamber, B, is to afford
portunity for the use of the two head gates, G,G, to control the
mission of water, and consequently the head acting on the wheel,
lere is also a head gate at the point where the penstock. A, takes
water from the first level canal. A small penstock, F, about 3
!t in diameter, takes water from the chamber, B, independently
the gates and leads to a turbine wheel, H, set in an iron casing,
the chamber, C, in order that this wheel can run when C and the
leel pit, D, are empty. The wheel, H, discharges through the
or at the bottom of C, and through the arch, I, and the supple-
ntary tail-race, K, into the second level canal. This wheel is
id to operate the repair shops ; also to operate the gates, G. The
imber, C, is bounded on one side by a tier of stop-planks, L, and.
366
Turbine Testing.
k.
The Holyoke Testing Flume.
367
on another side, by a tier of stop-planks, M, The object of the
stop-planks, L, is to afford a w^ste-way out of the chamber, G
This is of especial use in regulating the height of the water when
testing under low heads. The water thus passed over the planks*
L, falls directly into the taiUrace, K. and passes into the second
level. The stop-planks, M, are used when scroll or cased wheels
1 — BTHTiiwrinnrifTi
Fig. 228. —lasting Flume of Holyoke Water Power Co, Arranged for Teeting
Horijtmitfll Turbinefi.
are tested. In such cases D is empty of water and the wheel case
in question is attached by a short pipe or penstock from an open-
ing cut in tile planks, M. Fhimc wheels are set in the center of the
floor of D, and D is filled with water. They discharge through the
floor of D and out of the three culverts, N,N,N, into the tail-race^
E, Horizontal wheels are set in tlie pit, D, with their shafting
projecting through a stuffing-box in the side of the pit (See Fig.
228). At the down-stream end of the tail-race is the measuring
wetr, O (Fig. 227), The crest of the weir is formed of a strip of
planed iron plate twenty feet in length. The depth of water on the
weir is measured in a cylinder, P, set in a recess, Q, fashioned in
the sides of the tail-race. These recesses are water-tight, and the
observer is thus enabled to stand with the water-level at convenient
368 Turbine Testing* I
height for accurate observation. The cylinder, P, is connected wit^
a pipe that crosses the tail-race or weir box about ten feet back of
the weir crest. The pipe is placed about one foot above the Soar
and is perforated in the bottom with i inch holes. A platfonn, K
surrounds the tail-race, and is suspended from the iron beams thai
carry the roof. Above the tail-race is the street, over which xht
wheels to be tested arrive on wagons from which they are lifted
by a traveling crane that runs on a frame-work over the street, and
by means of which the wheels are carried into the building and art
lowered inEo the wheel pit, D. Spiral stairs lead into a passageway
that leads in turn to the platform, R. In the well-hole of these
stairs are set up the glass tubes which measure the head of water
upon the wheeh These gaug^e tubes are connected with the pit, D.
and the chamber, C, by means of pipes, one of which enters the
wheel pit through a cast iron pipe^ T, built into the masonry dam
which forms the down stream end of the wheel pit, D. The other
pipe passes back under the wheel pit, D> and crosses the tail-race
at the extreme back line and close under the pit floor. This pipe
is perforated throughout its length across the race in a manner
similar to the pipe used for determining the head on the weir. To
enable the observers at the brake wheel, head gauge and measuring
weir to take simultaneous observations, an electric clock rings
three bells, simultaneously, at inter\^als of one minute.
The usual method of testing a wheel is as follows: After tlie
wheel 15 set in place (See Figs. 227 and 228) a brake pulley and
Prony brake are attached to the shaft, the gates arc set at a fi-xcd
opening and water is admitted. The runaway speed of the wheel
is first determined with the brake band loose, after which a wci^hi
is applied and the brake tightened until the friction load balances
the weight. As soon as this balance is attained, which requires
only a few seconds, the revolution counter is read and the head?
in the head-race, tail-race and on the weir are observed. Obsen^^i'
tions are repeated simultaneously each minute at the stroke of the
bell and for a period of from three to five minutes. The weight
is then changed and the observations repeated for a different load
and speed. After observations are made over the range of speed?
desired, the gate opening is changed, and a similar series of obser-
vations are made for the new gate opening. This is repeated (of
each desired gate opening, usually from full gate to about one-half
gate.
The results are calculated and reported in the form shown in
Table LX. It is usually stated in the report whether the test is
^
The Value of Tests. 369
de with a plain or conical draft tube, whether plain or ball bear-
s are used, and also the pull necessary, at a given leverage, to
rt the turbines in the empty pit. No attempt is made in these
orts to describe the bearings or finish of the wheels in detail.
The maximum head available is about 17 feet under small dis-
Tges and this decreases to about 9 feet under a discharge of 300
)ic feet per second. The capacity of the tail-race and weir is
dly sufficient for the accurate measurement of the latter quan-
r
7a. The Value of Tests. — ^There can be no question as to the
•y great value of carefully-made tests of any machine. It must
borne in mind, however, that any test so made represents results
ler the exact conditions of the test, and, in order to duplicate the
ults, the conditions under which the test was made must be
plicated. Any changes in the design or finish of the wheels, any
orations in the method of setting, or in the gates, draft tube or
ler appurtenances connected with the same are bound to affect
: power and efficiency to a greater or less extent.
it is unfortunate for the world's progress that the records and
iditions of failures are seldom made known. The record of a
lure, while of great value from an educational standpoint, may
isiderably injure the reputation of an engineer or manufacturer,
i consequently results of tests and experiments, unless fully
isfactory, are seldom published or known except by those closely
crested. For this reason, the published tests of water wheels
lally represent the most successful work of the maker and the
;t practical results he has been able to secure. Tests, unless
iy representative, do not assure that similar turbines of the
ne make, or even similar turbines of the same make, size and
tern, will give the same efficient results unless all details of their
ign, construction, and installation are duplicated. There is no
ibt that in many cases the published tests of water wheels are
final consummation of a long series of experiments, made in
!cr to secure high results, and do not give assurance that such
ults can be easily duplicated. The manufacturers have acknow-
g^cd this by calculating their standard tables on a basis of power
I efficiency below that of the best tests they are able to obtain,
I it is only a matter of reasonable precaution for the engineer,
3 is utilizing the results of any such tests for the purposes of
design, to discount the test values to such an extent as will
ire him that his estimates will be fulfilled.
372
Turbine Testing,
i
The total losses given above correspond well with current prac-
tice. Under the best conditions efficiencies greater than 83 per
cent, are often obtain ed^ and, under unfavorable condition's with
poor design and poor construction, efficiencies much less than the
minimum of 72 per cent, are common. While these losses can never
be entirely obviated they should be reduced to the practical mini-
mum that good design and good workmanship will permit,
175. Measurement of Discharge* — The discharge, q, of the wheel
is commonly measured in cubic feet per second and should repre
sent only the actual discliarge through the wheel itself. This dis-
charge is usually measured, after it has passed the wheel, by the
flow over a standard weir. Any leakage around the wheel into ibe
weir box or from the weir box around the weir must be determined
and deducted from or added to the amount passing the weir. The
actual weir discharge must be known either by a direct calibration
of the weir or by the construction of the weir on lines for which
the discharge coefficients are well established. Errors in weir
measurements often reach values of nearly 5 per cent due to the
erroneous use of coefficients obtained from other weirs not strictly
comparative.
The head on the weir must be accurately determined by nican^
of a hook gauge which should usually read to *ooi of a foot. An
error of .01 foot in reading the head on the weir represents about 1
per cent,, and an error of ,001 about .1 per cent,, in the computed
discharge with a 1.5 foot head on the weir and a much greater error
at a lower head.
The construction of weirs in the tail-race of power plants, es-
pecially where large quantities of water are used under low heads,
involves an expense which is often prohibitive. In addition to thi^
the construction of such weirs in plants working under low heads
wculd often seriously reduce the head and alter the working
conditions.
Other methods of accurately determining the flow should be
developed. There are two methods which seem to give proinise]
of good results:
First : By the careful determination of the velocities of flow io I
the cross-section of the head or tail-race at points far enough fromj
the wheel to guarantee steady flow. This may be done by meatisj
of a carefully calibrated current meter, a pitot tube, or by floats (
To secure good results these instruments must be in the hands otl
Measurement of Head.
37J
familmr with their use and with the sources of error to which
xh is liable if carelessly used. (See Chapter XL) This method in-
>lves no loss in head.
Second: By the construction in tlie head or tail race of sub-
ergcd orifices of known dimensions and of a character for which
c coefficient ol discharge has been determined. Some work in
is line has been done at the University of Wisconsin (See pages
; to 45) which will soon be made accessible in detail in a bulletin
>w in press. This method will involve only small losses of head
id by a sufficient range of experiments can perhaps be made
sarly as accurate as weir measurements.
Fig. 229.— Doble Tangential Wheel Arranged for Brake Test,
176* Measurement of Head* — ^The power of water applied to the
^lieel depends on both quantity and head. The head is more easily
iieasured than the quantity* but, nevertheless, requires consider-
ble care for its accurate determination.
The head on the wheel must be measured immediatly at the
heel both for the head-water and tail-water. If measured some
istance away it is apt to include friction losses, which should not
! charged against the wheel in raceways, penstocks and gates,
he measurement of head should usually be to about .01 feet, al-
ough this depends on the magnitude of the heads involved.
i77< Measurement of Speed of Rotation. — The speed of the
iccl is usually recorded in revolutions per minute and may be
J
374
Turbine Testing,
Fig, 230,— Section and Pliiii of App«mtiis for Testing SwAin Ttirbini (bj
James B. FmnciH).
^^^^^B^^flr Measurement of Powen 375
determined by a revolution-counter which records the number of
revolutions made in a given interval of time; or by a "tachometer*'
which, by means of certain mechanism, indicates at once on a dial
the revolutions per minute* The latter method is more convenient
if the instrument is correct, but frequent calibration and adjustment
are necessary and a correction must usually be applied to values
thus observ'ed.
The revolution-counter is more accurate, and» while not so con-
venient, is to be preferred.
178* Measurement of Power, — ^Tbe power of the wheel may be
determined by placing a special brake pulley on the turbine shaft
^nd applying a resistance by means of a Prony brake or some other
(arm of dynamometer. This resistance is then measured by some
form of scales (See Figs. 229 aijd 230). The power thus consumed
by the friction of the brake can be calculated by equation (i)
*,^ „ 2?f 1 n w ,
P = Hor&e power
^^^^^ 1 = length of lever or brake arm from center of revolutioiii in ft
^^^^H n s revoluiloQ per minute,
^^^^V jr = ratio of the circumference to the diameter of a circle = 3.1416*
^H^ w = weight on the Bcale in pounds.
This is the method applied in all laboratory work (see Fig. 229) and
is that used at the Holyoke Testing Flume. If properly applied,
it is probably subject to minimum error- When wheels are tested
in place, it is sometimes more convenient, and often essential^ to
determine the power output from the current generated by elec-
trical units, which, when measured by aid of the known efficiency
of the generator, will give the actual power of the wheeL If these
units be direct-connected so that little or no transmission loss is
involved, and if the generator is new and its efficiencies have been
accurately determined, the errors involved by this method are
comparatively smalK The transmission of the power before mea-
surement through gearing, through long shafts and bearings or by
other means, involves losses, the uncertainties of which must be
avoided if accuracy is essential.
179, Efficiency* — The efficiency of a machine is the ratio of
energy delivered by the machine to that which was supplied to it
and it may have various significations.
In an impulse wheel (See Section 152) the theoretical energy of
the water in the forebay in foot pounds per second is;
(2) E ^ qwh
3/6
Turbine Testing*
The energy just inside the outlet of the pipe is
(S) El =qwth' ^^h')
The energ^^ of the jet is
(4) B. = -S5^
and the theoretical power delivered to the bucket is
(fi)
E. =
qw (1 — <p) V {1 — cos a) tp v
If e represents the actual ft lbs* of work delivered by the wheel
per sec. then I
(6) -p- = the efficiency of the entire higtallation including pipe, jet, 1
wheels et^. '
(7) -g— ^ efficiency of the water wheel, including nozzle and bucket
(8) -^^ = efficiency of the nuiner, and
(9)
K,
hydra alic efficiency of the bucket
In the testing of water wheel s» the efficiency (7), -^^ is the ratW
j^i J
ordinarily to be determined since it involves the losses in tlie no
1 L* MUM J
T
li
--f— ny H I ra— —
1 r
I i
\ I
1 I
« I
> I
I I
IM
4 I
!>
zle, jet and buckets as well as from residual energy in the
discharged by the buckets, all of which are properly chargeable •
the operation of the wheel.
Measurement ot Power.
377
r.ar«iir PwtSldeSlavAUon
Fig. 232.
SadElavatloD
vr.aiMir
Fig. 233.
efficiency represented by (9) involves only the effects of
of energy by the water in passing over the buckets and
joretical value is 100 per cent, for all values of ^. It dim-
the effect of uneconomical speed of rotation of the wheel
leaves residual lost energy in the water discharged by the
s and not properly chargeable to bucket imperfections. It
23
^H 37S Turbme Testing, ■
^m would be determmed only in a detailed study or test made for ik
^m first purpose above mentioned*
H 180 Illustration of Methods and Apparatus for Testing Wat«
^1 Wheels: — Fig. 230 shows the apparatus used for testing turl^ina
^^^ on a vertical shaft, by Mr. J, B, Francis to test a Swain wheel at tht
11
"^
^
y.
^
"^
-^
'X'
^
^
^
^
V
s.
7
1
_f-s
^
.^
—
"%
/
^
^
h
^
■
^-
f
J
^\
r
J
/
1
IC
u
}
y
y>
/
i
>
Y
4\
^
s
y
f
/
7
s.
u ^
IBSD
^
^
/
/
/
3
7^
J
f
/
>m
/
/
SI-
dfli
/
7
/
/
1
IN
7
/
f
4
Boo
peril
Tl
testi
T]
In
cour
shaf
moti
1 dasli
for 5
Fi
tails
9 10 ID 70 la KB
fsm GEirr batc oPEMmt
Fig. 234.
tt Mills, Lowell, Massachusetts (Sec ''Lowell Hydraulic
ments/*)
^e section represents a vertical turbine in the testing plant
ng apparatus in place.
iie plan of the plant shows the arrangement of the Prony bf
these drawings P is the friction pulley; b is the brake; c
iter balances to remove the load of the brake from the w
t; L is the bent lever or steel beam for transferring horizc
on to a vertical lift; S is the scale pan for the weight; d is
i-pot; w is the weir for measuring the water, and r is the i
stilling the water after leaving the wheel
gs* 231, 232, 233, show the brake wheel and Prony brake
used by Mr. William O. Weber for determining the effici*
Ex-
•akt
are
bed
Wltll
the
rack
d^
Tests of Wheels in Place.
379
of various turbine water wheels as described by him in a paper on
"The Efficiency Tests of Turbine Water Wheels," (See vol. 27, No.
4, American Society of Mechanical Engineers). (See also Section
171, Experiments at the Holyoke Testing Flume.)
181. Tests of Wheels in Place. — In April, 1903, a Leffel turbine
was tested at Logan, Utah, at the station of The Teiluride Power
Transmission Company, by P. N. Nunn, Chief Engineer. The
wheel was dir^ectly connected to a General Electric generator the
efficiency of which has been determined as follows :
125 per cent load 96. 7 i>er cent, efficiency
100 per cent load 96.2x)ereent. efficiency
75 per cent load 95.3 per cent efficiency
50 per cent luad..... 98.5x>ercent. efficiency
25 percent load 88.0i>er oenk efficiency
The output of this generator was used as a basis for calculating
the work done by the water wheel.
The results of the tests and methods of calculation are shown in
Table XXXV and graphically illustrated in Fig. 234.
TABLE XXXV.
Tht of High Head Liffel Horizontal Turbine at Lagan StoMon of Telhirids
Power Trans, Company^ Logan^ Utah, Efflciencif of Teat at Constant Speedy
AprU £8,1905.
P. N. Nunn, Ohief En^neer.
Grate opening
0.75
1.394
81.85
0.85
1.98
80.72
86.5
199.3
10.4
209.7
1921
1152
0.965
1600
0.833
0.75
0.50
1.132
59.76
0.85
1.98
58.63
87.3
201.2
10.6
211.8
1409
739
0.952
1041
0.738
0.50
0.40
0.969
47.27
0.85
1.98
46.14
87.5
201.6
10.8
212.4
1112
500
0.935
717
0.644
0.40
0.50
1.129
59.66
0.85
1.98
58.63
87.2
200.9
10.6
211.5
1405
737
0.952
1038
0.739
0.50
0.75
1.368
79.65
0.85
1.98
78.42
86.5
199.3
10.4
209.7
1866
1123
0.965
1560
0.836
0.75
0 96
^ead on 1& feet weir in feet
^^harge of weir in cubic feet
Der second
1.475
88.94
^^eakage around weir in sec-
ond feet
0.85
Bzciter water in second feet
VVater through turbine in
second feet .• .
1.98
87.81
Pressure at shaft center in
pounds per square inch. .
Elffective head above shaft
renter in feet
86.2
198.6
Vacuum head measured in
feet
10.3
Total working head in feet
rheoretical horse power
C. W. output at Sw. Bd
Jenerator efficiency
Jrake horse power of turbine
^ciency of turbine
rat*» ooenins
208.9
2082
1210
0.967
1677
0.806
0.96
NoFB— Speed. 400 R. P. M. (normal).
Generator efficiency taken from test of machine made by The Greneral Electric
ompany. (Record of test in office of chief engineer).
38o
Turbine Testing,
A similar test of one of a number of wheels installed by Tlie
James Leffel Company in the plant of the Niagara Hydraulic
Power and Manufacturings Company was made in December, 1905,
by Mn John L. Harper, engineer of that company. The following
table XXXVI is the condensed data of the test of wheel No* 8
which is also illustrated by Fig. 235,
9400
a too
auQQ
eiDo
eeoo
yi£40a
BBOO
oeo6o
imo
IBDD
1400
1200
IDOO
- 00
■ 00
■ 71
' 70
- 00
yiO
u
ae
w
5"
IL
liflO
-
^
ITS
llOo
y
^
^^
--
/
/'
y
y
^/
/
/
/^
^
71
jf
/
/
/
ICO t
/
\/
/
/
J
¥
/
100 o
■0
■b|
TOO
00
so
f
/
/
/
i
f
/
/
^/
/
' 11
^ 10
- tl
/
7
/
/
i
(
\
i
40 46 so 19 10 OS 70 7S 00 99 SO 19
pen GCHT SATE OPCMlMa
Y\t^ 235.
The water was measured by a standard contracted weir 16.25
feet long and discharge computed by Francis* formula:
q==3.33{L— 0.2h) h*
The load was computed from the voltmeter and ammeter rca<l-
ings of two generators Nos, 5 and 12 which were both driven by j
this wheel and then corrected for the generator loss by a fact<:j
estimated from the shop tests of the generators.
Wheels io Place.
TABLE XXX VL
T€*t of a Douhh Horhfmtal Leffet Turbine ijtst ailed in the plant of the
Niagarn Ui/drauHc Company, Niagara Fa 11% N, F,
Gatk Ofxkhto.
.45
Dec. 5th
Time -,,,,,.....* , . .
Hook gauge reading (corrected)
rHscharge of wheel by Francia* formula .
Hc^ad on turbine .,-,..
lEydraulic horse power* » .«,,,,,.* .
r;f- M,*- .,...
Gen f rat or No. S*
Volta_...„. ..,.-..., ,
Amperes. , , , , , ,
Efficiency
HorEe power taken frora wheel by generator. . . .
Gftieratar No. 12*^
Volta , ...„,.
Amperes ,.,...... , » , .
Effciency . , , . ^ > , ,
Horse puwer talcen from wheel by gt^nerator
Total horse power output of wheel ,..,.,
EfSciem-y of wheel ........,...,,, , . .
3;2l p- m.
1,3155
84.76
213.0
2045
255
178
5065
1314
Friction
Load
Only
17
1331
,fi5l
5:01 p, m.
1.978
146.6
212.4
S52S
259
178
5020
.92
1302
12200
57.7
.1*5
1720
3022
.So6
fDOQ
4QQ0
saoa
Fig. 236,
lODQ
lODIP
4:59 p. 1
2.2.57
17S.3
212.7
4320
250
184
5S33
.92
15^3
13000
60.5
.955
1912
3475
.Ra5
leaQi
• Generator No, 5 is a G. B, 5000 A. 175 V., D. C. tnachlneu
•• Generator No. 12 is a Bullock 1000 K. W„ 3 phase A C. senerator.
Turbine Testing,
The 10,500 h.p, turbine manufactured by the L R Morris Com-
pany for the Shawinigan Power Company was also tested in a
similar manner. A brief outline of this test is given on page 416
The graphical result of the same is shown by Fig, 236. Fig. 237
illtistrates the test of a 25" Victor High Pressure Turbine, manu-
factured by the Piatt Iron Works Co*, at the Houck Falls Power
Station at Ellensville, New York,
The results of various tests at the Holyoke Testing Fluniep zd^
lected from divers sources^ are given in the appendix. Most of ik
later tests have been furnished by manufacturers and represeat the
best results of modern turbine manufacture.
mo 40D 100 •DO loog ibdd 1400 iioo ibod eoos itOQ i4oa
Fig, 237-
Literature. 383
LITERATURE.
TUBBINB TESTINO.
1. Smeaton, James. "An Experimental Inquiry, read in the Philosophical
Society of London, May 3rd and 10th, 1759, concerning the
Natural Powers of Water to Turn Mills and Other Machines,
Depending on a Circular Motion."
2. Morin. "Experiences sur lea Power Hydraulicques." Paris, 1838.
3. Pourneyron, H. "Memoire sur les Turbines Hydraulicques." Bnussels,
1840.
4. Francis, J. B. Tests of Several Turbines Including the Tremont-Fourney*
ron and the Boott Center Vent Wheels. Lowell Hydraulic Ex-
periments, 1847-1851.
5. Francis. J. B. Test of Humphrey Turbine, 275 h. p. Trans. Am. Soc.
C. E.. vol. 13, pp. 295-303. 1884.
6. Webber. Samuel. Turbine Testing. Elec. Rev. Oct 18. 1895. p. 477.
7. Wiebber, Samuel. Instructions for Testing Turbines. Eng. News, 1895.
Vol. 2, p. 372.
8. Cazin. F. M. F. The Efficiency of Water Wheels. Elec. Wld. Jan. 9, 1897.
S. Report of Tests of a 28-inch and 36-inch "Cascade" Water Wheel. Jour.
Fr. Inst May, 1897.
10. Hitchcock, E. A. Impulse Water Wheel Experiments. Elec. Wld. June
5, 1897.
U. Hatt W. Kendrlck. An Efficiency Surface for Pelton Motor. Jour.
Franklin Inst, June, 1897, vol. 143, p. 455.
^2. Thurston. R. H. Systematic Testing of Turbine Watei* Wheels in the
United States. Am. Soc. Mech. £!ng. 1897, p. 359.
13. Results of Tests of Cascade Wheel. Eng. News, 1897, vol. 2, p. 27
14. Results of Tests of Hug Wheel. Eng. News. 1898, vol. 2, p. 327.
15. Efficiency Curves. Eng. News, 1903, vol. 2, p. 312.
18^ Houston. W. C. Tests with a Pelton Wheel. Mech. Engr., May 30, 1903.
n. Henry, Geo. J., Jr. Tangential Water Wheel Efficiencies. Am. Inst Elec.
EIng., Sept 25, 1903.
IS. Crowell. H. C. and Lenth. G. C. D. An Investigation of the Doble Needle
Regulating Nozzle. Thesis, Mass. Inst, of Tech. 1903.
19. LeConte. Joseph N. Efficiency Test of an Impulse Wheel. Cal. Jour, of
Tech. May, 1904.
20. Groait, B. F. E^xperiments and Formula for the Efficiency of Tangential
Water Wheels. Eng. News, 1904, vol. 2. p. 430.
21. Webber, Wm. O. Efficiency Tests of Turbine Water Wheels. Am. Soc.
of Mech. Ehigrs., May, 1906.
'2. Horton. R. E. Turbine Water Wheel Tests. Water Supply and Irriga-
tion Paper 180, 1906.
}. Westcott. A. L. Tests of a 12-lnch Doble Water Wheel. Power, Dec
1907.
CHAPTER XVI.
>
THE SELECTION OF THE TURBINE,
182* Effect of Conditions of Operation.^-For high and moder-
ate falls the variations in head under different conditions of limtr
are of small importance and water wheels can commonly be
placed high enough above tail- water to be practically free from
its influences. In such cases variations in head are comparaiivclj
so slight as to have little eflfect on the operation of the wheels
which can therefore be selected for a single head. Such condi-
tions are the most fa%^orable for all types of wheels.
When low falls are developed the rise in the tail-water is oftcB
comparatively great, and, as the head water cannot commonly
be permitted to rise to a similar extent on account of overflow]
and damage from back water, the heads at such time are consider-
ably reduced. As is pointed out in Chapter V, under such con-|
ditions and for continuous power purposes wheels must be se*
lected, if possible, that will operate satisfactorily under the eniirci
range of head variations that the conditions may demand, or at,
least under as great a range of such variations as practicable-
In some cases the change in head is so great that no wheel cat]
be selected which with work satisfactorily under the entire rangej
of conditions. In other cases, the head becomes so small that
the power which can be developed is insufricicnt without a ht\
and unwarranted first cost. Jn many such cases the use oi
water power plant must be discontinued, and, if the deliver}'
power must be continuous, it must be temporarily supplement!
or replaced by some form of auxiliary power.
In Chapter XVII it is shown that^ almost without exceptu
great variations take place in every power load and that a pbi
must therefore be designed to work satisfactorily under consid<
able changes in load. Most plants are called upon to (umii
power for a considerable portion of the time under much lei
than their maximum load, hut must occasionally furnish a ni;
mum load for a short period.
Basis tor the Selection of the Turbine. 385
If power IS valuable, and the quantity of water is limited, it is
desirable to select a wheel that will give the maximum efficiency
for the condition of load under which it must operate for the
greater portion of the time and that will also give, if possible,
high efficiency under the head available at the lowest stages of
the water. High efficiency is not essential to economy during
high water, for there is plenty of water to spare at such times;
neither is high efficiency as important during unusual load con-
ditions, which obtain for only brief intervals, as it is during the
average conditions under which the plant operates.
183.. Basis for the Selection of the Turbine. — In Chapter XV
the testing of water wheels has been discussed and a number of
tabulated results of such tests are given. (See appendix D). The
standard water wheel tables are calculated from the results of
these tests but the values of power and efficiency, as given therein,
are usually reduced somewhat for safety from the results deter-
mined experimentally. Such tests also give data for a much
broader consideration of the question, and for the determination
of the results that can be obtained under the actual conditions
of installation and operation, even when such conditions are sub-
ject to wide variations.
In Chapter XIV the hydraulics of the turbine are discussed,
various turbine constants are considered, and the constants are
calculated for a number of standard American turbines in accord-
ance with the conditions of operation as recommended in the cata-
logues of their makers. It will be seen from a study of the tables
that the turbines designed and built by various manufacturers
Sometimes have widely different constants, indicating that each is
l>est adapted to certain conditions of which the values of these
Constants are an index.
It is also shown that the various constants for a homogeneous
Series of wheels may be calculated from experimental data for
iny desired condition of gate opening and fixed value of <f>, and
ihat from these constants the operating results, that is, the dis-
charge, power, speed, and efficiency for any wheel of the series,
^ith the given gate opening and value of <^ and for any desired
lead, can be calculated. For most purposes, where the head is
constant or where the range in heads and other conditions to be
ronsidered are not extreme, the necessary calculations can be
eadily made from a satisfactory test, by applying some of the
386 The Selection of the Turbine.
formulas developed and discussed in Chapter XIV. The forraih
las of greatest value for this purpose are as follows:
, D n
1 q> = r^
1842V h
^ 1842 <P , , ^
2 ni= — g— , when h =s 1
Dn _ D, n, ,
S A = -7== w^ when <p 10 constant.
4 -y== = -7= when q> and D are constant.
^^ •
5 n = n , i^h when <p and D are constant.
q Qi
7 -7== = --r== when <p and D are constant.
8 q = Qi "^h when (p and D are constant.
10
-7-5- = -TT when <?) IB constant,
hi lilt
11 P = P h' when (p and D are constant and hi = L
In using these formulas it must be remembered that each i^
essentially correct only when the condition specified after each
equation obtains; also that as long as </> remains constant the
efficiency obtained by the test will remain practically constant
for the same wheel, under all conditions of head. It should aba
be noted that, with a fixed diameter of wheel and a fixed head, ♦
and n are in direct proportion, and most calculations can be made
by a direct consideration of the values cf n without a determina-
tion of the value of <f>.
When the operating results are calculated for a wheel of a given
series but of a diameter differing from that on which the experi-
ments were made, the results are liable to differ from the true
results on account of variations in manufacture, and allowance
must be made for such differences, at least until the art of manth
facturing turbines has further advanced.
urbme tor unti
leac
P 184- Selection of the Turbine for Uniform Head and Power.—
X he conditions of operation, as catalogued, 'are usually based upon
tests of a few turbines oi the series, and represent the best coo-
ciitions of operation for that series of wheels as determined by
such tests. Where the conditions of installation and operation
are fixed, and are not subject to radical changes in head or to great
x-ariations in the demand for power, the selection of a wheel may
tie made by inspection directly from the catalogues. This method
of selection is based on the assumption that the catalogue data is
correct, which assumption should be verified by the records of
an actual test of the series of wheels and, if possible, of the size
and hand which are actually to be used.
The examination of the many catalogues of turbine manufactur-
ers, in order to determine the wheel best suited to the conditions,
is a tedious method of procedure and can be greatly shortened by
brief calculations which are described in the following sections:
i85. The Selection of a Turbine for a Given Speed and Power
to Work under a Given Fixed Head. — It is frequently necessary
to select a turbine which must have a given speed and power in
order to successfully operate machinery for v'*Mch such require-
ments obtain. It is desirable to select a wheel which will furnish
essentially the amount of power required as all machinery will
work more efficiently and more satisfactorily at or near full load
conditions. It is also desirable to use a single turbine rather than
two turbines, and if more than one turbine is required, the least
number found practicable should usually be selected because the
multiplication of units involves an increase in the number of bear-
ings which must be maintained and kept in alignment.
To determine the best installation of turbines necessary to ful-
fill the given conditions, the value of K^ as given by equation (12}
should be determined. Having determined the value of K^, a
turbine should be selected having a constant Kb not less than the
amount determined, and if it is desired to operate the turbine at
its maximum efficiency, the value of K^^ for the turbine selected
should not greatly exceed the value found by computation. If
the value of Kq as computed greatly exceeds the value of Ks for
the various makes of turbines, then the power must be divided
between two or more units in order that the conditions may be
satisfied. As K^ is in direct proportion to P, one- half, one-third or
any other fraction of K^ will give the value of K, for a wheel
having a similar fractional value of the power, P, atid will there-
388 The Selection of the Turbine. ^^^^m
fore show the type of wheel which must be selected in order that
two, three, or more will do the work in question. The great vam-
tions in the value of K^ for different types of wheels and the in-
fluence of this variation on the relation of speed and power will
be seen by reference to Fig, 222 which shows the curves of r^
lation between revolution and power of various wheels for mt
foot head. This may be used for any other head by considering tk
revolutions in proportion to the square root of the head and the
power in proportion to the three-halves power of the head* A
brief study of this diagram will show its use more plainly. For
example : under a one foot head, and for 30 revolutions per minuU,
turbines may be selected that will deliver from 1*3 to 6.6 horse
power.
Suppose we desire to determine the power that wil! be available
under a 16' head at 100 revolutions per minute, 100 revolutions
per mintite at 16' head would correspond to 25 revolutions per|
minute at i' head.
For since
vr
therefore n^ = -7= 100 = .25 X 100 = 2S.
vlti
At 25 r. p, m. the diagram shows that turbines are obtainable j
that will give 1,8 to 10 horse power at one foot head.
The power at 16 foot head will be to the power at one foot head
as the three-halves power of the head. The three-halves power of
16 is 64; hence the power at 16 feet will be 64 times the power at
one foot head, and, hencCj wheels under a 16 foot head operated ai
100 revolutions per minute, will furnish from 122 to 657 horse
power and the most satisfactory wheel within these limits far Llic
problem at hand can be selected.
The diagram, however, is a convenience, not a necessity, and a
problem can often be more readily solved by the direct applica-
tion of equation 12. If, for example, it is desired to operate a
turbine at 100 revolutions per minute under i6 foot head to de-
velop 400 h. p., the corresponding value of K^ will be
n»P 100 X 100 X 400 ^^^
K, = -7= = 7^^ = 5906
By examination of Table XXXII it will be found that the Victor!
Standard Cylinder Gate or the United States Turbine wheels havtl
To Estimate Probable Results From a Test. 389
radically this value of K^ and will therefore fulfill the conditions,
laving determined from the calculated value of Kj the makes and
fpts of the several wheels which will satisfy the requirements, the
ize of the wheel may immdiately be determined by determining
he value of K, for the same series of wheels from Table XXX,
lap. XIV, and calculating the size of the wheel by the use of for-
lula 9.
Thus for the Victor Standard Cylinder Gate wheel the value of
C, is 0.00205. Therefore from equation (9)
^ = ^ = ^
^ =56.2-
.00205 X 64
vhich is the size of this series of wheels needed to fulfill the as-
umed conditions.
Having thus selected several possible wheels, tenders for these
vhccls may be invited from their makers. These tenders should
ic accompanied by an official report of a Holyoke test for the
wheel in question, or, if this is not available at the time, for the
acxt larger and the next smaller wheels of the series which have
^cn tested. From these tests the catalogue values of Kj and K5
which were used in their selection can be checked. In addition
^0 this the several prospective wheels may be compared as to their
operation at part gate, which comparison is equally important
for the final choice to be made.
As the wheels are seldom or never tested for the head under
which they are to work, and as tests are not always available for
-he size of wheel to be used, it is necessary to predict from the test
^ata furnished by the wheel makers the efficiency, power and
^ater-consumption curves which can be anticipated under the
f'vcn head. This can be done as illustrated in the next two
tides.
X86. To Estimate the Operating Results of a Turbine under
lie Head from Test Results secured at another Head. — ^For the
iirpose of illustrating the methods of calculation. Table LXXIII.
ay be considered. This table gives the results of certain tests
a 33* special, left-hand turbine wheel, with conical draft tube
Id balance gate, manufactured by the S. Morgan Smith Com-
Uiy. While the heads in the different experiments of this test
iry slightly, they are so nearly uniform that the table may be
■nsidered as developed under a uniform head of 17.15 feet. If
eater accuracy is desired, however, the square root of the actual
ad can be considered each time.
39^
The Selection of the Turbine.
Let it be assumed that the wheel is to be operated under a ao
foot head and with a speed of 200 n p* m. with the average load
at about .765 gate. The maximum efficiency at .765 gate is ^epr^
sen ted by experiment No. 43 of this table* In order that tfai
wheel shall work under the new head with this efficiency, equaticm
(4) must be satisfied. In all of these equations the primed cliaf*
actcrs are used to represent the experimental conditions* Tbf
most efficient revolutions under the tiew head will therefore be
determined as fallows:
172.75 X 4.46
4.14
= 186 f* p* m.
The wheel to be chosen must, howeveri in this case operate it
200 revolutions per minute. At 200 r. p. m. the wheel will i!Ot
run at its maximum efficiency* The actual efficiency at this sp«d
may be determined by finding what speed at the e^erimerittl
head corresponds with the speed to be used, and notin|f the ei
ciency corresponding to the same. This is done on the asstnn)
tion that the efficiency remains constant as long as ^ remri
constant which is shown to be essentially true by Fig, 214,
XIV,
The revolutions under 17.15 ft. head corresponding to 200 r
p. m, under 20 feet will be determined as before:
200 X 4.14
n' =
4,46
' = 187 T. p. m.
The result, 1S7 r. p, m., lies between the conditions of exp
ments 41 and 40, By proportion, the efficiency corresponding Ml
187 r p. m. will be found to be about ^.25 at ,765 ^^te.
If the efficiency corresponding to 187 r, p, m, in the table is no
determined from each g^te opening, it will be found that at full gat^i
the efficiency will be slightly below that shown in experiment tS«|
and can be determined by interpolation, or graphically, £0 ^\
About 81%, At gate ,948 the efficiency can be determined In !
same way to be about 8275%. At gate .883 the results will
between experiments 69 and 70 and the efficiency will be found 1
he about 86% » At gate .851 the result falls below experiment
and, by calculation from a graphical diagram or by interpolatioi
the results are found to be about .86. At gate 702 the rcvduti<^
correspond closely with experiment 56, and the efficiency from'
table is found to be 81,35%. At gate .636 the revolutions f.Mt I
tween experiments 25 and 26 and, by proportion, the efficiency
L
iilL.
Effects of Diameter on Results.
39»
found to be 80.62%. At gate .556, the efficiency is found, by pro-
portion, to be 77%. To determine the power of the wheel under
the new conditions, and for each condition of gate, the power of
the wheel as found by the test must be determined for the same
value of ^. The power of the new head can then be calculated by
use of formula (11).
In the same manner the discharge of the turbine can be deter-
mined by finding the value of q corresponding to the value of ^
for the experimental head, and from this value so determined the
value of q under the 20 foot head can be calculated by formula (7).
The results of these calculations, together with the efficiency as
determined for 20 foot head and for 200 revolutions per minute,
are given in Table XXXVII.
Having computed a similar table for each of the several pros-
pective wheels the one best suited to the given conditions can be
chosen.
TABLE XXXVII.
9mring H^ru Power, Ditekarge and Efficiency of »ineh Speeial Uft Ecmd
8. Morgan Smith Turbine, wUh tChfoot head and tOO R P. ML
OUcoUtfid from lest of dMuch. wheel under a head of 17.15 feet
Proportional Gate Opening.
Horse Power
Discbarge,
cubic feet
per second.
Efficiency.
i.ooo
222.1
220.1
217.7
212.7
188.1
165.1
154.7
136.7
120.4
117.0
111.3
109.2
97.5
87.8
81.5
75.0
81.6
.948
83.2
.883
85.6
851.........
86.8
.7ft5
88.2
.702
81.8
.©6
80.7
.556
79.0
187. To Estimate the Operating Results of a Turbine of one
Diameter from Test Results of Another Diameter of the Same
Series. — It is always desirable for the purpose of calculations to
Use the results of a test made on a wheel of the same size and hand
^ that which is to be used in the installation for which the wheel
is being considered. It is seldom, however, that all of the various
lizes of wheels in a series of wheels have been tested, and the
Manufacturers therefore frequently base their estimates and guar-
mtees of wheels of an untested size on the test of some other
vhcel of the series which may be larger or smaller than the whee'
i
i
392 ■ The Selection of the Turbine,
offered* Sometimes tests of wheels both larger and smaller thm
the wheel to be used ate available, in which case both sets of tests
should be used as a basis of calculation.
Let it be assumed that a 40" wheel is to be installed of the same
series as the 33'' wheel just considered, and that no tests of such
a wheel are obtainable. The tests of the 33" wheel may thercfort !
be used as the best information available* Let it be assumed thai
the 40" wheel is to be operated under a 9 foot head* For these J
calculations formula (3) must be satisfied.
Let it be assumed that the wheel is to operate at nearly full load
and the best efficiency is desired at about .85 gate. From the tests it I
will be found that at .85 gate, and with a 17,15 foot head and 191 J
revolutions, the wheel gave 85.97% eflSciency and 170,08 horse
power. Substituting these values in equation (3) there results:
— ^-j^ — = g , from which n = 114 r. p. m.
One hundred and fourteen revolutions per minute is therefore
the speed under which the wheel must operate in order to give
this maximum efficiency at this gate.
Let it be assumed, however, that the wheel must be run at i^
n p. m., on account of the class of machinery to be opentd
By substituting the value n^i20j in equation (3)/ 't is found
that n' = 202. The experimental efficiency at 202 n p- m. under
the 17*15 foot head and with the 33" wheel, will therefore* corres-
pond to 120 revolutions tinder a 9 foot head with a 40" wheel and
will indicate the efficiency under which the wheel will operate under
these conditions. Tliis is found to be about 81.5 at ,85 gate.
In order to determine the horse power of the wheel under the
new conditions, the horse power of the wheel under the test con*
ditions must first be determined for that gate; the resulting horse
power can then be determined by equation (9),
For 202 r p. m. at 17J5 foot head for this 33* wheel ?=B
which, substituted in equation (g), gives
S3 X 33 X 71 - 40 X 40 X 27 ^^^^ ^^^^^ P -^ 88.
In the same manner, the discharge of the larger wheel under the'
lower head can be determined by equation (6)* and q is found tt>
equal 104 cu. ft. per second.
To Estimate Results with Variable Heads.
393
I this way the discharge, efficiency and power of the larger
el under the chosen r. p. m. can be determined for each condi-
of gate, as shown in Table XXXVIII.
TABLE XXXVIII.
Hng Horse Potcer^ Discharge and Efficiency of a 4Mnch Special Left Hand
S. Morgan Smith Turbine, with a 9-Joot head and ItO R P. M.
Calculated from test of 3d-inch wheel under a head of 17.16 feet.
Proportional Gate Opening.
Horse
Power
Discharge
cubic feet
per second.
Efficiency.
)
I
>
I
3
5
100.
100.
92.
88.
76.
68.
64.
58.
119.
112.
108.
104.
91.
83.
76.
73.
82.1
84.2
82.5
81.5
78.1
77.8
78.8
75.1
J8. To Estimate the Operating Results of a Turbine imder
iable Heads from a Test made under a Fixed Head. — ^Where
variations in the head under which a wheel is to operate are
siderable, the variation in <^, and consequently in n, are some-
5S found to be beyond the limits of the test. Where the test
ditions are not greatly exceeded, the experiments may be ex-
ied graphically without any serious error.
,et it be assumed that the 33" wheel above considered is to be
rated under a maximum head of 25 feet, and that the head will
rease to 16 feet at times of high water; also, that the wheel is
be operated for the major portion of the time under about .75
e. The best condition for operation is shown by test 43, which
ws an efficiency of 86.3% at n'= 172.75 r. p. m.
may be calculated from equation (4) for the 25 foot head as
ows:
172.75 X 5 ^^^
n = jj^ = 208 r. p. m.
It is : the best number of revolutions for a 25 ft working head
lid be 208 r. p. m. The best number of revolutions for a six-
i foot head would be determined as follows:
n =
172.75 X 4
4.14
= 166 r. p. m.
24
394
The Selection of the Turbine.
I
The wheel, for the best efficiency, should be run at a different
speed for each head, but under practical conditions of semce
must be run at a constant speed.
Let it be assumed that, on account of the machinery operated,
it is desirable to adopt for the plant a speed of 200 r, p* m. Let
the 25 foot head be first considered. For considering the 25 foot
head the equivalent value of n under the test conditions is foiin^
as follows;
n'= a»X4.14 ^ 167 r. p. 01.
5
It will be noted from experiment 44 that at 169.25 r, p, m. the
efficiency is 85,55, A* 167 revolutions per minute tbe efficieoqr
would therefore be about 85%. Under a sixteen foot head n must
also equal 200 r. p, m., hence^ for this case^ the equivalent value of
n' for the test conditions is
^,^ _200X4a4_ ^ 208 revolutions.
4
Test 39 shows that, with 206.25 revolutions, the efficiency
76,66, At 208 revolutions the efficiency is therefore less than thil
amount and the probable efficiency under these conditions cao
be estimated by platting the relation between revolutions and tUm
ficiency as shown in Fig, 238. By prolonging the line from tJii
actual experiments, the efficiency indicated for 208 revolutioi
under the experimental condition s^ is found to be about 76'
As far as efficiency is concerned, therefore, the arrangement is v^
satisfactory, for a sufficiently high efficiency will be obtained ««*
der conditions of high water, and when the quantity of water tis<
is immaterial.
The relations of efficiency to speed, under the experimental coft-|
ditions and at various gate openings, are shown by the poii
platted on Fig, 238, Through these points mean curves ai
drawn, which are extended where necessary to intersect tfie i
scissa of 167 revolutions, which corresponds to the condition 1
efficiency for 25 foot head, and to the abscissa of 20S revolui
which corresponds to the condition of efficiency for a 16 foot
From these results the relations of efficiency at various gates
at the two heads named are platted in Fig, 239.
The relations of power to speed are shown by Fig- 240, whi£
has been platted in the same manner as Fig. 238, From Fig*
Estimate of Efficiency with Variable Head.
395
^^
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lev
0
(urrtDi
II nfi
uiiu
«,«
ID
n
ID ^
238. — Curves Showing the Efficiency Obtained at Various Speeds un-
der a Test Head of about 17.15 Feet from a 33-Inch Special Left-
Hand Wheel with Balance Qate, Manufactured by the S. Morgan
Smith Co.
i>A
A
V
^
^
p^
L
/
\
1 _ n 1 ♦>
f
r
^
\
.A
X
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•
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70
. o
IB FO
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PER C
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CNT 6i
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fkTE or
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9
0
101
239.— CuFYes Showing Estimated Efficiency at Various Gate Openings
and at Two Heads for 33-Inch S. Morgan Smith Wheel. (Taken
from Fig. 238.)
39*5
The Selection of the Turbine,
the power of the wheel at 25 and 16 feet can be determined by
equation (10).
The power at 25 feet will be
h* 12s
— I = ^g-g = 1.77 liraes Ibe power determined by theeiper
^' ' imeiit at 17.15 feet aud 167 r* p, m*
The power at 16 feet will be
b* 64
— I =£ =g-g = ,91 timed tbe power, as determined by the ei»
^' * peri men t at 17,15 feet, and at 216 r. p, m.
I
leo eoa
hEVQuniDHS nn minutc
Fig. 240.— Curves Sbowlng th© Power Obtained at Different Speeds uflder »
Test Head of about 17.16 Feet from the S, Morgan Smith
33-rDcb WheeL
.91 times the power, as determined by the experiment at 17.15 f«t*j
and at 216 r, p, m. Curves of the power of this wheel under 25 u^M
16 foot heads, and at various gates, as determined in this irianner,"
are shown by Fig. 241
The experimental relations of speed and discharge for the wl
are shown in Fig. 242 which was platted in the same manner
the diagrams for efficiency and power. A graphical represenU-
lion of the discharge under 25 and 16 foot head and at vari<
gates is shown in Fig. 243
1 89. A More Exact Graphical Method for CalculatioiL— -'
method outlined in section 188 is subject to some error as iht
suits arc platted regardless of head. The graphical method
therefore applicable without correction only when the experimd
A Graphical Method of Calculation.
397
head remains nearly constant. For a more complete^ accurate
1 satisfactory analysis the discharge, power and revolutions
)uld be reduced to their equivalents i. e. at one foot head
qi =
i/iT'
Pi =
hj
n
m
»o
!80
'80
140
too
,
1
•
%1
;i^
^
^
f/
f'
r
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♦5^
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te
t^
p.
\
90
8
D
7
PCR C
0
CNT 6i
8
Kit Of
0
'CNIN8.
8
0
m
f. 241. —Curves Showing Estimated Power Obtained at Various Gate
Openings and at Two Heads for 33-Inch S. Morgan Smith WheeL
(Taken from Fig. 240.)
I platted as shown in Fig. 244 where the r. p. m. under one foot
id is used as abscissas, and the power, discharge and efficiencies
used as ordinates. The condition at any given number of
olutions under a given head can be calculated by dividing the
•n number of revolutions by the square root of the head. The
398
The Selection of the Turbine,
ISO eoo
nCVOLUTIONS WEM ynHtftt
Fig. 242.— Curves Showing the Discharge at Various Speeds under tteTMtl
Head of about 17.16 Feet oC Uie 33-Iiich S, Morgan Smith Wh^l
140
^
X
o
u
LJ
^^
fk^
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<^
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BO
'r^
SO
e
0
7
D
a
0
9
a
li
pen CCNT SATC 0PCW1I6
Fig. 243* — Curves Showing the Estimated Discharge at Various Gate Op"
lugs and at Two Heads for the 33-Iiicli S. Morgan Smitli Wfa
Taken from Fig. 242J
^^^ A Graphical Method o£ Calcuiaiion. 399 1
w
80
76
72
I
i
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1 3a 40 42 44 48 46 5Q 52 54
RPM UNDER DNC FOOT HEAD.
244.— -Curves of the 33-1 uch S- Morgan Smith ^bee\ tot Oiie VoQlU^sj&i
V^
400
The Selection of the Turbine,
result is the comparative revolutions under one foot head, and a
line drawn vertically at the point so located on the diagram will
give the basis of calculations for power and discharge by muJti*
plying by hi and h^, respectively, for each gate opening and by
reading the efficiency direct.
For the wheel under 200 revolutions at 25 and 16 foot heads the
etjuivalent speeds on the diagram are 40 and 50, respectively,
Lines drawn vertically at these points will intersect the curves oi
efficiency, power and discharge and if reduced by a similar method
will give curves essentially the same as those shown in Figs, 239,
241 and 243. This is probably the best method for common use
in studying, from test data, the operation of a wheel under a
riable head.
190. The Construction of the Characteristic Curves of a Ter-
bine. — It is frequently desirable to make a more thorough analy-
sts, based on the available test, of the conditions under which 1
wheel can operate* For this purpose, the writer finds the use
what he has termed "the characteristic curve" o^ a turbine to he
the most comprehensive method for such an analysis*
For this purpose, prepare a diagram on which the ordinate^ rep-
resent the values of <^ and the r, p, m. under one foot head, ad
the abscissas the discharge of the wheels in cubic feet per second
under one foot head. It is also found desirable to show on the
upper margin of the diagram the horse power under one fo<^^ hea4
with iao% efficiency, corresponding to the discharge shown below.
For each experimental result the values of <p and of the discharge
under one foot head are determined by formulas (l) and {])*
The point representing these values is then platted on the dts-
g^ram, and the efficiency, as determined by the test for that exp^n-
ment, is written closely adjoining the platted point. This is don^
for each experiment at each condition of gate. After all the cX'
perimental points are platted^ and the resulting efficiency at each
given point is expressed, lines of equal efficiency are interpolitrf'
on the drawing, and will indicate the general law of the variation
of efficiency as represented by the test
It is, of course, possible to reduce the horse power determine
for each experiment to the theoretical horse power under one f<
head, and record it at the corresponding point, and then interpolate^
horse power curves, as in the case of the efficiency curves. It
been found by the writer, however, to be more satisfactory to ul
KU^iii
The Characteristic Curve. 401
Ac horse power scale at the top of the diagram, together with the
efficiency lines already drawn, for the calculation and platting of
the horse power curves. The horse power at any point will, of
course, equal the theoretical horse power expressed at the upper
margin, multiplied by the efficiency at the given points.
In determining the horse power curve, it is best to assume the
horse power of the desired curve, and then determine its location
in regard to the theoretical Morse power from the equation.
A. H. P = T. H. P. X Efficiency.
For example, on Fig. 245, if it is desired to plat the curve rep-
resenting 2 A. H. P. it may be done as follows: — The line repre-
senting two actual horse power will intersect the 70% efficiency
line at two paints whose abscissae are determined from the T. H.
P. scale by the equation
m rr T. A. H. P. 2
T.H.P.=-nEl- = -770 =2.86
If, therefore, the two points of intersection of the abscissa 2.86,
as indicated on the upper T. H. P. scale, with the 70% efficiency
line, are marked, two points will be established on the 2 A. H. P.
line. As many of the lines of equal efficiency and equal horse
power can be drawn on the diagram as may be desired, but if the
lines of the drawing or diagram are too numerous, confusion will
result rather than clearness.
One of the most complete sets of experiments with, or tests of,
a turbine water wheel which the writer has been able to obtain
is the set of experiments made for the Tremont and Suffolk Mills
at the Holyoke Testing Flume, December 3-5,1890, on a 48 inch
Victor turbine, with cylinder gate (See "Notes on Water Power
Equipment,*' by A. H. Hunking), which is given in full in Table
LX.*
From this table, and in the manner above described, a char-
acteristic curve of this wheel has been prepared, and is shown by
Fig. 245. In this Figure the efficiency curves are shown in black,
the horse power curves are shown in red, and the lines showing
the relations of discharge and <^ at various gate openings are
shown by the dotted lines connecting the experimental points.
191. The Consideration of the Turbine from its Characteristic
Curve: — From this characteristic curve the action of the wheel
under all conditions of operation within the experimental limits
of ^ can be readily determined. The use of the characteristic
• See Appendix — D.
MOQSC POWER UNDEP
[ ta I -i* 11
04
lo n
19 IS 1^ I a ro ?o ei
Fif, 24o. — *^Ch«raeti*ni4tir Cm
D wiTM lOo PCPicciMT crriciewcr
Idof Ta r b f ne* wi th C v 1 i n der G ate.
404
The Sdection o£ the Turbine*
curve is based upon the assumption that the efficiency will rcmiffl ^|
constant for a variable head as long as i^ remains constant, ^|
The efficiency and horse power lines as interpolated, are sift- |H
ject to errors of interpolation, the extent of which can be readily' ■*-
judged from the diagram made< The conditions of the test m H^
approximately checked by this diagram, for any marked irregularis V
ties in these curves must be doe to errors in testing, or to poor H
workmanship. H
By inspection it is possible to decide immodiately the vake fl
of i> that must be maintained in order to maintain the maximum ■
efficiency at any particular condition of gate. For example: KB
the maximum efficiency at full load is desired, 4> with this wheel ■
should equal about .69, If the maximum efficiency at 75 gate is 1
desired, the value of <^ should be about .65, and for maximum ei- J
ficiency at .50 g^te, 1^ should be reduced to about .64, ■
Knowing the head under which the wheel is to operate, the nec-^
essary number of revolutions at any head can be calculated by
formula (i) or by multiplying the r* p, m, at one foot head by tk
i/Fand the conditions of operation, in regard to both power and |
efficiency at all gates, will be determined by the intersection of a J
horizontal line through the chosen value of <^ with the efficiency -B
and horse power lines. If, for example, it is decided that <^ shall ^
be .66, a horizontal line running directly through the diagram at
<^=.66 will, by means of the various points of intersection with ,
the gate opening, efficiency and horse power lines, give all infor-
mation desired and from it can be calculated the efficiency, speed,
discharge and horse power of the wheel for the head under which
it is to operate. The intersection of this .66 <fi line with the va-
rious efficiency curves will give the relation of efficiency to dis-
charge with one foot head. The discharge tinder the required
head can be calculated by equation (8). 1* e, by multiplying the dis^
charge shown at the bottom of the diagram (one foot head) by V^-
The efficiencies at each gate position will remain unchanged by
this change in head since ^ is fixed at *66. If a 16 fool head be
considered, the discharge at any point will be four times tlie dis-
charge read from the diagram.
The relation of horse power to discharge is also shown by the
intersection of the <^ line with the horse power curves. The ac-
tual horse power under any head can be determined by equation
(11) i. e, by multiplying the horse power, as read from the dia-
laractenstic Uurve.
405
^m (one foot head) by h\ The horse power at 16 foot head will
^refore be 64 times that given by the diagram.
If it is desired to utilize the characteristic cun^e for the consid*
atioo of a wheel of another size but of the same series^ the power
D *
nd discharge must be multiplied by the ratio -^r
All of the various types of curves showing the results of opera-
iniiiiiiiiiiiimii
UIIIIIIIIIIIIIIIIJ
::aH::;:;;::;::::::::s»B»»»»:»:::»:s»:n:::n!;s'^i\s.vi::
4o6 The Selection of the Turbine: ^^^^
tion of the wheel as hitherto described are shown by, or ^di
L calculated from, the characteristic curve. ^M
^^ Fig. 246^ showing the relation of the number of revolutions touj
^" efficiency and discharge of the wheel, is one example of such ul
1 192, Other Characteristic Curves. — Fi^, 247 is the character^
L curve of a 44 inch "Improved New American" turbine showing tl|
^K HORSE POWER UNDER ONE FOOT HEAD WH^H 100 PEftCOIT eTFIDIENCy
^H ..^ 2.0 2.5 3,0 3.9 4.0 4.5 5,0
1
. . .^^
42
40
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^B 16 W 20 22 24 26 26 30 32 34 31 36 40 42 44 4S 48
^H DI3CHARGC IK CURlC FCET PER 8ECDND O«J0eR CMC FOOT MEAD
^H Pig, 247.— Chara<'ter1etlc Curve of a 44-Ineh "improved New Amei
^^1 Turbine. .
1
The Characteristic Curve.
407
ion of the wheel through a considerable range of heads,
utcr line entitled "Head at 120 r. p. m., shows the values of <f>
I at which the wheel would have to operate to maintain 120
n. at the indicated heads. The location of these points may
termined in two ways: First. — By calculating the values of
^
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^
— -*
4
;^
fJ"
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48. — Curves Constructed from Fig. 247 Showing the Power at Two
Speeds of Six "Improved New American" Wheels.
a given head and number of revolutions, and locating the
•ponding point from the scale on the left of the diagram:
d. — By dividing the number of revolutions by the square
A the head and fixing the point by the corresponding revolu-
under one foot head, as shown on the scale of r. p. m. at the
of the diagram.
4o8
The Selection of the Turbine.
At 14 foot head the wheel will operate at about the maximum ef- \
ficiency. If the head be decreased to 12\ the relative efficiencies |
will still reniaiii fairly satisfactory, but will decrease rapidly at
to' as shown by a horizDntal line drawn through the corresponding ^
point. It is also evident that at 8' the efficiency becomes very lo^v,
and below this head the wheel would probably be unable to maio-
tain 120 r, p, m.
HO REE POWER UNDER QNC FQOT MCAD WTTM lOD l»ERC{3fT CFnCEfCr
9r* 9,1 i.t 4.0 4.3 4 4 4.« 4.1 l.U »,J 9.4 ** t.i
I
Fig. 249, — CliaracterlBtle Curves of & Wellman-Seaver-Morgan 51-lQdi M^
Cormick Wheel,
The second line at the right shows the value of 4^ and xij at va-
rious heads when operating at lOO revolutions per minute. At
this speed the wheel will operate satisfactorily under heads from
14' to as low as 7', or even less. The efficiency at 14 foot head io
this case will be less than at 120 n p. m*, and the efficiency 0! oper*
at ion will increase as the head diminishes to the g and 10 foot
point, where the best efficiencies are obtained at 100 r, p. m. Be*
low this point the efficiency of operation will gradually decrease.
Provided the revolutions per minute are satisfactorily selected, \\
will be seen that the wheel will meet successfully a wide variatiofl
in the operating conditions.
The Characteristic Curve,
409
Fig. 248 IS a diagram constructed from this characteristic curve
nd shov^rs the power of six turbines of this series but of 49" diam-
ttr connected tandem to a horizontal shaft and operated at the
'^arious heads and revolutions above discussed. The curves show
ht condition both at full and at part gates. The gradual change
HDUSC power UtlDEA 0N£ FOOT HEAD WTH 100 PERCENT EFnCEIIS:Y
1.5 g.Q 2,5 3.0 3>S 4.0 4.S 5,0
I
10 12 14 16 fS 20 22 24 26 2B 30 32 34 36 39 40 42 44
0JSCHAR6E IN CUiiC FEET PER SECOND UNDER ONE FOOT HCAO
W^ 260,~Char^cterlstlc Curves of the 99i4<Tnch Tremoiat Fourneyron WheeL
H 410 The Selection gf the Turbine.
H in the relative position of the 100 and the 120 r. p. m. curves, as
H the head ehanges, should be noted.
H Fig, 249 shows the characteristic curve of a 51" McCormick tur-
H bine, as manufactured by Jolly Brothers for the Wellman-SeaveH
H Morgan Company, At the right of the diagram are shown tlm
H^ relative values of tf> and at the left the values of n for heads ironfl
^^^^V MDnsc powcn unua oni: foot hcao otth ido fCRcmf trnaocir ^|
^^^^H ^ t3 ft 77 2a 25 3Ct 3J 3i 3J 3* 23 IB 17 3M IB Aa 4\ *i Al ** 4^ *& ^ *t *9 * 1
^9i
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OiaCNAUSC M4 CUBIC fECT f>£fl SUOMQ UMOPI OhC rOOTT HUO
ff. 2S1. — Gbaracteristic Gurvea of a 4o-IiicJi "Samsoa* Wheel. (Jim^
Leffel ft Co.)
0 8 feet, at go and loo r. p. m. This curve shows that this
el will work satisfactorily under a wide range of conditions,
suitable speed is chosen.
g. 250 is the characteristic curve of the Tremont turbine tcstw
ames B. Francis, and described in the "Lowell Hydraulic E*"
ments," This wheel was a Fourneyron turbine of about 7^'
e power at 13' head,
g, 251 is the characteristic curve of a 45" Leffel turbine, wbitl
been selected for the Morris Plant of the Economy Light m3<
er Company, now under construction on the Des Plainfi*
;r, about twelve miles south of Joliet, Illinois. 1% is to be op
fd at 120 revolutions per minute and under variations in ht^
The Characteristic Curve.
411
n 16 to 8 feet- Eight units, each consisting of .eight of these
^wheels, connected tandem, are to be installed to operate eight 1,000
K. W. alternating generators. This diagram was prepared from
the test sheet accompanying the bid of the James Lcffel & Com-
panj. In the construction of the wheels for the plant, an attenipt
w^as made to so alter them as to maintain a high efficiency for a
'liO
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3« it i
WTTH IDQ PEH CEMT
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Fig. 252.— Characteristic Curves of a 45-lnch **Samsoii" WlieeL (James
Leffel & Co.)
greater range of gate conditions than ordinarily obtained. Fig,
252 shows a characteristic curve of one of the new wheels as con-
structed for this plant* The analysis was made for the purpose of
estimating the results which would probably be secured under
service.
In Fig. 253 are shown the discharges, powers, and efficiencies
of one unit of eight wheels under all heads from 8 to 16 feet at
full and seven-eighths gate. Allowances would have to be made
in order to take into account the difference between the operation
of the eight ^vheels in the horizontal position connected in tandem ,
and in the position in which they were tested; but the diagram
■ ^12 The Stileclion of the Turbine.
H shown gives an analysis from which fairly satisfactory coodu*
H stons can be drawn.
1 193. Graphical Analysis as Developed by H, B. Taylor under
H supervision ofW, M, White* — A valuable method of grapbbl
^^^ HEAD
^^H S 9 ^ 10 12 tl U IS IS
1400
1700
isoa
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$
I30D
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FULL iATE trrft'i
lioS
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■ Fig.
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ana
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and
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and
253.^ — Curves Showing the Efficiency and tlie Maximum and (MlBtfM
Power and Discharge of One Unit ol 8 4&-Iiich Bamaon Wh^da ■
ysis is shown in Bulletin No. 2 of the I. P. Morris Company, fl
:h is discussed the variations in power and efficiency of a turbiaff
el capable of giving 13,500 horse power under a head of 65 feet,
at a speed of 107 revolutions per minute. This wheel 1^
gncd by this Company for the McCall-Ferry Power Company,
was to work under heads varying from 50 to 70 feet. -
Graphical Analysis of W. A. Waters.
413
414 '^^^ Selection of ihtt Turbititf. ^^I^^|
Figs, 254, 255 and 256 and the following description arc talccatB
with slight alterations, from the above named Bulletin* ■
Curve No, i, Fi|^, 254, shows the power which the wheel will 1
give for heads varying from 70 feet to zero» provided that the revo I
luttons are allowed to vary as the square root of the head, anl is I
based on equation (lo). I
From Curve No. 1, Fig. 254, it will be noted that at 70 foot htui |
the wheel will develop 15,000 horse power, and from Curve No. ^i. J
of the same Figure, it will be noted that the best speed of t«
wheel under the conditions of 70 foot head will be ni revolMtlonM
per minute. It will also be noted from Cun^e No. i that, undtrH
50 foot head, the wheel will develop 9,150 horse power, if it he ntd
at 94 revolutions per minute. That is to say, by keeping a consta™
ratio between the peripheral speed of the runner and the sqmPM
root of the head the efficiency of the wheel at varying heads is nofl
changed for any given setting of the gate, I
In order to properly utilize the output of the wheel, it is occevl
sary that the speed be kept constant. In order to determine ik
amount of power that will be lost by keeping the speed conftant
while the head varies, the curves of Fig. 255 were platted from
actual obser\^ations.
Curve No. i, Fig. 25s, is the full gate readings of the 10,500
horse power turbine* which was installed for the Shawinigan Wa-
ter and Power Company, This wheel was designed for 10.500
horse power when working under a head of 135 feet, and when
running at 180 revolutions per minute. The observations wWch
are platted on this curve were obtained by using the generator as
a brake for the wheel, and a water rheostat was used as a meatisof
loading the generator. The speed was then adjusted to 180 revolu-
tions per minute at the wide open gate and an observation mzdt
Ey varying the field of the generator, the speed of the unit was
varied without materially affecting the power and without moving
the gate of the wheel. Observations were made above and bebw
the normal speed through as wide limits as the rheostat in the
field circuit of the generator would permit. The power oaiiptit
was determined by means of accurately calibrated electrical to-
st rumen ts. The speed was determined by an accurately calibrat-
ed tachometer. The curves on this sheet give the relation between
^ and horse power.
Rcterring back to Fig. 254, and taking the 50 foot head 1
tionSi it should be noted that for a constant speed of 107 t^
dWitfHI^^I
'Graphical Analysis of W. A, Waters.
4»S
^Cujve& of tp and Power of Several L P, Morria Wheals. { Repro-
duced from Bull. Ho, 2 of I. P. Morn*. Co.)
4i6
The Selection of the Turbine,
tions per minute 4> would have to increase from the normal vilutj
of about ,68 to ,8a By referring again to Fig. 255, it will im
noted that when 0 was 0.8, with full gate opening, the power
dropped from 10,650 horse power to 10,250 horse power, or al>oui
3,3 per cent. From this fact the normal power as shown by Fig. 1
may he corrected for the new speed of rotation and a point on
Curiae No, 2, Fig, 254 obtained, giving the actual power whkli
would be developed by the wheel under the 50 foot head, anri
running at the constant speed of 107 revolutions per mimittJ
Curve No, 2 is platted in this manner from Curve No. I. I
As a check to Curve No, 1, Fig. 255, Curves Nos. 5* 6, 7, and Si
have been platted, all of which were made from actual obseni-l
tions, in the same manner as Curve No* i* All of these wheelfl
are of the Francis inflow type, and were designed for ^=,7, txceptj
Curv^e No, 6, which is an outward flow Fourneyron wheel, andB
was designed for <^ — -5. Curve No. 5 is for a 6,000 horse powcrl
wheel with gates in the draft tubes. The shape of the cunw
shows that the gate was probably not entirely open when the olhB
servations were made. ^
In Fig. 256 has been platted efficiency curves, which the df-
signed wheel would give under varying heads, and running at 2
constant number of revolutions. Curve No. i is an exact dupli*
cate of the efficiency curve which was obtained on a 3,500 horse
power wheel workini^ under 210 foot head, and making 250 revob-
tions per minute. The wheel is of the Francis inflow type* with 1
double runners, fitted with movable guide vanes, similar to \hostm
which are proposed to be used in the wheels for the McCalKFcirfB
Power Company, ■
It will be noted that the efficiency of the wheel reaches S2.3 p*"*
cent, at about seven-eighths power, the efficiency dropping to 81 *«
per cent, at fttll gate. It will be noted that the efficiency \$ nrfm
high at part load. This was accomplished ^n the design of the wMB
by sacrificing a higher efficiency at full load. This curve has !>ftr«B
taken as typical of the efficiency which would be obtained by thcB
wheel proposed for the McCall- Ferry Power Company, when wortj
ing under a 65 foot head. The efficiency curve of the io.50ol^^|
power wheel which \vas supplied by the I. P, Morris Compa^^H
the Shawinigan A¥ater and Power Company (See Fig, 236), giv'*H
higher results than the curve selected, but it was thought Jhal«
Curve No. 1 is the he^t for a typical curve. ^^^^^^^^^^|
Graphical Analysis of W. A. Waters. 417
Curve No. i, Fig. 256 was platted by assuming that, at full gate,
1,500 horse power corresponded to 13,500 horse power in the
vhcel to be designed. The part gate points of the curve were ob-
aincd by proportion. Curve No. 3 represents the efficiency and
X)wer of the wheel when working under 50 foot head, and at 94
r. p. m.
Point X on this curve was obtained in the following manner:
First, read on Curve No. 1, Fig. 254 the power which the wheel
would give under the 50 foot head, and revolutions best suited.
This is found to be 9,150 horse power. On Scale B, Fig. 256 a
line is drawn from 9,150 horse power to zero, forming Curve No.
10. To find what the efficiency would be at 8,000 horse power un-
der the 50 foot head, take the point at 8,000 horse power on Scale
B, projected horizontally until it intersects Curve No. 10, and
11,800 horse power will be read from Scale A. From the effici-
ency curve directly over 8,000 horse power on Scale A, the point, X.
will be found on Curve No. 3, which gives the efficiency of the
wheel when developing 8,000 horse power under the 50 foot head,
and running at the revolutions best suited, namely 94.
This wheel is to run, however, at 107 revolutions per minute,
under all conditions of head, and it is necessary to correct Curve
No. 3 for the drop in power and efficiency due to the increase in
speed.
Referring to Curve No. i. Fig. 255, it will be noted that the pow-
er varies when the speed varies, and in the calculations of effi-
ciency in Fig. 256, it has been assumed that the efficiency varies
directly as the power. In other words, it has been assumed that
the quantity of water does not vary when the revolutions are
changed with the constant setting of the gate. This is not strict-
tytrue but for the observations as platted o.n Curve No. i. Fig. 255
the quantity of water would probably vary only one-half of one
percent., increasing as the revolutions increase from 158 to 201.
Referring to Fig. 254, and the 50 foot head, it will be noted that
'vhen the speed is increased from the best speed of 94 revolutions
0 the desired speed of 107 revolutions, the power falls 3.3 per
ent. and the power and efficiency of the full gate point on Curve
^o, 3, Fig. 256 can be decreased 3.3 per cent, resultinjg in the full
^te point on Curve No. 2.
Referring to Fig. 255, Curves Nos. i, 2, 3, and 4, it will be noted
lat the slope of these curves between <^ = 0.7 and <^ - 0.8 is about
le same, and, therefore, the power afnd efficiency of all the points
4tH
The Selection of the Turbine,
imsi»»mHiniiii2tiim^:»iHii:?^iiifi!P^^^
t^^ riiiiiii tiliiMi
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ftft1±if»tmiH^ H
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Fl|f. 256.— Eat i ma ted Efficiency— Power Ciirvea of ilie Proposed McC*ll-F€JTy
Wheel, (Reproduced Uoin BuW, ISq, 2 vX I. P, Morris Co, )
Graphical Analysis of W. A. Waters. 419
n Curve No. 3, Fig. 256, can be reduced by the same percentage,
amely, 3.3 per cent. In this manner Curv^e No. 2, Fig. 256. is ob-
lined, which gives the power and efficiency of the wheel when
rorking under the 50 foot head, and running at the speed of 107
evolutions per minute. In the same manner Curves Nos. 5 and 7
re platted, Curves Nos. 4 and 6 being deduced therefrom, respec-
ively. In the same manner Curve No. 9 is platted, and Curve No. 8
educed therefrom. It will be noted that Curve No. 8 lies on the
pposite side of the parent curve to that of the other curves,
urve No. 8 crosses Curve No. 9 at 13,500 horse power on Scale
., and beyond this point would drop below Curve No. 9. The
Jason Curve No. 8 falls to the left of Curve No. 9, and shows
reater efficiency at part gate for the 70 foot head, is because when
changes from 0.7 to 0.65, Fig. 255, the partial gate Curves No«s. 2>
. and 4, Fig. 255, show the increase in power and efficiency,
hese points, however, cannot be very definitely determined, but
docs show that the assumption is correct that the designed
heel, working under the head of 70 feet, and running at 107 rev-
utions, will show higher percentage of efficiency at part gate
lan when running at the 65 foot head and the same powers.
The curves on Fig. 256 show that the efficiency is not serious-
affected by keeping the speed of the wheel constant under the
irying conditions of head. They do show, however, that the
)wer is seriously affected by keeping the speed of the wheel con-
ant under the varying conditions of head. The endings of the
irious curves show the maximum power, as read on Scale A,
hich the wheels will give under that head.
These curves, therefore, give the performance of the wheel when
inning at a constant number of revolutions, and working under
arying heads from 50 to 70 feet. The curves, of course, are not
bsolutely correct. They show, however, fairly accurately, the
mount of variation in efficiency and power which may be cx-
ected from the actual conditions obtained with the proposed
*ccl under the head for which it was designed.
CHAPTER XVII
THE LOAD CURVE AND LOAD FACTOR, AND THEIR
INFLUENCE ON THE DESIGN OF THE POWTR
PLANT
194. Variation in Load. — All power plants arc subjected to more
or less change in load» and this continually changing load has an
iTTiportant bearing on the economy of the plant, and should be car^
fully considered in its design and construction.
If the power output of any plant be ascertained, minute by mm-
ute or hour by hour, either by means of recording devices or by
reading the various forms of power indicators usually provided
for such purposes, and a graphical record of such readings bf
made, a curve varying in height, in proportion as the power varies
from time to time, will result. This curve is termed the daily
load curve. The load curve itself will vary from day to day ^
the various demands for power vary, hut it usually possesses cer-^
tain characteristic features which depend on the load tributary l<
each plant and which vary somewhat as the seasons or other con-
ditions cause the load to vary.
The characteristics of the load curve, due to certain demands,
can be quite safely predicted. A power plant in a large city, fofj
example, will carry a comparatively small continuous night l<Da4j
This, in dark weather and in winter, will he increased by the earl]
risers who are obliged to go early to shop and factory* Tkse
demands usually begin to affect the load curve about 5 A. M. and
may cease wholly, or in part, by 7 A, M., depending on the seisoi
and latitude. From 7 to 8 A. M. the motor load begins to be felt
This may reach a maximum from 10 to T2, and usually decreases
from 12 to 2 during the lunch hours. The maximum load usually
comes in the afternoon when business reaches a maximum, and
when the largest amount of power and also light (in the late after-
noon) are used. The. load begins to decrease after the evenmg
meal, as the demand for light lessens, and may again increase soP^
what as the theatres and halls open for evenings' amusements, Tht
■character of the load curves, due to various loads, is best under-
stood bv a study of the actual curves themselves.
LfOad Curves of Light and Power Plants. 421
195. Load Curves of Light and Power Plants. — ^The curves
shown in Fig. 257 are from the plants of the Hartford Electric
Light Co., of Hartford, Conn., and will illustrate variation of the
Load curve at different seasons of the year. These curves were
taken from an article in "The Electrical World and Engineer" of
March 8th, 1902. This plant is a combined water and steam pow-
er plant, and is provided with a storage battery to assist in equal-
izing the load. These curves are described as follows:
"On a week day in March, 1901, the maximum load was 1720
k. w. and the total energy output was 30249 k. w. hours. The aver-
age hourly load was then 1260 k. w. or 46 per cent, of the maximum
load. On this same day the battery discharged at the rate of 260
k. w. at the peak of the load. In the early morning hours of this day
the load on the system, apart from battery charging, reached its
minimum at 612 k. w., or only 22.5 per cent, of the maximum load.
In June, 1901, the maximum load on a certain week day was 1390
k. w., and the minimum 250 k. w., or 18 per cent, of the former.
The total output on this day was 2505 k. w. hours, so that the
average load during the 24 hours was 1046 k. w. or 75 per cent, of
the maximum. In January, the maximum load came on between
4 and 5 P. M., when lighting was the predominant factor, but in
July the greatest demand came on the system in the latter part
of the forenoon, and must have been made up in large part by re-
quirements for electric power. By December 1901, the maximum
load reached 2838 k. w. and the minimum 612 k. w. The approxi-
mate capacity of all connected lamps and motors in that month
was 8530 k. w. The maximum load for the December day of 2838
k.w. is only 33 per cent, of the connected capacity. On this day
the total output was 3219 k. w. hours, so that the average load
during the 24 hours was 1342 k. w. This average is 15 per cent, of
fte total capacity."
Fig. 258 is a combined annual load curve for several years, and
'Jot only shows the increase in the electrical output of this system
for the years from 1898 to 1905, but also the annual monthly
i^hange in load from a maximum in December or January to a
minimum in June or July. This variation fortunately accompanied
'imilar variation in the flow of the Farmington River on which
fiost of the power was developed.
Up to the middle of 1898 the entire load of this Company was
arried by a single water power plant. The natural increase in
emand for power necessitated the construction of a second plant
121
The Lfoad Curve,
Kilowatts.
§ I
,5i
^J'--'' ' ^^
f ^^¥— --.^
____ ^ ____^.„ ____...
.»s
^ «
s
;i *
1 "3
" »- * = 1 ^ ^ ,
^ It 1 — T—
L^^_i ^tfttrii 1 1 1 1 1 ff
X i — . .— ^ _— , P*- ^ =,, , L , Hi—,
< C
1 1 1 M M M M 1 1 1 1 1 1 lyjl 1 1
-fc ;»;
= 5
a ^
' 6
5
i
Load Curves of Light and Power Plants.
423
the same river, and up to January 1905, the two water power
mts were able to carry most of the load, steam auxiliaries, how-
er, being occasionally used, as indicated by the dotted line.
Fig. 259 shows daily load curves from the Christiania Power
ations, of Christiania, Norway. In this figure are shown the max-
lum, the minimum, and a mean curve for the entire year. • The
1000000
750000
&00000
anooo
Jan. JuL Jan Jul Jan. Jul. Jan. Jul. Jan. Jul. Jan. Jul. Jan Jul. Jan. Jul.
1898 1800 1900 1901 1906 1908 1904 1006
Steam
Water
Total
Fig. 258.— Eneigy Output of Hartford Electric Light Co.
Electrical World and Engineer. )
(From
fFerence between the maximum and minimum curves is here very
irked. This is readily ascribed to the high latitude of Christiania
the long twilights of summer render lighting at that season
Host unnecessary, while the very short and dark days of winter
eate not only a high maximum but a high continual demand dur-
g the entire day. No data as to kind of load is available.
Fig. 260 is a power curve from the New York Edison Company.
On August 1st, 1905, there were connected up to the system of
e New York Edison Company an equivalent of 1,651,917 incan-
scent lamps, 22,093 arc lamps, 2,539 ^' ^- ^^ storage batteries
424
The Load Curve.
and 99i258 H. P, in motors. The lighting load forms 52.2 per cent^
of the connected load.
The effect of extraordinary conditions on the load curv^e and I
necessity of some kind of storage to provide for the same, is wd
illustrated by Fig. 261 which shows the effect on the load cunci
1000
€00
^ GOO
o
400
«D
/
/
\
1
I*
/
j
e
II f
1 f
\
L
1
\
\
X
4
t'
^^^
\
\
J
/
\
'.i^^
V
.<?:
\
\
\
\
^
'^
_-
^
/
,^
f
M \
Ml ti
y<uih
A
JUL
V
Y , 1 ft .
n
w
/
\\
—
-^
=d
fed
bd
bd
=d
bd
t=
td
b=d
t=J
tzj
4 0
A.M.
M
Fig, 259.— Typicai Electric Lighting Load Curves. Christiana, Norwiy.
Power Smtioni.
of a lighting plant of a sudden thunderstorm. When such a st<
occurs in the late afternoon the light load from schools, offio
stores, etc., may be suddenly thrown on, and the result may be
extraordinary load which the plant must meet.
196, Factory Load Curves. — Shop and factory loads are suf
posed to be the most uniform in character, yet they are subject W
great variation, due to the sudden turning on or off of the itul-
chines. Fig, 262 shows the load curve of the Pennsylvania Rail*
road Shops at Altoona, Pennsylvania.
The shops of the Pennsylvania Railroad are located in and arooni
Altoona, Pennsylvania, in groups, each group being supplied by its
own power station* No data as to the number and power tA motort
connected up is available, but the following shows to some extent
how the load is divided. The Machine Shop power plant embnrti
Factory Load Curves.
42s
-300 k. w. generators, i Brush arc generator (power unknown),
id a 40 H. P. Thompson-Houston arc generator for lighting shop
id grounds. At the Car Shops 4-250 k. w. and 1-625 k. w. gen-
•ators are used. Current is supplied to 75 arc lights in shops and
ards. At the Junita shops 3-300 k. w. generators are used for
)wcr purposes only. At South Altoona the generating station
00000
* —
-
V
BOOOO
^
/
^
4000O
\
8000O
10000 '
^
/
f
y
N
N
N,
(
>-
—
V
/•
/
\
10000
s
i
^
/
— 1
\
*^
""^
\%
6
A. M.
12
M.
0
P.M.
10
2,1904.
18
New York Edieon Co., Load Curve, day of Max. load, Dec.
•IncluiHiis 3900 K. W. delivered directly at 6600 Volts A. 0.
Fig. 260.— Typical Electric Lighting Load Curve.
ibraces 1-50 k. w., and 2-500 k. w., and 2-300 k. w. generators,
e loads are quite variable, as would be expected in a railroad
)p, there being some very heavy machines in intermittent opera-
n, one planer running as high as 80 H. P., while 20 H. P. motors
: numerous. The normal load is less than the maximum, but the
ier is frequently reached.
V, B and C, Fig. 263, are three typical factory lo5ad curves which
resent types of load curves from three different electric power
jonSy A in an Eastern, B in a Central, and C in a far Western
e. These curves are taken from an article on "The Economics
Electric Power" in Cassier's Magazine for March, 1894. The
uits from these stations are exclusively motor circuits, the num-
of motors connected being given in the following tables ;
426
The Load Curve.
o
6000
1
4000
i
8000
J 1
Mfln
1
-
-
K
i A
/
"-V
\.
/ "
1/
^:
lUW
-rf'^v^
/
V
\
0
/
\
6
10
18
6
P.IL
Fig. 261. — Sharp Thunder Storm Peak, Dickenson St Station, Mancheitr.
Eng.
A
B
C
Size of
Motor
<H. P.)
No. in
Use.
Com-
bined
H. P.
Size of
Mot or
(H. P.)
No. in
Use.
Com-
bined
H. P.
Size of
Motor
(H. P.)
No. in
Use.
Com-
bined
ap.
i
3
li
J
3
1
J
4
1
1
2
31
10
31
20
}
2
1
1
1
1
6
1
5
3
19
57
1
15
16
2
8
6
5
10
50
2
14
28
3
4
12
7i
3
22}
3
6
16
6
3
15
10
12
120
5
12
60
6
6
30
13
5
75
7*
12
90
Bi
3
25J
20
2
40
10
16
150
10
6
60
25
4
100
16
9
135
14
6
84
50
1
50
20
6
100
16
1
15
25
3
76
17*
1
17»
30
40
3
1
90
40
26
30
40
60
70
1
8
1
2
1
25
90
40
120
70
Total...
100
667
100
7991
60
616J
Factory Load Curves.
i1i§§i§§§§§a
427
428
The Load Curve*
|£5
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(
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>
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m KDURS '
100
114
.1 KW.\
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176
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S 100
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6 7 S 0 JO n IS 1 2 3 I 5 fi 7 » 0 10 11 It
A.M. M. P. IL
Flff. 2S3.^Typlca] Factoir Load CtirvdB, (Caffller's Mammal oe,)
Load Curve of London Hydraulic Company.
429
he circuits covered by the diagram B some of the motors are
miles and more distant from the power stations.
le deduction which may be made from a study of these curves
at in an electrical power system where a considerable number
otors are employed the initial dynamo plant need not be equal
le total motor load. In the case in hand the curves show that
generator need be but from 25 per cent, to 40 per cent, of the
lOJ
tM
h .
w
Ai
nV
\
K .
V
\
00
m/
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1
V
V
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NOVCMBCR S,I804
\
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100
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t
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SOCTOBCR I4,^I8S7
\
000
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-—
6
iuM.
10
M.
G
P.M.
264. — Maximum Days of Pumping. — London Hydraulic Supply. (Ca»-
Bier's Magazine.)
d capacity of the motors connected. In order to check off this
lomenal condition actual meter readings were taken monthly
1 fifty-three different shops covering a period of from four to
months, current to these shops being sold on the meter basis,
results showed that only 25V^ per cent, of the nominal capacity
he motors was employed, thus practically checking the condi-
s indicated by the diagrams of the central power stations.
17. Load Curve of London Hydraulic Supply Company. — Fig.
is a load curve of The London Hydraulic Supply Company,
:h is rather exceptional in that the power is used almost en-
y for running elevators and is therefore almost exclusively a
38
^L 430
The Load Curve. ■
^^^^^^ sooo
] \ \ i \ \
T
JUN
t-
SI
11
04
f
1
<
1
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1
1
lurfAio
1 1 1
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t
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h
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TAILS POWCH lUrFALOJ
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t _. i i 1 ,
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rig. :6\ ^
Kilowatts
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tr
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Fig. 2C6.
■
13 s 4 ft e 10 13 s 4 e 8 ia iiH
A. A{, at p. BL ■
— T/picAl Railway Load Curve&j Internatioikal Ry. Co. (From £^i^|
trical World and Engineer.) H
Railway Load Curve. 431
lay load. The London Hydraulic Supply Company furnishes
/ater under a pressure of 750 pounds per square inch through a sys-
era of mains 86 miles long. In 1894, 2915 machines were connected
0 this system, of which 650 were passenger elevators, 2000 freight
levators and cranes, 90 presses of various kinds, 95 motors, and
to fire hydrants. Each 1000 gallons of water pumped represents
1.738 H. P. hours, therefore, the maximum on the diagram repre-
ients about 1200 H. P. The preponderant influence of the elevator
oad is shown in the rapid rise from 6 to 10 A. M. and the some-
what slower decline from 4 to 12 P. M.
198. Railway Load Curves. — ^The power load most subject to
nolent fluctations is that utilized for railway purposes. The sud-
fcn changes in the demand for power occasioned by stopping and
itarting of cars, which may, under some conditions, occur simul-
taneously are often very rapid and the resulting load fluctuations
rcry great
Figs. 265 and 266 show two sets of curves taken from the power
charts of the International Railway Company of Buffalo, which
may be considered typical for electric railways. Each chart has
two sets of curves, one for the city lines, on which the trafiic is
purely urban in character, and the other for the Tonawanda, Lock-
K)rt and Olcott Line, which is an interurban line. In either set the
otal load at any time is represented by the ordinate to the highest
urve in that set. The amount of load carried by any portion of
le system is represented by the difference between the ordinates
> the curve of that portion and to the curve next below. On the
'ban lines two peaks will be observed, one at 8 A. M. and one at
P. M., for both winter and summer, the afternoon peak of the
rmer being nearly 75 per cent greater than the latter, however,
he load curve of the interurban line appears to be nearly uniform
roughout the year.
The data, on page 432, concerning these curves are taken from
The Electrical World and Engineer'* of December 10, 1904.
199. Load Conditions for Maximum Returns. — It is manifest
at no plant will receive its maximum returns without operating
full load all of the time ; that if it operates at less than full load
$ income will be reduced unless more is charged for power so
jlivcred; and that if the load carried for a large portion of the
ne is comparatively small and the returns for such power are not
oportionately large the plant may be found to be an unprofitable
433
The Load Curve-
investment. On every plant the fixed charges, which include in
terest on first cost, depreciation charges and taxes, continue at i _
uniform rate every hour of the day and every day of the year*
operating expenses increase somewhat with the total amount ofl
power furnished but not in proportion. An increase in the total l
Data from Curves of Figure iSS.
Pus€HASKD Power.
Tonawand^
Buffalo.
Lock*
port.
nicott
Total.
Sto&aqe Battkbiis^'
TonawandtL,
Buf-
falo.
Lock-
port.
Toil]
Told.
Maximum H. P
Mtnifnum H. P.
Average H. P..
R P,, houna, .,
1.667
4,6345
111,272
S;J,009
1,985
319
1,221
29,302
21,859
8,09S
1,985
6,857
140,674
104,868
3,752
79
1,262
8,406
6,271
6S5
40
274
3.480
2,596
113,'
Maximum number of cars in sei vice in BuMalOj 406.
Average voJte at B. C» buflbarfi, 692.
Btata of weatber^ S a. m., cloudy; 6 p. m., fair.
TemperatuFft; 8 a, m., 66 degreea F.; 6 p. m., 74 degrees F,
Data from Curves of Figure JKfi*
PuaciiAHE^o Power.
Tofiawandot
BtifEftlo.
Lock*
port,
Oicott
Stbim Powi
Total*
Niag-
ara St
Vir-
ginia
8t.
Total.
Buf-
falo,
Mflximam H. P.
Minimum H. P.
Avera^f* H. P...
H. P*, hours, ..*
K. W„ hours.,.
7,622
5,303
6,002
144,046
107,458
2,026
199
1.149
27,584
20,578
9,647
2,502
7, 151
171,630
]28,03H
3,414
969
2, 115
38,442
28,678
2,064
715
1,641
4,367
3,238
5.478
l,6tt8
3,756
42,809
31,93<'
3,970
79
U224
7,344
&,47W
Average volte at D, C. busbare, 592.
State of weather: 8 a, m,, cloudy; 6 p. m.^ cloudy,
Tainperature: 8 a, m., 20 degrees F.; 6 p. m. ^ degrees F»
output of a given plant, therefore, means a direct mcrease in 1
net earnings of the plant and unless the power plant is constifl
operating at its maximum capacity, its earning efHciency is not
the highest point.
The Load Curve in Relation to Machine Selection. 433
It will be noted at once that if a machine can be operated at its
full capacity for the entire time, that the work done will be done
under the most economical conditions as far as each unit of output
(Horse Power Hour or Kilo- Watt Hour) is concerned. The in-
terest on the first cost and other fixed charges will be distributed
among the maximum number of power units. The cost of wear,
and the repairs, while they increase with the amount of power fur-
nished, are not in direct proportion thereto, and decrease per unit
as the average load carried reaches nearer the maximum of the
machinery used. The same is true of the cost of attendance and
most other operating expenses.
200. The Load Curve in Relation to Machine Selection. — A com-
parison between the average load carried and the maximum load
will show the relation between the machinery which it is necessary
to install and the active work which it has to do, and furnishes a
basis for the study of the possible earnings of the plant.
The ratio of the average to the maximum load is called the **load
factor." Some engineers use the term **load factor" as represent-
ing the ratio between the average load actually carried and the
maximum capacity of the machinery operated. The writer however,
prefers the. term '^machine factor" to represent this ratio. The same
term is also sometimes applied to the ratio of the average load to
the machinery in hourly operation, but to this the term **hourly
niachine factor" seems more applicable. The ratio of the average
load to the total capacity of the station would seem best represented
by the expression **capacity factor."
In order to have a plant work at the maximum advantage, it
niust be designed to fit the contingencies of the load. The opera-
tion of a machine at partial load is not only expensive on the basis
of fixed charges, but is still more so on account of the decreased
efficiency under such conditions.
With a varying load, efficient operation usually involves the in-
stallation of two or more generators of such capacity that a single
Unit will furnish the power required during the hours of minimum
demand and at the same time operate at a fairly efficient rate. As
the daily demand for power increases, additional units are started
tad operated, still under economical conditions, and at the peak
of the load one or more additional units may be cut in and operated
For the limited time during which the maximum demands prevail.
Such an arrangement assures reasonable economy of operation at
all times, even when great changes of load are of daily occurrence
434
The Load Curve*
aoi. Influence of Management on Load Curve* — ^The relations oi
the "load curve," the "load factor," the "machine factor" and the
"capacity factor" are, or may be, to an extent controlled by tbt
business management of any plant, and by the selection and the
character of the load to be carried, where such selection is possiye.
Each consumer of power will develop a particular curve due to tk
character of the work donCj and it is frequently possible, by a ju-
dicious selection of customers, and especially by a proper gracing
of rates, to raise the load factor and thereby decrease the cost of
operation and increase the net profits from the plant. A study oi i
the probable plant factors is necessary for the judicious selectio
of machinery in order to attain the most efficient operation an(|
in a hydraulic plant, in order to properly design it and conscr
the maximum energy of the stream that is being developed
202. Relation of Load Curve to Stream Flow and Auxiliaiy]
Power. — Some of the relations between the load factor and tlifr,
conditions under which a hydraulic plant may have to be operatc4|
are shown by Figs. 267, 268 and 269.
In Fig. 267, diagram A shows a typical daily load curve from tk
terminal station at St, Louis, a curve quite similar in general char-
acter to those previously shown.
Diagram B shows the power that must be developed by a stream
in order to take care of the load represented by this load cunre.
under conditions where no auxiliary power or storage arc available.
In this case, it will he noted that the available water power mustbej
equivalent to or greater than the maximum peak load, and that all J
power represented by the area above the load line, amounting in thtl
case illustrated to about 40 per cent, of the total available pofttfjj
will be wasted.
Diagram C illustrates a condition where the average load aw
water power are equal. In this case, pondage or storage, rep"
sented by the cross-hatched area below the average Iine» may
utilized to furnish the peak power represented by the cross-KatcWl
area above the average line. Without pondage, the cross-hatcM
area below the average load line will represent the energy wasted,
and the crQss-hatched area above the average load line will Tepf^
sent the energy which must be supplied by auxiliary power. With-
out pondage the power of the stream must be utilized as it parses,
and in tlic diagram B, of Fig. 267, the power represented above th^
load line under such conditions must be wasted.
Relation of Load Curve to Water Power.
435
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ITORAOE OR AUXILIARY POWER REQUIRED^
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RELATION OF POWER SUPPLY AND DEMAND
Fig. 267.
43^
The Load Curve,
These same conditions are shown both by diagram C, Fig* 26I
and diagram A, Fig. 269. In the latter, with water power above
the average load of the plant, the peak load must be supplied by
auxiliary power, although more water power than would be suS
cient to handle it is daily wasted.
Diagram E, Fig. 26S, shows a condition with low water power
no storage available, and the power less than the average load. In
this case the water power wasted is comparatively small, and tliij
amount, and especially the capacity, of the auxiliary power
comes large.
Diagram C, Fig. 268, represents a water power conditionf whert
the power available is less than the average load, where stoi
is practically unlimited, and some auxiliary power is necessary ii
order to carry the peak of the load. Under these conditions, th*
water power, which would otherwise be wasted during the \Mi
of minimum load, is impounded, and can be utilized together witli
the auxiliary power at times of maximum load* The diagramj
shows a, method of utilizing the minimum capacity of auxiliai
power by utilizing the stored water power to its greatest advii
tage, and utilizing auxiliary power uniformly throughout th
period where auxiliary power is demanded.
Diagram A, Fig. 269, represqnts the same conditions where stof^
age is limited, and auxiliary power is necessarily required to hdj
■out the peak load conditions. In this case only a certain amounl
■of the spare water can be stored, the balance being wasted at tim<
where it cannot be continuously utilized.
The conditions for reducing the total amount of auxiliary powi
hy utilizing the storage to advantage is shown in the same rnanm
as in diagram C, Fig. 268*
Diagram B, Fig. 269, shows a method of utilizing the minimui
capacity of auxiliary power in a plant where the water power
below the average load and the pondage is practically unlimiW
This is accomplished by the continuous operation of the auxili!
plant and the storage of water power during the hours of low c<
sumption^ for utilization during the hours of peak load*
A careful and detailed study of the load curve and load factor;
the method of increasing the latter and of designing the most
economical plant to take care of the condition to be met ; and the
adjustment of rates to attain equitable returns to the investor it
reasonable price to the consumer, are matters of plant design
worthy of the best efforts of the engineer.
Relation of Load Curve to Water Power.
437
•••
400
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AUXILIARY POWeil RCQUIIIEO . NO ITillABC AVAIUIU .
WATER POWER ORCAUR THAN AVCRAOC LOAD •
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AUXILIARY fOWER REQUIRED . OTORAOE UNLiMITED
WATER POWER LESS THAN AVERA6E LOAD
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RELATION OF POWER SUPPLY AND DEMAND .
Fig. 268.
433
The Load Curve.
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AUXtLIARY POWER [mIRIMUM RERUIRED] IN CONTtMtlOUa OCIVICE
ITORAOE UNLIMITEO
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Fig. 26S,
I
Literature on Load Curve. 439
LITERATURE.
REFERENCES OF LOAD CURVES AND LOAD FACTORS.
1. Load Curves of Electric Central Station. Elektrotechnische Zeitschrift
Vol. 25, page 68. Jan. 28, 1904.
2. Influence of Load Factor on the Cost of Electrical Energy. Edmund L.
Hill. Electrician (Lon.). Feb. 10, 1905.
3. Load Factor — Its Effect upon an Electricity Station. Alex Sinclair. Else
trician, London, June 30, 1905.
i Distribution of Power Load of EUectricity Works. Electrician (Lon.)
July 28, 1905.
5. The Load Factor of EHectric Generating Stationa Norberg>^hultz.
Cotistfania. Elektrotechnische Zeitschrift. Vol. 26, p. 919, Oct.
6, 1905.
6. The Effect of Load Factor on Cost of Power. E. M. Archibald. Eng.
News, Vol. 53, p. 169. Feb. 16, 1905. Elec. Age, Nov. 1906.
7. Electrical Transmission of Water Power. Alton D. Adams. Chap. I and
IL New York. McGraw Pub. Co. 1906.
8. Economy of Continued Railway and Lighting Plants. Ernest Ganzen
bach. St. Ry. Review, Feb. 15. 1906. EHec. World and Engr
Jan. 27, 1906.
9. Central Station Power. E. P. Espenschied, Jr. Proc Engrs. Soc. Wes.
Penn. Mar. 1906.
10. Relation of Load Factor to the E^rolution of Hydro-Electric Plants. S. B.
Storer. Am. Inst. Elec. Engrs. Mar. 23, 1906.
U. Notes on Design of Hydro-Electric Stations (With Reference to the In
fluence of Load Factor). David D. Rushmore. Proc. Am. Inst.
Elec. EngTB. April, 1906.
U. Effect of Day Load on Central Station Economy. J. P. Janes. Elec. Re
view, N. Y. May 12, 1906.
2. Sale and Measurement of Electric Power. S. B. Storer. EUectrical Age,
Aug. 1906.
4, Sale of Water Power from the Power Company's Point of View. C. E.
Parsons. Eng. Record, Aug. 11, 1906.
5. Contracting for Use of Hydro-Electric Power on Railway Systems. O. A.
Harvey. Elec. Age, Sept. 1906.
C. The Sale of Electric Power. Eng. Record, Nov. 3, 1906.
7. Flat Rates for Small Water Power Plants. J. S. Codman. Elec Wld.
and Engr., Nov. 3, 1906.
CHAPTER XVIIL
THE SPEED REGULATION OF TURBINE WATER
WHEELS.
203. The Relation of Resistance and Speed. — ^The power delivered
by any water wheel may be expressed, in terms of resistance over- '
come by the wheel through a known distance and in a known time
by the formula (See equation i, Section 177, Qiap. XVI).
2jrl wn
(1)
P=:
33000
The second term of this equation may be divided into two fa^
tors: first,
2irlw
33000
which may be called the resistance factor and which is the resist-
ance overcome or power produced by the wheel per revolution per
0
a
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IS
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i
M
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a
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aCVOUuTIONS PCR HMUTC
Fig. 270.
minute ; and n, the number of revolutions per minute. The product
is the horse power of the wheel.
In any wheel operating with a fixed gate opening and under a
fixed head the speed, n, will always increase as the resistance, w,
decreases, and will decrease as the resistance increases.
Self Regulation with Variable Speed and Resistance. 441
n Fig. 270 the line AB shows the relation of speed to resist-
e in a turbine operated with a single fixed gate opening and
the full range of load conditions (as determined by experiment)
m A, at which the resistance, w, was so gp-eat as to hold the
"tor stationary, to B where the resistance was completely re-
'ved and the entire energy of the applied water was expended
overcoming the friction of the wheel, or rejected as velocity en-
Fig. 271.
f in the water discharged therefrom. From this figure it is
lent that if, at any fixed gate opening, a wheel is revolving at
ven speed, n, and the resistance, w, is decreased to w" the speed
increase to n', while if the resistance increases to w' the speed
decrease to n'.
34. Self-Regulation in a Plant with Variable Speed and Resist-
t. — ^At Connorsville, Indiana, is a pumping plant (Fig. 271) in
ch a horizontal shaft turbine is directly connected through
tion clutches to two rotary pumps. For operation the turbine
\s are opened until the pump, or pumps, speeding up to a suit-
r. p. m., produces the desired pressure in the distributing sys-
442 The Speed Regulation o£ Turbine Wate " Wheels,
tern. The work of the pump under these conditions in pumpinf
water at the speed of operation against the desired pressure equals
the work done by the quantity of water q passing through the m-
bine, less friction and other losses. If the pressure falls, the loads
become unbalanced: i. e., the resistance is reduced and the tur-
bine and pump increase in speed until the balance is restored. If
the pressure rises the machine slows down until there is agsin
a restoration of balance between the power of the turbine, the
pump load and friction losses.
Fig. 272.
To pump water against an increased pressure, it is necessary to
increase the gate opening of the turbine. In its regular daily work
the varying demand for water is thus supplied by the self-regfula-
tion of the two machines used and no governor is needed The
conditions of operation are similar to those illustrated in Fig.
270.
205. The Kelations Necessary for Constant Speed. — Fig, 273
is a diagram drawn from experimental or test observations afld
similar to Fig. 270 except that the relations between speed and de-
sistancc are shown for various gate opening.
It IS evident that if the wheel must operate at a fixed speed, ft,
the resistance, w, increases to v/ or decreases to w*^, it will be m
sary to increase the gate opening from % gate to full gate in
first case and to decrease it to % gate in the second case in order to
maintain the speed uniform.
k ana
Bthe ^
^. The Ideal Governor. 443
An examination of the load curves described in Chapter XVII
shows that changes in load are constantly in progress. For the
satisfactory operation of water wheels, under these constant and
irregular changes in load, automatic regulation of the turbine gates
becomes necessary* This is accomplished through the water wheel
governor which regulates the gates through the various classes of
gate mechanisms described in Chap. XIII.
206. The Ideal Governor. — ^The power output of a water tur-
bine in terms of energy applied to the wheel is expressed by the
formula.
(2) P = gg- where
q s en. ft. per second of water used by the wheel.
H' = net available head.
E = efficiency of the wheel.
P = hone power developed.
Any sudden increase or decrease of load, w, will produce a cor-
esponding decrease or increase, respectively, in the speed, n, of
he machine as shown by Fig. 270 unless the energy applied to the
Urbine is immediately changed to correspond. The ideal turbine
rovernor would effect a change in output by varying only q, thus
obtaining perfect water economy by conserving unneeded water
or future use. This is not possible in practice as head, water, and
herefore efficiency are usually wasted when operating a wheel un-
i«r other than its normal load and dttring the change in load.
207. Present Status. — ^The success of the comparatively recent
pplication of hydraulic power to the operation of alternators in
►arallel and to the generation of current for electric lighting street
ailway and synchronous motor loads has been largely dependent
ipon the possibility of obtaining close speed regulation of the gen-
rating units accompanied with good water economy and without
indue shock upon machinery and penstocks while working under
iictremely variable loads.
The degree of success thus far obtained in the development
necessitated by the above conditioais) of automatic turbine gov-
-rnors, although achieved from the experimental standpoint almost
Exclusively, has been remarkable. Instances a»e now by no means
iDcommon where hydroelectric units working upon variable loads
^rc controlled as, satisfactorily as modern steam driven units. To
iccomplish this result the conditions must be especially favorable.
444 The Speed Regulation of Turbine Water Wheels,
Success in this feature of hydra-electric design is by no meani
uniform, however, and the frequent failure to realize satisfactoryj
results can often be ascribed to the lack of proper consideration (
the arrangement of the mechanical, hydraulic^ and electrical clfr
merits of tlie plant, wheels, and generators, rather than to anyift
herent defects in the go\*ernor itself. The power plant, the tuts^
bineSi the generators, and the governors are commonly designed I
four different parties without proper correlation of study and de-
sign. At present neither experimental data nor theoretical fomuh
are available by^ which the hydro-electric engineer can design m^
plant for an assumed speed regulation, or can predetermine eIii
speed regulation which is possible with a given installation or t
?oiCENT or ntntnAi iionglc pcwu
Fig. 273.
time required for the return to normal speed, — and yet the fp
ernor builder is commonly required by the engineer to gnaratita
these operating results. The predetermination otf speed v^riatio
during portions of the steam cycle and at load changes has receive
careful study in the design of reciprocating steam engines and 1
desirable per cent of speed regulation is freely guaranteed
readily obtained through careful study and analysis by the desi^tf
The same amount of study is warranted but seldom or never giva
to the problem of speed regulation in water power work,
2o8, Value of Unifonn Speed. — Uniform, or nearly tinifo
speed is of great economic value in the operation of a plant but add
to the first cost and may also result in a waste of water. The c^
rect solution of any given problem of speed regulation invoh^^
compromise between first cost, water economy and speed reg
tion,
A pecuniary value cannot well be placed upon good speed reg
lation. It differs fr»m poor speed regulation chiefly in procuring i^
more satisfactory operation of motor driven machinery and in pr^
ducing a more constant incandescent light. Fluctuations in tl
bright ness of a light are annoying, and tend to create dissatisfi
tion among consumers. Fig. 273 shows the general way in wHdll
The Problem.
4i5
lie candle power of an incandescent light varies with the impressed
oltage.* A pressure variation of S per cent., and hence also a
peed variation of a similar amount, is shown to produce a much
irger variation in candle power of the light, — in this case about
5 to 30 per cent.
309. The Problem. — ^Where (as in Fig. 271) a turbine is operating
nder balanced conditions and the resistance changes in magni-
ude, the turbine does not at once assume the new speed relations
orresponding to the change in resistance. The inertia of the mov-
ig parts of the wheel and of the column of water in the penstock,
Fig. 274.
Fig. 275.
urbine and draft tube, tends to maintain uniformity of speed, and
he wheel gp-adually changes in speed to that corresponding to the
lew conditions. In such cases the speed of operation is not essen-
ial and the delay in reaching the speed corresponding to the re-
istancc or work the turbine must perform is usually unimportant.
When, as in Fig. 272, the wheel is designated to operate at a
bccd speed, the uniformity of speed becomes a matter of greater
n less importance depending on the character of the work the wheel
3 to perform. In this case the inertia of the wheel and of all rotat-
Dg parts of other machinery connected thereto tends to maintain
L constant speed. On the other hand, the flow of water in penstock,
urbine, and draft tube must be changed in quantity, (Eq. 2),
icnce in velocity, and its inertia therefore tends to produce a change
n head and to produce effects opposite to those desired for efficient
egulation.
The conditions of installation have a marked effect on the diffi-
ailties of turbine governing. If (as in Fig. 274) the turbine is in-
tailed in an open pit and has only a short draft tube, and the water
•See American Electrician, Vol. XIII, No. 7. July, 1901, by F. W. Wilcox.
27
4^6 The Speed Regulation of Turbine Water A^heela,
1I0WS to the gates fram every direction, the velocity of flow km
all directions is very low. The quantity of water which moves at a
high velocity is confined to that in the wheel and draft tube and
the change in the velocity and momentuni, due to, a change in the
gates, produces no serious effects. If, however, water be con-
ducted to and Jrom the wheel throfugh a long penstock and dfaft
tube (as illustrated by Fig. 275) the conditions become quite differ-
ent. In this case a large amount of energy is stored in the movii
column of water and a change in its velocity involves a change in
its kinetic energy which may, if an attempt is made at too rapid rej
ulation, leave the wheel deficient in energy when increased power 6
desired, or, when the power is decreased, may prodtice such shocks
as will seriously affect regulation or perhaps result in serious iojui
to the penstock and wheeh
210. Energy Required to Change the Penstock Velocity,— j
increase or decrease of load requires an ultimate increase or ii
crease in velocity of the water in the penstock. Work has to
done upon the water to accelerate it and must be absorbed in ordi
to retard it. The total available power which can be expended h
all purposes at any instant during the acceleration is (since vH
proportional to qH) proportional to the product of the instantan^
ous velocity and the supply head. This total power is thus defi-'
nitely limited and, hence, the work required to accelerate ihi imtir
must be obtained at the expense of the work done upon the tvheiL
Thus, when an increase of load occurs the gate is opened by tiie
governor, and the immediate result is a decrease in the power out-
put of the wheel, even below its original value, and is diametriallT
opposed to the result desired. This counter effect may last for sev-
eral seconds, and, unless sufficient reserve energy in some form
is available to partially supply this deficiency^ the speed of tl
wheel may fall considerably before readjustment to normal pow<
can take place*
In the same way an excess of energy must be absorbed to d<
crease the velocity at time of decreasing load* This may be
pended upon the wheel thus increasing the speed above normal,
it may be dissipated in one of several ways to be discussed later
The water in the draft tube must be accelerated and retarded 1I
each change of gate opening and its kinetic energ>^ changed at the
expense of the power output in exactly the same manner as that in
the penstock. For this reason it should be included in all calcub*
tions as a part of the penstock. One additional precaution must k
Hunting or Racing,
447
n : if the draft head is large a quick closure of tlie turbine gate
may cause the water in the draft tube to run away from the wheel
(actually creating a vacuum in the draft tube) and then return
again causing a destructive blow against the wheeL
211. Hunting or Racing. — ^The regulation of both steam engines
and hydraulic turbines as now accomplished is one of degree only
since a departure frocm normal speed is necessary before the gov-
ernor can act. Since the immediate effect of the gate motion is op-
posite to that intended, the speed will depart still further from the
normal. This tends to cause the , governor to move the gate too
far with the result that the speed will not only return to normal
' as soon as the inertia of the water and of the rotating parts is over-
come, but may rush far beyond normal in the opposite direction.
, The obvious tendency is thus to cause the speed to oscillate above
I and below normal to the almost complete destruction of speed reg*
lalation.
A successful governor must therefore "anticipate" the effect of
sny gate movement. It must move the gate to, or only slightly be-
yond, the position which will give normal speed when readjust-
ment to uniform flow in the penstock has taken place. A governor
-vtnth this property or quality is commonly said to be "dead-beat/'
In Chap. XIX several expedients are shown for the automatic clin>
ination of excessive racing.
aia- Nomenclature. — The following symbols will be used in the
Tnathematical discussions which follow:
A = cropfl iectional area of penstock m eq. ft^
C = friction eoefflcient for flow in pipe Ifnes = -^ (1 -|- f-^ + etc.)
D. — miximaiii rise of watar in standpipe above^the forebay wh^ti fuil
load ( V =2 V|) ia rejected by the wheels,
V* = drop of water id atandpipe below original friction gradient all in-
fluoncea considered,
D = ditto, friction in penstock neglected,
Dt = drop of level in standpipe below fore bay*
d ~ diameter of penMock (closed circular) in feet.
e — 2.7182S = base of nattiral Byeteni of logarithms,
F = cross -Be ctional area of the atandpipe in equare feet*
f = ^'friction factor'' in penstock.
g — acceleration due to gravity in feet per Becx>nd per eecond.
H = total available power head in feet.
H' ^ effective head at the wheel = H — hf for any given uniform velocity,
Vj in the penstock.
44^ The Speed Rt^^ulation of Turbine Water Wheels*
h ^ InstantAneous efieci.ve liead at the wheel dtiring chftngee of v^locltf
in the peti-tock.
fas = he^ wbich la effective at any logtaiit In accelerating the waitr bi
the peiietock and draft tube.
hr — friction lo^s in penstock for normal flow with a given head aad pit
opening.
bf = variable head lost by friction entrance, etc., in penstock wbaniln
veloc'ty is v*
I = moment of inertia or fly wheel effect of revolring parte in poimdiit
one ft. radius = ft* lbs.
K = energy delivered to the wheel,
^K = excess or deficient energy delivered to wheel during change of loii
^ Ki = excess or deficient energy delivered to wheel due to excels orddSf
iency iti quantity of water during load change.
^Ki= ditto, — due to energy required to accelerate or retard the wiittin
the petutock.
^ K|-= ditto^^due to sluggishness of gate movements
K* = kinetic energy in foot pounds of revolving parte at speed S.
A K'i^ increment (+ or — J in K' due to load change
2ifH
k'
1
M = elope of the v- 1 curve when v =
2.3IV
• leii^ah of penstock in feet^
V. + Vi
(equation I@),
pft = initial horse power output from the water wheel.
Pl — the horse power i utput frn m the water wheel corresponding tfltk]
new load.
Q ££ discharge of the wheel under normal effective head H' foranjPii^l
load,
q = instantaneous diachai^e of wheel in cubic feet per second dunnf l«<d|
change.
R = ratio of actual deScient or excels work done on wheel to ibtl^i
puted*
S ~ normal r. p. m. of the wheel and other rotating parts.
AS ^ S — Si = temporary change in speed.
Si ^ speed in revolutions per minute after load change,
T* = approximate time required lor acceleration or retarding of *i^l
from velocity v^ to vi,
T^ = the time required for the governor to adjust the gate after %t^^.
of load.
t = variable time after gate movement.
V = normal (and hence maximum possible) velocity in the penstock i
given head and gate opening,
T == instantaneous variable velocity in tlie penstock while i4lQi'higt0l
new value,
T» = velocity in penstock at the in&tant of gate change^
Vi = velocity in the penstock required for new lond.
Water Hammer-
449
w = weight of a cubic unit oE water ia lbs.
Y = ma?cimtim depanure of head^ b^ from normal with use of stand-
pi pe,^Kli9 charge gf wheel aesumed conBtant at the abnormal baa J
(see Dp and Dt)*
y = vanaiion of water level in thestondpipe from forebay level = H — li
d — speed rei^ulatiori or per cent variation of speed from rjormal,
^213, Shock or Water Hammer Due to Sudden Changes in Ve-
locity.— The acceleration or retardation of a moving body requires
an unbalanced force. Since acceleratiom and retardation are iden-
-4
'V
WJ/'^j^V4v^'fVJjj^//J^/////m^
tical, except as to sign, the required accelerating force may in all
cases be expressed as follows:
Force = masi X Rcceleratioii,
Acceleration, or the rate at which the velocity increment in-
creases per increment of time, is expressed by the formula:
Pdv
(3 ) Acceleration — —^
The mass of water to be accelerated is
P (4) MaB8=^
Figs, 276 and 2yy show the conditions existing during an in-
crease and decrease of velocity respectively. If the draft tube were
closed at the lower end and no water leaving, there would be a
total force, equal to the hydraulic pressure over the arta of the
penstock, or wAH. tending to move the water.
450 The Speed Regulation of Turbine Water Wheels.
If the water is flowing with a velocity v the turbine offers a re-
sistance to flow represented by the effective head, h, at the wheel
and the penstock offers a resisting head hr composed of friction, en-
trance, and other losses. If the velocity remains uniform, h==ir,
and the forces are balanced thus :
(6) H = H' + hr
If the opening of the turbine gate is now suddenly increased, the
head H' at the wheel, will fall to the value, h, (shown in Fig. 276)
which is required to force the given amount of water, Av, througli
Fig. 277,
the wheel. On the other hand, if the gate opening is decreased the
pressure head must rise above H' (as shown in Fig. 277) in order
to discharge the water through the wheel. This change h, in the
head H' disturbs the equilibrium of forces shown by equation
(S) making
(6) h. = H-h-h,
Only the head h^ is effective in accelerating or retarding the
water and the force resulting from this head is wAh^^. Substitut-
ing this value and those of equations (3) and (4) in equation (2)
we obtain:
. , A Iw dv
wAh. = — • -gr
1 A'^ 1
(7)
or
I J 1
h» = — • -rr- = — X (™te of velocity change)
Permissible Rate of Gate Movement. 451
The value of h^ given by formula (7) is a general expression for
le change in. pressure-head due to a change of velocity or for the
ead which must be impressed to -produce a desired change in
elocity. When in excess of the static pressure as shown in Fig.
77, it is commonly called "water hammer." (See Appendix — .)
If the closure of the gates is rapid the value of h^ is large and
le column of water is set into vibration or oscillation. If the
artial closure of gate is sufficiently slow to allow a distribution of
ich increment of pressure along the pipe, this oscillatory wave is
voided and the pressure produced at ,any instant during closure
given by equation (7) is that which is necessary to retard the
loving column of water at the rate at which its velocity actually
ccreases at that instant and can be reduced below any assumed
laximum allowable value by a sufficiently slow. gate movement.
When a penstock is long, these oscillatory waves become • a
ource of great danger to .the turbines and also to the penstock,
specially at bends. The extinction of a velocity of 4 feet per
econd at a uniform rate in one second in a pipe 1,600 feet in length
fould create a pressure-head of about 200 feet, or a total longitud-
lal thrust on the pipe line at each bend, and upon the wheel gate,
f 24" in diameter, of abo,ut 20 tons.
These dangers are further augpnented by the fact that several
/aves, if succeeding each other by an interval which is approxi-
nately a multiple of the vibration period of the pipe, may pile up,
o to speak, crest upon crest and cause a pressure which no possi-
)lc strength of parts could withstand.
Fig. 278.
214. Permissible Rate of Gate Movement.— Gate movements
niust be sufficiently slow to avoid oscillatory waves of dangerous
amplitude. No general quantitative rule can be given for the re-
quired rate oif movement. It can be more rapid the shorter the
penstock and the smaller the velocity in the same. The danger
is much smaller during opening than during closure of a gate and
452 The Speed Regulation of Turbine Water Wheels,
the rate of gate .movement could well be made much more rapitl
in the former than in the latter case,
The rapidity with which a gate should be opened Is limited for!
feeder pipes with an initial flat slope as shown in Fig* 278.
Let h' be the lowest head obtained in opening the gmte at an as-
sumed rate and AB, the resulting hydraulic gradient. In case thd
gate opens so rapidly as to cause the distance, a, at any point alon^
the pipe to exceed suction limit, the water column it* the penstock
will separate (the portio,n of the column above A not being able
to accelerate as rapidly as that below) and will agiiin reunite wiili
a severe hammer blow. Failure to observe this precaution probably
caused the destruction of the feeder pipe of the Fresno, Caiifomta,
power plant. The rate to be used can be chosen after a determina*
tion, by the method discussed in Appendix — , of the pressures re-
suiting from several assumed rates of movement. The method is tt
dious but justifiable in many cases*
215. Regulation of Impulse Wheels. — It is impracticable, if not
impossible, to build a pipe line strong enough and well enougii
anchored at all points to withstand the enormous pressures and
longitudinal thrusts which would result from rapid gate closures
in a long closed penstock such as commonly used for impulse
wheels, Tbe adjustment of quantity, q, for changes in load
short duration is hence impossible in such closed penstocks and till
expedient usually adopted is to 'Meilect*' the jet from the wheel by
changing the direction of discharge of a pivoted nozzle. This
quires that the '^needle valve" (See Fig^iflS") or gate maintain a )i
sufficient to carry peak loads; hence causmg a waste of water at all
other times. This condition is commonly improved somewhat by
adjusting the valve about once each hour by means of a slow niotiofl
hand wheel for the maximum peak load liable to occur during thi
hour.
An automatic governor has recently been invented which mty
the needle valve or gate slowly, thus adjusting for changes of loai
of long duration while it still retains the deflector to provide l(
abrupt changes in the load curve. (See Fig. /\ .)
Another device proposed for use in this connection is a by-pasi
nozzle arranged to open as the needle valve rapidly closes, and then
automatically close again at a rate sufficiently slow to reduce thccs-
cess pressure to safe limits. One advantage in fa%'or of this
rangement is that the jet would theu always strike the center
the buckets which is found to considerablv reduce tl*eir wear
of.
r^«
ar-l
Influence Opposing Speed Regulation. 453
in automatic relief valve of hydraulic or spring type is nearly
ays used but serves more as an emergency valve to reduce water
nraer pressures than as a by-pass to divert water from the wheel
the purpose of governing? For this latter use the spring type
valve has proven unsatisfactory.
n some cases the water discharged from high head plants is used
ow for irrigation and must be kept constant, thus doing away
h the necessity of varying the velocity in the feeder pipe for a
ying load.
At. Raymond D, Johnson proposes for these high head plants,
use of large air chambers or "Surge Tanks," placed near the
eels, of a sufficient size so that the governor can control the
idle valve directly, thus dispensing with the deflector and by-
;s and doing away completely with the waste of water occa-
ned by their use. He has derived formulas by which he claims to
rurately proportion these tanks for an assumed maximum allow-
e range of head fluctuation or surge.*
116. Influences Opposing Speed Regulation. — ^Abrupt changes
the demand for power of a considerable proportion of the total
)acity of a plant, take place at times in modern power plants.
ree causes tend to make the change in output of a wheel lag he-
ld the change in demand placed upon it; viz.: (i) the fact that
J governor, however sensitive, does not act until an appreciable
ange of speed occurs, and then not instantly ; (2) the fact that
me time is required for the readjustment of penstock velocity,
en after the gate movement is complete; (3) the necessity of
anging the velocity, and hence of overcoming the inertia of the
Iter in the penstock and draft tube at each change of load.
Each of these influences is directly opposed to speed regulation,
will appear in the succeeding articles, since each causes the
)wer supplied to a wheel, at time of increasing load, to fall short
the demand, the deficiency being supplied at the expense of the
•ecd from the kinetic energy stored in the rotating parts. The ex-
ession for the total deficient work, i. e. foot, pounds, is:
(8) A K = A Ki -f A Ki -h A Ki
r which see equations 22 and 23 and Section 221.
217, Change of Penstock Velocity.— Assuming the gate move-
?nt to take place instantly, we will have the condition illustrated
See "The Surge Tank In Water Power Plants," by R. D. Johnson. Trans.
. See. M. E.. 1908.
454 The Speed Regulation of Turbine Water Wheeb.
in Figs. 276 or 277, for which equation 7 was derived (Sec Sec
213). Solving equation (7) for -g^ we have:
(9) Acceleration = -^-- = -f" X (accelerating head) = ■?- h«
The accelerating head as shown in equation 6 is H — h — h^
is the general principles of hydraulics that the head lost in
through any opening, pipe, orifice, etc., varies as the square
velocity.
It was shown in Section , Chapter XVI, that the quai
flowing through a turbine varies as the square root of the h
Remembering that the quantity is proportional to the pensi
velocity, we have:
(10) -g = ^ = T/S* ^^ which
(11) h = -^r H' Now
(12) h, = (1 + f i. + etc.)-g- • Hence,
(13) -t-jr or
(14) h,=^hF
From equation (6)
h. = H — h — h, =x H — H' -^ — hr -^ 6r
(16) h. = H-(H'+hF)-^
And from equation (5)
(16) h. = H-H-^ = H(l — ^)
Hence from equation (9)
U7) dt " 1 ^ V« '
The integration of this equation as given in Appendix — g
the following equatiom for the curve of velocity change in the ;
stock following a sudden change of gate opening:
^^^^ ^"" ^Bantilogk't+1
As shown in Appendix B this value of v approaches but i
equals the value of V. The form of the curve for an increa
velocity is shown in Fig. 279.
♦ See Merrlman'B Treatise on Hydraulics, p. , equation.
Effect of Acceleration on Water Supplied to Wheel. 455
218. Effect of Slow Acceleration on Water Supplied to Wheel. —
nee velocity in the penstock, discharge of wheel, and load
e approximately proportional to each other, the ordinates of
g. 279 may be taken to represent loads. The load demand remains
a constant value v© from A to B, where it suddenly increases
Vj, foillowing the line A B C D T. The supply, howiever,
suming an instantaneous gate movement, follows the line
B D F. Now, the total quantity of water supplied to, and hence
Pig. 279.
le work (not power) done by the water upon the wheel, is propor-
onal to the area generated by an ordinate to the latter, and the
emand upon the wheel to the area generatd by the power curve,
he area B C D B therefore represents a deficiency of developed
ork which must be supplied by the energy stored in the rotating
irts.
For practical purposes this area may be assumed equal to the
ea L of the triangle B' C D^ where the line B' D' is tangent to
e curve B M D at the point of mean velocity 2^^
The slope of the line B' D' for this mean velocity is readily ob-
ned from equation 17. Call it M, then
B' 0' _ VI - vo _ gH r (vq 4- vi)' 1
T' ~ 1 L 4V2 J
(19)
M =
C D'
and
456 The Speed Regulation of Turbine Water Wheels.
(20) T'=.Il^
(21) Area B'C'D' = L JJ^lIZloK = <^'-^o)'
This value of L is expressed in feet and represents the dcfidcncy |
of lineal distance moved by the water column in the penstock. Tke i
deficiency of supplied water in cu. feet is, hence, A L and the fc j
ficiency of undeveloped work is
(22) A K, = ALwH = 4^ (^» - ^•)'
219. Value of Racing or Gate Over-Run. — ^At D, Fig. 279, 4e
supply line B D F crosses the load line C D E, and the speed wWdi
was lost from B to D begins to pick up again.
The necessity also for an overrun of the governor is shown by
Fig. 279. If the demand line were A B N F and the gate opened
to the same place as before, giving the supply line B D F, the sup-
ply of power would approach, but theoretically never equal, the
demand and the speed would hence never pick up to normal. The
^__ I \ , MORMAI. OATC » MCW L.OAO ^
. NOWMAL Ot\T£ - OCO COAO
Fig. 280.
«fate movement should therefore be similar to that shown in Fig.
280 in order to give the gate the small overrun which is necessary
to bring the speed hack to normal.
220. Energy Required to Change the ,Penstock Velocity. — ^The
energy involved in the change of velocity above described result^
in an excess or deficiency of energy delivered to the wheel (See Sec-
tion 210). The amount of this excess or deficient energy is readily
determinable. The kinetic energy in foot pounds stored in the
moving column of water is K? = —^ or
0*? 5Alv«
K, = •;, ' = .972 Alv«
The amount which must be diverted from the wheel or dissipated
when the velocity changes is therefore
(23) A K, = 0.972 Al (vi« - Vo«)*
In this case 1 should be taken as the combined length of penstock
and draft tube.
The Fly- Wheel. 457
Tfiis deficient energy must be supplied, or the excess absorbed, by
sans of a flywheel or the installation of a stand-pipe connected
th the penstock closely adjoining the wheel.
aai. Effect of Sensitiveness and Rapidity of Governor. — Referring
ain to Fig. 279, suppose the increase of load to take place at B"*"
ring the load line AB''' C' E. After an interval from B''' to B",
e speed has dropped an amount depending upon the sensitiveness
the governor. The gate will then beg^n to open ; the velocity in
e penstock accelerating meanwhile along the dotted line B"Tf.
le lack of sensitiveness of the governor has therefore added a de-
ient work area of B'" B" C" C", and the slug^shness of its mo-
rn an additional area CB" B C, approximately. This deficiency
K, can be only roughly approximated without the detailed analy-
I given in Appendix — .
aaa. The Fly-WhceL — A fly-wheel is valuable for the storage
energy. Work must be done upon it to increase its speed of rota-
Mi,and it will again give out this energy in being retarded. From
i« laws of mechanics the number of foot pounds of kinetic energy
ored in a body by virtue of its rotation is given by the formula :
^,_2Iir'8«_ 2X8.1416' ^ c,. «,
^ "T^ " 32.15 X60« ^^ ""^
(24) K' = .00017 I 8«
Hie amount of energy which must be g^ven to or absorbed from
• fly-wheel in order to change the speed is
(25) A K' = 00017 1 (So« — Si« )
f^us a fly-wheel can store. energy only by means of a change in
^d. By means of a sufficiently large moment of inertia the speed
^ge of a fly-wheel, for any given energy storage, AK', can be re-
'ed to any desirable limit.
^e n ed of a fly-wheel effect to carry the load of a hydro-electric
t during changes of gate, and while the water is accelerating in
penstock at an increase of load has led to the development of a
« of revolving field generator, whose rotor has a high moment of
rtia and is therefore especially adapted for speed regulation usu-
'^ making the use of a fly-wheel unnecessary.
Varren* has simplified the expression for AK' (See equation
substantially as follows:
Bee "Speed Regulation of High Head Water Wheels." by H. E. Warren.
rechnology Quarterly, Vol. XX. No. 2.
458 The Spt^ed Regulation of Turbine Water Wheels*
From equation (24) :
.^„. Ki' _ .00017 I Si'
(27)
K/ " S," " 8,-
PtitSi — Si = AS
and Ki' — K/ = £\ K'
For small differences between S* aKd S3 equation (27) bc'
■approximately; ' ^
A K^ _ 28 X A S 2 X A 8
(28)
K'
Hi
B
or
At. g
V
Or the percentage change in speed is
(•iO) <S = ^7 —
_ »|
92^, The Stand-Pipe. — ^Thc function of the stand-pipe is t
iold : (i) to act as a relief valve in case of excess pressures iji
penstock; (2) to furnish a supply of energy to take care of sui
increases of load while the water is accelerating, and to dissipate
■excess kinetic energy in the moving water column at time of s^id
drop in load. For these purposes it should be of ample diametci'i
placed as close, to the wheel as possible.
The analytical detemiination of the effect of a given stand-p
upon speed regulation is very difficult if not quite impossible. F
thermore, it is not necessary, since the drop in effective head al
increase of load may (except in the case of maximum possible toi
be compensated for by an increase of gate opening, hence na
taining a constant power and speed or at least a satisfactory iem
of speed regulation. Thus the action of a stand-pipe in sto^
energy differs radically from that of the fly-wheel as the latter
store or give out energy only by means of a change of spe;.
the generating unit.
The determination of the range of fluctuation of water level i
assumed stand-pipe, and the time required for return to normal I
for various changes of load on the wheels will assist greatly in
design of the stand-pipe.
Fig, 281 shows the condition when a stand-pipe is used. Assi
that the wheel is operating under part load. The water nom!
stands a height h^ below the supply leveL If the load stidcenl|
creases, the gates open, and the water level begins to fallp tl: js
ing an accelerating head h. = H — h — hf. Equation 9 the 1 ap
as before, where h^ becomes (h — cv').
tanc
Ipe.
+59
IF the governor keeps step with the change in head by increasing
gate opening to maintain a constant power then
q h ^ Qi hi
q (H - y) = Avi (H — hr ) =^ Avi (H — cvi') or
_ Ayi{H — CV|')
J rate of water consumption by the wheel at any instant is q;
■it at which the water i: nipplied by the penstock is Av; and
^« I ate of rise or fall of the water surface in stand*pipe is there*
.31)
q =
(J3)
dy _ _dh^ _ Ay — q - ^ f _ ^i (H — cvi') 1
dt ~ dt ~ F ~F L^ H--y J
Tl solutions of equations g and 32^ which are necessary for
^eter nining the curves of variation of head and velocity, is imprac-
"TJS?*^ 'Hi^b-wuDre -^ibmi
T
ttcablt , if not impossible, hence a different treatment is proposed and
considered in Appendix.
If q be assumed constant (s^Avi) during the adostment of pen-
stock velocity and the friction loss, cv*, in the penstock be neg^lected,
then equations 9 and 32 simplify and become integrable. The re-
suiting equations, showing the variations of v and y, are true bar-
monies or sine curves. The effect of friction and governor action is
to produce a damped or somewhat distorted harmonic as discussed
ID Appendix — ♦ Any change of load thus starts a series of wave like
fluctuations of penstock velocity and stand*pipe level which con-
tinue until this wave energ\'- has been entirely expended in friction.
460 The Speed Regulation of Turbine Water Wheels,
Analogous to all other wave motions these waves may pile up. fif
tv^ro or more gate movements succeed each other by short inten-ali
which are approximately multiples of the cycle, 2T) causing a fcir
great flucuation in head and velocity. In fact by assuming a proper
combination and succession of circumstances no limit can bcas-j
signed to the range of fluctuation or "surge" which may occur,
probable combination of circumstances which will occur in an?
plant depends largely jupon the character of the load. Overflon
from stand-pipes due to these surges have been known to do co
siderable damage and it is desirable to either provide for this ova
flow either at the top or by relief valves at the bottom, or builj
the stand-pipe high enough to prevent it and thus gain the ad
tional advantage of conserving the water which would othcrwil
waste.
If the change of load is assumed to occur iftVen the water is (
its normal level then the analysis given in Appendix — furnishes I
followinir formulas-
(33)
(34)
(35)
(36)
(37)
Y^^in-y.}
'Fg
n i A , / I cT \
The value of T from equation (33) is one-half a wave cycle i
the time required for return to normal head after a change of loa^
It is obtained by neglecting both friction and the compensatini
effect of the governor, Tliese influences increase T in very ijeafl|
the ratio that D exceeds Y*
Y from equation (34) is the maximum head fluctuation, or max
mum value of y, also obtained by neglecting friction and govctnaj
action.
D from equation (35) is the maximum drop in standpipc lev^
corresponding to Y except that governor action is included.
this value of D is added as shown in equation (36) to the ixiilil
friction loss, cv^*, the result agrees very closely with the value <
the maximum drop D where friction is included and is much mort
simple than the more exact equation given in Appendix — ^.
A reasonable assumption for determining the probable maxinni
height to which the water will rise in the stand-pipe is thtt ft
Predetermination of Speed Regulation. 461
id is instantly thrown off the unit when the normal full load ve-
rity Vf exists in the penstock. This assumption leads to equa-
« (37)-
The verification of these formulas and some additional ones is
^en in Appendix — , and an example of their application in sec-
n 23a
124. The Air Chamber. — ^There is a practical limit to the height
which a stand-pipe can be built. A high stand-pipe is also less
ective due to the inertia of the water in the stand-pipe itself which
ist be overcome at each change of load, thus introducing to a
scr degree the same problem as in a penstock without stand-pipe,
r some such cases the top of the tank can be closed and furnished
:h air by a compressor. The design of air chambers has been in-
tigated by Raymond D. Johnson.* An air chamber is less effec-
: in equalizing the pressure than a standpipe of the same diam-
r.
25. Predetermination of Speed Regulation for Wheels Set in
tn Penstocks.— The influences which oppose speed regulation
e been partly discussed. At an increase or decrease of load there
deficiency pr excess of developed power due to (i) the inability
:he governor to move the gate upon the instant that the load
nges ; (2) the necessity of accelerating or retarding the water
he penstock and draft tube as previously discussed. If no stand-
5 is used, reliance must be .placed upon the fly-wheel effect of
Mne, generator and additional fly wheel, if necessary, to absorb
rive out the excess or deficiency of input over output of the plant
his time.
Tie first influence opposed to speed regulation, that of slow gate
irement, is of chief importance (a) where the plant is provided
h large open penstocks and short draft tubes ; (b) where an am-
stand-pipe, placed close to the wheel, and a short draft tube
used; (c) in the regulation of an impulse wheel where no at-
pt is made to change the velocity of water in the feeder pipe.
[f. H. E. Warrent has analyzed this case essentially as follows:
As long as the output from the wheel is equal to the load, the
ed S and kinetic energy K' of the revolving parts will remain
stant. The governor is designed to adjust the output of the
•el to correspond with the load, but it cannot do this instanta-
See Trans, of Am. Soc. M. B., 1908.
See article by H. E. Warren on "Speed Regulation of High Head Water
els/' previously referred to in Section 222
28
462 The Speed Regnlation of Turbine Water Wheels,
neously. Consequently, during the time T required to makcfc
adjustment of the control mechanism after a load change there wi
be a production of energy by the water wheel greater or less tfai
the load. The entire excess or deficiency will be added to or sab-
tracted from the kinetic energy of the revolving parts, and will In-
come manifest by a corresponding change in speed.
Neglecting friction losses, and assuming that the power of the
water wheel is proportional to the percentage of the governor stroke
and that the movement of the governor after a load change is ati
uniform rate, the excess or deficient energy which goes to or comes
from the revolving parts after an instantaneous change of load from
Lo to Lj is measured by the average difference between the powtr
of the wheel and the new load during the time T^, while the gover-
nor is moving, multiplied by T" or expressed in foot pounds:
(38) AK' =-5^^=^XT'X550
From equation 24 the kinetic energy of the rotating parts is:
K' = .00017 IS^
From equations 24, 30 and 38
^_60X(Po-P.)T^X550
2 X .00017 IS* °'
(39) d = 81,000,000^ (po — pi)
226. Predetermination of Speed Regulation, Plant with Closed
Penstock. — In this case the rotating parts must absorb or deliver
up an amount of energy AK' (equation 29), equivalent to that given
for AK in formula
(8) AK = AKi+ AKf+ AKf
where, from equation 22,
(22) ^Ki=4^(vi-v«)«
M being obtained from equation
The value of A K, is obtained by equation
(23) AK, = 0.972 Al(v/-.Vo»)
There is no simple way, as discussed in section 221, of determin-
ing K3. It must be estimated or analyzed graphically as in Appc"*
dix C.
From equation
(24) K' = .00017 I S«
Predetermination of Speed Regulation. 463
If R is the proportion of this theoretical energy which is given to
he rotating parts at a decrease in load,, or which the rotating parts
nust give out during an increase of velocity and load then
(40) AK'=BXAK
md we have from equation
(30) ^^.^50XRXAK|
50X RX AK
"• .00017 I S» °'
(41) ^ = 294,000 5^A5
Solving for I we find the moment of inertia of the rotating parts,
rhich is necessary to obtain any desired percentage of regulation to
e
(42) 1 = 294,000 ^^s^^
Although there can be no doubt as to the accuracy of the form of
[uations 41 and 42 yet their value for other than comparative pur-
)ses depends upon the accuracy with which we can estimate R.
'ith perfect efficiency of the wheel under all conditions, R would
unity, but in actual cases R must be determined by experiment or
' the graphical method given in Appendix — . It will be less for
creasing than for increasing loads since the indficient operation
the wheel assists speed regulation in the former case, and hinders
in the latter. In addition to this fact, the excess energy at a de-
ease of load can be partially dissipated through a relief valve, or
by-pass, etc. For practical cases it is therefore necessary to in-
stigate only the case of increasing load.
A detailed analysis of a particular problem can be made, as in
ppendix — , by which the velocity in the penstock, effective head,
>wer of wheel, speed, etc., can be determined for each instant dur-
g the period of adjustment. From this also the time of return to
>rmal speed can be determined. The method is somewhat tedious.
It justifiable nevertheless.
227. Predetermination 'of Speed, Regulation, Plant with Stand-
pe. — If the stand-pipe is of suitable diameter and close to the wheel
e speed regulation will approach that obtainable in open penstock
id as investigated by Warren in Section 225. Otherwise the prob-
n becomes that of a plant with a closed penstock, of a length equal
that of the draft tube, plus the penstock from stand-pipe to wheel.
464 The Speed Regulation of Turbine Water Wheels,
228. Application of Method, Closed Penstock.— An example of
the analysis of a problem in speed regulation is as follows :
Assume the 48" Victor cylinder gate turbine, whose characteristic
curve is shown in Fig. 245, page — . Suppose it is supplied with
water through a penstock whose diameter is 8 feet, jand whose
length combined with that of the draft tube is 500 feet. The head
is 50 feet which for ^=.664 gives 180 R. P. M. = S.
Neglecting all losses of head except that in the turbine, we find
from the characteristic curve for various loads as follows :
Full load.
.8 Load
JiLoad.
•
XLoii
Brake Horse Power
1120.00
240.00
4.77
.82
900
210
4.18
.764
660.00
145.00
2.88
.68
280.00
Quantity of water per sec. (cu. ft
Velocitv in Penstock. V
97.»
1.91
KfBciencv of wheel
.505
The above values will be considered as applying to the entirp
plant since the loss in the penstock is small in this case.
Assume the load to increase suddenly from one quarter load to
0.8 load, while the gate at the same time opens to full load posi-
tion. The nti|mber of foot pounds of work which must be done to
accelerate the water from a velocity of 1.94 feet per second to 4.18
feet per second is found from equation 23 to be
AK, = 0.972 Al(vi«-.Vo*)
= 0.972 X 60.3 X 600 (4.18» — 1.94«)
= 0.972 X 60.3 X 600 X 13.73
= 335,000 foot pounds.
Referring to section 226, p. — , to find the amount of deficient
work due to insufficient supply of water we have
Vq + Vl _
From equation 19, section 226
32.15X60 A
M =
600
_ 82.15X60
"" 600
= 2.88
= 3.06,
3.O61 y
4 X 4.77«J
897
From equation 22,
^^ 50.3 X 62.6 X 60,, ,^
^^^ = 2 X2.88 ^^•^^■
= 187,000 foot pounds.
1.94) •
Predetermination of Speed Regulation. 465
The total deficiency for which formulas have been derived is
bence,
A K = A Ki + A K« + (A K, undeterminable)
= 335,000 + 137,000
= 472,000 + ft Iba
By means of the detailed graphical analysis given |in Appendix
- this deficiency is found to be 600,000 foot pounds for gate move-
nent in one-half second showing that the estimated value should
lave been increased in this case by 12.7 per cent. (R = i.i 27) to
:ompensate for neglecting the effect of slow (V^ second) gate move-
ncnt, or K,. It must be remembered that this quantity, AK, is
he deficiency of jtheoretical hydraulic work done upon the wheel.
For reasons discussed in Appendix — , it will, however, be found to
Jiffer but slightly from the deficiency of wheel output, in this case
)86,ooo ft. pounds.
To determine the speed regulation which can be obtained, as-
sume a generating unit whose rotor has a fly-wheel effect, or mo-
ment of inertia, I, of 1,000,000. lbs. at one ft. radius. The normal
Jpeed S = 180, AK = 472,000 ft. lbs., and R (in general to be esti-
nated, but in this case obtained iby the graphical method given in
Vppendix — , is 1,127. Therefore from equation (43)
A - 9Q4 ,^1.127 X 472,000 _ . .«^
* = ^'^1,000,000X180* - ^^^
If a fly-wheel is to be designed for a given regulation say 4 per
cnt., then the required moment of inertia of same is, from equa-
ion (42).
I = 294,000^5^5
= 294,000 ^^^, Of
1 = 1,365,000 ft.* Ib0.
229. Application of Mediod, Open Penstocks — ^As the penstock
itid draft tube are shortened, the excess or deficient energy area,
^^^Kj, obtained during the gate movement becomes an increasing
proportion of the whole until for a large open penstock and short
Iraft tube the developed power ceases to lag and follows practically
'le same law of change as the gate opening. The estimation of
*xcess or deficient energy, and consequently of speed, is then very
simple by means of Mr. Warrens equation (39). For illustration:
issume the same wheel as in the preceeding section, obtaininff 1
outputs of 280 H. P.=Po at one-fourth load and 1120 H. P;=-
^.66 The Sptfed Regulation of Turbine Water Wheels.
full load, as in the other installation* Assume the same momtnl
of inertia 1,000,000 and that the gate movement takes place in ^^
second as before. Then T''= H j S = 180.
This gives
0.5
tf ^ S1.000,000^■
■(1120— 280) ^ UOSjl
1»000»OOOX 180'
This is a much closer regulation than obtained with the longpefr
stock.
230* Application o! Method, Plant with Stand-pipe-— Assume I
plant virhere the wheels develop 39,000 H. R under 375 head, thereb;
requiring about 1100 cu. ft- of water per second (assuming 83 pfl
cent, efficiency of the wheels). Assume this water is supplier
through four f pipes about 4800 feet long, requiring a velocity in t
feeder pipes at full load of ahout 7.15 feet. Suppose four pipes i
connected at the lower end to a stand-pipe 30 feet in diameter lia
sudden load change, of about one third of the total is to be provided
for this would require an ultimate change of velocity in the penstock
from about 4.76 feet per sec. at two-thirds load to 7.15 feet at is
loadf or v^ ^= 4.76, and v^ ^= 7.15. Now,
4 X TT -j- = 154 aq. It
F = ff
30'
= 707
From equation 33 the time required for return to normal head, of |
the half period of oscillation, is
'4
707 X 4B0i^
= 82 eecotidi
'154 X 32.15
This would perhaps be increased to nearly 100 seconds, due to the
use of additional water during this period of low head, as disciissea|
in Appendix — , but the value 82 should be used in equation 35.
Equation 34 gives for the drop in water level in the stand-ptp**
v=V:
154 X 4800
(7,16 — 4.76)
707 X S2.15
=^•30 X 2*39 - 13.6 feet.
The more exact equations, 35 and 36, give for D and D^
D. - a X 3-5 D = -2-^ [^(7.15. - 4.76.) + ?!|^17.15-1«)H
or
D«— 750 D + 11, 120 = 0
Governor Specifications- - - 467
Solving this quadratic equation gives
r>_760 — •750^"^4 X 11,120
D ^ or
^ 760 — 719 ,,,-,,
D = 2 = ^^'^ ^®**
Db = 16.5 + fc X 4:.76» = 15.6 + .176 X 4.76» « 19.5 feel
No attempt will be made 'to estimate the greatest drop in level
hich might occur, due to an addition of waves.
331. Governor Specifications. — ^The present practice of requiring
!C governor builder to guarantee the speed regulation of a plants
I the design of which he has had no voice, without even giving
im the necessary information regarding the hydraulic elements
hich are considered in this chapter is wrong. It is partly the out-
rowth of the modern tendency to specialize, but perhaps more
Tgely due to a lack of understanding on the part of the engineer of
le nature of the problem, and a resulting desire to shift the respon-
ibility for results upon some one else who is better informed upon
le subject and thus protect results financially as well as save his
wn reputation in case of failure.
Governor specifications should call for a guarantee of the
(a) Sensitiveness or per cent load change which will actuate the
:overnor;
(b) Power which the governor can develop, and force which it
an exert to move the gates ;
(c) Rapidity with which it will move the gates;
(d) Anti-racing qualities, such as number of gate movements rc-
luired to adjust for a given Iqad change (See figure 280), or per-
cent, over-run of the gate, etc.
(e) General requirements of material, strength, durability, etc.
Beyond this point the governor designor has no control. The
-ngincer can, however, by choosing a generator whose rotor has a
"^igh moment of inertia (which quantity should be stated in tenders
^or supplying the generators), by the addition of a fly-wheel, if
"Accessary; by the construction of a stand-pipe; by means of a re-
icf valve, and very largely, also, by the general design of the pen-
Uocks, draft tubes, etc., greatly improve the governing qualities,
^nd, in fact, reduce the speed variation to any desirable limit which
the nature of load to be carried, magnitude of load changes antici-
pated, and economy of first cost will warrant
^68 The Speed Regulation ot Turbine Water Wheeli.
LITERATimm
Ttr RHINE ReOyLATIOTT.
1» Wini&niB, Harrej D. A New Method ol Governing Water Whfteli. Stfc
Jour, of Engng. ^^larch, 1896,
2. Electric Governors. Eng, News, 1896, T<si 1, p. ^76-
3. Parker, M. S. Governiag of Water Power Under Variable Loada, Tnm
Am. Soc a K June* 1S97,
' 4. Regulat[on of Wheels. The Chavanne Nozzle Regulator. Mining I Sci-
entific PreBi, Oct, 30, 1897*
5. Kntght, Samuel N. Water Wheel Regulation, Jour, of Elec. Not., ml
$♦ Replogle, Mark A, Speed Government In Water-Power PI a tits. Jeur. ft
Inst., VOL 145, p. 81, Feb., 1898.
7- Regulation of Water Wheels under High Pressure. Pioneer Electric
Power Co/b Wheels, Eng. Rec, Feb. 5, 189S.
8, Garratt. Allan V* Elements of Deeign Favorable to Speed Reguiatioa.
Eng. News, 1898, voL 2, pp, 51-159.
9. Modern Practice In Water Wheel Operation. Elec World, May S, 1100.
10. CasBel, Elmer F, Commercial Requirements of Water-Power Goveniiii&
Eng, Mag., Sept.. 1900.
11, Garratt, Allan V. Speed Reg-ulatlon of Water Power Plants. Ciasliri
Magazine, May, 1901.
12* A Water-Wheel Governor of Novel Construction. Eng. News* Xov. 13.
1902.
13. Thurso, J. W. Speed Regulation la Water Power Plants, Eng. NfWf^
1903, vol. 1, p, 27,
14. Governing Impulse Wheel by an Induction Motor. Eng. News, 1903, ^oi 1'
p. 24(3,
1£. Garratt, Allan Y. Speed Regulation of Water Power Plants, Elec kg^
May, 1904.
16. Goodman, John. The Governing of Impulse Water Wheels. Enp?-
Nov. 4, 1904.
17, Church, Irving P. The Governing of Impulse Wheels. Eng. Record.
Feb. 25, 1905.
15. GradenwitE* Alfred. The Bouvler Governor for Water TurhlQes. Marb
N. Y. June, 1905.
19, Henry, Geo. J„ Jr. The Regulation of High-Pressure Water-wheelB for ,
Power Tranamission Plants, Am. Soe. of Mech. Engrs. May l^l
1906.
20. Replogle, Mark A. Some Stepping Stones In the Development of t Mo(
ern Water-Wheel Governor. Am. Soc. Mech. Engrs. May. W
21, BuTtnger, Geo, A, Turbine Design as Modified for Close Regulitioa
Am. Soc. of Mech. Engrs. May, 19p6,
22. Lyndon, I^mar. A New Method of Turbine Control, Proc. Am. Init (
Elec. Engra. May, 1906,
Literature. 469
ater Wheel GoyemorB. Elec. World. June 30, 1906.
New Water Wheel Governor. Eng. Rec. Current News Sup. July 14.
1906.
arren, H. E. Speed Regulation of High Head Water Wheels. Tech.
Quar. Vol. 20, No. 2.
hnson, R. D. Surge Tanks for Water Power Plants, Trans. Am. Soa M.
B. 1908.
CHAPTER XIX.
THE WATER WHEEL GOVERNOR.
a 3a, Typ«5 of Water Wheel Governors. — In all reaction turbinei
md in all impulse turbines, with the exception of tangential wheels,
the governor affects regulation, i. e, controls the output, and henq
the speed of the wheel, by opening or closing the regulating \
thus varying the amount of water supplied to the whecL
gential wheels, under high head, this method of control, for i
reasons (See section 215), becomes difficult and in extremd
impossible and in such cases the governor must be arranged
feet regulation by the deflection of the jet from the bucket
Fig. 2S2).
Fig. 282. — Governing Iinpnlae ^beel with Automatic Needle and DeieetiD| ;
Nozzle (after Warreii)*
The force required to move the turbine gates is large (somctiflid
50,000 lbs, or more) and it is therefore evident that they cannot I
moved by the direct action of the centrifugal ball governors, 35 wtlj
steam engines, but must be moved by a "relay/'
The relay* as its name impHes, is a device for transmitting energ
from a source of energy independent,*— as to quanlity^-of the ceft*
trifugal governor balls but controlled by them in its appliettiQ'^
Typt:3 of Water Wheel Governors.
47r
may is of 'UneckaukQl type" the power required to operate
the gates is transmitted, when needed, from the wheel by
of shafts, gears, friction-clutches, belts and puUeys or other
lica! devices. In mechanical governors the flyballs may
' pawls, friction gears or other mechanical devices which will
he relay into action,
Fig, 2i3.^Woodward Standard Governor,
» relay is of the hydrauHc type^it usually consists of a piston
ted by some mechanical device to the gate rigging and moved
ins of the hydraulic 'pressure of water taken from the pen-
)r other source, or by oil supplied under high pressure from
troin The pressure of the oil in the reservoir is maintained
ipressed air supplied by power taken from the wheel itself,
thus used in moving the piston is exhausted into a receiver
hich it IS pumped back into the supply reservoir* The hy-
ssi^y is commonly controlled by the ball governor through
47^
The Water Wheel Gov ernon
the medium of a ^rnall valve which by its motion either admits thel
actuating water (or oil) directly to the cylinder or to a secondaryj
piston controUing a larger admission valve.
Electrical methods of actuating the relays controlled by mms^
of governor balls have been used to some extent but arc not ntarlVj
so common as mechanical or hydraulic devices.
Fig.
2S4.— Dlagramatlc Section af Woodward Simple Mech&alcal
233, Simple Mechanical Governors, — Fig, 283 is a view and Fi?
284 a diagramatic section of a simple mechanical governor of tlif
Woodward* Standard type. On the upright shaft are two frictio«
pans (a and b). (See also Fig. 2S7). These pans are loc^c ot) tlif
shaft, the upper one being supported in position by a groove in thf
hub and the lower one by an adjustable step-bearing. Between
these pans, and beveled to fit theni^ is a double-faced, friction whff'
(c) which is keyed to the shaft* This shaft and friction wheel nio
*Woo4ward Governor Co.^ Rock ford, III,
Anti-Racing Mechanical Governors. 473
msly and have a slight endwise movement. They are
:d by lugs on the ball arm and therefore rise and fall as the
of the balls varies with the speed.
the speed is normal, the inner or friction wheel revolves
itween the two outer wheels or pans which remain station-
hen a change of speed occurs, the friction wheel is brought
the upper or lower pan as the speed is either slow or fast,
uses the latter to revolve and, by means of the bevel
, turn the gates in the proper direction until the speed is
)rmal. As the gate opens, the nut (d) travels along the
t) which is driven through gearing by the main governor
d as the g^ate reacts, the nut (d) coming in contact with
• (f) throws the vertical shaft upward and the governor out
ission.
t3rpe of governor may be used to advantage where the
heels operate a number of machines, connected to a main
d where, in consequence, the friction or constant load is
lerable percentage of the total load. In such cases the
in load may not he a large percentage of the total load
temporary variations in speed, which occur at times of
of load, may not be of sufficient importance to necessitate
nation of a quick acting governor.
the water wheel is direct connected to a single machine,
friction load is comparatively small, the relative change in
I the consequent possible changes in speed, is much larger.
:h cases the type of governor above shown will result in
s hunting or racing (See Section 211) of the wheel during
able changes of load, and in unsatisfactory regulation. In
ses governors with compensating or anti-racing devices
used for satisfactory regulation.
kiiti-Racing Mechanical Governors. — ^The Woodward Com-
g Governor. — Fig. 285 is a view and Fig. 286 is a dia-
: section of a Woodward vertical mechanical governor of
pensating type.
: simple Woodward governor (See Figs. 283 and 284) the
ecessary to actuate both the centrifugal governor balls and
' is transmitted through a belt to a single pulley, P. In the
ird compensating type of governor the relay is operated
lilar manner by la single pulley, P, while the centrifugal
• balls are actuated by an independent pulley, q, having an
lent belt connected to the wheel shaft or to some other re-
474
The Water Wheel Governors.
volving part connected therewith. From the driving pulley, %
power is transmitted to the governor balls through a sliaft andj
gearing. The shaft supporting the centrifugal governor
is hollow, and on the ball-arms are two kigS which connect wilbl
Fig. 2S5.— Woodward CoaipeiLaatiiig Govtirnor.
spindle Cd which therefore rises and falls as the positions ottf*^
governor balls vary with the speed*
The movement of the centrifugal governor balls causing *h|
spindle^ f» to rise and fall changes the position of tlie tappet ann.
g, to which it 19^ connected, and causes one or the other of the two
tappets, tt', to engage a double-faced cam, h. This cam is contifr
uously rotated by means of the pulley above it, driven by a belt com
nected with the main veftical shaft of the relay. The tappets arc
J
Anti-Racing Mechanical Governors.
475
nnected to a common suspension arm. to which the vertical spin-
5, f, IS attached. The suspension arm is hinged to the lever arm, j.
le lever arm is connected to the shaft, K, which can be rotated
its bearings and which is connected with a tension rod, 1, by an
centric at the bottom. The tension rod, 1, is in turn connected by
^ 2S6. — ^Diagramatic Section of Woodward Vertical Ck>mpen8ating Mechan-
ical Governor,
ever, m, with the vertical bearing, e, on which the main shaft of
e friction cone rests. This bearing is movable around the ful-
jm, n, and is counterbalanced by an arm and weight, u.
When either of the tappets engages the rotating cam, the resulting
>vement turns the rocker shaft, K, and, through its connection,
ses or lowers the vertical bearing, e, which causes the friction
leel, c, to engage either the upper or the lower of the friction
ns, a and b, as in the case of the simple governor.
Ihe compensating or anti-racing mechanism is just below the
ating cam. It is essentially alike in all of the Woodward com-
isating types of governors and is described in the govem6r cata-
ue as follows :
476
The Water Wheel Covernor,
**0n the lower end of the cam shaft is a friction disc, r, (Fig. 2%)
which rests on a rawhide friction wheel on a diagonal shaft. The
hub of the friction wheel is threaded and fits loosely cm the diago
shaft which is normally at rest The effect of the continiiallT*
rotating friction disc upon tlie rawhide wheel is evidently to cau^
it to travel along the threaded diagonal shaft to the center of the
disc. When the governor moves to open or close the gate, tb
diagonal shaft, which is geared to it, is turned and the friction 1
is caused to travel along the shaft away from the center of the &k
d
I
Fig. 297. — Friction Cone and Pans of Woodward Govereo^,
and thus raise or lower the cam shaft so as to separate the cam ftm
the tappet which is in action, before the gate has moved too far,
thus preventing racing. As soon as the gate movement ceases tlie
disc causes the friction wheel to return to the center of the disc
along the threaded shaft,"
To prevent the governor from straining when the gate is follj
open or closed, suitable cams are mounted on tiie stop shtll
'*When the gates are completely opened, the cam engages the s
lever and holds it down so that it cannot raise the lower tap
sufficiently to engage the revolving cam; this does not, howeve
interfere with the upper tappet, to prevent the closing of the gate
should the conditions demand. The closed gate stop acts in a sin
ilar manner on the upper tappet but docs not interfere with
lower tappet being engaged, should the conditions demand that tl^
gate be opened. In addition to these stops, the governor is pt'i
vided with a safety stop whose function is to immediately close 1
gates should the speed governor stop through breakage of the I
or any other cause."
tfUU
The Woodward Governor,
477
235. Details and Applications of Woodward Governors. — Fig. 2S7
ows the constniction of the friction gearing of the Woodward
echanical Governor. In the inner friction driving cone, corks
? inserted in holes drilled in the rim and these are ground off true
that they project about one-sixteenth inch. This seems to give a
y reliable friction surface not readily affected by either water or
|. 288. — Woodward Horizontal Compensating MecMntcal Governor at. Hy-
dro-Electric Plant of U. S. Arsenal, Rock Island. 11 L
I
and it is claitned to he superior to either leather or paper for
LIS purpose. In order to cause the friction wheel to engage
noothly and nniselessly, a plunger attached to the shaft, just
slow the inner friction wheel, fits rather closely into a dash-pot
ffmed in the lower pan.
Fig. 288 shows a horizontal compensating type of Woodward
l?emor as installed to control the gates of the turbines in the Hy-
lulic Powder Plant of the U. S. Arsenal at Rock Island, Illinois,
he cables shown at the back of the cut operate the gates of the
rbine. On the gate shafts of the latter are sheave wheels to which
cables are attached. These sheave wheels are fitted with
478
The Walter Wheel Governor*
clutches so that any gate may be disconnected from the fovemsfj
Each gate is provided with an indicator showing its position TIM
provides means of cofiipling properly, after being disconnccteU
without closing the gates of the other wheels. Each governi^i
arranged to control six turbines, belonging to two different unit!
Two behs are provided so as to drive from either unit. The gove
Fig- 2i^, — LoiJibarU-Ktf^iUtgHl Mechauical Go\*ernori
nor can thus be used to control three wheels on either side or all
six when the two units are running in multipl<\
236, The Lombard-Replogle Mechanical Governor* — Fig >
shows a Lombard-Replogle mechanical governor. The princ:
of operation of this governor are better illustrated in the diagram,
Fig. 29(1
In the diagram A is a spherical pulley with its shaft turned r
and treaded as at X. B and B are revolving concave discs Innu
with leather which are continuously revolving in opposite dircc'
tions, C and C are lignum vitae pins flush with the leather* 0
and D are compression springs for controlling the pressure betft^ccB
the disks and tlic sphere. When the spherical pulley A is shifted
from its central position in the line of its axisi the springs ait
♦The Lombard-Replogle Governor Co., Akron^ Oliia I
The Liombard-Replogal Mechanical Governor.
479
tightened automatically, causing increased traction as the smaller
diameters of the sphere engage the larger diameters of the disc.
E and E are the centrifugal governor balls so poised as fo require
:hc weight of the pulley A to balance them at normal speed. F is a
oose collar to allow independent revolution of the balls EE. G
5 the point of connection between A and the gates or valve rigging
f the wheel to be governed.". X is the compensating devise, and is
Flf. 290. — ^Dlaffram of Lombard-Replogal Mechanical Gtoyemor.
w the purpose of reducing and controlling racing. Z is a sta-
aonary spindle or comnecting link between the collar F and the
-hrcaded shaft or pulley A. Z is only stationary in reference to
revolution, as it rises or falls with the variations of the governor
balls.
The spherical pulley A is normally at rest while the discs BB are
continually revolving. A movement of the governor balls raises or
lowers the shaft so that the spherical discs rotate the pulley.
The greater the displacement of the shaft the more rapid the
revolution since the circle of contact on the disc is increased. The
•Qtation of the spherical pulley A either shortens or lengthens
:hc distance to collar F by means of thread X. "This shortening
rauscs A to be pulled back to the disc centers, thereby cutting the
governor out of action" and preventing the gates from moving
oo far or racing.
Essential Features of an Hydraulic Governor. 481
237. E^ssential Features of an Hydraulic Governor. — ^The essen-
tial features of an hydraulic water wheel governor are :
1. A tank for storing oil under air pressure.
2. A receiver tank for the collection of oil used by the governor.
3. A power pump driven from the water wheel shaft.
4. A hydraulic power' cylinder for operating the gates.
S- A sensitive contrifugal ball system for controlling a valve
which cither admits oil directly to the power cylinder or to an inter-
mediate relay cylinder the piston of which operates the admission
valve to the power cylinder.
6. An anti-racing or compensating mechanism.
The power pump is continually using power from the wheel to
pump the oil from the receiver back to the pressure tank thus
gradually storing the energy which is used intermittently to oper-
ate the gates.
Fig. 291 illustrates the Lombard Type "N" Governor and shows
clearly the relations of the various parts of an hydraulic governor.
The centrifugal governor balls are connected by belt to the wheel
shaft. These balls control a small primary or pilot valve of the
cylinder type which admits oil from the large pressure tank under
about 200 pounds pressure into one side of a cylinder where its pres-
sure is exerted against one of two plungers. These plungers control
a large valve, also of the cylinder type, which admits oil from the
pressure tank to one or the other side of the power piston. The
rectilinear motion of the piston is converted, by rack and pinion, into
rcitary motion for transmission to the wheel gates. The oil used
for operating the power pistons and the plungers of the relay is
exhausted into the vacuum tank from which it is pumped back into
^he pressure tank by means of the power pump shown at the left
^hich is driven by belt from the wheel shaft. The speed variation
'Necessary to actuate the governor depends upon the lap of the pilot
^alve and is adjustable.
238. Details of Lombard Hydraulic Governor.— The details of
^he Lombard Type N Governor are best shown by the enlarged
^'iew of the upper portion of the governor (Fig. 292) and by the sec-
tion of the relay valve (Fig. 293). The following description of the
Operation of this governor is taken from the Directions for Erecting
^nd Adjusting Governors.*
**The oil from the pressure-tank is supplied to the working cyl-
inder 62 through the large relay-valve 106, arranged to discharge
^'Published by The Lombard Governor Co., Ashland, Mass.
483
Hie Water Wheel Governor*
or exhaust oil directly and rapidly into or from cither end of to
cyUnden The relay-valve 106, through the hydraulic system con^
nected therewith, is under the simultaneous control of the rtg-
ulatitig-valve 14 and the displacement-cylinder 107. This is
aadl
Fig, 292. — Upper Portion ot Lombard Type N Goveroor,
brought about in the following manner The relay- valve A|
(See Fig, 293) is moved hydraulically by plungers B
C contained within cylinders D and E forming parts
the relay- valve heads F and G, Plunger B has about om
half the area of plunger C, consequently plunger C can OVCI
power plunger B, if the pressure in cylinders E and D is nearl]
The Lombard Governor.
483
al. The cylinder D is permanently in communication with the
n pressure supply through the pipe H which also furnishes liq-
to the regulating-valve 14, Therefore the teadency of plunger
lalways to move valve A towards the relay-valve head G. Cy lin-
ing. 293.— Section Lombard Relay Valve,
I £ is in communication through pipes I and J with the adjusting-
ve 14, and also through the pipes J and K with the displacement-
iiadcr 107. The regulating valve 14 is capable, when moved
One direction, of admitting liquid under full pressure into the pipe,
aod, when moved in the other direction, of exhausting liquid
%ugh the pipe L In the former case the action is to increase
& pressure back of the piston C until it overpowers the piston B,
ereby naoving valve A towards the relay-valve head F, simulta-
iisly opening the upper cylinder-port to the main exhai'-'*^ *
484
The Water Wheel Governt
the lower cylinder- port to the main pressure supply. Instantly tJill
main piston of the governor and with it the displacement-plungefj
109 are set in motion.
''As the displacement-plunger begins to move, a space is create
back of itj into which a portion of the liquid flowing through ih
pipe I is diverted. As the motion of the displacement-plunger 1
comes more rapid, a condition is reached v^hen all the liquid flomnj
through I continues on through K into the displacement-chambcr|
The relay-valve A then ceases to move any further. The motid
of the main governor-piston, however, continues as long as thi
regulating- valve 14 is open. When this valve 14 closes, the rclaf
valve A is immediately thereafter closed, because the liquid in ih
cylinder E instantly escapes through the pipes J and K into 1
space beneath the moving displacement-plunger; thus the who
governor is brought to rest,
"When the regulating- valve 14 is moved in the opposite directioi
by the centrifugal balls so as to allow liquid to escape through th<j
pipe I, there results an immediate loss of liquid in the cylinder ]
back of the plunger C j this allows the plunger B to force the relay
valve A towards the relay- valve head G, thus opening the iowe
cylinder port to the exhaust ^ and the upper cylinder-port to t^e
pressure supply. The main governor-piston instantly begins tjo
move down, carrying with it the displacement-plunger^ thus forcing
liquid through the pipes K and I, reducing the flow outward throagli
J, until finally the downward velocity of the displacement-plungtr
becomes rapid enough to entirely check the outward flow through J
Relay-valve A then remains stationary until the valve 14 has moved
to a new position. As soon as regulating- valve 14 is closed, the liq-
tiid which has been flowing out through T immediately flows into]
and^ acting upon the plunger C, restores valve A to its closed posi-j
tion, stoipping further movement of the governor. It will be se
fthat the governor when moving has a constant tendency to do
the relay- valve which keeps it in motion, and this relay-valve t^
'ht maintained open only so long as the regulating- valve 14 is a<i(^|
ing or subtracting oil to or from the system consisting of the pip^
If J, K, and parts connected therewith*"
Fig. 294 shows the Lomard Governor, Type R, the smallest of t^]*
various governors made by that company* This is a vertical, s«lf*j
contained oil pressure machine. The oil is stored in a tank forme'
by the main frame. The go\*ernor is designed to exerl 2500 poufi^
k.
The Lombard Governor.
4^5
pressure and will make an extreme stroke of eight inches in one
second.
239. Operating Results with Lombard Governor. — Fig. 295 is
^ cut from a spead recorder strip taken from the Hudson River
Fig, 294,— The Lombard Type R Governor.
Power Transmission Companies plant and shows the regulation of
Jhe Lombard Type B Governor regulating S. Morgan Smith tur-
Iliincs on an electric railroad load. The cars are large and the
change in load rapid and large.
486
The Water Wheel Governor.
a
o
m
n
- P^
f:^ o
£
'hi
Fig. 296 shows the comparative repla-
tion of two generators in the same plant
(See Bulletin No. 107 Lombard Gow
crnor Company,) The load was Quiltj
variable on account of beaters whiclbd I
to be driven from the same shaft as tliej
paper making machinery. The ori^nall
governor used, the work of which isshoviti
in the upper cut, was replaced by a Lom-
bard Type D Governor* The work qU
the latter is shown in the lower tacho
meter chart, and the improvement m i
uniformity of operation is readily seen i
a comparison of the two charts,
240. The Sturgess Hydraulic Go?er-j
nor,* — The Sturgess Type **M'* Hydratf
lie Governor, with the omission of thr
pump and storage tank, is shown in Fig
297 and in section in Fig. 29S. This gov*
emor consists of a shaft- tj^pc ccolnfugii
governor G attached to the topof them*i-
chine and operated by a belt and pullef
P from the turbine shaft. The govemar
balls BB in this machine control directly h
means of a long vertical lever D a fiuall
primary or pilot valve S of cylinder type
which admits oil to a cylinder controlling
the main admission valve S, The main
valves, attached to the side of the cylin-
der, admit pressure directly into the cyl-
inder S and on either side of the piston ^
which, by its motion, rotates the gatf
shaft by means of the concealed steel rack
R and pinion N, shown in the scctioDal
view, Fig, 298.
The valves for the admission of oil or
water, as the case may be, in the cylinder
are of the poppet type which avoid '*lap*'
and therefore increase the sensitivciv -? >
the governor. The anti-racing mechdji
^SturgeeB Enpneering Dept. of
Valve Mfg, Ca, Troy, N, Y.
J
.Vheel Governor.
The Walter Wheti ^
¥Vf
-^297
^StiJrg*^'^
,,.M Hydraulic Oovemc
The Sturgess Hydraulic Governor,
p r~t)B
489
Fig* 29R.— Section Slurgess Type M G^>vernor.
nsts of a rod A which is attached to the cross head of the
Svernor* At the top of this rod is a projection to which
attached an adjustable piston rod reaching down into the open
p dash pot F. The piston rod has a piston attached at its lower
kitting freely into the bore of the dash pot the top of which is
49©
The Water Wheel Governor,
formed into a cup which receives the excess oil. The bottom of tliej
dash pat is closed and ts attached to a tail piece connected to tkj
coonter weighted locker lever, C
The piston rod and piston are hollow and near the bottom ^thel
pistotti is a small by-pass which can be regulated by an adjusting
screw which controls the rate of flow of the oil in the dash poL The
lever, C, is fixed on the rocker shaft the opposite end of which car-
ries the short arm from which a link is carried to the bottom of the
valve lever D which is free to move. Two weights, EE, are
It * I, TA^MOIICTIft N». lOpHt
_Ti*t «. 1 H4 M _-
o^iU^
^gf omar ta4 Oat*':
m.
w
E-^;--
ii
m
UmA ™ -
r-H-
f-
'~ 1
-T-----
"="F""B--
f- +
^■-
-i""-
t:::::::-;^:::^
---pd^. 1..
Fig. 21>9.— Test Results wilti Sturgess Goveruor.
hung loosely on the rocker shaft but a pin on the shaft engager wit^
either one or the other of the weights and raises them whenevertb
rocker shaft moves. The function of the weights therefore is '
keep the rocker shaft, and consequently the bottom of the valv
lever, in normal position. When the main piston moves, it is ok
vious that it will tend to raise or lower the dash pot, F, throwg
its connection to the rod I and this movement will swing the kv
C and rocker shaft H thus deflecting the bottom of the valve Icvd
Dsoas to compensate in the correct manner. The same movemcntj
raises one of the weights E, but as the dash pot permits a iioi
movement the weights will finally restore all parts to the middle*
k.
Test Results with Slurgess Cxovcmor.
491
normal position. In the smaller sizes the pilot valve is omitted
and the centrifugal governor balls actuate directly through the
lever the main valves of the system.
241. Test Results with Sturgess Governor* — ^The action of any
governor in maintaining a uniform speed may be shown graphi-
cally by attaching a recording tachometer to the turbine shaft. In
order to fully understand and appreciate the action of the governor,
the tachometer chart should be considered together with the load
curve and a diagram showing the movement of the governor dur-
ing the same period*
Fig, 299 shows a governor test made by Mn John Sturgess on an
1 100 K* W, unit, 'The curves were traced by a special Schafer &
Budenberg tachometer, the readings being sufficiently magnified to
bring out the characteristics of the governor. * * * The load
changes and governor movements are platted below. Note that when
the whole load was thrown off (at 1 155 ), the speed accelerated about
S per cent, in an incredibly short time (under i sec), and the gov-
ernor had the gate shut in 14 sees, after the load went off, • * ♦
It is to be noted that after the first quick result at 2:00 mins. the
governor slowly oscillated for about another minute, but with
gradually increasing gate opening, the speed and load being prac-
tically constant. This was due to the water rismg in the forebay,
and gradually subsiding in a succession of waves, the governor tak-
ing care of these fluctuations, in effective head, in a very intelligent
manner."*
**The plant in which these tests were made was by no means a
good one from the regulation standpoint, for it will be noticed that
when the whole load was instantly thrown off the momentary rise
of speed was about 8 per cent, although the governor shut the
gate from full open position in the extremely quick time of 1,4
sees. There were five wicket gates, having a total of 96 leaves, and
a heavy counter-w^eight to be moved a considerable distance in this
interval, **
342, General Consideratijon. — Mechanical governors are cheaper
than hydraulic, biit^ assuming the same gate movement, they are
less effective at increasing loads since the power to move the gates
must be taken as needed from the wheel itself instead of being taken
• See American Society M, E.» Vol. 27. No, 4, p. 8*
•• Catalo^e of Water Wheel Go?ernorB, Sturgess Engineeringf DepartmeDt
of tfae Ludlow Valve Co.* p. 23,
I
I
493
The Water Wheel Governor
from a storage tank as with hydaulic gfovernors. This is t factor
of more or less importance in accordance with the degree of regu-
lation required. The difference is manifest principally at low loads
when the energy taken by the governor relay from the water wheel
is a considerable percentage of the total energy being generated ^3
the power exerted by the relay is usually comparatively small, the
difference in action from this cause between the two types of go^
ernors is often unimportant-
Fig, 300,— Governor Conneeiion by Briw BodiL
The hydraulic governor possesses an additional advantage in its
ability to start a stationary wheel into action by means of iu
stored energy. The mechanical governor depending as it does on
the power of the wheel itself is only effective after the wheel has
been started by other means.
243, Control From the Switchboard.— Electrical devices caa now
be purchased by which the normal speed of the wheels can be con-
trolled from the switchboard in case the governor is so designed,
that it can be adjusted while in motion^ which is true of most higli|
class machines. It is also possible to start and stop the wheeb
electrically from the switchboard or from a distant station.
im^
B ConoectioD of Governors to Gates» 493
■ 344. Connecton of Governors to Gates, — ^The following discussion
mi this subject and the accompanying figures are taken with slight
changes, from a paper by Mr, A, V, Garratt.*
" ♦ * * The most successful methofi of connecting the cylinder
gates of several turbines to the same governor is shown in Fig. 300*
In this case each pair of drawrods is connected to a pair of walking
beams which carry counterweights on their opposite ends. Each
walking beam carries a gear sector which engages a rack on a long^
horizontal reciprocating member terminating at the governor-
The racks on the reciprocating member arc **sleeved*' on it, and held
in place by pins, which may be removed if it is desired to discon-
nect any turbine from the governor.
"By this method any one, or any combination of turbines, may be
handled by the governor or any turbines by hand, at will, by means
of a lever shown in the end projection.
"Fig. 301 shows a good method of connecting a governor to a
pair of horizontal wicket-gate turbines. It will be noted that the
shaft connecting the two gear sectors on the gate stems goes di-
rectly to the governor, and is connected to it through a pin clutch
which may be opened, and a hand- wheel cm the governor may then
be used to move the gates by hand- The only improvement on
this design which can be suggested would be to eliminate the coun-
ter-shaft between the governor pulleys and the turbine shaft by plac-
ing the governor beyond the draught*tube quarter-turn, so that
the governor pulleys might belt directly to the turbine shaft. The
Kmitattons of available space prevented the location of the governor
in this manner on the drawing which shows the design used for
three units in a modern power plant.
"Frequently the only possible location of the governor prevents
anything like direct connection between it and the turbines* In
such cases experience has shown that it is wisest to avoid the use
of several pairs of bevel gears and long shafts, and in their place
use a steel rope drive. This method has great flexibility, and per-
mits of governor locations which would otherwise be impossible.
Fig. 302 shows a design of this kind. The governor is located in
the only available space, and yet its connection to the turbines is
perfectly adequate. The steel rope used is small in size, made of
very small wire, especially laid up, and its ends are fixed to the
grooved sheaves, which are provided with internal take-ups, so
• See "Speed Regulation of Water Power Plants,* by AJlaa T. Oajrutt Ct»
tier's MaemzlBe, May. 1901.
3a
t
494
The Water Wheel Governor.
Fig 301 — Governor Connection by Shaft and Sectort.
Relief Valves.
495
that the rope may be kept tight as a fiddle string. This general
method of connection is in successful use in many plants where
the requirements for speed regulation are most exacting.
"In the above examples the two ends which have governed the
design are simplicity and directness. These two factors should
never be lost sight of, and the more completely they are embodied
in the design, the better will be the sp^eed regulation. To these two
may be added another, and that is freedom from lost motion. These
IT
JlL
Fig. 302. — Governor Connection by Cable.
three factors are absolutely necessary if successful results are to be
expected. The slightest motion of the governor must be trans-
mitted in the simplest and most direct manner, and in the shortest
possible interval of time, to the turbine gates."
245. Relief Valves. — Relief valves are very necessary on long
feeder pipes and penstocks to avoid excess pressures of an acci-
dental nature as well as those produced by closing of the turbine
gates. A g^oup of such valves installed on the end of one of the
penstocks of the Niagara Falls Hydraulic Power and Manufactur-
ing Co. is shown in 'Fig. 303. Relief valves should be arranged to
open with a slight excess of the penstock pressure but should close
very slowly in order to avoid oscillatory waves. Spring hala*
496
The Water Wheel Governon
relief valves have proven objectionable for this purpose. If set
to open at a small excess pressure they are apt not to close on ac-
count of the impact of the discharging water against the valve.
In order that they may close, the balancing spring must be so stroaf
That a considerable excess is required to open the valve which does
not therefore ser\*e the desired purpose. All types of valves are
also hindered by the fact thaf corrosion is apt to sea! the valve so
that a considerable excess is required to open it,
246. Lombard Hydraulic Relief Valve, — Tlxe Lonibard Gov-
Fig. 30.1. Relief Valve on end c\i Penst-ock. Nla^ni Fn]h HyiJ rautie Pofftr
ManufactiiilnKCo, (Electrical World, Jao. 14, IKSaj
emor Company have designed a valve in which they claim to bvt
eliminated the difficulties of the spring valve. This valve is shown j
in Fig. 304* and is described as follows :
**The valve consists of the following parts, viz: — A valve disc c*
c&pable of motion to or from its seat, b, rigidly connected by mean?
of a rod, ij with the piston, f, in the cylinder, e. The whole valve ti ,
bolted to a flange upon the supply pipe, d, wherein the pressure is
to be controlled. The area of piston, f, is somewhat greater t^^^
that of the valve disc, c, so that when water at the same pressure j
is behind the piston and in front of the valve there is a positive afs^ |
strong tendency to hold the valve closed. For the purpose of a^'
• Lombard BuHetin Ne. 101.
Lombard Hydraulic Relief Valve.
497
ng the valve disc, c, to open at proper times to relieve excess
sure in the supply pipe, d, there is provided a regulating waste
e, C. This valve is opened or closed by a piston, n, opposed
very oblong and strong spiral spring, p. Piston, n, is a loose
i its cylinder, o, so that it moves upward freely in response
Fig. 304.— Lombard Hydraulic Relief Valve.
le least excess in pressure upward due to the water in the cyKn-
0, apposed to the downward pressure of the spring, p. ♦ ♦ ♦
piston, n, is connected by means of the stem, m, with a double-
ed balanced valve, d, which of course, opens simultaneously
I any upward movement of the piston. Water under existing
sure IS admitted into the cylinder, e, through the pipe, k, and
ttle valve, t.
498
The Water Wheel Governor
k.
**Tbe spring, p* is adjusted by means of the screw, s, and lock-niit,
jf so that the effective normal pressure of tlie water in the chamber
13 jtist insufficient to overcome the downward pressure of the
spring. The valve, D, will therefore remain closed normally: con-
sequently the main valve disc, c, will also remain closed norinaUy,
because water Bowing in through the pipe, k, and throttle %^alvf, L
will produce an excess closing pressure upon the piston, f. When
thus adjusted any increase in pressure above the normal will
immediately force the piston, n, upward, and will thereby oper
the balanced valve, D* This instanily reheves the pressure back
of the piston, f, which of course then gives way to the superior pres-
sure back of the piston, f, which of course then gives way to the
superior pressure in front of valve, c. In this manner practially
the whole pressure in front of the valve disc, c, is available fof
opening it, * * • Valve disc, c, will continue to open until
the limit of its travel has been reached, or the pressure in
the supply pipe, d, has been reduced to a point where the
piston, n, will close the balanced valve, D. Immediately on the
closing of balanced valve, D, water begins to accumulate behind
the piston, f, flowing in through the throttle valve, !• This water
gradually and surely forces the valve disc, c, to close. The speed oi
closing is adjustable by the opening through the throttle valve, i.
and may be made as slow as several seconds or even minutes, Tlie
closing motion is * ♦ uniform and there is not the slightest ten*
dency to set up vibrations in the water column, a very serious ob-
jection to the ordinary types of spring balanced valves which open
and close suddenly and are liable in the latter operation to set np
water hammer effects even more dangerous than those which tky
are designed to relieve/'
247- Sturgess Relief Valves, — The Sturgess Engineering IV
partment of the Ludlow Valve Manufacturing Company makes two j
forms or relief valves, the "Automatic" and the "Mechanicai
The Automatic Relief Valve is shown in Fig. 305 and is described j
as follows ;
"The essential element in the Automatic Relief Valves is a largti
very sensitive diaphragm nf special construction* This is under
the influence of the water pressure in the pipe-line and its move
mcnts are communicated to a small piiOt valve controlling a hr
draulic cylinder, which in tiirm operates the relieving valve on the
relief valve proper. After the pressure in the pipe-line is restored I
normal, the relief valve gradually closes automatically.
Sturgess Relief Valve.
499
'The action of .this valve is almost instantaneous, and it will
fully open on a very small rise of pressure.
"These valves can either be made in self-contained form, or
the sensitive parts (diaphragfm, pilot valve, and hydraulic cylin-
Fig. 305.— Sturgess Relief Valve.
dcr) may be mounted on a pedestal placed in the power house,
and the relief valve proper attached to the penstock or wheel cas-
ing, a rod or link being provided to connect the two (as in Fig.
305).
CHAPTER XX.
ARRANGEMENT OF THE REACTION WHEEL
248. General Conditions. — ^The reaction turbine may be set or ar-
ranged for scnrice in a water povirer plant in a variety of ways, and
tlie best way may differ more or less with each installation, Tlie
arrangement of wheels should always be made with due regard to
machinery to be operated, the local conditions that prevail, and es-
pecial consideration should be given to securing the greatest
economy in the first cost of installation, maximum efficiency and
facility in operation, and minimum cost of operation and maiflte-
nance.
Impulse water wheels of the tangential type have always been
set with their shafts horizontal » An installation with vertical shaft
was proposed for one of the first Niagara plants but was not con*
sidered on account of the lack of actual experience with such a
form of installation. Impulse wheels of the Girard type have been
used with both vertical and horizontal shafts* In general* how-
ever, because of the high heads under which impulse wheels usually
operate, the horizontal shaft arran^gement is readily adapted.
When an impulse wheel is installed it must be set above the level
of maximum tail water, if it is to be operated at all stages of water,
The wheel arrangement is therefore dependent principally on the
arrangement of the machinery to be operated. By far the greater
proportion of such machinery is built with horizontal shafts and
hence in most cases wliere machinery is not special, horizontat
shaft arrangements are desirable.
Reaction wheels are often used on streams where the relative
varjation in position of the tail- water is considerable, and it is both
desirable to utilize the full head and to have the wheel set at an ele-
vation at least above the lowest elevation of the tail- water in order
that they may be accessible for examination and repairs. By the
use of the draft tube this can often be done without the sacrifitc
of head.* Tf the wheel must be set below tail-water» gates must be
provided for the tail-race with pumps for the removal of the watcf
when access to the wheels is necessary.
Necessary Submergence of Reaction Wheels. 501
The arrangement of reaction water wheels is susceptible only of
rencral classification, which, however, may assist in the under-
tanding of the subject and the selectioa of the best methods to be
dopted under any set of local conditions. Wheels may be set
ertically or horizontally, as the conditions of operation demand,
without materially affecting their efficiency, provided that in each
istance the turbine case, draft tubes, etc., are suitably arranged,
'he improper design of the setting may materially affect the effi-
iency of operation in either case.
249. Necessary Submergence of Reaction Wheels. — In order to
revent the formation of a vortex or whirlpool, which will draw
ir into the wheel and often seriously affect its power and efficiency,
is necessary that the g^te openings of the wheel be placed from
ne to one and one-quarter wheel diameters below the water
urface. The head under which the wheel is to operate, however,
reatly affects the formation of the vortex. High velocities of flow
all facilitate their formation ; therefore greater heads will require
greater water covering or other means for the prevention of
ortex formation.
As the wheel usually has a greater diameter than the height of
he gate it can be set vertically with less danger of air inter-
crence than when set horizontally. For this reason the vertical
vheels are more readily adapted to low heads and have in the past
>een more widely used for developments under low and moderate
leads.
With both horizontal and vertical wheels the wheel may be pro-
jected from the formation of the vortex by a solid wooden float, or
Tiay be partially encased or covered with an umbrella-shaped cover
the edges of which can be brought below the level of the upper
^tes of the turbine thus allowing the wheel to be set near the
tiead water surface without the serious interference above men-
tioned- In all such cases the float or cover must be so arranged as
to admit the water to the wheel gates without undue velocity in
^rder to prevent the loss of head. If this is done the efficiency and
>ower of the wheel will not be affected (see Appendix — ). Arrange-
rnents of this sort were designed by the writer, in the fall of
1^906, for the water power plants at Kilbonrn and at Dresden
Heights.
250. Arrangements of Vertical Shaft* Turbines. — Figs. 306 and
507 show twelve typical arrangements of reaction turbines. Figs.
A. B, C and D of Fig. 306 show typical arrangements of vertical
502
Arrangement of the Reactiott WheeL
vmmd^^^
^ ■ :n
-^z^
M
Fli. SM.
Arrangement of Vertical Siiaft Turbine.
503
rficels. Diagram A li the most common arrang-ement of the re-
auction turbine in an open penstock for low head. In this case the
•^jvhecl is set in a chamber called the wheel pit, the ftume, or some-
times the penstock; and is connected with the head race from which
it should be separated by gates. The wheel pits in the smaller
fplartts have commonly been constructed of timber; but in the larger
plants they are usually built of a more substantial character, —
often of iron or concrete, usually reinforced. Sometimes two or
more wheels are set in a single pit; but in the better class of con-
struction, a pit is supplied for each individual wheel or each unit
ccM-nbination of wheels so that each unit can be cut off from its
fellows, disconnected from the transmission mechanism to which
it is attached, and examined or repaired without interference with
the remainder of the plant. Open pits are commonly used for
heads up to 18 or 20 feet and may be used for considerably higher
heads under favorable conditions*
For higher heads» the arrangement shown in diagram E, or sone
other form similar thereto, is often found more desirable. In this
case closed flumes of steel or reinforced concrete are used, and are
connected with the head race by metal, wooii, or reinforced con-
crete pipes to which the term "p^^^^^^ck" is commonly applied.
This form of construction permits of the use of vertical wheels
with almost any head. In Diagram E the turbine is shown as di-
rect connected to an electrical generator of special design with ver-
tical shaft.
In Diagram A the shaft of the turbine is shown as directly at-
tached to a crown gear which in turn is connected by a spur gear
with a horizontal shaft. This horizontal shaft may be direct-con-'
nected to a generator as shown in Fig. 325, or may be attached by
belting, ropes, cable or other mechanical means with one or more
machines which it is designed to operate.
Diagrams C and D show two vertical types of settings of tnn-
dem or multiple wheels. Such arrangements are introduced when
it is necessary to reduce the diameter of the wheels on account of in-
creased speed, and at the same time maintain the power of in-
stallation by increasing the number of wheels for the purpose of
direct connection to some machine to be operated .
In all cases where two wheels discharge into a common draft
tube sufficient space is necessary between the wheels to prevent
interference and consequent loss in efficiency. The arrangement
5^4
Arrangement of the Reaciioa Wheel
of wheels in this manner therefore requires a considerable amount
of vertical space and, under low or moderate head, involves the
construction of a %vhcel pit of considerable depth in order to se-
cure proper submergence of the upper wheeh This arrangcmcni
results in the lower wheel being often considerably below the tail-
water and necessitates the use of tail gates and a pumping plant
to remove the water in order to make the lower wheels accessible
With this design the plant is made comparatively narrow but iht
greater depth of construction means an additional expense in the
foundation work. Vertical wheels of all types involve a design
of satisfactory vertical bearings which are usually less accessible
than in the case of horizontal bearings which can be placed at an
elevation above the power house floor, and are consequently matt
readily accessible. The stop bearings for single vertical whcdi
have been long in use and are reasonably satisfactory. The su
pension bearing, which is involved in the use of large vertical in
stallations, is not universally satisfactory and, in fact, considerable
difficulties have been encountered in so designing a bearing that it
will operate without undue expense for maintenance.
251, Arrangement of Horizontal Turbines.^ — Single horizODtal
wheels of the common type are shown in Diagrams E and F of Fig.
306 and in Diagrams A, B, C, and D of Fig. 307. In each case thej
gates of the turbine must be readily accessible to the entcring|
water without undue velocity, and the wheel pit, or penstock^ must
be designed with this requirement in view.
Diagrams E and F, Fig. 306, and A, Fig. 307, show horizontal
types of wheels set in an open wheel pit or penstock.
In Diagram E the wheel has the quarter turn set entirely in the|
pit, and the main shaft passes throug'h a bulkhead in the wall 1
the station with a packing gland to prevent the passage of watcfJ
In this case the water must flow by the quarter-bend and hence,'
in order to secure sufficiently slow velocity, the wheel pit must be
wider or deeper than in the case shown in Diagram F of Fig. i-
Here the gates of the turbine are placed toward the entering w:itr
and the (low is interfered with only by the pedestal bearings wl.ic];.
being placed in the center of the crown or cover plate of the wheel
occupy but little space and oflFer practically no obstruction to fiow.
Diagram A of Fig. 307 is essentially the same in arrangement
as Diagram F in Fig. 306, except that in this case instead of a m^
tallic quarter-turn and draft-tube, the quarter-turn and draft-tube
are constructed in the masonry of the power station and the hnW-
Arrangement of Horizontal Shaft Turbine. 505
Fig. 307.
3o6
Arrangement of the Reaction Wheel-
head IS reduced to simply a packing gland through which thcshaM
enters the power station. I
Diagrams B, C, and D, Fig. 307, illustrate three methods of en-
closing a turbine in a closed flume which is connected with tht
head water by a closed penstock. I
In Diagram B the turbine case is spiral, the water enters tan^cnlj
to the wheel and at right angles to the shaft and is discharged!
through a metal quarter-bend into a concrete draft-tube. I
In Diagram C the water enters the metallic flume in which thei
wheel is placed at right angles to the shaft, and is dischaigeU
through a metal quarter-bend and draft-tube- I
In Diagram D the water enters the wheel case parallel to t«
shaft of the wheel and is discharged through a metal quarter-be™
^nto a concrete draft-tube. I
Figs. E and F of Fig. 307 show methods of setting homontaT
shaft wheels in tandem. Diagram F is for setting in an opeti
flume or penstock. The two wheels discharge into a common
shaft chest and use a common draft-tube. In Diagram E the wbeela
have a common closed case or flume cotmectcd by a penstock witH
the head waters and each discharges through an independent qtiar-
ter-turn and an independent draft-tube into the tail- waters beneatkJ
With the closed flume removed, this arrangement can also be usefl
in an open penstock. These diagrams are simply typical of T»*arioiii
possible arrangements of wheels that can be adapted with variousj
modifications of detail to meet the local requirements of the eiJ
gmeer for any hydraulic plant which he may be called upon todoJ
sign. I
252, Classification of Wheels. — The classification of the amuigM
ment of wheels as shown in Figs, 306 and 307 may be reviewe™
bncfly as follows: I
In this review reference is given to various figures in the prw
ceding and following text in which the type of wheel described Wm
illustrated with more or less modifications^ I
rst* Vertical single %vheel, open wheel pit (See Diagram i.^
Fig, 306, also Figs. 329, 331, 333 and 334,) I
2nd* Vertical single or tandem wheels in metal casing cofM
nectcd by cylindrical penstock with supply, (See Diagram B, Flil
306, also Figs. 132, 181, 3T0. 31 r.) |
3rd. Vertical tandem wheels, — two or mare wheels in open l^Jt
(See Diagrams C and D, Fig. 306, also Figs. 134, 138. 173, 330.)
k
Classification of Wheels,
507
Horizontal turbine, open wheel pit, quart er-bend and draft-
tube within wheel pit, — quarter bend of metaL (See Diagram E,
Fig. 306.)
5th* Horizontal turbine, open wheel pit, quarter-bend, and draft-
ttibe exterior to pit, — quarter-bend may be of metal or concrete
construction, (See Diagram F, Fig. 306, also Diagram A, Fig.
307 and Figs, 314, 322)
6th* Horizontal turbine in spiral case at end of penstock, single
or double draft-tube. (See Diagram B, Fig, 307, also Figs< 159,
162, 338.)
7th* HorizcHntal turbine in cylindrical or conical case at end of
penstock. (See Diagrams C and D, Fig. 307, also Fig- 335.)
8th, Tandem horizontal turbines in open wheel pit, single dis-
charge through common or independent draft tubes. (See Diagram
F, Fig. 307, also Figs, 315, 319 to 324 inclusive.)
9th, Tandem horizontal turbine in enclosed cylindrical case with
enrnmon penstock and common or independent draft*tubes, (See
Diagram E, Fig 307, also Figs. 13, 140, 152, 317.)
253- Vertical Wheels and Their Connection. — The vertical set-
ting of single wheels is usually the cheapest in first cost, which
fact IS an important factor that has been largely ins trn mental in
tbe adoption of this arrangement in most of the older plants. Ver-
tical wheels are most commonly set in open wheel pits. They may,
however, be set in a cast iron or steel casing which is then con-
nected to the headrace or dam by a proper penstock. Single ver-
tical wheels can be connected to the machine they are to drive by
various means. Belting, transmission ropes, cables, and shaftings,
arc in common tise for such connections. The shaft is usually placed
hnrizontally and is connected by a crown beveled gear and pinion
to the wheel. Frequently belts, ropes, and cables are connected by
pulleys or sheaves to a short horizontal shaft driven in the same
manner When the power of a single vertical wheel is insufficient,
two or more may be harnessed by gearing to a line shaft which may
be directly connected to the machin*" or machint;s to be operated,
or otherwise connected as convenience and conditions may require.
254. Some Installations of Vertical Water Wheels. — Figs. 329 to
332 inclusive, show the plans, elevations, sections, and details of
a small plant of vertical water wheels designed by the writer for
the Sterling Gas, Light and Power company of Steriing, Illinois.
The details of this plant are clearly shown by the illustrations and
will be discussed at some length later. This plant is located on the
So8
Arrangement of the Reaction Wheel.
J!
f^l^-^rjf?^
Some Installations of Vertical Water Wheels.
S09
ng side of the Rock River (See Fig» 345) and is next to the
lant on the Sterling Race. The head developed h about eight
and the power of each wheel is about 115 h* p. under this head.
:h wheel of the installation is set in an independent pit or pen-
:k which can be closed by means of a flume gate. The wheels
connected to a common shaft extending into the power house
Connected with pulleys and belts to the generator.
Tie plan of the South Bend Electric Company at Buchanan,
iiigan, is of similar type and is shown on page 544, Fig. 334. The
!l shaft IS here connected with ten turbines and is in turn
rtly connected to an electric alternator.
Fig* 309, — ^1x3 w Head French Water Power Plant
me adaptability of the vertical shaft turbine to low head is well
Im in Figs, 308 and 309. Fig. 308 shows three turbines manufac*
M by The Trump Manufacturing Company of Springfield, Ohio.
ese turbines are 61 , 56 and 44" respectively, and by suitable gear-
, are connected with a common shaft. These wheels were in-
ed at Bologna, Italy, and operate under a low water head of 4^
[under a high water head of 28^ It was necessary to set the
lis rnnsiderably below the level of the tail water in order that
SI
Sio
Arrangement of the Reaction Wheel.
the turbines should have a sufficient submergence for ope
Fif' 3C>9 is a similar plant installed at Laches, France, In?
case the water is conducted to the turbines by means of a syphtinj
supply pipe in order that the turbine might be placed high eni ■:;,'''
above tail-water that tt be accessible at all times without the
_^ use of a tail-gate. Air i^
exhausted from thecrowo
of the syphon by mt of i
steam ejector whciicvertiK
plant is to be started up.
This plant operates under
the low head of thirty-one
inches and is said to woA
very satisfactorily.
Fig, 310 shows a venici]
shaft turbine of theVictof
cylindrical gate type maj\-
ufactured by The PUtt
Iron Works, This wheel
is set in an independent
case with provision made
for the attachment of a
cylindrical penstock con*
ducting the water fromtk
head work to the wheel
This figure shows a special
design by which the spec-
ial generator is set on col-
umns resting directly on
the wheel case.
Fig. 31 1 shows the plant
of Trenton Falls, NVw
York, of the Utica Gas and Electric Company, The wheel is a
Fourneyron turbine, manufactured by The L P* Morris Company,
operating under a 266 foot head, the water being conducted to the
wheel through a penstock the length and arrangement of which art
shown in Fig. 353. The wheel is provided with a draft- tube and is
regularly connected with the generator above. The moving parti
of both machines are carried by a vertical shaft bearing, shown in cut
355, Some Installations of Vertical Wheels in Series. — In the
last three illustrations wheels are shown of suf^cient size and operat-
Fir 310.
Some Installations oE Vertical Water Wheels.
S^i
111.— The lYentoo Falls Plant of the Utlca Gas and Electric Co. (L P.
Morris Co.)
5i2
Arrangement ot the Reaction Wheel.
ing under sufficient head to be suitable for the independent operatt!
of the machine attached to them. In many cases, however, eif<
cially with low head, the arrangement shown in Fig. 308 and
Figs. 325 to 329 inclusive, becomes necessary. In such OK
considerable loss is entailed by the use of shafts, gearings, and belt
Fig:. 312.— Vertical Turbine for Sew airs FftlU Plant of the Concord Elect!
These losses are so large that it is desirable to avoid oe rt
them If possible. For this purpose vertical wheels are somel
placed tandem as shown in Diagrams C and D, Fig, 306.
type ol plant is also illiisLrated by Figs, 312 and 313 whicj
illustrative of wheels tnstaUed in the plant of the Concord El
Company, at Concord, N. H.
Some Instalialions of Vertical Wheels in Series.
5U
"ig. 3T2 shows tandem wheels for this plant as designed and
nufactured by The AUis-Chalmers Company of Milwaukee,
s,, and are described in further detail on page
Fig. 313 is a view of a
double vertical unit, designed
and built for the Concord
Electric Company by The S*
Morgan Smith Company of
York, Pa. This form of in-
stallation has the advantage
of a greater concentration of
the machinery This type of
installation, while quite com-
mon in Europe^ is somewhat
new in this country* and pre-
sents several novel and desir-
able features.
256, Some Installations
of Horizontal Water
Wheels.^Most machines to
be operated by water wheels
are built with horizontal shaft,
and, as a direct connection of
wheels to the machinery to
be operated involves a min-
imum loss in power and con-
sequent greater efficiency
than with the various com-
plicated arrangements often
necessary with vertical
wheels, the horizontal wheel
becomes desirable and is
opted whenever practicable in a modern water power plant. The
pe of such a plant is well illustrated by the power plant at Turner's
4is, Massachusetts^ shown by Fig. 314. The single horizontal wheel,
*ect-connected to the machinery to be operated, is perhaps already
Rficiently described in the preceding pages. The arrangement of
o or more wheels for such purposes deserves careful consideration,
gs. 315 and 316 show a plan and section of a double unit, for use in
open penstock, as manufactured by The Dayton Globe Iron
orks Company of Dayton, Ohio, These figures show a plain.
Fig. S13.
Some Installations of Horizontal Water Wheels. 515
idrical, draft-chest connected with a common draft-tube. The
ils of the arrangement can perhaps be better seen from the half-
, Fig. 320. which illustrates two of these units connetcd
ther tandem.
^ggr>ii*r<i>tiii^'i.rt«y
315. — Section Double Wheel with Common Draft Tube. (Dayton, Globe
Iron Worics Co.)
Fig. 316.— Plan.
igs. 317 and 318 show a similar double unit manufactured by
same company. This unit is shown set in a closed flume for
nection by a penstock of suitable size with the head works. In
. 318 the chest, into which the turbines dischargee, is designed
IS to give a certain independence to the discharge of the two
)incs until they come to the draft-chest below the wheel. The
)ine case, shown in Fig. 316, seems to have more room than
s^
Arrangement of the Reaction Wheel
necessary lo the upper portion of the case in which interference o[
the two streams and much eddying are possible, all of which is ob-
viated in the the design, shown in Fig. 317. The writer knows of
no experiments which show conchisively that such loss actually
occurred* More information is needed a!ong this line than is now
accessible to the engineer.
Fig. 317. — Double Horizontal Tiir!>Jne In Closed Penstock ^ Dayton Globi IroJ*
Worki Go.)
Fig. 318.— Flan-
Fig* 319 is a cross-section of a double unit of the Samson tur*
bine, manufactured by The James Lcffel and Company of Spriof
field, Ohio. This shows a design in which careful attention i*
given to the maintenance of a uniform and slowly decrcasinf ^e-
loKrity frosi the time the water reaches the wheel until it passes
from the common draft-chest into the draft-tube below.
Some Installations of Horizontal Water Wheds.
5^7
257, Some Installations of Multiple Tandem Horizontal Wheels,
J— Two double units of the wicket gate type, similar to the double
pnits shown in Fig. 315, are illustrated by Fig. 320, These turbines
%vere manufactured by The Daytosi Globe Iron Company of Day-
ton, Ohio, and are shown with the tipper portion of the case removed
teo that the arrangement of the wheels and the gate mechanism are
learly visible. The gates are moved by a cylindrical ring to which
r
F1& S19, — Double Horizontal Turbine for Open Penstock. (James Leftel & Co.)
each gate is attached independently. The ring is moved by the
link connecting the gate ring to the governor rod which, by its ro-
tating, opens or closes the gate as the power needed requires.
Two double units with cylindrical gate, as manufactured by The
S, Morgan Smith Company of York, Pennsylvania, are shown
in Fig_ 321, The bulkhead casing and the coupling to which the
machinery to be operated must be attached, are shown at the left.
In this case the governor rods have a horizontal movement, the
upper rod moving backward and the lower forward in order to
open the cylinder gate.
Figs. 322 and 323 show a section throitgh one of the main units
and a plan of the power house and turbines of The Southern Wis-
consin Power Company now under construction at Kilbourn, Wis-
consin, on the designs and under the supervision of the writer.
This plant consists of four main units, each generator having a
capacity, at full load, of 1650 kilowatts and an overload capacity
of 25 per cent. Each unit is direct-connected to six 57* turbines
now under construction by The Wellman-Seavcr-Morgan Com-
.i-L
Some Installations of Horizontal Water Wheels.
5^9
e
e
-a
&
i
530
Arrangements of iht Reactioo WheeL
pany of Cleveland, Ohio. Each turbine unit is set in i separate
penstock controlled by three independent sets of gates. The four
center wheels discharge in pairs into common draft-tubes, while the
two end wheels have independent draft-tubes. All of the hearings
within the flume are accessible by independent wrough iron man-
hole casings.
Fig. 324 shows four pairs of 45" Samson horizontal turbines ma:]-
ufactured by The James Leffel and Company of Springfield, Ohia
These wheels have been installed for The Penn Iron Mining Com-
pany of Vulcan, Michigan, where two such units are now in opera-
tion. Eight similiar units» designed to deliver 1400 H, P, under H
foot head| are now under construction by The James Leffel and
Company and are to be installed in the plant designed' by the
writer for The Economy Light and Power Company at Dresden
Heights, Illinois, the general arrangement of which is shown by
Fig, 350.
When the head increases above 20 or 30 feet, it may become de-
sirable to convey the water frorn the head-work by means of a
closed penstock as shown in the case of the plant of The Winnipeg
Electric Railway Company (See Fig, 340),
In this plant are shown four wheels in tandem, direct connecied
to a generator. The bell-mouthed entrance to the penstock should
be noticed, also the air inlet pipe which is designed to admit ihc
air into the penstock when the same is to be emptied, and to acirok
the water gradually and without shock when it is again fillcd|
When the head becomes still higher the closed pemstock becomes ii
perative as in the case with The Shawinigan Water and Power Com-J
paoy's plant shown in Fig, 33S where a head of 135 ft. is utitiKdj
Similar arrangements and connections for single and double wheefsl
with penstock are those of The Dodgeville Electric Light and[
Power Company* shown in Fig. 337, and that of The Hudson River j
Power Company's plant at Spier's Falls, as shown in Fig. 335.
The plant of the Nevada Power and Mining Company sbown i^\
Fig. 341, involves tangential wheels operating with needle nouki
and discharging freely into the tail race below.
In the selection and installation of reaction wheels a con-
siderable latitude in the choice and details of arrangement is r^^si*
ble and it is only after a careful examination and consideration of
all the conditions of installation that the correct size, speed, and [
arrangement of the wheels can be obtained. Numerous failuf^^
more or less serious, in the past have fully shown the fact that
Some iDStallations of Horizontal Water Wheels. 5^'
S2»
Arrangement o£ the Reaction WheeL
524
Arrangement o£ the Reaction Wheei
this work demands the most careful attention and investigation of I
the engineer and should be attempted only after the most thor-|
ough study and mature deliberation.
358. Unbalanced Wheels, — In installing horizontal wheels it is!
usually desirable to use them in pairs with two, four, six or tlghil
turbines in tandem. It is, of course, possible to introduce an oddl
number of wheels and this is frequently done where it seems to be
desirable* There is an advantage is an even number of wheels tor
in this case the wheels may be, and should be, so arranged as to
balance the thrust by the union of a right hand and left hand whe«l
in eacli pair. Where an odd number of wheels is introduced, an
unbalanced condition arises which can only be taken care of by a
thrust-bearing which, at the best, is an additional complication
cj^ten unsatisfactory and should be avoided if possible*
There is another cause of unbalanced condition which mty be
here mentioned. If a pair of wheels is so joined tog^ether as to
use a common draft-tube then, on starting the wheels the vacmim
formed in the draft- tube is common to both wheels and therefore
balanced. If, on the other hand, the wheels have separate draft-
tubes, when the wheels are started a partial vacuum is commonly
created in one of the draft- tubes in advance of the other, or even
when the wheels are in operation the vacuum in one draft-tube is
not as gfreat as in the other, creating thereby a thrust in one di-
rection or the other which must be balanced by the connection of
the two draft -tubes by an air pipe or must be taken up by a thrust-
hearing as in the case of a single whceL
CHAPTER XXL
THE SELECTION OF MACHINERY AND DESIGN OF
PLANT.
250. Plant Capacity. — The selection of machinery for a power
ant depends upon numerous conditions. In the first place, for
rmanent and constant operation, the machinery must be so
lected that its total capacity shall be great enough to take care
the maximum load and have at least one unit in reserve so that
it becomes necessary to shut down one unit for examination or
pairs, the plant will still be capable of carrying the maximum
ad for which it was designed.
The desirable reserve capacity of any plant depends on the con-
ngencies of the service or the degree of liability to disabling acci-
ent involved in the operation of any plant, and on the relative
ost of such reserve capacity and the damages which might be sus-
ained if the plant should at any time become disabled as a whole
►r in part and incapable of furnishing all or any part of the power
or which it was designed. In many manfacturing plants the occa-
sional delays caused by the entire suspension of power on account
rf high or low water, or for the necessary repair to machinery, are
*ot serious if cheap power is available for the remainder of the
ear. For the operation of public utilities, and the furnishing of
&ht and power for diverse municipal and manufacturing purposes,
>e matter becomes more serious and necessitates a sufficient du-
'cation of units to practically assure continuous operation.
Por paper mills and other manufacturing purposes water powers
- utilized in which the head and consequent power is practically
•stroyed during high water conditions. For continuous and un-
^errupted service such powers are available only with auxiliary
^'Wer that can be used during such periods. In the same manner
s^rve capacity may be unnecessary, desirable or absolutely essen-
^' as the importance of maintaining uninterrupted power in-
^ses.
^Co. Influence of Choice of Machinery on Total Capacity. — A
^dy of the week day load curve of The Hartford Electric Light
S2
5^6 The Selection of Machinery and Design of Plant
Company as shown by Fig. 257, page 422, will show that the load
for December, 1901, represents the maximum load which that plant
was called upon to carry during the year, and, consequently, was
the maximum load for which the machinery must have been se-
lected, A considerable variety of unit sizes w^ould be possible
which would fill the requirements of this load curve to a greater
or less extent The maximum or peak load shown in Decembefi
1901, was about 3,000 k, w. If a single machine were selected of
3,000 k w, capacity for regular operation, then, in order to have
one unit in reser\^e, it would be necessary to purchase two 3,000
k. w. machines or a total capacity of about 6,000 k. w. It on the
other hand, machinery should be purchased with units of joo
k» w. capacity each, it would be necessary to have six of such units
in order to carry the maximum load of 3,000 k. w*, and a sevenih
unit of 500 k, w. capacity would be all that would be needed for the
reserve. This would give a total capacity to the plant of 3,500 k, w.,
giving the capacity of the machine purchased some 2,500 k. w.
less than the plant first discussed.
261* Effect of Size of Units on Cost — The cost of machinen- ii
not in direct proportion to its capacity. The larger machincn- is
somewhat less in price per kilowatt capacity than the smaller ma-
chinery. Hence the cost of the last plant suggested would be more
than 35/60 of the cost of the first plant On the other hand, the m-^
s t alia t ion of such a large number of units complicates the plant an
is undesirable. For this plant it would therefore be desirable
select five units of 750 k. w. capacity each, or four units of to
k. w. capacity each, giving in one case a total plant capacity
3,750 k. w, and in the other case of 4,000 k. w.
A plant having units of 750 k, \v. or 1,000 k- w. capacitj' ead
would have a less total kilowatt capacity and, consequently, a le
first cost compared with a plant having units of 3.000 k, w. capacity
Such a plant would also have a less number of units and coo*
quently less complication in the arrangement than a plant haviii
units of 500 k, w. capacity.
262, Overload.^ — In the above consideration no mention is miA
of overload capacity. The ordinary direct-current machinery
be operated at about 25 per cent overload for short periods ol |
haps one hour at a time without danger to the machinery, Altei
nating machinery can be operated at 50 per cent, overload at sin
times or at 25 per cent overload for two hour periods. In <
quence of this condition it is frequently possible to purchase 1
Economy in Operation. 527
nery of considerable less capacity than the total load would in-
ate, depending on the overload capacity of the machine for short
"lods of maximum load. Unless, however, the estimated load
•ve covers all possible contingencies for maximum power it is
lirable to retain this overload capacity as a provision for a second
idition which has not been fully covered in the estimate of the
ly load curve; or, in other words, it is desirable to retain the
jrload capacity as a factor of safety.
{63. Economy in. Operation. — A second matter that needs the
eful consideration of the engineer in the selection of machinery
the question of economic operation under variation in load. A
erence to the efficiency curve of most machines will show that
machine will operate most efficiently at some particular load,
lally some .75 to full load, and will perhaps give the best results
from .75 to 1.25 load, or to 25 per cent, overload. It therefore
:omes important to so select machinery that it will operate effi-
ntly at all conditions of load.
Kn examination of the load curve of The Hartford Electric Light
mpany for the full week day load in March, June, September
i December, will show that for securing the most efficient results
all times in the day, and at all times in the season, units of 500
w. capacity would apparently be the best. Such units would
:e care, efficiently, of the minimum loads that occur at 6:00
M., between 12:00 and i :oo P. M., and at about 7:00 P. M. At
:h times one of these units would operate efficiently; but in
)st cases the period at which it could be operated singly would
for a few minutes only, or perhaps for an hour at the most, when
t additional unit would have to be cut in. A 750 k. w. generator
mid operate with almost as great an efficiency at these times and
would, with its overload capacity, take care of the load for a much
eater period of time each day. The 1,000 k. w. machine would
rhaps fulfill these requirements even to a greater degree. While
would be less efficient at the minimum point of the load, it would
ive the advantage of operating singly for a much wider range of
id and the additional advantage that, as a rule, the larger the ma-
ine the higher the full load efficiency curve.
The complications resulting from the numerous machines, and
i losses entailed thereby, have also to be considered and must be
iefully weighed in this connection.
Hbe circumstances of operation and many local conditions, which
^rtain particularly to the plant in question, must be weighed in
Sa8 The Sekction of Machinery and Design of Plant
k.
connection with the selection of this machinery- There is n<j dcS
nite law by which the selection of machinery for any plant ad
be reduced to an exact science, and several combinations of mi-
chinery are possible in almost any plant and will give reasomk
satisfaction.
In the above discussion only units of a uniform capacity hail
been considered and it is usually desirable, other things being cqiK
to have similar machines so that a minimum number of rep
and duplicate parts may be kept in stock. On the other haniiij
long, low night load is probable, it may be desirable to insialii
or more units of a capacity suitable to carry such load efficienik |
264. Possibilities in Prime Movers. — A third matter for
careful consideration of the desigfnin^ engineer is the possibiW
of a prime mover that is to be used for operating the machines i
question. If a steam or gas engine is to be used as the moti^
power, there is a w^ide range of selection in speed, capacity, ad
economy of such machinery, and, as a general rule, the prime racut
may be selected to conform to the generator or other machine ill
is to be operated thereby* In the selection of ^^-ater wheels foT
prime movers the conditions are radically different and the selection
of the size and capacity of the units to be operated is often modi-
fied or controlled by the water wheels and the conditions unj
which they will be obliged to operate.
In the selection of the water wheel one of the most importam
matters is the head and the range of heads under which the wheel
will he called upon to operate. While it is possible to select a whc
so that it will operate at almost any reasonable speed under a <
siderahle head, yet the capacity or power of the w^heel rapidly '1^"
creases in amount with the speed, and if the speed be too hisli i^
will he necessary to join two or more wheels in tandem in order!
furnish the power necessary to operate the machinery selects
This is perfectly feasible and is done in a great many eases.
365. Capacity of Prime Movers. — It is important to note that i
the generator or other machinery to be operated is to be operator
under overload conditions, the maximum powder to be generatei^
must be kept fully in mind in the selection of a prime mover
the case of steam engines, these engines can be commonly opemte
under overload conditions. They are usually rated at their m<3i
efficient capacity and can sometimes be operated to 50 per cenil
above their normal rating, although their economy under such
ditions is apt to materially decrease. Gas engines, on the othe
Power Connection. g ^
and, are commonly rated at very nearly their full capacity aiid
hence tlie machinery which they are to operate can be operated only
to about the normal rated capacity of the engine.
Water wheels are commonly rated in the catalogues of manu-
, facturers at very nearly full gate and consequently at full power.
In some cases they are rated at abotit seventh-eighths gate so that
^ a small margin of additional power is availalble. In the selection
I of a water wheels therefore, it is important that a careful study
I be made of the actual power that the wheel can generate under full
|i g^te and at minimum head. This should be sufficient to operate the
I machmery at its niaximum load,
266. The Installation of Tandem Water Wheels. — ^The installa-
U±ion of t%vo wheels set tandem, either horizontally or vertically,
nnd directly connected with the machine by a common shaft, is
[very common and this may be increased to four, six, or occasionally
I to eight turbines. Every additional machine, however, involves the
f introduction of increased diameter in the shaft, of additional bear-
ings Avhjch must be set and held in alignment, and a compHca-
■yjon in the design and construction of the machinery which should
Pbc avoided wherever possible. The excuse for the attachment of a
numDer of turbines in tandem arrangement, and the com-
plexity of the plant of water wheels installed, lies in the sim*
plifi cation of the machinery to be operated by them, and in the de-
sign and arrangement of other portions of the plant. The extent
to which the application of any principle is to be carried is a matter
of Judgment and can be answered only by experience and the con-
sideration of all of the conditions involved in each particular case.
267, Power Connection.^\Vith the turbine, as with every other
prime mover, it is important to convey the power to the machine
or machinery to be operated as directly as possible. The turbines
should be connected as directly as possible to the machinery to be
driven without any nnnecessary intervention of gearing, shafting,
bearings, belts, cables, or other still more complicated methods of
power transmission. Every shaft, every gear, every belt, every
bearing and every other means of transmission that intervenes be-
tween the power generated in the wheel and the machine in which
the power is to be utilized means an extra loss and a decrease in
the efficiency of the plant. The machine to be operated should,
therefore, whenever practicable, be direct connected to the slmtr
of the turbine instead of being connected with the turbine by any
intermediate mechanical means. (See Figs, 310, 314 and 322-
330 The tielecUon of Machinery and Desiga ot PlaaL
Various Methods of Connection,
531
£t connection of machinery and turbine involves a careful selcc*
of both machinery and turbine so that both will work satis-
rily at the same number of revolutions per minute. This
(Cntly involves extra expense that may not be justified in plants
lany purposes,
acr methods of connection or of power transmission are,
fore> frequently necessary* With many low head installations
k connections are impracticable for a number of reasons,
itmes various machines with diverse revolutions are to be
U by the same wheel and the revolutions of the turbines in*
d must differ from some or all of the machinery to be operated
jomc form of connection other than the direct must be used*
■where the importance of the plant makes it desirable to use di-
^onnection, it frequently happens that a single turbine gives
sufficient power at the speed desirable for connection to a
Ine of the desired capacity. Under such conditions it is nec-
f to unite two or more turbines in order to generate sufficient
r for the purposes for which the plant is to be designed. Tlie
sfty of using a large number of turbines in a single unit may
rise to very long shafts and a large number of bearings, and
iss due to such an arrangement is sometimes considerable, and
^rly arranged will be almost or quite as inefficient as gearings
ihafting well maintained.
w Various Methods of Connection in Use. — ^The most common
of turbine used is a single vertical turbine, connected by a
jed crown gear and ^pinion to a horizontal shaft. Several of
tiirbines are commonly coupled up to the same shaft and may
i in a single or in separate wheel pits. Such types of installa-
are sho%vn in Figs, 329 to 334, Fig. 325 shows the turbine
►ss in the plant of The Oliver Plow Works at South Bend,
ma, installed by The Dodge Manufacturing Company, The
Igement of the wheel is quite similar to that illustrated by
334, Three or four vertical wheels Jire here each connected
^ear and pinon with a horizontal shaft, w^hich, in turn, is con-
kl to an electric generator. In all such cases more or less
[y is lost in transmitting the power throtigfh the gearing and
ITQUS bearings to the generator. Sometimes it is found desir-
tiot to connect the generators directly with the main shaft,
© connect the generator or other machines to be operated by
^wer plant by belting them to driving pulleys attached to the
[horizontal shaft, as shown by Fig. 326, which shows the power
jj
53a The Selection of Machinery and Design o£ Plant.
Vairous Methods of Connection,
S33
plftat of The Trade Dollar Mining Comp*iny near Stiver City, Idaho,
This, however, introduces another source of loss through these
b«lt5 but possesses a certain flexihility due to the abihty to thereby
drive various small units at a variety of speeds by the simple process
of changing the diameter of the pulleys used to drive such machin-
ery. Sometimes rope drives can be used to advantage in place of
Fig- 327, — Haruesa and Driving Sheaves^ Soutliweat Missouri Light Oo,,
belts. This is especially true where the distance is great or the
alignment other than direct. Examples of such connections are
shown by Figs, 327 and 328,
Direct connected plants are shown in Figs. 310, 314, 322, 335, etc.
269* Use of Shafting. — A shaft connecting a machine to a prime
tnover, or imposed in any manner in any power transmission, must
lie carefully designed and constructed. It must be carefully aligned
and have its bearings carefully adjusted. Each bearing may be con-
sidered as a point in the alignment of a shafts and, as two points
determine the direction of a straight line, it will be seen that each
additional bearing is objectionable for it increases the difficulty of
Staining and maintaining a satisfactory alignment. When more
than two bearings are used each must be brought and maintained in
* Dod^e Manufacturing Co., Mlsbai^ aka, Ind,
534 Tht Seleciion of Machinery and Design ol Plant
the best practicable alignment, both honzonally and vertically. All
bearings must be of sufficient size that the limit of bearing pres-
sure shall not exceed good practice and they must be sufficiently
adjustable so that the shaft shall have as complete and uniform bear-
Ftg. 323. — Flan Showing Harness,. Rope Drive una Jaeksliaft. Sotitbw«^ j
Missouri Light Co.*
ing as possible over the entire surface of the box Boxes and bear-
ings must be arranged for satisfactory lubrication so that m^^
the hardest service they will not become unduly heated. In ortftf
to secure good results the best class of workmanship is nec«ssirf
and it is also necessary that the plant shall be carefully and prop-
*Dodge Manufac^turliig
r The Wheel PiL 535
crly maintained, A poor shaft, running in poor boxes ^ poorly
aligned, may consume most of the power generated. Shafting, to
be reasonably satisfactory, demands frequent and proper inspectioUj
constant lubrication^ and proper maintenance or it will soon become
a source of great energy loss»
270, The Wheel Pit. — The wheel is usually set in a chamber
called the wheel pit, flume, or sometimes the penstock, which is
connected with the head-race from which it can be separated by
suitable gates.
The wheel pit in the smaller plants has commonly been con-
structed of timber but in the larger plants is usually built of a more
substantial character, — of concrete, plain or reinforced, stone or
iron.
Open pits are commonly used for heads up to 18 or 20 feet, and
may be used for considerably higher heads; however, for higher
heads, closed flumes of reinforced concrete or steel are commonly
used, and such construction is usually connected with the head-
race by metal, wood or reinforced pipes, to which the term penstock
is commonly applied. This latter form of construction admits of
the use of wheels with heads of almost any height
A number of wheels can be set in the same wheel pit, and are
commonly so set, especially where they are used together to
operate one machine* It is frequently desirable, however, to sep-
arate the turbines and set them in separate pits so that one or
more wheels can be shut down at any time without interfering
with the operation of the plant. The exent to which this arrange-
ment is carried is a matter of policy and depends upon a variety of
conditions which the engineer must settle for each particular case.
271. Turbine Support. — The arrangement and construction of the
wheel pit must be such as to furnish a proper support for the tur-
bine in order to secure satisfactory operation. In many of the
earlier plants, the wheel pits were built of timber, with the turbine
case resting directly on the timber floor, which was often improp-
erly supported. The result of such conditon has been that the tur-
bines settle out of alignment and much energy is expended in un-
due friction in the transmitting mechanism. The floor or founda-
tion on which the wheel case rests should be of a substantial char-
acter and of such a nature that it will not readily deteriorate and
allow the wheel to settle. It is usually desirable to support the
wheel by a column directly below the wheel case, which should rest
upon substantial foundations below the bottom of the tail-race.
536 The Selection of Machinery and Design of Plant 1
(See Fig* 331) In all events settlements and vibrations must be
prevented or reduced to a minimum in order to eliminate one of tlic
very important causes of loss which is frequently encountered in
water power plants. In many cases, due to defects of this kimi
water power plants are givnig efficiencies of 50 per cent, and below,
where 75 or 80 per cent, should be obtained.
272, Trash Racks. — The water entering the wheel pit from tht
head-race commonly passes through a trash rack consisting af fiar-
row bars of iron, usually 14" by 3" in dimension, spaced iW^ ^^ ^
between and reaching from above the head- waters ^o the bottoiti d
the wheel pit, the purpose of which is to strain out such floatmf
matter as may be brought by the current down the head-race and
which, if not taken out at this point, might float into the wliceb
and if large and heavy enough, might seriously injure the same
These racks have to be raked or cleaned out at intervals depending
on the amount of leaves, grass, barks, ice or other floating matter
in the stream. In water power plants on some streams where largt
amounts of such floating matter occurs at certain seasons, it »s
sometimes necessary to keep a large number of men constantly
at work keeping the racks clear.
Tile accumulation of material on the racks will sometimes shut
off the entire flow of water if attention is not given to keeping them
clear; hence it is sometimes necessary to so design the racks and
their supports that they may sustain the entire head of water-
The racks are usttally made of bar iron held apart by spools l)^
tween each pair of bars and held together by bolts passing through
the spools and joining together such a number of bars as may I
convenient for handling. The spools should usually be placed neil
the back of the bar so as to allow the rake teeth to pass readilf«|
.The rack should be situated at an angle so as to afford facifiti«i|
for raking. The deeper the water, the greater should be tk iff
clination, as with long racks, and especially with high velocities, thij
clearing of the racks becomes more difficult
Chain racks and automatic mechanical racks have been attemptra|
but without satisfactory results.
Where trouble occurs from ice, involving much winter wortt rtj
is frequently desirable to cover the racks with a house in order t<^
protect the workmen.
CHAPTER XXIL
EXAMPLES OF WATER POWER PLANTS,
373. Sterling Plant — A rear elevation (Fig, 329) of the plant
wtiich was designed by the writer for The Sterling Gas and Electric
Company of Sterling, lUinois, shows three 50" vertical Leflfel wheels
connected to a common shaft by beveled gearings.
The genera! type of harness used is fully shown in the plan and
elevation and needs no further description.
This plant is located on the Steriing race and is next to the last
plant on the race on the Steriing side of Rock Riven (See Fig. 345,)
The head developed at this plant is about 8 feet, and the power of
each wheel is about 115 horse power. Each wheel is set in an inde-
pendent wheel pit which can be closed by means of a gate, as shown
in Fig. 332. In order to make repairs on any wheel without inter-
fering with the other wheels, the wheels and harness are well sup-
ported from the foundation, a very essential condition for perma-
nently maintaining a high efficiency. The discharge pit is of ample
size, so that the velocity with which the escaping waters leave the
draft tube is reduced to a practical minimum. A rack, to keep
coarse floating material from the wheel, is placed in front of the
penstock and is shown in Fig. 331, in section, and in Fig* 332,
in partial elevation. The shaft otf this plant is extended into the
adjacent building and to it are belted the generators which supply
electric current for light and power purposes in the city of Sterling.
An engine is also connected to this main shaft and may be utilized
in case of extreme low water conditions, where sufficient water for
power is not available, or for flood conditions where the head is
practically destroyed.
274. Plant of York-Haven Water Power Comparfy. — ^Figure 333
shows the arrangement of the power station of the York-Haven
Water Power Company on the Susquehanna River at York, Pa,
The power house is 478 ft long and 51 ft wide. The head-race
is 500 ft long and of an average depth of so ft. The wheel pits are
19 ft* deep and extend the entire width of the power house, open-
i
lant of the Sterling Gas and Electric Light Co* 539
6
^ be
Q B
a
8
540
Examples of Water Power Plants
H|Jiyyipnnyill|yHj iji^ .1 ffifi
k
^
i
I
^ ^ C T / O N
F1». S31.— Wheel Pit, SUrllng Ga* and Electric Ught Oo.'a Plut
Plant of the Sterling Gas and Ekctric Light Co. 54^
3
s
54-
Examples of Water Power Plants,
mg to the forebay. They are protected by iron racks and are made
accessible by lar^c head-gates of structural iron which weigh about
eleven tons each.
Fig. 333 — Plant of York Hfiiren Water Power Co,
(Electrical Engines.)
Each pit contains two 78.5'' inward flow ttirbines, hung fr<
spring bearings just above the runners. The turbines are set on t
floor of the pit and arc about 6 ft* above the lower water mark.
The draft tubes are 10 ft.^long and extend well under water The
net head under normal conditions is about 21 ft. Float ^it^c^ ^
the switch board show at a glance the height of head and tail
water.
Plant of South Bend Electric Company. 543
The turbines were built by the Poole Engineering Company of
Itimore, Mr., and are rated at 550 H. P. each, or 1,100 H. P. per
r.
rhe turbines are oi special design, the buckets being made of
issed steel. The shaft extends vertically from the turbines to
rel gears above the main floor and each is encased in a cast iron
»e to protect it from the action of the water and to secure long-
ty both to the shaft and to the bearings which retain it in line.
The present installation consists of ten pairs of turbines with
generators, equipped with Sturgess and Lombard governors.
The turbine bearings are supplied with oil from a gravity tank
ated on the switch-board gallery .
The generators are S. K. C, three-phase, 60 cycle alternators,
ed at 875 kilowatts, and generate a 2,400 volt current. The nor-
l speed of the generators is 200 revolutions per minute. Two 250
W., 125 volt, S. K. C, compound-wound, direct-current exciters
nish the exciter current to the generator fields.*
75. Plant of South Bend Electric Company. — Figure 334 shows
plant of the South Bend Electric Company at Buchanan, Mich-
n, built in 1901.
Tic dam, which was constructed in 1895, is of the gravity type,
It of wood, with two rows of sheet piling below and one above
It IS about 400 feet long, and affords an average head of 10 feet,
is is estimated to furnish a minimum of 2,000 h. p. for from
r to six weeks in a year, while the maximum will reach 5,000 h. p.
an average, 2,500 h. p. is available for about three months and
X) h. p. for the remainder of the year.
The power house, placed a short distance below the dam, is 273
t long and 40 feet wide. It is built of stone, with concrete foun-
ions, and slate roof. It parallels the river so that the water from
turbines is discharged directly into the same. The regulating
es are seven in number, and are operated by racks and pinions.
The water wheels are Leffel turbines of 68 inch vertical type,
• h. p- each. They are geared to a line shaft, which extends nearly
whole length of the building, and to the end of which the genera-
is coupled. A 40 inch vertical LeflFel wheel is used for driving the
:iter, which is belted to an intermediate shaft, driven by gears,
e line shaft is divided into three units, so that either four, seven
ten wheels can be used for operating the generator, depending
See Electrical World, vol. 49, March 2nd, 1907.
Spier's Falls Plant Hudson Water Power Co.
545
n the load carried. In addition, the gears on the line shaft can
:hrawn out of mesh, so that any water wheel can be repaired if
essary. The plant is governed by two Lombard water wheel
ernors driven from the line shaft.
. 20 ton hand-operated crane serves all the apparatus in the
ding.
335. — ^Plant of Hudson Water Power CJo. Spier's Falls Plant Double
Horizontal Turbines in Steel Penstock. Central Discharge. (E}Qgine-
ering Record.)
he generator is a 1,500 k. w., 60 cycle General Electric revolving
I type alternator supplying three-phase current at a pressure of
o volts. The switch-board and transformers are located at one
of the building. There are no high tension switches at the
^cr house.
he power is largely transmitted to South Bend, Indiana, a
ancc of 16 miles, where the company has a steam power plant
Si6
Examples of Water Power Plants.
which is always kept in such condition as to be put into immediate
operation. It is used, however, only in case of extreme low water,
at times of a heavy peak, or in case of accident to the transmissiciii
line. The steam power house is used as a stsb-station and distrib*
uting point.*
276* Spier Falls Plant of The Hudson River Power Transmission
Company^ — ^A cross section of the Spier Falls Power house is sho^-u
in Fig. 335* A head of 75 feet, for operation of this plants is derivtil
from a granite rubble, ashlar- faced, masonry dam across the Hud-
son River between Mount McGregor and the Luzerne Mountam
The dam consists of 817 feet of spill w^ay section, the remalndexy
of the dam, 552 feet, being- built about 12 feet higher, Wata
is admitted through arched gateways to a short intake canal dc-^
signed to carry 6,000 cubic feet per second with a velocity of three j
feet per second. This canal distributes the water to ten 12' circa
steel penstocks %vhich lead about 150 feet to the wheels.
The power house is divided into three parts with the transfonner j
and switchboard room in one end, the wheel room and generatoi
roon. being formed by a longitudinal partition wall extending^ th^
length of the building, with traveling crane in each.
Each unit consists of a pair of 42" or 54" cased S. Morgan Smiih
wheels^ governed by Lombard and Sturgess governors and directj
connerted to 2,000 and 2,500 k* w. 40 cycle, three-phase revolvinf
field generators, built by The General Electric Company,
The transformer room contains sc\ en 670 k. w. and thirty %J
k. w* General Electric air cooled transformers.
The power is distributed to Glen Falls, Schenectady, Sarata
Springs and Albany, f
377* Plant of Columbus Power Companyp — The plant of th
Columbus Power Company is shown in Fig. 356, It is situated *^9^
the Chattahoochie River just beyond the limits proper of tlte cityj
of Columbus, Georgia, at a shoal known as Lovers' Leap. At tiiC
point a dam of Cyclopean or boulder concrete with a cut stone sp
way surface was erected giving a head of 40 feet. The length of ^1^*^
dam is 975 feet 8 inches* with a spillway 728 feet long*
The power house is located at one end of the dam» so that no p*^"]
stocks are necessary. This applies to power house No. i. PDwct
to drive the plant of The Bibb Manufacturing Company is ^^'M
•(See Electrical World and Engineer. May 30, 1903 and July 14. IW
tR^ Engiiieering Record ^ June 27th, 1903.
Plant o[ Columbus Power Co,
547
tiished from power house No. 2, being^ transmitted to the mill by a
rope drive system. The power house is supplied with pressure
water by means of penstocks let through the bulk-head wall, which
extends from house No. i to the river bank. In both cases the
tail water is discharged into the excavated river bed beneath the
power houses. Power House No* i is designed to develop 6,000
h, p. ia six units, and No* 2 about 3,ocX3 h. p, mainly in two umta.
pmw Jm J^ J M t.T^Jyf TJ^^i; il'i'P^ 'ljfc»
Fig. 33S. — Plant of Columbtis (Gaj Power Co. Double Horizontal Turbines
In Open PenBtock. (EnirtneeTing News.)
Power house No. 1 is 137 feet long and 52 feet wide. It rests on
heavy stone foundations, the up-stream portions of which form the
heavy bulk-head which is pierced by six large openings for plant No,
I, by a smaller opening for the exciter units and a larger one for
the penstock leading to power house No. 2.
The openings for power house No. i are short flumes or chambers.
The back end of each of the wheel chambers is closed with a
heavy plate or bulkhead of cast iron and steel separating the wheel
chamber from the generator room. The racks are of the usual con-
548 Examples of Water Power Plants.
struction and are supported on a framework of I-beams, giring
them an inclination of about 12** with the verticaL The gates to the
wheel chambers are of timber and are raised by hand bj means 0(1
rack and pinion.
Each of the main wheel chambers Contains a pair of horizontal
39 inch Hercules turbines, which discharge into a common draft
tube. The center line of the wheels is 15 feet below normal head
water level and 25 feet above normal tail water leveL Under the
total head of 40 feet, each pair of wheels develops 1,484 h. p. at 200
r. p. m. The draft tubes are 7% feet in diameter at the turbine cas-
ing and 10 feet at the discharge end.
Each pair of wheels is direct connected to a two-phase alternator
built by the Stanley Electric Manufacturing Company. Each ma-
chine has a rated capacity of 1,080 k. w. at 6,000 volts and driven at
200 r. p. m. gives current at 60 cycles. Each is connected to the
wheel shaft by a flexible leather coupling.
There are two exciters directly connected to a single 18 inch
Hercules wheel. Each exciter is of the Eddy type, having a capac-
ity of 60 k. w. at 75 volts and running at 450 n p. m. The exciters
are under the control of mechanical governors-*
278. Plant of The Dolgeville Electric Light and Power Ca— In
Fig. 337 is shown the plant of The Dolgeville Electric Light and
Power Company at High Falls, New York, on what is now known
as the Auskerada River.
The dam is built of limestone masonry. The height at the spill-
way is 20 feet, with each abutment 6 feet higher. The total length
is about 195 feet. The width at the top is 7 feet and at the bottom
26 feet. The upstream side is perpendicular, the downstream side
being curved in order to properly receive and discharge the water.
The head gate, 12 ft square and built in two sections, is fitted with
a by-pass gate to relieve the pressure when filling the flume. The
steel flume extends from the head gate to the power house, 520 feet
away. This flume is 10 feet in diameter, and is made of % inch
steel plate, all longitudinal seams being double riveted. Just out-
side the dam is a vent pipe which assists in relieving the flume
from any sudden strains.
There are two 36 inch horizontal Victor turbines, each direct
connected to one 450 k. w. 2,400 volt two-phase Westinghousc gen-
• See Electrical World and En^neer. Jan. 23, 1904 «r Bng. Record, Jin. 1^
1904.
Plant of Dolgeville Electric Light and Power Co, 549
5 so Examples of Water Power Plants.
erator. Each of these wheels will develop 600 h. p. at 300 r. p. m^
under the working head of the water, which is 72 feeL They are
mounted in cylindrical steel casings, and discharge downward
through draft tubes, which extend a few inches below the sur-
face of the tail water. Each wheel is supplied with a Giesler elec-
tro mechanical governor.*
279. Plant of the Shawinigan Water and Power Company.— The
power plant of the Shawinigan Water and Power Company is lo-
cated on the St. Maurice River, Canada, at a point about 21 miles
from Three Rivers, 90 miles from Quebec, and 84 miles from Mon-
treal station. Fig. 338 shows a cross-section of their power station.
The St. Maurice River has a total length of over 400 miles, and is
supplied from a great many lakes and streams, the drainage area
being about 18,000 square miles. The water flow is very steady
throughout the year on account of the dense forest covering this
area, and is in the neighborhood of 26,000 cu. ft. per second, seldom
going below 20.000 cu. ft per second. At the crest of the falls the
water flows over a natural rock dam and then down over the cas-
cade, making a fall of about 100 feet, then on in a narrow gorgt
through which the water rushes swiftly and in which there is a
further fall of 50 feet
The intake canal is 1,000 ft. long, 100 ft wide and 20 ft deep. Its
entrance from the river is located in a rather rapidly flowing stream
at the crest of the falls where the water is 20 feet deep, for the reason
that at times of rather high water, when the ice is flowing out d the
river, the current is expected to carr\- the ice past the mouth of the
canal. Tlie end oi the canal where it comes out at the face of the
hill is closed by a concrete wall from which the water is led through
steel penstock pipes down to the power house 130 feet below.
The concrete wall or bulkhead in the canal is 40 feet in height.
about 30 feet in thickness at the bottom and 12 feet at the top.
On top of this wall are set hydraulic cylinders for lifting the head-
gates and ov top. covering the cylinders, is a brick gate hous^ Tlie
steel penstocks are 9 feet in diameter.
The electrical apparatus was supplied by the Westinghouse Elec-
tric & Maruifac::ring Conipanv and the turbines by the I. P. Morris
Co.
^The three turbine units of the original installation are horizontal
^.louble units of 6 000 h. p. These are direct connected with single
• See American Elev trioian. April. !$$«, VoL 10, Xo. 4.
Plant of the Shawnigan Water Power Co.
551
552
Examplei of Water Power Pla^^ts,
5,000 h. p* generator units of the rotating field t>"pc, «iih imuSi
poles. They are designed to operate at 180 r. p. m. ^vii^i
currents at 30 c^xles per second and 2,200 volts. A Islsr i
»
Fig, 339,— Plant of Concord Electric Qi.
blnes Connected in Taodem.
S^ V, -aIVs Falls PlanL T«rt!<«l 1
( Engineer tug Reconi)
tion consists of two 10,000 h. p. water wheels each driving a6.6o®|
Ic w. generator. (See Figs. 159 and 236.)
A separate penstock is provided for the exciter units which COn-|
sist of two 400 h. p. turbines direct connected to exciters.*
• See references as given: Eng. Rec. Apr. 2S, 1900; Can. Engr,i Apr. l**!*!
May, 1901, and May, 1902; El. Wld, and Engr., Feb. 8, 1902: CaMler » MU^
June, 1904.
Plant of the Concord Ekctric Company,
553
aSo- Plant of the Concord Electric Company. — This plant, shown
in Fig, 339, is situated at Sewairs Falls on the Merrimac
River about four miles from the State House in Concord, New
Hampshire, The dam is a timber crib- work structure about $00'
long and gives a fall varying from i6' to I'f, The addition to the
old plant is the one shown in cross-section by Fig» 339 and is of
special interest due to the vertical shaft generating units which
ivere here installed. Comparative estimates showed that all other
features of the plant, except the machinery could be built cheaper
ivith the vertical shaft installation and the machinery added only
a few thousand dollars to the total cost, while other advantages de-
«rmined its installation.
The new installation consists of two units, each consisting of
3 — 55" bronze runners of the Francis type, mounted on a vertical
shaft and hung on a step bearing. The machines are of the Escher*
Wyss type built by The Allis Chalmers Company, American rep-
Tesentatives of the Escher-Wyss Co. The gates are of wicket pat*
tern, controlled by Escher-Wyss mechanical governors, also built
l)y The Allis Chalmers Company. The generators, which are direct
connected to the vertical shaft wheels, are of 500 k, w., 3-phase,
60 cycle, 2,000 volt, TOO n p. m., revolving field type. Excitation is
furnished by one 75 h. p., 3-phase, 2,600 volt induction motor, direct
connected to a 45 k, w., 125 volt, compound wound D. C generator.
The exciter unit runs at 680 r. p. m»*
381, Plant of Winnipeg Electric Railway Co. — In Fig. 340 is
shown the power plant of the Winnipeg Electric Railway Company.
It is situated on the Winnipeg River at a point a few miles from
Lac du Bonnet, which is on a branch line of the Canadian Pacific
Railroad, 65 miles distant from the City of Winnipeg*
To obtain the necessary water, a canal 120 feet wide and with a
clear depth of 8 feet at normal low water was cut to the upper river
near Otter Falls. The canal is 8 miles long, with a drop of 5 feet
to the mile, equaling a total head of 40 feet. At the point where the
dam is located there is a natural fall, and the dam crosses almost at
the crest.
With the head and discharge available it is claimed that 30,000
electrical horse power can be developed.
The water wheels are all McCormick turbines regulated by Lom-
bard governors. The turbine pits are protected by racks to keep
out ice, logs, etc,
• See Engineering Record, Jftnaary 6th, T906L
Plant of Nevada Power Mining and Milling Co.
S5S
electrical units consist of four i,ooo k. w. and five 2,000 k. w.
ig field, 60 cycle, 2,300 volt, three-phase generators and two
V. 125 volt, direct-current exciters, all coupled to turbines,
> 175 k. w. 125 volt direct-current exciters, coupled to three-
f,300 volt induction motors.
I are 15 transformers, comprising five banks, by means of
lie voltage is stepped up from 2,300 to 60,000 volts for trans-
to the sub-station at Winnipeg over a distance of 65 miles.*
^i^miiw^*'(^*w^'^^'f"i'''^'''' ' ^^" '>' '■■'■'^■^^'■'^^^^■^''^
Fig. 341 — Plant of Nevada Power Mining and Milling Co.
(Engineering Record.),
^lant of Nevada Power Mining and Milling Co. — Fig. 341
. section through the plant of The Nevada Power Mining
ling Company on Bishop Creek, near Bishop, CaL The
:nt of the station consists of two 750 k. w., 60 cycle, 2,20c
ee-phase alternating-current generators, running at 450
and a 1,500 k. w. generator running at 400 r. p. m. This
inerator is shown in the sectional drawing. There are two
of 60 k. w. each, delivering current at 140 volts pressure,
citers are operated by water wheels, and, in addition, one is
i with an induction motor. The water wheels were made
Pelton Water Wheel Company of San Francisco. The two
llectrical World, June 23, 1906.
556 Examples of Water Power Pbnta.
750 k. w. machines have Sturgess governors, and die 1,500 k. w.
machine has a type Q Lombard governor. Hand-cootrol mecfaaO'
ism is provided for each wheel. Oil is snppfied to die governor bjr
two oil pumps operated by water wheels.
Water is taken from the creek at a small diverting dam and can-
veyed along the moontain-side in a pipe line. The pipe line is aboot
12^000 feet long, and consists of 6,700 feet of 42-inch wood-stare
pipe. 2.150 feet of 30-inch wood-stave pipe, and 3,150 feet of 24-iiidi
steel pipe, all diameters being inside measurements. The 42-indi
pipe lies on a nearly level grade, the static head at the lower end
being about 30 feet. At this point are placed two jo-inch gate
x-alves, one opening into the 30-inch pipe and the other provided for
a future line. The 30-inch pipe descends the hill to a point that
gives a static head of 265 feet. Here it joins the 24-inch steel pipe,
which descends a steep hill to the power house, die total static
head being 1.068 feet.
The power generated at the plant is transmitted, over a line (rf
stranded aluminum, equivalent to No. o copper, to Tonopah and
Goldfield, Nev., making a total length of line of 113 miles. In
crossing tlie WTiite Mountains the line reaches ain elevation of over
TO.500 feet^
LirFRATTRR
1. Hydro-Electric Development at North Mountain. CbL Elea World vA
Engineer. March 4. 1905.
2. The Northern California Power Companj's Srstems. Electrical World and
Engineer. Sept, 10. 1904.
3. The Power Plants of the Edison Electric Company of L06 Angeles. Eng-
ineering Record, March IS. 1905.
4. The Fresno Transmission Plant. The Journal of Electricity, April, 1W€-
5. The Edison Company's System in Southern California. Electrical World
and Engineer, March 11, 1905.
6. An S3-Mile Electric Power Transmission Plant, GaL Caaaier'a Magiiioe,
November, 1899.
7. Bishop Creek. Cal. Hydro-Hectrtc Power Plant Electricml World. June
30, 1906.
8. The Hydraulic Power Development of the Anim^ Power and Water Com-
pany. April 14. 1906. Enginering Record. Electrical Reriev.
Jan. 30. 1904. Engineering News, Jan. 4, 1906,
9. Power Transmission in Pike*s Peak Region. Electricml World and Ear
ineer, July 26. 1902. Electrical Worid. Ifay 26, 1906. Engineer
ing Record. 3klay 19. 1906. Engineering Record. Jnly 19, 1901
♦ See Engineering Record, June 80, 1906, or Electrical World of June 30.
1906.
Literature,
557
New Water Power Development at New I^Iilford. Conn. Engineering Rec
* ord, Feb. 13, 190^,
ill. Berlishire Power Company, Catiaan, Conn. Eiectrical Review, Sept 7» 1907.
12. PlEDt of Hartford Electric Light Company, American Electrician, March
1900.
lS.Hydrt>-Electric Power Plant and Trauemisslon Lines of the North Georgia
Electric Company. Electrical Review, Oct. 20. 1906.
P 14. Atlanta Water and Electric Power Comt>any"s plant at Mor^n Ealla, Ga.
K Engineering Record, Apr. 23. 1904.
I IS. Plant of The South Bend Electric Company, South Bend* Ind. ESectricaJ
^ World and Engineer, May 30. 1903.
i 18, Plant at Rock Island Arsenal, Rock Island, III. Western Electrician. Nov,
^ 23* 1901.
f 11. The Hydraulic Development of the Sterling Hydraulic Company. Engln-
eering Record, Dec. 16, 1905.
It. Joliet Water Power of Chicago Drainage Canal. Engineering Record,
Apr. 19, 1902.
3$. Development of Electric Power at Shoshone Falls, Idaho. Western Elec-
trician, Mar. 9, 1907.
20, Cbandiere Palls Power Transmisalon Company, Maine. Electrical World
and ESnglneer, June 15, 1901. Engineering News, May 7, 1903.
21, "Water Power at Portland, Me. Electrical World and Engineer, Jan. 10,
1903,
Z2. Plant at Deer Rips, Me. Electrical World and Engineer, Apr. 8, 1905.
23. Great Northern Paper Company's Kew Mill, Me. Engineering Record,
Dec. 15, 1900.
^4, A Submerged Power Station. Md. Engineering Record. Aug. 24, 1907,
as. High Pressure Power on the Housantonic, Mass. Electrical World and
Engineer, Feb. 13, 1904.
26. Development at Turner^s Falls, Mass.
Aug. 12, 1905.
27- Power on the Blackstone River, Mass.
Oct 14, 1905.
1 3S, New Plant of Holyoke Water Power Company.
Sept. 15, 190G.
29, I^whead Hydro- Electric Developments in Michigan. Engineering Record,
Oct. 19, 1907,
30. Plant of the Mlchrgan-Lake Superior Power Company, Sault Ste. Marie.
American Electrician, August, 1S98. Engineering News, Sept,
25, 1902, Electrical World and Engineer, Nov. g, 1902.
31. Transmission Plant of Kalamazoo Valley Electric Company, Mich. Am-
erican EHectriciafi, July, 1901.
32, Water Power IJevelopment at Little Falls. Minn., and Its Industrial Re-
sults. Engineering Record, June 13, 1905.
SS, SL Anthony Falls Water Power Plant, Minn, American Electrician, Maj
1S9S.
34
Electrical World and Engineer,
Electrical World and Engineer,
Engineering Record,
558
Examples of Water Power Plants.
34. Or«&t Northern Power CompaDy of Duluth, Minn. Electrical World.
July 2S, 1906.
31. Electric Power TraiiBiiiiBftiQii Plant, Butte, Mont American Hlectrtclas,
Febraar^i 189$.
36^ Generating System of Tho Portland General Electric Company. Eneineer
tng Record* Aug. 12, 190^.
t7. Tbo Water Power Plant at Hannawa Falls, N* Y, EngiueerlBg Beeorl
Dec. 7, 1901.
35. The Water Power Development at Massena, N. Y. Power, December, 1901
3». HudJion River Power Plant at Mechanic ¥ 111 e, R Y. American U«y
trlclan, September, ISSS. Engineering News* SepL 1. U^$. Ele^
trlcal World, Nov. 13, 1807.
40. Hudson River Power Plant at Spier Falls, N. Y. Engineering Reoorl
June 27, 1903. Electrical Review, July 21, 1906.
41. Hydraulic Developments at Trenton Falls, H. Y. Electrical World, SUf
19, 1906.
42. 8 tat ton of Rochester Gaa and Electric Company, Snectrical World tod
Engineer, Nov. 13, 1903.
43. Now Hydro-Electric Power Plant of Cornell University. EngineerlBj
Record, May 20, 1905,
44. HydrO'Electrlc Developments tn the Adlrondacks. Electrical World, Apr.
26, 1906.
45. Hydraulic Development. ^liddletown, N. Y. Electrical World and Ear
lueer, Aug. 8, 190S.
4G. Niagara Falls Power Developments. Cassier's Magazine (Niagara f<tnf
number). Engineering News, 1901, vol. 1, p. 7L
47- Power Plants of The Portland Railway Light aud Power Company, Port-
laud, Ore. Engineering News, June 27. 1907. Engineer. Apr.
15, 1907.
4S. Qarrln'a Falls Plant, Manchester, N. H. Engineering Record, Jan, !l
1903. Engineering News^ March 19, 1903. Electrical World i
BTngineer, May 2S, 1904.
49. Concord, N. H. Water Power. Electrical World and Engineer, July It, Wt~
50. Plant at Se wall's Falls, N. H. Engineering Rocord, Jan. 5, 1906.
61. Water Power at Manchester, N. H. Electrical World and Engineer, jta
17, 1903,
62. York Haven, Pa. Tran amission Plant. Electrical World and Engine*
Sept 19, 1903. Electrical World, March 2, 1907.
63. Developments at Huntingdon, Pa. Electrical World and KUglneer.
23, 1906.
54. Hydro-Electric Plant of the McOall-Ferry Power Company, Fa. Enginet
Ing Record, Sept. 21, 1907. Electrical Review, June t, 1907,
55, The Warriors Ridge Hydro-Electric Plant at Huntingdon, Pa. Engtnt*
Ing Record, Dec. 22, 1906,
66, Hydro-Electric Developments on the Catawba River, South CaroUfl^
Electrical World, May 25, 1907. Engineering Record* July
1904. Electrical World and Engineer, July 23, 1904,
Literature 559
67. Construction of the Neals Shoals Power Plant on Broad River, S. C. Eng-
ineering Record, March 3, 1906.
58. A Large Hydraulic Plant at Columbia, S. C. The Engineering Record,
Jan. 1, 1898.
59. Greenyille<^rolina Power Company, S. C. Electrical World, June 22,
1907.
€0. Water and Electric Power Plant of the Utah Sugar Company. Engineer-
ing News, Apr. 13, 1905.
€1. Bear River Power Plant and Utah Transmission Systems. Electrical
World and Ehgineer, June 18, 1894.
42. Plant of the Chittenden Power Company, Rutland, Vt Engineering Rec-
ord, Dec. 9, 1905.
€3. Plant of Vermont Marble Company, Proctor, Vt Electrical World, Feb.
3, 1906.
^. Water Wheel Equipment in the Puget Sound Power Company's Plant.
Electrical World and Engineer, Oct. 22, 1904.
^. Hydraulic Power Plant on the Puyallup River, near Tacoma. Engineer
lug Record, Oct. 1, 1904. Engineering News, Sept 29, 1904.
Electrical World and Engineer, Oct 1, 1904.
^6. Snoqualmie Falls Water Power Plant and Transmission System. Eng-
ineering News, Dec. 13, 1900. Western Electrician, Aug. 20, 1898.
Electrical World and E^ngineer, May 7, 1904.
^7. Apple River Power Plant, Wisconsin. Electrical World and Engineer,
Dec 8. 1900.
^^ 8t Croix Power Company, Wisconsin. American Institute of Electrical
Engineers, 1900. Engineering Record, March 3, 1906. Western
Electrician, Oct 27, 1906.
«. The Lachine Rapids Power Plant Montreal, P. Q. Engineering News,
Feb. 18, 1897.
*^0. Shawinigan Falls Electrical Development Electrical World and Eng-
ineer, Feb. 1, 1902. Cassier's Magazine, June, 1904. Engineer-
ing Record, April 28, 1900. Canadian Engineer, April and May,
1901 and May, 1902.
^L 60,00a-volt Hydro-Electric Plant Winnipeg. Manitoba. Electrical World,
June 23, 1906.
^1 DeCew Falls Power Plant Engineer, Apr. 2, 1906.
"^ Development of the Montmorency Falls. Electrical World and Engineer,
June 17, 1899.
"^i The Rheinfelder Power Transmission. Electrician, March 26, 1897.
"^5. The Bellinzona, Italy, Hydro-Electric Station. Electrical World and Eng-
ineer, Sept 16, 1905.
n^i A Norwegian Water Power Plant Electrical World and Engineer, Apr.
4, 1903.
^. An Italian 40,000-volt Transmission Plant Electrical World and Eng-
ineer, Aug. 19, 1905.
^ Tyrol Hydro-Electric Power Station, Keiserwerke. EZlectrical World, May
1. 1907.
- : :i3f
CHAPTER XXIII.
rHE RELATION OF DAM AND POWER STATION.
I3. General Consideration. — In any water power plant the
IT must be taken from some source, conducted to the wheels,
discharged from the same at the lower head. To accomplish
object there must be a head-race leading from the source of
)ly to the plant which may be of greater or less length and in
:h more or less of the available head may be lost in order to
luce the velocity of flow and overcome the frictional resistance.
Pig. 342.
iter entering the plant the water is discharged through the
>ine T into a tail-race of greater or less extent in which there
Iso a loss caused by friction and velocity of flow, similar to that
ady expended in the head-race. In Fig. 342 the total head
tlable is H ; the head lost in the head-race is indicated by hj ;
the head lost in the tail-race is indicated by hj. The net energy
lie wheel is h = H — hj — hj, and a portion of h is also lost in
slip, leakage, and friction of the machinery and transmission*
Tie power plant should be located with reference to the dam*
liat (i) the greatest amount of head may be utilized at the least
«nse; (2) the plant constructed should be as free as possible
H interruptions due to floods or other contingencies; (3) the
ition chosen should be at such' a point where security of con-
tction can be accomplished at the minimum expense.
-ach of these influences is of importance and the relative location
tlie power plant and dam must depend upon these and various
er conditions which must be carefully considered.
56a The Relation of Dam and Power Station. ■
284. Classification of Types of Development, — For the pufpOH
of a dear understanding of the principles invoh^ed, the type ■
development may be grouped or classified into : ■
First: Concentrated fall, in which the plant is built on tbedifl
or closely adjoining thereto, with a short or no race. In this cafl
the entire fall is concentrated by means of the dam and as a nfl
this class of development is adaptable only to central power ?l^
tions where one or two plants only are to be installed oa M\
power. ■
Second: Diversion type with dam. In this case the fall is M
vcloped by means of a dam in the manner conforming to tiic lifl
type but the water is distributed to one or more plants by meaafl
of a long head-race canal throug^h which the water flows to tk
power station, after which it is discharged either into the stream
at some point below the dam or into a tail-race from which it is
finally discharged at a point lower dowTi the stream.
Third: Diversion with or without dam. In this case the develop*
ment is installed with or without a dam at the head of the rapids
or fall which is to be utilized and the water is conducted througfi
a long head race, if land of a suitable elevation is available, or*,
otherwise, through a tunnel to a point immediately above the site
of the power station. From the end of the tail-race or tunnel tf^e
water is carried to the plant through a metallic penstock.
Fourth : The fourth type is similar to the third except that where
the head-race or tunnel is used (the ground being unfavorable tp
such construction or the expense of the same being unwarranted)
a long penstock of metal is provided to conduct the water horn
the head works to the station.
Fifth : The fifth type is the tunnel tail-race type and involves con-
ducting the water through metallic penstock direct to the wheels
located at the minimum level and, after the water is dlschargtd
therefrom, the provison of a tunnel tail-race for conducting the
water from the turbine to the point where it is to be discharged
back into the stream-
It is important to note in this case, as in the case of all other
classifications attempted, that such a classification is for the pur-
pose of systematizing the consideration of numerous diverslfiecl
types and bringing them to a similar basis for examination* In
the actual adaptation of plans of development, it is seldom any sin-j
gle type will be found in its simplicity; in most cases modifications'*
of the same become desirable or essentiaL
m m
Classification of Types of Development.
56s
5^4 The Relgtioo of Dam and Power
285. Concentrated FalL^ — ^lo most of Cbe low bead wmter powers
ihe portioci of the fall of tlie river which can be txtlfized is d^tiib-
tited over minor rapids and small falls and occttpies m coosidcfable
length of the stream. Where the head is small and the expense of
m dam to eoncentrate the head entirely at one point is permissibirp
the power house may sometimes be located to advmntage tn tiie dm
itse'tf. In this case the power bonse will constitme a part of tk
dam itself. This is possible only where the lepgth of the spillway
remaining is sufficient to pass maximum flood without an undue
rise in the head of the water above the dam* lit many stich cases
this plan, which is represented by Diagram C Fig. 343, mefti
economical construction as it may both cheapen tke cost of the
dam and reduce the excavation nec^^ary for the wheel pit and t2il>
race. The power house built at such point is* however, usmllv
directly in the line of the current and must be so constructed w^
protected as to prevent its injury or destnsctioo by floods^ ice or
other conting^encies of river flow.
In other cases, where the spillway available by the above plan is
not sufhcient or where the plant is not properly protected b]r such
forms of constniction, the plant may be constructed on one side
of the dam, receiving its waters from a head-race which jom thf
river above the dam and discharges it into the river below, ^
shown by Diagrams C and D, Fig, 343. Or, where the capacity i*
si^tablep the plant itself may receive the water directly from sl^
head gate from the river above the dam and discharge it through
a tail-race which will enter the river at some point below the dam.
as shown in Diagram A» Fig. 343.
In other cases, where the power is to be distributed to a number
of independent plants, raceways may be constructed on either of
both sides of the stream and from the dam, following the stream
downward along the bank and more or less approximately parallel
thereto as the nature of the conditions demand The plant drawing
the water from this head-race may be distrbtited at various pomi^
along the same, and from these plants the water will be discharged
after use either directly into the stream itself or into a tail race con-
necting such plants with a lower point farther down the streajHi**
shown in Diagram E, Fig, 343,
a86. Divided FalL — An independent tail-race is usually coi^-
structed to advantage where the dam concentrates only a portioci «
the head or fall, leaving certain additional portions to be develop
by the use of the tail-race, which may, if desirable, enter the strewti
Classification of Types o£ Development 565
566 The Relation of Dam and Power Station. I
at a point much tartlier down the ri%^er and at the foot of the rapiB
Where the fall of the stream is considerable, and the expensed
construction of the dam to suitable height to concentrate Uie entfl
fall at a single point is inadvisable, it is often desirable to btiilM
dam to less height at perhaps considerably less expense and devdn
at the dam only a portion of the total fall From this dam a heafl
race may extend to some considerable distance, and the ^vaterfral
this head-race may be delivered to the power plant a mile or t<rl
lower down the stream. From this head race, the water, after pa<?
ing throw gli the wheels, is carried directly into the stream at tie
lower point, as shown in Diagram G, Fig. 344.
Under other conditions, where the topography of the country is
suitable, the head-race may be much less in extent, and a tail-race
substituted for receiving the waters after they have been usd ifl
the wheel and then conducted to the river at or near the ^nd of tk
rapids, as shown in Diagram F, Fig. 344.
Under still other conditions the plant itself may be located Immt-
diately at the dam and the tail waters may be conducted from the
turbine to a tail-race or tail-water tunne! to the lower end of the
rapids, as in Diagram H, Fig, 344.
The relation of head-race and tail-race is merely a question d
developing the power plant at the least cost and securing the max-
imum head, and the topographical conditions at the power site will
therefore determine which line of development will be best. In a
number of cases, where the head or fall ip considerable and thf
power development is large, and where the cost of land for head-
races w^ould be almost or quite prohibitive, the stations have b«Ji
located in the immediate vicinity of the river and have delivered the
water into a tail-race tunnel, which frequently empties at a coo-
siderable distance down the stream and at the lowest point of deliv-
ery that is practicable. In other cases it is more economical tonin
open raceways for a portion of the distance and then conduct the
water under pressure by closed pipes to the wheels at the lower
point.
This last method is used particularly under high head and where
the water must be conducted for a reasonable distance over an irreg-
ular profile.
The quantity of water to be used, the head available, and the
value of power modify the arrangements which must be carefully
studied in view of the financial, topographical, and otheT modifyin|
conditions.
J
Distribution of Water at Various Plants.
567
287. Examples of the Distribution of Water at Various Plants. —
ig. 345 is a plan of the power development on the Rock River at
:erling, Illinois, The dam at this point is about 940 feet in length.
he power is owned by various corporations and private individuals
ho have combined their interests in the dam and raceways and
345.— Raceways of Sterling Hydraulic Company.
wve organized The Sterling Hydraulic Company, whose function
s to maintain the same. The individual plants are owned, installed,
ind operated by the various owners or by manufacturers who lease
he power. At this location races have been constructed at the foot
>f the rapids, but these rapids continue to a point near the lower
nd of the tail-race, and the plants farthest from the dam have the
ighcst falls. The fall varies from abooit 8 to 91^ feet
568
The Relation of Dam and Power Station.
Tig. 346 shows the general arrangement of the canal of The Hoi*
yoke Water Power Company at Holyoke, Mass* The total fall d
the river at this point, from the head water above the dam to t!ir
tail water at the loivvest point down the stream, is about sixty feci
The fall is divided into three levels by the variotis canals, martd:
ist level canal t 2nd level canal, and 3rd level canal.
Fig. 3-4lj.^Caaals of Holyoke Water Power Compimy.
The first level canal, which has a length of about 6,ooa feet, {5c»:ju*
structed as a chord across the bend of the river and is approximatd|j
some 3,000 feet from the bend. The canal is about i^c^ wide near^
the bulkhead and decreases to about loo' at the lower end, Tbe
water depth is about 20' at the upper end and about lo' at the bwtr*
The canals are all walled throughout their length to a height twoorj
three feet above the maximum water surface. The fall from M
first level to the second is about 20', Various mills draw^ their watfrj
supply from the first level as a head-race, and discharge into the
second cana! as a tail-race. Near the upper end of the canal ar^*
few factories that draw water from the first level and dischargcil^*|
same into the river with a head of some 35 or 40 feet
The second level canal is built parallel to the first and at a &r\
tance of about 400 feet nearer the riv^er. The main canal is about
6,500 feet in length, but near the left hand of the map is shown toj
Distribution of Water at Various Plants.
569
Fig. 347. — 'Kilboum Plant of Southern Wi8con«ln Power Co.
570
The Reiatioo of Dam and Power Station*
sweep round towards the river and attain a reach of about 3,005
feet in length parallel thereto. The mills drawing their supply frous
this canal discharge either directly into the third level or into tlie
river. The water supply frotn each of the lower levels is the tail
water from the next level above, but is also supplemented by over-
flows wheti the mills fed from the level above are not discharginf
Fig, 348. — Plant of The Lake Superior Power Cq»
sufficient water to maintain the quantity needed in the lower levd.
The fall from the third level of the river is essentially the sanat
for all the mills drawing water therefrom, but according to the stag?
of the river ranges from 15 to 27 feet.
The flow of water in the first level is controlled by gates and its
height limited by an overflow of about 200 feet in length whkB
acts as a safety overflow and prevents any great rise in the hm
water during times of flood.
fl88* Head-Races Only. — Fig* 347 illustrates the general plan of
the hydraulic power development of The Southern Wisconsin P<>wef
Company at Kilbourn^ Wisconsin, Here the entire cross-section of
the stream is necessary in order to pass the maximum volume of
Distribution of Water at Various Plants.
571
a
o
I
o
I
^
^
Distribution of Water at Various Plants.
573
water, which amounts to about 80,000 second-feet The plant has
therefore been constructed at one side of the river, receives the flow
through a series of gates built just above the dam, and discharges
the water into the river just below the bend in the river, as shown.
The plant now under construction is only a portion of that which
it is designed to ultimately install. The proposed future extension
of the power plant is shown by the dotted lines.
/P -*^^^^-"^ ^
^j^ ^"-
TWIM FMAi
F1?. 351. — Possible Canal for Peshtlgo River Development
Fig. 348 shows the water power plant of The Lake Superior
I^owcr Company at St. Mary's Falls, Michigan. The canal on the
American side begins just above the entrance to the American ship
c^anal and above the Soo rapids. The water is cond^ucted through
this canal to a power house located below the rapids at the point
shown on the map. On account of the value of the land this canal
"Vas designed for a velocity of flow of about 714' per second with
*ull load of the plant, which was designed for about 40,000 h. p.
JPcquiring a capacity with available head of 16.2 feet, of about 4,200
^^bic feet ner second. (See Engineering News of August 4th, i8g8.)
36
574
Tne R.-^aroii at Dam sad Power Statioa.
F!g: 345 rioiws -iie alaa at zhe aydrxsEc development of The
Ecrinamy Lighr and Power Gmpaznr at JoIiMt, Illinois. The entire
installatiaii 3S ^cwn is owned by dtfs companr. The fall available
is about ix fiest and is dcTeioped by a concrete dam which creates
the upper basin alon^ wrrrrh die power plant has been constructed
The water f ows rfiron^ the finmc gates directly on to the wheels
and is discharged iatD a tail-race bnxlt parallel with the river A
!
k
t
s
u
tM
(
840
tM
\ i
SIO
/
...s
1
— -— — 'T^ i
800
z
' ! 1
790
YZ
! \
7tO
)
i
770
i
1
m
60
61
60
64
66
MIUBS
Fig. 352.— Profile of Peshtigo River.
certain amount of water is necessary for feeding the lower level of
the canal and this is supplied by a by-pass tunnel shown in dottco
line above the dam. This by-pass, which is slightly higher than
the elevation of the tail-race, is fed by the discharge of one of the
wheels, which operates under a less head than the other wheels ifl
the installation.
289. Plant Located in Dam.— In Fig. 350 is shown the general
plan and elevation of the hydraulic plant at Dresden Heights 00 the
Des Plaines River just above its junction with the Kankakee Ri^^^-
1 licse two streams unite at this point to form the Illinois River.
In this case the dam is built across a very wide valley and the
length of the dam is much greater than necessary or desirable to
High Head Developments
575
i
o
I
&
a
o
•4-*
a
0)
u
a
B
O
•33
►
Q
u
9
accommodate the flood flow of the
stream which is approximately 25,000
second-feet. In consequence, the pres-
ent power plant, as well as the pro-
posed extension to the power station^
will form a part of the dam itself and
the spillway will occupy only a portion
of the entire length of the structure
and is so designed as to maintain a sat-
isfactory head at times of flood flow
The head of the water above the dam
is controlled both by the length of
spillway and by six tainter gates by
means of which the level of the water
above the dam can be controlled at all
stages of flow.
290. High Head Developments. —
Fig. 351 illustrates the general plan of
a possible method of development of
the Peshtigo River for The Northern
Hydro-Electric Company. The fall
available is shown by the profile, — Fig.
352. It is proposed to construct a dam
above High Falls of sufficient height
to back the water over Twin Falls^ and
to either develop the power at High
Falls and Johnson's Falls independently
or conduct the water by a canal to Mud
Lake, thence to Perch Lake, thence to
the head work to be be built above
Johnson's Falls, where a head of about
110' will be available. If a single de-
velopment is chosen the water will be
be conducted from the head works
through penstocks to the power plant
to be built at the base of the bluff below
Johnson's Falls. The canal in this case
will conduct the head waters with very
little fall to the immediate site of the
plant, thence by penstocks to the tur
bine located in the gorge below.
and Power Station.
Fig* ^&4---Niagara Falls Fower Dev«i»piiieiii*
Hi^h Head Developments.
577
^^E' 353 *s a plant of the power devclcpment at Trenton FalJs,
^^ew York. The upper portion of the fall is developed by a dam
ibout 60^ in height, which is connected by an 84" pipe line with the
tirbiTie located in the power house about two miles below. The
^urbines used in this development are the Fourneyron turbines,
^^wrhich are described in Chap, XIX, and are illustrated by Fig. 311,
Fig. 354 is a general plan of the water power de%^etopments at
^^iagara Falls, The first development was that of The Niagara
Falls Hydraulic and Manufacturing Company. By means of a
canal the water is taken from the upper end of the rapids and con-
ducted to the lower bkiff on the American side, and distributed, by
open canals, to various plants located along this bluff..
Ttie second plant constructed was that of The Niagara Falls
Power Company; in which power is developed by the %^ertical shafts
connecting with a tail-water tunnel %vhich discharges into the river
just below the new suspension bridge*
578 The Relation of Dam and Power Station.
On the Canadian side are shown three plants.
The Ontario Power Company secures its water supply from the
upper portion of the rapids, conducting it through steel conduits
to a pc«nt above the power house and thence by penstocks to the
wheel, located in the gorge below the falls.
In the plants of The Toronto and Niagara Power Company md
The Canadian-Niagara Power Company, the water is taken from
above the Falls and discharges through penstocks to wheels looted
at the base of a shaft and thence into tunnels, discharging intofte
river at a point below the Falls.
Fig. 355 illustrates the plant of The Niagara Falls Hydraulic tod
Manufacturing Company, which is supplied by water from Ae
hydraulic canal above mentioned. The water is conducted from fte
forebay by a vertical penstock to which is attached several wheels
which deliver the water into a tail-race tunnel and thence into Ae
gorge below.
The plant arrangements ab©ve described are typical of many not
in use both in this country and in Europe. It is at once obvious ttat
in considering this subject each particular location is a problem by
itself which must be considered in all its bearings; but an under-
standing of the designs and arrangements already in use forms t
satisfactory basis from which a judicious selection can be made
with suitable modifications to take care of all the conditions of
topography and other controlling conditions.
CHAPTER XXIV*
PRINCIPLES OF CONSTRUCTION OF DAMS.
agi. Object of Construction. — A dam is a structure constructed
with the object of holding back or obstructing the flow and elevat-
ing the surface of water. Such structures may be built for the fol-
lowing purposes :
First: To concentrate the fall of a stream so as to admit of the
economical development of powen
Second : To deepen the water of a stream so as to facilitate nav-
igation and to so concentrate the fall that vessels may be safely
raised from a lower to an upper level by means of locks.
Third: To impound or store water so that it may be utilized as
desired for water supply, water power, navigation, irrigation, or
other uses.
Fourth: In the form of mine dams or bulk heads to hold back
the fiow of water which would otherwise flood mines or shafts or
cause excessive expense for its removal.
Fifth : As coiTer-dams for the purpose of making accessible,
usually for construction purposes, submerged areas othervvise inac-
cessible.
39a* Dams for Water Power Purposes. — The primary object of
a dam constructed for water power purposes is to concentrate the
fall of the stream so that it can be developed to advantage at one
point and so that the water thus raised can more readily be delivered
to the motors through raceways and penstocks of reasonable length.
This object is sometimes accomplished in rivers with steep slopes
or high velocities by the construction of wing dams which occupy
*only a portion of the cross-section of the stream, but cause a head-
ing up of the water and direct a certain portion of the flow into
the channel or raceway through which it flows to the wheels.
Usually in streams of moderate slope the dam must extend entirely
across the stream in order to concentrate sufticient head to be of
practical titility.
£3o Trindpies of Coostractkn of Dams.
\\':r.^ dzzr.s can be used at the head of high tails where onlv a
portior^ of the volunie of flow can be utilized, as at Niagara Falls,
or in rapid rivers where a portion of the flow is to be directed into
a narrow channel for txtilizing low heads by means of midershot or
•!oat wheels as is frequently done for irrigation purposes. Where
the full benefit of both head and volume is to be utilized the dam
must extend from bank to bank and be constructed of as great a
height as possible.
293. Heig^ of DaoL — ^To utilize a river to the maximnm extent
the highest dam practicable must be constructed.
The height of a dam may be limited by the following factors:
First : The overflow of valuable lands.
Second: The interference with water power rights above the
point of development.
Third : The interference with other vested or public rights.
Fourth : The cost of the structure.
The value of the power that can be developed by means of a pro-
posed dam will limit the amount that can be expended in the pur-
chase or condemnation of property affected by backwater from the
dam and the cost of its construction. These are among the cl^
ments of the cost of the project and must be considered together
with other financial elements before a water power project can be
considered practicable.
In considering backwater and its effect on riparian rights both
high and moderate conditions of flow must be considered. The
former condition gives rise to temporary interference, often of little
importance when affecting purely farming property, and the real
or fancied damages from which can commonly be liquidated by re-
leases at small expense. The latter conditicwi will permanently
inundate certain low lands which must be secured by purchase or
condemnation. In many states where the laws of eminent domain
do not apply to the condemnation of property for such purposes it
is necessary to secure such property by private purchases before
the work is undertaken, and usually before the project becomes
known publicly, for in such cases the owner of a single piece of land
may delay the project by a demand for exorbitant remuneration,
from which demand there is in such cases no escape- In every case
it is desirable that riparian and property rights be fully covered
before the construction of the project actually begins.
The Foundalion of Dams. 581
294. Available Head* — Beside the question of backwater the ques-
tion of head at the dam is important both in relation to the question
of interference and in relation to the question of power. In relation
to interference it is an easy matter with a known length and height
of dam to determine by calcalation from a properly selected weir
formula the height of water above the dam under any condition of
flow. To determine the head available under all conditions of flow
the weir cur\^e must be studied in connection with the rating curve
as discussed in Chapter V.
Two conditions of flow often require consideration in this con-
nection :
First: Where a considerable portion of the flow is being utilized
by the wheels and therefore does not aifect the head of the dam*
Second: Where the water is not being used by the wheels and
consequently aflfects the head of the dam.
Both of these conditions should be studied and determined in rela-
tion to their influence on both backwater conditions and power.
295, The Principles of Construe tian of Dams, — The general prin-
ciples for the construction of all dams are similar, and are as fol-
lows :
First : They must have suitable foundations to sustain the pres- *
sore transmitted through them, which must be cither impervious or
rendered practically so.
Second: They must be Stable against overturning.
Third: They must be safe against sliding.
Fourth: They must have a sufficient strength to withstand the
strains and shocks to which they arc subjected-
Fifth : They must be practically water-tight.
Sixth: They must have essentially water-tight connections with
their beds and banks* and, if bed or banks arc pervious, with some
impervious stratum below the bed and within the banks of the
stream.
Seventh: They must be so constructed as to prevent injurious
scouring of the bed and banks below them.
The application of the ab(ive principles depends on the material
from which the dam is to be built and on local conditions-
396. The Foundation o! Dams. — The materials used for the eon-
struction of dams may be masonry, which includes stone-work and
concrete-work, reinforced concrete, timber, steel, loose rock, and
earth. Each may he used independently or in combination.
Masonry and concrete dams must be built upon foundations which
55*3
PfVtC^llcS' oc
are practically free frooi possHife setticEneiii:. SataH masoory siiac-
torn ntxf soinetiincs be saMj eoBStractcd cw piles or piUi^
bsaed on flofter ntatemis ; bnt tbe lafger and more tm-
ilfiscliuesip if coostmcted of sBsoorf* oa be safely buiU
only tipofi solid rock. Ressforced coocrefe is now betn^ exteosheh
osed for small structtires and is not as sctioosly affected by sUgiit
s^Uemeat as in tlie case o( dams ct sofid masoeiy. There is, hew-
ever, little fle^dbility in structures of this kind, and die foniKlition
^
I I
^ K^i.
-"^
V^
Fif. 356,— Timber (Mb Dmm mi JkntrnwUlt* Wis.
must be selected in accordance with this fact. Timber and steel
possess a flexibility not possible in concrete construction and ire
much better adapted to locations where the foundation may be sob-
jcct to settlement.
In construction on rock foundation it is usually desirable to exca-
%'ate trenches therein in order to give a bond between the stniciure
of the dam and its foundation. It is also essential with rock foun-
dations to determine whether cracks or fissures in the foundation
extend below the structure, and if such are found, they must be
completely cut off, «
On earth, sand or gravel foundations, when such must be ti^»
the flow which would take place through these materials and nni^f
the structure of the dam must be completely cut off by the use of
steel or timbi^r sheet piling* which, if possible, should be driven
from the structure to the rock or to some other impervious strattsm.
If no impervious stratum is accessible, the sheet piling must he
k.
Strength o£ Dams.
58j
ren to stich a distance below the base of the dam that the friction
of the flow of water nnder it will reduce or destroy the head and
consequently reduce the flow of water to an inappreciable quantity,
297. Strength of Dams.^ — A dam to be built in a flowing stream
should be designed with a full appreciation of all the stresses to
which it may be subjected* Of these, stresses that are due to static
pressure can be readily estimated from the known conditions. The
strains due to dynamic forces are not so fully understood or easily
Fig. 3->7.— Janes vj lie Dam with Mcderate Watcn
calculated. Where the structure is constructed to retain a definite
head of water without overflow, as in the case of reservoir embank-
ments, the problem becomes one largely of statics and the only
other stresses to be considered are those due to ice action and the
action of waves on the structure. When a dam is constructed in a
running stream and is subject to the passage of extensive floods of
water over it, frequently accompanied by large masses of floating-
ice, logs or other material which in many cases may strike the
crest of the dam, and bring unknown and violent strains, the prob-
lem becomes largely one of experience ?.nd judgment.
298, Flood Flows. — The passage of great volumes of water over
a dam involves the expenditure of the power so generated upon or
immediately adjoining the structure, and unless preparations are
made for properly taking care of this immense expenditure of
power, the power may be exerted in the destruction of the structure
itself.
584
Principles of Const rucliDEi o£ Dams,
f^igs. 356 to 358 show three views of the timber crib dam
Janesville, Wisconsin, under various conditions of flow. In Fi§*
356 the flow of the river is comparatively small and all of the water
is bcin^ used in the power plant, none passing over the dam. In
Fig, 357 the river is at a moderate stage and the greater part of the
(low is passing over the crest of the dam. In Fig. 358 some four
or five feet of water is passing over the dam and the power tliat h
developed thereby is causing the standing wave and the roup
Fig. 358,^Jftne8vine Dam under HtgU Water.
water shown in the picture below the dam. At this point the power
developed by the fall is being expended in waves and eddies, whidu
unless properly controlled, will attack and injure or destroy the
structure. On rock bottom the rock itself will sustain the impact of
flow over small dams. But where the rock is soft, or the bottom is
composed of material that can be readily disintegrated, it becomes
necessary to extend the structure of the dam itself in the form of
an apron to cover and protect the bottom.
Fig, 359 shows the preliminary design of a dam for the SontTiern
AVisconsin Power Company, now under construction at Kilbourn.
Wisconsin^ This dam will be about 17 feet in height above low
water and will be subject at times to the passage of floods to a
depth of 16 feet above its crest. For section of dam as constructed
see Fig, 373, The two ends of the dam will rest upon a rock
foundation. Cribs are also carried to the rock at the face of the
dim and at the edge of the apron. The center of the dam is stis-
I
586 Principles of Construction of Dams.
tained by piles reaching to rock but surrounded by sand which is
retained by the cribs.
The dam proper is built of cells 6 feet squarCp the walls of eadi
<reli being built of solid timber, and each cell carefully filled with
stone and sand. At the face of the dam and at the toe of the aproa
triple sheeting has been placed and sscurely fastened to the 4mi
and cribs from the rock up, thus eflfectively preventing the passage
of water below or through the dam.
During high floods the amount of power which must be wasted ib
the passage of water over the dam will exceed 100,000 horse powtr
In order to prevent the expenditure of this power in the destruction
of the dam, the dam is extended in an apron of about lOO feet in
width, the total wfdth of the structure including the dam and the
apron, being about 150 feet.
To further protect the structure, rip-rap is deposited both above
and below the structure itself. The surface of the dam exposed at
times of low water is constructed of re-inforced concrete, attached
directly to the timber work of steel reinforcement* By this design
a structure is obtained having all the advantages of the flexibility nf
timber, with the lasting qualities of masonry, for the concrete only
will be exposed at times of low w^ater, all timber work being sub-
merged under every ordinary condition.
299. Impervious Construction- — Masonry dams are commonljf^
made impervious by the structure of the masonry itself. ■
In timber crib dams ordinarily no attempt is made to make the
structure itself water- tight, but the top and upstream side are usu-
ally covered with water-tight sheeting to prevent the water pass-
ing into and through the cribs* Such water as reaches the timber
cribs usually passes away readily through the open structure on thc^
down stream side of the dam. ■
In the construction of rock-filled dams the same condition ordi*
narily obtains. The dam is fairly porous with the exception of its
upper face which is made practically water-tight by the use of con-
crete, puddle, or some impervious paving.
In earthen dams the finer and more water-tight materials are
used on the inner slopes of the embankment, and, in addition
thereto, it is customary in large and important works to use a corf
of concrete or puddle to effectively prevent the passage of water
through the structure*
300* The Stability of Masonry Dams. — The external forces act-
ing on a masonry dam are the water pressure, the weight of iht
Stability of Masonry Dams. 587
masonry, the reaction of the foundation, ice and wave pressure near
the top, wind pressure, and back pressure of the water 00 the down
stream side. The action of these forces may cause a dam to faU by :
(i) Sliding on the base or on any horizontal plane abonre the
base.
(2) Overturning.
(3) Crushing the masonry or foundation.
If the dam be built of rubble masonry there will be no danger of
failure by sliding on a horizontal joint above the foundation and
experience has shown that where a good quality of mortar is used
it can be depended upon to prevent sliding in concrete and stone
dams having horizontal bed joints. The joint between the dam and
its foundation is a more critical point In rock foundation steps or
trenches should be cut so as to afford good anchorage for the dam.
In the case of clay, timber or similar foundations the dam will have
to be made massive enough so that the tangent of the angle be-
tween the resultant pressure on the base and a vertical line is less
than the co-efficient of friction between the materials of the dam
and the foundation.
It is customary in the design of masonry dams to proportion the
section so that the lines of resultant pressure at all horizontal
joints, for both the conditions of reservoir full and reservoir
empty, shall pass through the middle third points of the joints.
If this condition is fulfilled, the factor of safety against overturn-
ing at every joint will be 2, and there will also be no danger from
tensile stresses developing in the faces of the dam.
Investigation has shown that there is no danger of crushing the
masonry except in very high dams, with the consideration of which
we are not here concerned-
301. Calculation for Stability. — ^The general conclusion may there"
fore be stated, that, in the case of ordinary masonry and con-
crete dams, not over 100 feet in height, to be built on rock foun-
dations, the design can be based upon the condition that the lines
of pressure must lie within the middle third of the profile
This rule must be modified at the top of the dam to resist the
stresses due to waves, ice, etc. The force exerted by ice is an in-
determinate quantity and the tops of dams must therefore be pro-
portioned in accordance with empirical rules. Dams are built with
top widths varying from 2 to 22 feet, the broader ones usually
588
Principles of Construction of Dams.
carrying a roadway. Coventry suggests the following empirical
rules for width of top and height of top above water level*
(1) b = 4.0 + 0.07 H
(2) y, = 1.8 + 0.05 H
Where b is the width of top, y© the height above water level and
H the greatest depth of water. Both faces of the dam will be ver-
tical until the depth vi, is reached, where the resultant force passes
through the middle third point. Below this depth the general nilc
will apply. In computing the water pressure against the dam, it
Fig. 360.
is best to consider the water surface level with the top of the dam
in order to allow for possible rises due to floods, etc. Having de-
termined the top width, b, and assuming a section of the dam one
foot long, the height, y^ of the rectangular portion can be deduced
from the formula
(3) y, = hVr
in which s is the specific gravity of the material of the dam.
The down-stream face of the dam must now be sloped so as to
keep the resultant pressure, with the reservoir full, at the Hmit of
the middle third of the length of any joint. Dividing the remainder
of the height of the dam into lengths convenient for computation,
the IciiL^th of any joint, (see Fig. 360) as "GH may be found by the
formula
Calculation for Stability, 589
rhich
em(ATeftABFE) BH» ,
FH 1 FH ^*^
frliere m = distance from F of the line o£ action of the weie^t of
tDasonr>^ above EF and
r4 (Areit ABFE)
=i[i^^^5^UKF]
rhc value of n is given by the equation
Mom. of ABFE + Mom. ©f EFHO
(5)
(AreaABHG)
moments being taken about the point H,
Equation (4) can be used as long as n is greater than one-third
the length of the joint When this condition can no longer be sat-
isfied with a vertical face, it will be necessary to batter the upstream
face also^ so that the lines of pressure with reserv^oir full and empty
both lie at the limits of the middle third of the length of any joint.
The length of the joints, as IJ, may now be found by the formula
I
• ,fl\ TT ^rSK" , /(TTT . (AreaABHG)\ (Aw« ABHG) "gR
and the value of KJ, is
— 2 (AreaABHG) (TJ — l^m) — fHK X 55"*)
^ ' " 6 (Area ABHG) +irK C2GH + IJ)
In high dams two more stages, governed by the compresstve
strength of the masonr>% would have to be considered, but, within
the limit of height set above, the formulas given are sufficient
The position of the line of pressure may be readily determined
also by graphical methods.
In the case of overfall dams, which are necessarily subjected to
dynamic forces, which are more or less indeterminate, the design
cannot be so closely figured.
302. Further Considerations.— The preceding analysis does not
take into account the possibility of an upward pressure from below
the dam, due to the previous character of the foundation, or to
cracks and fissures, by means of which the pressure of the head
water may be transmitted to the base of the dam. This factor is
_commonly ignored in dam construction, but should be considered.
59»
PriiKiples of Constructioii of Dama.
ilf^ Ul,
Uon of Dam of Hdlroke Wat«r Power 0^
Fig. 3S2.— liraMary Dam of Holyoke Water Power
Further Considerations,
591
ind, when occasion requires, the foundation shouM be so prepared
i& to obviate or reduce it to a minimum. This may tistially be done
Ijy the careful preparation of the foundation to prevent inflow, or by
."he construction of drains from the interior of the foundation to the
lower face.
The construction of a dam with a vertical overfall, unless pro-
vision is made for the admission of air, will result in the formation
a partial vacuum below the sheet, and a certain extra strain on
I ' ^
Fig. 363.^Holyoke Dam During Flood.
istnictiire due to the same. The vertical overfall is also fre-
llly objectionable, on account of the action of the falling water
tc bed of the stream immediately adjacent to the dam, and
foimdation of the dam itself. It is frequently desirable to give
jwer face of the dam a curved outline, in order to guide the
Bf smoothly over the dam, and deliver it approximately tang-en-
the stream bed. The convex surface of the dam should be
eb form that the water wilh through gravity, adhere to it,
example of a dam with a curved face is shown by Fig, 361
is a section of the dam of the Holyoke Water Power Com-
^uy. Two views of the dam, one during law water (Fig* 362)
and one with about ten feet of water flowing over the crest (Fig.
592
Principles of Construction of Dams.
363) are also shown. A section of the McCall's Ferry dam, built of
Cyclopean Concrete (height 53 feet) is shown in Fig. 364 and awe-
tian of a small Concrete dam at Danville, 111,, is shown in Fig. 365.
The cur\^e for dams of tliis character should be kept at or above the
Fir 3S4.— Section of McCall Ferry Dam (Eaag, RecX
parabolic path that the water wouJd take in a free fall with iht h
itial horizontal velocity corresponding to the depth of water on iW
flam.
From equation 50, page 64, the flow over one foot of crest will
equal,
q — vb — m(|)\^2ihl, hence,
v = m(!)/2iF
The abscissa of the parabola is x = vt, in which t^ tim« in
seconds.
/5teis* BmtM
^"^i>
!
mjs^;,^
'^Tifnimnfiffx^'
I ^ md Dam
"--C! il
^\\ 't'Ml
Fig. 365— Concrete Danir D«nville, HL
594
Pnncipltts of Construction of Daou.
TIic ordinate is, y ^ ^^4 gt*, hence,
is the equation of tlie pnrabola*
When a curved face is impracticable or undesirable and the bd
of the stream, below the dam, is not of suitable material to resist
the impact of the falling water, some form of apron must be prfr
vided. Sometimes the dam is divided into steps over which tf.e
water falls in numerous cascades. Such a dam is shown in Fig.
366, This is the timber crib dam constructed for the Monuni
Fig. 367.— Timber Dam at Sewall Falls. (Eng, News» vol. XXS^^
Power Company, near Butte, Montana. In this case the cells a^r
composed of timber, laid alternately in each direction, with a con-
siderablc space left betw^een them, instead of being built solid 3^
in the Kilbourn dam. These cells were filled with broken stone
and the upstream side of the dam was planked with sheeting i"
order to make the structure water-tight. When the water wa&|
admitted behind the dam a portion of the structure was k^^^j
out of alignment by the crushing of the timbers, at the points
contacts The amount of this displacement and the cause of tt«fj
same is quite clearly shown in the cut.
Fig^ 367 is a section of the Sewall Falls dam, showing a stoi^^
method of resisting the impact of the overflow.
304. Types and Details of Dams. — The types of dams are so ^^^
merous, and the details of construction vary so greatly with evi
locality, that an entire volume w^ould be necessary to adequately
cover this subject. As the subject is already well covered ip ^"?j
special treatises and articles, no attempt will be made to discn*
this subject in the present edition. Numerous references ire p^^]
to books and articles in which special forms of conslniction s^j
discussed and described,
•Turtieaure A UunseW^ * 'Public Water Supplres/* Seclion 446
LfiteratuTti.
595
LlTETRATURm
PHijfCTPiJEa or coNBTBUCTiaji or hams^
TTirneaure and RusBell. Public Water Supplle*. Chaps. 16 to 13. John
Wiley and Sons, 1901.
Church, I. P. Mechanics of Engtneerlng. John Wiley and Sons. 1904*
regmann. Edward. The Design and Gonstniction of DairiB. John Wiley
and Sons, 1S99.
L^ffelU James. Construction of Mill Dams. James Leffell and Company .
Springfield. Ohio. 1831.
Follet, W. W. Earthen vs. Masonry Dams. Eng. Newg, Jan. 2, 1892»
et aeq. Eng. Rec. May 14. 1S92. et eeq.
Hall, F. F. Investigation of the Distribution of Pressure on the Base of
Dams, Trans. Assn. C. E. of Cornell, 1900.
Kalght. FranK B, Building an Impounding Dam for Storage Reserroir,
Mtn^s and Mining. May, 1900»
Schuyler, J as. Dix. Reservoirs for Irrigation, Water Power and Domes-
tic Water Supply. New York. Wiley and Sons, 1901.
Gregory, John H. Stability of Small Dams. Eng. Rec. Sept 21, 1901.
Fielding, John S. EseeDtial Elements In the Design of Dams. Can,
E:ngr, Jan. 1M05.
Wilson. J. S., and Gore, W, Stresses In Dams. Engng. Aug. 4, 1905.
STABILITY or MASONRY I^AMa
Coventry, W. B. Design and Stability of Masonry Dams. Proc Inst.
C, E. ToK S5, p. 2S1. 1SS6.
Morley, Isaac. On the Determination of the Profile of High Masonry
Dams. Eng. News, Aug. 11, 1S8S.
Vischer and Waganer. The Strains !n Curved Masonry Dams, Eng.
News, Meh. 15, 1890; Sept, 27. 1890.
Van Buren, John D. Notes on High Masonry Dams. Trans. Am. Soc
C. E. vol. 34, p. 493. Dec. 1895.
Pelletlau, M. Profiles for Masonry Dams. Ann. des Ponts et Chausseea.
Feb. 1, 1897,
Levy, Maurice. Trapezoidal Formula. Cora p tea Rendus. May 2, 1898,
Levy, Maurice. The Elastic Equilibrium in a Masonry Dam of Triangu-
lar Section. Comptes Rendus. July 4, 1898.
Specifications for a Large Concrete Dam. Eug. Rec. Oct 29. 1898,
Bainet, M. The Computation of Masonry Dams for Reservoirs. Ann dea
Ponts et Chaussees. 2 Trlme-stre 1898,
Baibet M. L. The Conditions of Refli stance of Masonry Dams for Reser-
voirs. Ann des Ponts et Chaussees. 1 Trlme^tre 1899.
>lllm&n. Geo. L. A Proposed New Type of Masonry Dam. Trans. Ajn.
Soc. C. E. vol. 49. p. 94. 1902.
59^
Principles of Construction of Dam&
12,
DaiBil
Wlsnen Geo, Y. The Correct Design and StabiUty of Hlgli MasooiXa
Dams. Eng. News. Oct 1, 1903.
13. Stability of Masoarj Dams. ^^ngng. Mcb* 31, 1906,
14. Review of Paper of AtcherlF ^ Pearaoa on StabiUtj of Mbsqutj
Engr,» Load, Mch. 31. 1905,
15. Unwin, W. C. Note on the Theory of 0naymmetrlcal Masonry Dtm
EngGg. Apr. 21. 1905,
Unwin» W, C, Further Notes on the Theory of Unsymmetrlcal Maaoarr _
Dams. Engng. May 12, 190§. ■
Tin win. W. C. On the DlstribtJtton of Shearing Stresses In Masonry I>ami^
Engng. June 30, 1905,
Pearson, Karl. On the Stability of Masonry Dams. Engng. fOL M*
July 14. 1905,
Wlsner, Geo. Y., and Wheeler, Edgar T, Investigation of Streesea to
High Masonry Dams of Short Spans. Kng, News. Au^, 10. VM
20. Pearson, KarL On the Stability of Masonry Dams, Engineeritig, vd. B,
p. 171. Aug. 11, 1905.
21. Th« Determination of Pressures on Masonry Dams. Oest. Wochfiisciir,
f d Oeff, Baudienst. Aug. 19, 1905,
22. Bletch, S, D. Internal Stresses in Masonry Dams. Sch. of Min» Qr.
Nov 1905.
23. Ende, Maxam. Notes on Stresses in Masonry Dams. Engineering. Det
1905.
le.
17.
18.
19.
EARTHEN DAMS,
1. Fitzgerald^ J. L. Lreakage Throtigb aa Karthen Dam at Lebanau, W-j
Eng. Rec. May, 1S93, pp. 474^5.
2. LeConte, L, J. High Earthen Dam for Storage Reservoirs. Proc Am
W. Wks. Assn.. 1S93, and Eng, Rcc, Sept. 16, 1893.
3. Fitzgerald, D., and Fteley, A. Construction of Reservoir Emhaakineiiti
Eng. News. Oct. 26, 1893. pp. 330-1,
4. Earth Dam of the Honey Lake Valley, California. Eng, News, Mch. 1^-
1&94.
5. Earth Dam at New Britain, Conn. Eng. Rec. June 23, 1S94.
6. Dinirultles with Earth Dams in Great Britain. Eng. Ret. Set. 3, l^^
7. Strange, W. L. The Conatmcilon of High Earth Dams. Eng. ^
Apr. 15. 1899,
8. The Limiting Heights of Earth Dams. Eng. Rec. Dec, 7. 190L
9. A Remarltable Core- wall for an Earth Dam. Eng. Rec. Dec, 21, 1^^^
10. Concerning the Design of E]arth Dams and Reservoir f^tmnkmf^^
Eng. News, Feb. 20, 1902. j
11. The Tabeaiid High Earth Dam, near Jackson, Cal. Eng. News. Julj 1^'
1902.
12. Baasell. Burr. The San Leandro Eartb Dam of th« Oakland WiW |
Worlds. Eng, News, Sept 11, 1902.
IS. The New Earth Dam for Water Works of Santa Fe, N. M. Enf. Ki^"^ <
Apr, 13, 1903, p, 348.
iriMiiiiidLi
Literature
597
An Earth Dam with Loam Core at Clinton, Mass, Bng. Rec. Aug. 20,
1904.
Brown, R. H. Grouted Rubble Core Walls for the Wetrs of th© Delta
Barraee, Egypt Eng, News. Feb, 9. 190&,
Walteri Raymond P. Belle Fourclie Dam, Belle Fonrche Project. S. D.
Eng. Rec. Mch. 3, 1906. Vol. ^3. p. 307.
Herechel, Clemens. Eta^rtli Dama with Concrete Core Walls. Eng> News,
Sept. 7 1905,
Leonard, J, A, A proposed Earth Dam with a Steel Core and a Rein-
forced Concrete Spillway at Ellsworth, Me. Eng. News, Sept* 7,
1905.
Scbnyler, J. D. Recent practice In Hydraulic Fill Dam ConstmctloiL
Froc, Am. C, E. Oct 1906.
BOCK FH-t DAM9,
I, The Otay Dam. Eng. Rec, Sept. 28, 1895, p. 310.
(S. The Nevada County Electric Power Company's Dam, Mln. ft Set Pr*
Felj. 8, 1$96.
3. A Rock-fill Dam with a Steel HeartwaJl at Otay, Cal. Eng. News, Mch.
10. 1S98.
4. Welles, A. M. The Castlewood Dam. Eng. Rec. Dec. 24, 189S. Vol, 39,
p. 69.
5. Hardesty, W, P. The Castlewood Rock<flll Dam and the Canal of the
Denver Land & Water Co. Eng, & Mln. Jour, Feb, 9. 1899.
6. Parker, H. S, East Canyon Creek E>am, Utali, Eng. Rec. Sept 2, 1899.
7. Dumas, A, Rock Dams with Metallic Reinforcement Genie CItIL Oct,
21, lg99.
8. The Goose Neck Canyon Dam. Eng. Rec Mch. 10, 1900.
9. The Cascade Rock-ftll on the Erie R. R, Eng. N#ws, Dec 27, 1900, toI.
44, p. 440.
10. Hardesty, W, P. A Rock-fill Dam with Steel Core Across East Canyon
Creek, Utah. Eng. News. Jan. 2, 1902.
11. Reconstruction of the Castlewood Dam. Eng. Rec, July 12. 1902,
12. The Plant of the Pikes Pe«ik Power Co. Eng. Rec. July 19, 1902,
13. Lake McMillan Dam, Pecoe River, N. M, Eng, Rec June 9, 1S91
MA so NaT DAMS.
1. Aflhhurst, F. H. Reconstruction of the Bhlm Tal Dam. Kumaon, India.
Proc Inst. C. K toI. 75, p. 202. 1881.
2. Hill, John W. A Masonry Dam. Trans. Am. Soc. C. E. June, 1887,
3. Tonsa Dam. Bombay Water Works. Eng. News. June 30, 1892, pp, 646-7.
Eng. Rec. Dec 19, 1891, p. 40.
4. New Croton Dam for the New York Water Supply. Eng. News, June 2,
1892, pp. 552-3. R. R. Gaz. Oct 14. 1892. p. 163-
5. Folsom Dam at Folsom, Cal. R. R. £ Eng. Jour. July, 1892. pp, 315-S.
f. Vyrnwy Dara for the Liverpool Water Works, England. R. R. ft Eng.
Jour. Sept 1892.
598
Priociples of Constructioa of Dams.
i
f. Goneraie Madonrr Dam of the ButU Cltf W^ter Compan?. Mq&ual
Ens. NewB, D«c. IS, 22^ 1192^ pp, 554 ft 58i.
8. Pfirl&r Concrete D&m ia India for IrrtKSilon Parpooea. Lon. Esr.
Not. 25, Dec 2, $. 1892. Eng. Eac Dec. Si, 1892, pp, &2-4.
S. Report of the Austin Bo&rd of Public Works, Austin. Texas, En& N«wi.
Jan. 26. 1S93. pp, 8S-90,
!(», Dam at AustEn* Texas. Eng Newo, Jan. 26. 18$3, pp, ST-SS,
11. HcCulloli, Waltar* Sodani Dam, New York, Trana Am. Soc, a E. M^^i
1393. YoL 23, pp. lS^-ld9. Dlacassion hj Members of Socuiy
Trani. Am. Soc. C. E. May, 1893, voL 2S. pp. 348-351.
11 McCuHoh, Walter Tbe ConstructfoQ of a Water Tigbt Dwn. Tin*
Am. Soc. C. E. Apn 18B3.
13. Ba«tn Creek Dam for Water Worka of Butte^ Mont Eof. News. Auj r,
1893, p. 130.
H, Dam & of the Stone Brook Portion of the Boston Water Works. Eaf
Rec. Nor. 4, 1893, p, 3G1.
15. Bettea, Stockwell. Determtnfng Minimum Section for DfarCaU MMom
Dams. Eng. News. Dec. 28, 1S93, toL 30, p. 511.
16. Masonry Dam at LaGrange, Cal, Eng, Ntwa. Harcb Z% ItH Eat
Rep. March 3. 1894.
17* Pellitveau, Albert Great Masonry Dam. Ann, 4aa Ponta et Cbausieci
May, 1894. -
18. Masonry Dam, CbemnitE Water Works, Germany. Eng. Rec July !!. I
1894, Jour* f Gaab. u Waas^rv. Sept. 1, 1894. Scl. Am. Sup
Nov. 10, 1894.
19. Snyder, F* E, Tbe Colorado River Dam at Austin, Texas. Eng. St^^
Aug. 2. 1894. E^ng. Mag. Nov. 1894.
20. Dunn lug's Dam. Eng. News. Oct. 18, 1394. Eng. Rec Oct 29, 18W-
21. Gould. E. 8. The Dunnlng^s Dam, Partly of Eartb and Partly of M
sonry. Trans. Am. Sac. C. E. Nov. 1894.
22. New Masonry Dam at Lonsdale, R, I. Eng. News, Mar, 14, 1S95
23. Van Buren, John D. Hlgb Masonry Dams. Trans. Am. Soi'. C. E, toI,
34, No. 6. pp. 495-520. 1S95.
24. Haller, Prof. The Bouzey Dam. Jour. f. Gasb. u, Wasserr. .Tune 5*
1895, et seq.
25. Overflow of the Sweetwater Dam. Eng. News, Aug. 15, 1895, rol. K
p. 111.
2S. Marstraud, O. J. Curved Masonry Dam for Water Works of Remicii«'<J
Germany. Eng, News. Jan. 30, 1896.
27. Flrtb. Charles. Concrete Dams on the Coosa River, Ala Eng. New^
Feb. 20. 1896.
2S. Sayagd, H. N. Repair and Extension of tbe Sweetwater Dam. En$, f^
March 12, 1896.
29. Tha Cold Spring, N. Y.. Concrete Dam. Eng, Rac. July 11, 1891
30. HcPMCheid and Cheminiz Water Works. Eng., Lend. Julv SI, 1S98,
31. New Arched Dam at Nashua, N. H. Eng, Rec. Aug. 8. 1S9S.
S2. Dahl, H. M. T A New Dam at Minneapolis. Eng'a Year Book UsJt oJ
Minn.. 1897.
Literature. 599
33. The Proposed Steel-Faced Concrete Arch Dam. Ogden, Utah. Eng. Rec.
Mch. 6, 1897.
34. Thompson, Sanford B. The New Holyoke Water Power Dam. Eng.
News. May 13, 1897.
35. Homey, Odns C. Ck)ncrete Water Power Dam at Rock Island Arsenal.
Jonr. W. Soc. Engs. June, 1897.
36. Schnyler, James D. The Construction of the Hemet Dam. Jour. Assn.
ETngng. Socs. Sept. 1897.
37. Schuyler, James D. The Hemet Irrigating Dam. Sci. Am. Sept 25.
1897.
38. The Muchkundi Dam. Engr. Lond. Oct 22, 1897.
39. The Hemet Dam. Eng. News. March 24, 1898.
40. Richter, Irving. An Unusual Small Masonry Dam. Eng. Rec. Nov. 26,.
1898.
41. Rafter, G. W., Greenlach, W., Horton, R. E. The Indian River Dam.
Eng. News. May 8, 1899.
42. Crosby, W. O. Geology of the Wachusett Dam and Aqueduct Tunnel.
Tech. Quar. June, 1899.
43. The New Masonry Dam at Holyoke. Eng. Rec. July 22, 1899.
44. Gould, E. S. Earth Backing for Masonry Dams. Eng. Rec. Dec. 23,
1899.
45. The Bear Valley Dam as an Arch. San Bernardino Co., Cal. Techno-
graph No. 14, 1899-1900.
46. The Tariffvllle Plant Plans of Hartford Elec. Light Company. Eng. Rec.
Mch. 24, 1900.
47. The New Water Power of the Hartford Electric Light Co. Am. Electri-
cian. Mch. 1900.
48. Flinn, Alfred D. The Wachusett Dam. Eng. News. Sept 13, 1900.
49. The Wachusett Dam. Eng. Rec. Sept 8, 1900.
50. A Concrete* Power Dam at Middle Falls, N. Y. Eng. Rec. Oct. 4 1900.
51. Stewart, J. A. Building of the Great Wachusett Dam. Sci. Am. Sup.
Dec. 15, 1900.
62. The Dam ft Power Station of The Hudson River Power Company. Eng.
Rec. Mar. 8. 1902.
53. Heaman, J. A. Description of a Dam and Accompanying Work Built for
the Water Commissioners. Can. Soc. of Civ. Engrs. Apr. 24,
1902.
54. A Concrete Dam Near London, Ontario. Eng. Rec. July 26, 1902.
55. Frechl, H. Construction of the Lauchenesee Dam. Eng. Rec. Aug. 30,
1902.
56. The Spier's Falls Dam of The Hudson River Water Power Company.
ETng. News. June 18, 1903.
57. Morton, Walter Scott A New Water Power Development at New Mil-
ford, Conn. Eng. Rec. Feb. 13 and 20, 1904.
58. Harrison, Chas. L., and Woodard, S. H. Lake Cheesman Dam and Re^
ervoir. Proc. Am. Soc. C. E. Aug. 1904.
59. Galliot, M. Reinforcement of the Grosbois Dam. Ann. des Ponts et
Chaussees, 1905.
Boo
Principles of Construction o! Dams,
€0- *f!ie Rooieyelt Masonry Dam on Salt River. Arizona. Eng. News. Jui.
12. 1905,
6L A Quickly Erected Eel n forced Concrete Dam at Fen el on Fafla, Out ^H
News. Feb. 9. 1905*
62. A Concrete Dam on a Pile Foundatioii at St. John '8 Lake, Ijans Ulaai
N, y, Eng. News. Feb, 9. 1905,
63, Qnarinl, Emile. Barosaa Dam, Southern Australia. ScL Am. AprU i
1905.
HoHow Reinforced Concrete Dam at Sebuyldrrtlle, K. T. Bn^. Newa.
April 27. 1905.
Blodgett, Geo. W. The Wachuaett Dam of the Metropolitan Water
WorkB. R. R. Gai,, vol. 39, p. 100. Aug, 4. l%m.
Dams for the New Plant of the United Sttoe Machinery Comiiaiiy, Be^
erly, Mass. Eng. Rec. Sept 2. 1905,
Shedd, Geo. 0. The Garvin 'i Falls Dam, Canal and Hydro-Eleetrtc Ptaut
Jour. Aesh. Eng. Soc, OcL 1905.
G<iwes, Chas. S, Chaagcs at the New Croton Dam, Proc, Am, Soe, C E-
Mch. 1906.
69, The Pedlar River Concrete Block Dam. Lynchburr W. Wks. Eng. Rk.
May 13. 1906.
TO. The Streeses on Masonry Dams. Editorial Review of Paper by ProL
Carl Pearson. Engineering. London, September, 1907.
71. The McCall'a Ferry HydiauUc Electric Power Plant. Eng* News,
tembcr 12. 1907,
I
64
65
66.
67.
68,
TIKBiS DiLMS.
S€|h I
L Parker. M, S. Biack Eagl© Falls Dam at Great Falla. Mont Tnni
Am. Soc. C, E. July. 1 890. vol, 27, pp. 56-59. Eng. Rec Oct i
1892. p, 295.
2. Sewell Falls Dam Across Merrlmac River, near Concord » N, H. Eofi
News. April 19, 1894.
Z. Parsons, G. W. CI o slug the Timber ft Stone Dam at Bangor, Ma Eof
News. July 26. 18S4.
4. Brown. Robert Oilman. Additions to the Power Plant of the Stftflda^*^
Consolidated Mining Company. Trans, Am. Inst Mining Eur*.
Sept. 1896.
5, Ripley, Theron M. The Canyon Ferry Dam, Canyon Ferry » Mont Joar.
Assn. Engng. Soc. May, 189S.
6. The Butte. Montana, Power Plant Eng. Rec. Mch, 5. 1898.
7, Carrol t ETugene. Construction of a Crib Dam for Butte City Water O^-
Butte, Montana. Jour. Absu, Engng. Soc. April. 1899,
S, The Reieonatructed Canyon Ferry Dam, near Helena, Montana. Eni
News. Apr, 26. 1900.
9, A l^rge Crtb Dam. Butte. Mont. Eng. Rec. Feb. 3, 1900.
10. Harner. Jos H. The Reconstruction of Big Hole Dam, Big Hole. MW^
tana, Jour. Assn. of Engng. Soc. Apr. 1900
Literature. 6oi
11. Tower, G. W. Timber Dam at Outlet of Chesunoook Lake, Penobscot
River. Eng. News. Sept. 1, 1904.
12. Woermann, J. W. A Low Crib Dam Across the Rock River
STEEL DAJiS.
1. Fielding, John S. The Use of Steel In the Construction of Dams. Can.
Arch. Aug. 1897.
2. Steel Weir, Ash Fork, Arizona. Eng. Rec. Apr. 9, 1898.
3. Steel Dam at Ash Fork, Arizona. Eng. News.. May 12, 1898.
4. Fielding, John S. Proposed Design for a Steel and Concrete Dam. Eng.
News. Nov. 16, 1899.
5. Bainbridge, F. H. Struc ural Steel Dams. Jour. West. Soc. Enpr. 1905.
6. The Hauser Lake Steel Dam in the Missouri River Near lledena, Mont
Eng. New. Nov. 14, 1907.
7. Wheeler, J. C. A Collapsibe Steel Dam Crest. ETng. News. October 8.
1907.
BEINFOBCED CONCRETE DAMS.
1. A Large Reinforced Concrete Dam at Ellsworth, Maine. Eng, News.
May, 1907.
2. A Hollow Reinforced Concrete Dam at Theresa, New York. ETng. News,
Nov. 5, 1903.
3. Reinforced Concrete Dam at Schuylerville, New York. Eng. News, April
27, 1905.
4. A Concrete Steel Dam at Danville, Kentucky. Eng. Rec. Dec. 3, 1904.
5. Reinforced Concrete Dam at Fenelon Falls, Ontario. Eng. News, Feb. 9»
1905,
DAM FAILURES.
1. Washout at the Pecos Dam. Eng. Rec. Aug. 26. 1893.
2. Failure of the Bouzey Reservoir Dam. Lon. Engr., May 3, 1895, p. 588;
Eng. News, May 9, 1895, p. 312; Lon. Engr., May 31, 1895, p.
883; Eng. News, May 23, 1895, p. 332.
3. Catastrophe at Lima, Montana. Irrigation Age, July, 1894.
4. Rickey, J. U. Failure of Dam at Minneapolis, Due to Previous Weaken*
ing Through Ice Pressure. Eng. News, May 11, 1899.
5. Failure of Masonry Dams. Annales des Fonts et Chaussees, vol. 7, No. 7,.
pp. 77-89 (1895).
6. The Johnstown Disaster. Eng. News, June 18, 1899.
7. Recent Events at the Castlewood Dam, Castlewood, Colo. Eng. Rec
May 19, 1900.
8. The Failure of Two Earth Dams at Providence, R. I. Eng. News, Mch.
12, 1901.
3. Destruction of Datns In the South. Eng. Rec. Jan. 11, 1902.
1^0. The Failure of the Dam of the Columbus Power Company at Columbus^
Oa. Eng. Nef^'S. Jan. 23, 1902.
6o2 Principles of Construction of Dams.
11. Failure of the Lower Tallassee Dam at Tallassee, La. Eng. News. Feb.
13, 1902.
12. Johnson, Robert L. Some Thoughts Suggested by the Recent Failure
of Dams in the South. Eng. News, Mch 20, 1902.
13. Hill, W. R. A List of Failures of American Dams. Eng. Rec. Sept 27,
1902.
14. The Break in the Utica Reservoir. Eng. Rec. Sept 27, 1902.
15. Whited, Willis. The Failure of the Oakford Park and Fort Pitt Dam.
Eng. News, July 23, 1903.
16. Robinson, H. F. Construction, Repairs and Subsequent Partial Destruc-
tion of Arizona Canal Dam. Eng. News, Apr. 27, 1905.
17. Murphy, E. C. Failure of Lake Avalon Dam, near Carlsbad, N. H. Enf.
News, July 6, 1905.
CHAPTER XXV.
APPENDAGES TO DAMS,
305, MDvsiBle Dams, — The height of a dam is limited in the mati-
ler hereinbefore described. It will be noted that the limit is that
iposed by high water conditions and that, as a rule, the water sur-
icc during low stages could be raised to a considerable amount
nthout interference with the riparian owners, if at the same time
lood conditions could be provided for. In order to provide such
>nditions, movable dams are sometimes constructed which will
*rmit of raising or lowering all or a part of the structure as the
n^ 36S* — V. B, Movable Dam on PUe Foundation, McMeclien, W. Vi. (l?kif,
Newa, YoL 54, page lOOJ
stage of the water requires. These flexible portions of the dam
may consist of a gate or series of gates which can be raised or
lowered. Sometimes a considerable portion of the dam is made
flexible by the construction of a bear trap leaf, which is usually
raised and lowered by hydraulic pressure, and by means of which
the head of water can be readily and rapidly controlled. Sometimes
Movable Dams.
605
entire dam is made movable by the use of Cbanoine wickets
^«e Fig^, 368) and similar types of dams, a part of which may be
^novable while other parts are folded down on the bed of the
■r-eam, allowing the flood waters to pass over them. Most of such
Fig, 370,— Tainter Gates for Morria Plant, Ecanomy Light and Power Co.
onstructions are expensive and are used most largely on govem-
nent works for the control of rivers for navigation purposes.
The objection to movable dams for water power purposes is
hat the reduction in the elevation of the head water by their use
ommonly su reduces or destroys the head that the continuity of the
6o6
Appendages to Dam
power output is intemipted. The same objection also applies 10
any gate, flash board or other device designed to reduce tlie head.
Such reduction is usually made during conditions of flow undfr
which the natural head that would obtain is already at a minimum,
306. Flood* Gates. — Flood gates are quite commonly used h
water power dams to control or modify extreme flood hetgbti
These gates are commonly designed to be raised so as to perniitj
the escape of the water underneath them. The tainter gate,]
Fig. 371^— Hoist for Tainter Gates of Northern Hydro Electric Power Odl
some of its modifications, is perhaps most widely used for this pur-
pose. Fig, 369 shows a plan, elevation and section of a tainlj
g^te, designed by L, L. Wheeler* resident engineer of the
and Mississippi Canal, for the U. S, Government dam at Stef^
Illinois. This is one of a series of tainter gates designed
flood control of the Rock River at that point. The gates af
ated by an overhead hoist which can be moved from gate (ril
when it is desired to manipulate them,
Fi^' 370 is a section of one of six gates designed by the wild
for the Morris plant of the Economy Light and Power Conipani
FloodGatea*
607
Fig. 372,— Tainter Gates at Upper U, S. Gov. Dam, Appleton, Wis.
Fig, 373,— Ta!Dter Gatea at Lower U. S. Gov. Dam, Appleion, Wis.
Flashboards.
609
These gates are operated by a movable hoist, similar to Fig, 371,
irhich travels on a track on the brige above,
F>&s- 372 and 373 are views of the steel tainter gates constntcted
n the upper and lower U, S. Government dams across the Fox
^tvcr at Appleton^ Wisconsin.
In the dam of the Southern Wisconsin Power Company at Kil-
loum, Wisconsin, the rise of the flood water is so great (about 16
cet) that it was found impracticable to const met lift gates to re-
luce the flood heights. In this case the writer has divided the crest.
fig. 375. — Flush Boards and Supporta, Rock ford Water Powjipr Co,
by piers, into twelve sctions. Between each two piers a twenty-
five foot gate is placed (see Fig* 374) which can be lowered into the
dam six feet, thus reducing the extreme flood height by that amount.
These gates are of steel and weigh about seven tons each. They
may be operated by an electric motor or may be manipulated by
hand, should occasion require.
307. Flashboards. — ^Tbe control of limited variations in head is
commonly accomplished by means of flash-boards wliich are widely
ed for this purpose. The simplest form otf flash -board consists
6io
Appendages to Divms,
of a line of boards placed on the crest of the dam (see Fig. 3751
usually held in place by iron pins to which the boards arc com-
monly attached by staples* The object of Rash-boards is prind^
pally to afford a certain pondage to carty the surplus water itm
the time of minimum use of power to the time of maximum detnani
Incidentally, the head is raised and the power is also increased in
this way. The supports of the flashboards should be so arranged
that they will withstand only a comparatiyelly low head of water
flowing over the boards, and will be carried away if a sudden
m^-
Fig. 376. — Automatic Drop-Shutter for Betiva Dam, India.. (Bd£. Sttt
June it 1903J
flood should raise the head materially above a safe clevatioa If
the boards are so supported as to withstand the discharge of hetvj
floods, they will form a permanent portion of the dam and increase
its fixed elevation to such an extent as to create damage which their
use is supposed to avoid. Sometimes the pins supporting thCj
boards are made so light that they must be held in position bj ia
clined braces. These braces are sometimes supplied with stt
eye*boUs through which is passed a cable. A large steel washc
is attached at one end and a winding drum at the other* (Sec Fij
375), Commonly, if a flood is anticipated, the boards are removi
and stored for future use. If, however, a sudden flood should arii
the inclined braces are removed by winding up the cable an
the pressure on the flash-boards bends the pins and the hosLfi^
are washed away. The expense involved by the loss of flash^boards
Head Gates and Head Gale Hoists,
eii
is not excessive as one set will commonly take care of the entire
summer low water period. The expense involved in their use 1%
:herefore only the cost of one set of flash-boards per year.
Sometimes the flash-boards constitute a permanent bt!t adjust-
ible part of the dam and arc lowered automatically during stages
>f high water* (See Fig. 376). On some dams, especially at
jvaste weirs of canals and reservoirs where the fliictiiations in
leight are inconsiderable* the dam may be provided with a foot
>ridge which makes the whole crest of the dam accessible at all
imes and from which the flash -boards can be readily adjusted.
rhis plan is used on the dam across the Chippewa River at Eau
Fig, 377,— Adjustable Flaah Boards at Eau Claire, Wii.
Claire, although this river is subject to high floods. (See Fig. 377).
Ordinarily, on rivers stibject to such conditions, this type of con-
struction is impracticable*
In some dams, instead of gutes or flash-boards, vertical stop
planks or needles arc used. These consist of planks or squared
timbers that are lowered vertically into position, stopping off the
opening partially or wholly, as desired. They are commonly sup-
ported by a shoulder at the bottom of the opening and one or more
cross beams above.
308* Head Gates and Head Gate Hoists.^-It is usually desirable
to control the water at the inlets to the headrace by the use of gates
:iich may be closed in emergencies or for the purpose of making
6l2
Appendages to Dams.
I
fr
6 14
Appeodages to Dain^
necessary repairs or modifications in the race^^ay through which
the water is diverted to the plant. In northern rivers it is also
found desirable to prevent the entrance of ice into the raccwij
either by the construction of a Boating or fixed boocn In front oi the
gates or by constructing a system of snbmerged arches cither b
front of, or as a part of, the gateways. By means of snch constnjc-
tioo the floating tee or other floating material may be diYCfled froio
tlie raceway and passed over the sptliway of the dam^
The head gates must be sufficiently substantial to allow the net
to be emptied under ordinary conciitions of water and to pnsted
the race^vay under flood conditions.
Fig. 378 shows an elevation of the head gates, designed by ^
writer for the power plant at Constantine, Michigan* These ire
shown in detail "by Fig. 379. A rear view of these gates from the
race side is also shown in Fig. 38a These gates are double wooden
gates with concrete gateways and are arched over between the
piers so as to permit the passage of men and teams. These gata
are designed to pass about ^jooo cubic feet per second.
Fig. 3S1 shows a set of double wooden gates, the posts and braca
of which are made of structural steel designed by the writer f<K tke
power plant of Mr. Wait Talcott, at Rockford, Illinois,
In the Cbnstantine g^tes the gate mechanism is geared for fair!?
rapid operadoii by two meik The Rockiord gate apparatus is very
simple, the gate being handled with a capstan bar by a siogk m»st
but at a much slower ^»eed.
Ftg. 382 sho¥rs the movable head gate hoist designed by die
writer for the c^ietatiOQ of the head gates at the Kifbooni pbnt of
tlte Somthem Wisconsin Power Company.
J09. Fi^Ways^'^In almost eTcry state fishways are re«j
law in any dam constmcted om natural waterways. The^ fis!
imys smst be so arranged as to permit the free passage of fish tif ^
the stiemm,
Fif * 3S3 shows a concrete fishway bnilt by the writer in ccw^
necUoo with the og<ee conocte dam constructed across the Vc
million Riv^ at DAnviIle« ItEnois. Fig. 384 is a fishway deslgne
by Mr, L. L. Wlieeler and cottstraded in the dam at Sterling* '<
aojs. The Sterling dam is a thnb^ crib dam and the fishwty !
cmSElriicted of timber. Fig. 385 shows the type of Bshway
iMftied by the Fidi Comwis^oa of the State of Wi
onltnarilT used tn tliat state.
6i6
Appendages to Dams.
Head Gates and Head Gate Hoists,
Fig. 3S2.-Head Gatis Hoiet, Kilbourn, WIb. tScuthern Wisconsin Power Ca)
The purpose of these fish ways is to afford a gradual in c line
through which a continuous stream of water of comparatively low
velocity shall flow and against which the fish may readily swim.
Both the inlet and outlet should be below low-water and the out-
let should be in such a position that the fish, when they ascend the
stream and reach the dam, in passing from one side to the other in
searching for a passage, are naturally led to the point where the
6i8
Appendajjes to Dams
Fishwayi*
6x9
Fig. SS4,— Timber Flsliway In Dam at Sterling. IlL (Eng. Newe.)
Fig. 383.--FiBhway of Fish Commiaalon, State of WiBC^onslB.
620
Appendages to Dams«
flowing water is encountered. The slope of these Ushwars sbodd
not be steeper than one vertical to four horizontal, and the water
should be so deflected that the velocity will be reduced as low i5
possible. A fish way should be entirely automatic and free iituE
all regulating devices. It is usually desirable for the opening h
Si-£¥B*M
SPtLLWA r SECnOH
Log- Ways-
621
Jio. Log- Ways, — The free navigation of streams for legging
mrposes is provided by law in most states and it is therefore neces-
iry where logging is practiced to provide ready means for their
issage over or through the dam. This is accotnplishcd in the
Fir. 317-^ — Log Way at Lower Danij MioneaiwJIflp MtniL
Kilbourn dam (see Fig. 374) by the lowering of any one of the
flood gates.
Fig. 386 shows a plan and section of the log-sluice constructed in
the Chesuncook timber dam on the Penobscot Riven A section of
the spillway of the dam is also shown in the same figure.
Fig. 3S7 is a view of the logway in the lower dam at Minneapolis.
This sluice is only six or eight feet in width, and the depth and
quantity of water flowing is controlled by a bear trap leaf,
9ti
63a Appendages to Dams.
In most cases, to avoid an excessive waste of water, it is desk*
able to build the logway as narrow as possible. Under such ^
tions it becomes necessary to guide the logs into the sluice by 1
ber booms which, leaving the sluice at a low angle, are strung i^
stream to such points that the logs in floating down stream M
enter between them and be guided to the sluice opening*
UTERATUlia
1C07ASLS DAM3, FI.ASHB0ABD3« KTO^
1, Harcourt, Li V, FUed and Movable WeirB, Proc, Ins. C. E. VoL fii
p. 24. Jan. ISSO.
2, Cbittenden. Hiram ftl American Types of Movable D&ms. Eng, N«n
Feb. 7, 1S95. VoL 33, p, 81
B. StlckneTp Amos. Lifting Dam. Jour. Abbu. Eug. Soc Vol. 16, p. 33i
June, 1896.
4. Tbomas, B. F. A Design for a Movable Dam. Jour. Assn. E^g: Sdc»
VoL 16» p. 260, June. 1856.
5. Chittenden, H. M. Modified Drum Weir. Jour. Abso. Eng. Soc. Vd
IS, p. 249. June, 1S9G.
6. Powell, Archibald 0. Movable Dams, Sluice and Lock Gates of Ibe Bei^
Trap Type. Jour. Aaao, Eng. Soc. VoL 10, p. 177. Jaae, nU.
7. Marshall, W, L. Marshali*s Bear-Trap Dams, Jour. Assn. Eag. Sot
Vol. 16, p. 21S. June, 1896,
S. Jonea, W. A. Bear-Trap Weirs. Jour. Assn. Eng, Soc. Vol. Ifi, p. 2^
June, 1896.
9. Jolinson, Archibald. Bear-Trap Gates in the Navigable Pass, Sandy Uke
Reservoir Dam, Minnesota. Jour. Asan. of Eng. Soc, Vol li
p. 210. June, 1896.
to. Martin, Wm. Bear-Trap Gate lo Davis Island Dam, Ohio RiTer. Jour,
Asso. Bug. Soc. Vol. 16, p. 208. June. 1S96.
11. Movable Dama on the Great Kanawba River. Eng. News, ttdL S6, p. i2i
Dec. 31, 1896.
12. Needle Dams. Ann, dea Fonts et Chaussces. Part 11. IS 97*
13. Bear-Trap Dam. Chicago Drainage Canal, B. VL Gaz. Feb. 12, 1897.
14. The Use oC Rolling Shutters tn Movable Dams. Genie Civil. May I. Wl
IB. LArmlnie, J. C. Falling Shutters, Godavery, Anient* Ind. Eng. De:
18, 1897.
16. Thomas, B. F. Movable Dams. Tra^s. Am. Soc. C, E. Vol. 39, p. Ul
Mar 1S98.
17. Bear-.Trap Dam for Regulat[ng Works, Chicago Drainage Canal. Eag-
News. Mar, 24, 1898.
15. The Movable Dam on the Big Sandy River. Q^nta CirU. May II, ISftl
19. Marshall Automatic Movable Dam. Eng, News. May 29, 1S9S.
w.
Literature. 623
). The Management of Non-parallel Motion and Deficient Operating Head
in Bear-Trap Dams by Auxiliary ConBtructions. Bng. News.
May 26, 1898.
L New United States Qovernment Needle Dam at Louisa, Kentucky, on the
Big Sandy River. Eng. News, vol. 40, p. 2. July 7, 1898.
I. The Chittenden Drum Dam. Sng. Rec. Vol. 40, p. 356. Sept. 16, 1899.
I. Claise, M. The Resistance of Dam Framing. Ann des Fonts et Chaus-
sees. 4 Trimestre, 1899.
I. A New Automatic Movable Dam. EIng. Rec. Vol. 45, p. 222. March 8,
1902.
5. Reconstruction of the LAke Winniblgoshish Dam. Eng. Rec. Vol. 46,
p. 250. Sept. 13, 1902.
C. Hilgard, K. EL Roller Dams. Schwelzerlsche Bauzoitung. Bd. 43 8.
65 u. 86. Feb. 6-13, 1904.
.7. ^oechlin, Rene. Large Rolling Dams. Genie Civil, Feb. 27, 1904.
!8. Guarini, Emile. Rolling Dams at Schwelnfurt, Bavaria. Eng. News,
vol. 53, p. 57. Jan. 19, 1905.
M. Walker, Gilbert S. Pile Foundations for Movable Dam at McMechen,
W. Va. Eng. News, vol. 54, p. 100. July 27, 1905.
10. Movable Dam and Lock of The Rice Irrigation and Improvement Assoc.,
Mermentau River, La. Eng. News, vol. 54, p. 321. Sept 28, 1905.
|1 Movable Crest Dams at the Water Power Development of the Chicago
Drainage Canal. Eng. Rec. Vol. 56, p. 194.
H Johnston, C. T. Masonry and Steel Head Gates of the Grand Valley Ir-
rigation Canal. Engineering News, VoL 50, p. 141.
M. Hanna, F. W. Electrically Operated Gates for the Roosevelt Dam. Eng.
News, vol. 57, p. 586.
•i Qaona, F. W. Hydraulic Gates for Drainage Tunnel, Kern River Plant
Eng. News, vol. 51, p. 326.
US. Leighton, M. O. High Pressure Sluice Gates. Jour. West. Soc. Eng.
Vol. II, p. 381.
^ Gillette, H. P. The Rudder Boom. Eng. News, Vol. 47, p. 473.
nSHWATS.
^ Gerhardt, Paul. Flschwege and Flschteiche. Verlag Von Wilhelm En-
gelmann. Leipzig, 1904.
2- Leslie, Alexander. Salmon Ladders in Scotland. Institute of C. B. Vol.
89, p. 304.
CHAPTER XXVL
PONDAGE AND STORAGE^
311. Effect of Pondage on Power. — ^The terms "Pondage" and
"Storage" are quite similar in meaning, both having reference to
the impounding of water for future use. The term pondage us-
ually refers to the smaller ponds which permit of the impounding
of the night flow for use during the working hours of day. Stor-
age, on the other hand, is usually applied to the larger impounding
reservoirs that enable a sufficient quantity of water to be stwed
to carry the plant, to some extent at least, through the dry season
of the year. Between these limits every variation in capacity is
of course possible.
In Chapter IV, Section 54, the effect of pondage on the power
of a stream is briefly outlined and illustrated by hydrographs
shown in Figs. 41 and 42. The pondage illustrated by these dia-
grams is sufficient to store the entire flow of the river during the
parts of the day when the power is not in use and reserve it for
those hours of the day when the power is needed. Such a condi-
tion can frequently be realized for the low flows during the dry
seasons, but the capacity is seldom sufficient to store the larger
Hows, and if sufficient should be investigated in a different manner
to be discussed later. These hydrographs (Fig^. 41 and 42)
should therefore be examined with these points in view.
In many water power installations practically no pondage is pos-
sible and the power of the stream must be utilized as it flows or
otherwise it will be wasted. On continuous service, such as i**
sometimes required by cotton factories, paper mills, and electro-
chemical works that run twenty-four hours per day, pondage is not
so essential. With most power loads, such as are shown by the
various load curves in Chapter XVII, the night load is small and
the pondage of the night flow will frequently permit of more than
doubling: the power that can be otherwise utilized.
312. Effect of Lrimited Pondage on the Power Curve — Fit-
quently limited pondage only is possible and its influence on the
possible power that can be generated must be carefully investigated
Effects of Limited Pondage oii ine Power Curve, 625
I ( power IS to be used for a limited number of hours each day, the
^ate at which power can be used for this time withoiu pondage will
fee the same as for the continuous power of the stream*
Such proportions of the otherwise unutilized flow of the stream
^s can be impounded during periods of light load can be added to
t:he daily output. Thus, if power is used for 12 hours per day, and
\he night flow can be impounded and utilized during the day, the
day power will be increased to double what it otherwise would be.
If power is used for only ten hours per day, with' perfect pondage
the day power will be increased to 24 of what it would otherwise
be.
In twelve hours there are 43,200 seconds, and in each acre there
arc 43,560 square feet, it can therefore readily be remembered that
for twelve hour pondage there must be practically as many acres
one foot deep (or acre feet) in the pond as there are cubic feet per
second to be impounded. For ten hour use and foiirteen hour
storage, the pond area must be increased by one sixth above the
capacity needed for twelve hour service. For example: In order
to utilize the full flow of the Wisconsin River at Kilbourn in twelve
hours, (see Fig. 39) on the day of lowest flow (in August, 1904), a
pondage of 3,000 acre feet would have been necessary, and, to util-
ize this full flo%v in ten working hours, would have required a pon*
dage of about 3,5^0 acre feet.
Where the depth of pondage is considerable the effect of the
variation in head on the power should receive careful consideration,
313. Power Hydrograph at Sterling, Illinois. — In 1903 the writer
was retained to investigate the probable effect, on the water power
at Sterling, Illinois, of the proposed diversion of water for feeding
the Illinois and Mississippi or "Hennepen" Canal,
The pondage formerly available at Sterling, by using eighteen
inch flash boards on the dam, was about 42,000,000 cubic feet (al-
most 1,000 acre feet).
The diversion dam at Sterling has been constructed about one
mile above the dam of the Sterling Hydraulic Company and has
limited the available pondage to an area of about 5,000,000 sq. ft.,
and a pondage of about 7,000.000 cubic feet. This change has there-
fore caused a loss of pofidage of about 35,000,000 cubic feet, which
represents the night storage (i* e,, the storage during the fourteen
hours of night), of 700 cubic feet per second, which represents 980
hydraulic horse power for the ten hours of day. That is to say, —
the loss of 35,000,000 cubic feet of storage capacity caused by the
\^m Effects of Pondage oq Other Power. 627
construction of the U. S. Government dam near the mouth of the
mUnois and Mississippi Canal, has lost to the Sterling HydrauUc
*<;ompany about 980 hydrauHc horse power during such periods as
the flow of the river is more than 840 cubic feet per second, and
less than the capacity of the wheels installed (i. e., 4,450 cubic feet
per second).
Fig. 388 gives a graphical illustration of the effects of storage on
the normal water power at Sterling and the loss resulting from the
loss of storage. The lower flow line is the line of the normal hy-
draulic horse power of the Rock River for continuous (twenty-four
hour) service. It also shows the total power available for ten-hour
service without pondage. The flow line just above the Hne of
normal power, and parallel thereto, shows the additional ten-hour
power available from a pondage of 7,000,000 cubic feet. The upper
flow line sho%vs the tcn-hour power made available by the storage
of 42,000,000 cubic feet. The hatched area between lines two and
three represents therefore the loss in ten-hour power which has
been caused by the loss in storage of 36,000,000 cubic feet
From this diagram it will be noted that when the flow of the
river is sufficient to supply the wheels, no loss would be occasioned
by the loss in pondage, and, as the flow approaches this point, the
actual loss decreases. It should also be noted that when the flow
of the river is less than 840 cubic feet per second (above the
amount diverted by the canal) the total storage of 42,000,000 cubic
feet is more than necessary to store the night flow, hence the loss
at such times caused by loss of pondage also decreases.
The approximate total loss of power for the year caused by the
loss of 35,000,000 cubic feet of storage, as measured from this
diagram, is 980 hydraulic horse power for, approximately, 250 ten-
hour days.
314. Effect of Pondage on Other Power, — The pondage of water
during the night naturally interferes with the normal flow of the
stream and alters the regimen of the river at points below the point
of pondage. The effect of such interference on other power, and
the effect of other ponds on the plant contemplated, should be
carefully considered.
Fig, 389 is a hydrograph of the Fox River taken from observa-
tion by the Government Engineers at Rapid Croche, Wisconsin*
Above this point are a number of water power dams. Many of the
plants run twenty-four dally, but close down on Sundays. The cf-
628
Pondage aod Storajje-
S
<
OKOaiS Uld 133i 3Jan3 iJ 3Slftll39lll
ffect ofErnSed i^torage.
539^
feet of the Stinday shut-down on the stream flow is well shown in
the hydrograph and is evident even during flood periods.
315* Effect of Limited Storage. — When the pondage available is
more than sufficient to carry the night flow of the low water period
over for day use, it becomes possible to equalize, to a greater or less
extent, the variation in daily flow and to utilize excess flow to in-
crease deficient flows, thus raising the quantity of available contin-
uous power. The extent of this equalization depends on the quan-
tity of storage and can readily be in%^estigated graphically.
Fig* 390 shows the estimated daily flow of the Wisconsin River at
Kilbourn for July, August, and September, the low water period)
T904, From this hydrograph it will be seen that the lowest flow 19
3,000 cubic feet per second. From Sec, 312 it is seen that in order
to utilize the night flow during the twelve hours of day, a pondage
of 3,000 acre feet must be available. With such a pondage the
IBJQOO
ii 12,0
m
e 10.0
•^ 4.0
u
i 2,G
iiiliiHiiiiiiiifiniiiinniimis
': l?!!f ! !•! ! I'm !!i!E!il~!l ■! !~B!!P! ! !
Illi' illii[liiil!lflllil!SI^^!:ia:l ill!"!!! t 81! !!»;
III! 1^1! Il{l!l!l!l!ll! mill I »!!!!! 8!^! !8 I' III! 8j!
t^i4 n nil iiiiiiiiiiiii I Hill I iiiiiii mill III It iHi III
;jii mt IIIIIIIIIIIII I mil 1 iiiiiii iiiiii 111 ir 11 tii
III im iiiniiiiiiii I mv 111 in 11 111 m 11 rii
III uii ^iiiftiiiiii I liin I iiriiii III 11 III sir 1 11 1 m
III Jill niiiiiiiiiii I mil iKmm tmm 1111 luh 1 iiii 111
^MiiiminiiiifH
t iiiimiiii mmmummmu m ,^i ^^^^?^ yun^u 11 un mn in
raisi i!iiii;iSin i^iiyi iiiiiii i!i.i«ii^i 111 iiiii si
iiiiiiiiiii IIIIIII nil ] IIIIIII til III III nil III II mil ni
iiiiiiiiiii iiiiifiiiiii iiiiiii IIIIII iiiiiiiiii II. mil 'III
illlllllllllilliilliijijiiillllliilliiiiiiliiH^
JULt AUGUST SEPTEMBER
Fig, 390.— Low Water Flow at Kilbourn aad Storage Capacity Necessary to
Augment It to Various Amounts,
tiig^ht flow can ordinarily be distributed so as to be available either
for twelve hour constant power or to furnish power for any equiv-
alent load curve.
In Fig. 390 the horizontal spaces each represent a flow of i,Oqo
cubic feet per second, and the vertical spaces, one day. The area
of each space therefore, represents 86,400,000 cubic feet, or ap-
proximately 2,000 acre-feet.
To increase the low water flow of the river to 4,000 second feet
will require a storage capacity equivalent to that represented by ap-
proximately three spaces, or a storage of 6,000 acre-feet in addition
to the pondage, or a total storage of about 9,000 acre feet To b-
630
Poodage and Storage.
crease the flow to 5,000 second feet, a total storage of 28,000 acr^
feet in addition to the pondage would be required; and a flow of
6,000 second feet, will require a storage of 90,000 acre feet in iddi-
tion to the pondage. In this latter case the conditions to Sept. ekij
must be considered, for the increased flow from August 12th to 17th
is not siiflScient to fill the reservoir, although it will reduce the
capacity required, as will also the increased flow of August 201b.
The reservoir capacity represented by 90,000 acre feet is show
on the diagram both by the curved hatched area above the flow-
line and by the recta ngfular shaded area as welU
If the reservoir capacity is known, and Its equivalent repre-
sented on the drawing, its effect on the hydrograph can readily be
determined by trial, (See also Fig, 393.)
316. Effect of Large Storage, — When large storage is available,
the daily flow of a stream can be equalized and its variauons there-
fore becomes less important. In such cases the power of a plant
depends on the average weekly or monthly flow of the stream %n4
the possible storage capacity,
S* B. Hill, C E., has suggested a method of discussing the effect
of storage on the flow and power of a stream which is welt illu^
trated by Figs. 391 and 392. These hydrographs were prepared by
the writer to illustrate a report on the probable power of a pro-
posed hydraulic development in the South. Figs, 391 represent
the mean monthly flow of the river in question for the years rl
to 1906 inclusive. In this case the scale above the zero line sliowsj
both the mean monthly flow of the stream in cubic feet per se^|
ond and the mean monthly power of the stream in horse powci
hours per day with the head available. The available stoimg? >*^^
here 51.000 acre feet or 2,221,560,000 cubic feet. This sttiragt i
equivalent to a flow of 857 second feet for thirty days, or a
age of ener^, with the available head, of about sjogo,ooo horje|
power hours.
The maximum daily continuous power (see A-A» Fig. 391^ M
determined by the efl"ect of the driest year (viz. 1904) on the st€f-|
age. The eflfect of the dry periods on the storage is shown byi^^M
incisions into the lower or storage line of the diagram, h^^\
year 1904 the reservoir capacity would have been just exha
in order to maintain the power during the low flows of Septc
October and November of that year. The amount of available c^l
tinuous energ>' (i. e. the position of the line A*A) is deicmiifi^M
Effect of Auxiliary Power. 631
by equalizing the deficiency in flaw during the dry months with
the total reservoir capacity.
It is important in the study of storage to see that in the inter-
vening periods of excessive flow, such flows are sufficient to
supply the deficiency occasioned by previous demands on the res-
ervoir, otherwise the effect of one dry period must be considered
in its relation to subsequent periods in determining the available
continuous power (see Fig. 391, 1897 and 1898).
The daily flow of this river for the year 1904 is shown by the
hydrograph, Fig. 393, from which it will be seen that with pondage,
but without storage, the available power of this stream would be
limited to a minimum of 27,000 horse power hours per day.
317. ££Eect of Auxiliary Power. — In order to maintain a con-
tinuous power greater than that due to the minimum flow of the
stream plus the pondage, some source of auxiliary power must be
available. If it is desired to increase the power of the stream rep-
resented in Fig. 391 by 50,000. horse power hours per day, making
the total horse power hours delivered 163,400 (represented by line
B-B, Fig. 392), auxiliary power, as represented by the shaded areas
on this diagram, would be needed. As at all other times water
power would be available, the addition of steam auxiliary power
would apparently be warranted. The size of the plant needed to
furnish such excess power would depend on the method of power
utilization. It is evident that during the dry periods in 1899, 1904
and 1905, if the water power was first used to its maximum, and the
storage exhausted, an auxiliary plant would be needed of a capacity
almost equal to the maximum demand on the plant, and that a
plant of less capacity could be utilized satisfactorily only by operat-
ing it to a considerable capacity whenever a considerable draft be-
gan to be made on the storage. As the extent of the drought, or
deficiency of water, coaild not be anticipated such a use of the
auxiliary plant would require a greater expenditure of auxiliary
: horse power hours than is represented by the shaded areas in Fig.
f 392.
I An investigation of the capacity and amount of auxiliary power
^ needed, without pondage or storage, to maintain a given continu-
ous power, can be readily made from the hydrograph of daily flow
^s shown by Figs. 394 and 395 which represent such a study of the
Rock River at Sterling, Illinois, before the diversion of water for
^se in the Illinois and Mississippi canal, and the probable addi-
lasa
Fig. 3dh— Mean Monthly Flow of
2
O
m
IE
Ul
0.
Fig. 392.— Amount of AoxilaTrl
Sect Thereon o£ a Given ELeaervoir Capacity,
182000 £
I3S00O >
108000 ?
BIOOO-j
54000 10
27000 g
0 X
a
liM^eflfle Output by 50,000 B. F. H.
634
Pondage and Storage.
>:
I
8
I-
'""'"V
' i
O ' '
#
•Tf?"'"'
"^ i^t^' L
a
m
41 p
'-7
t
4
^.j -*"
. =k ^ ^^
-r- -"^''^
T f.
0
i
0
2
■3
SI
a
I
BO
'puoaag jaj iss j ^IQiiO ^T ^Si^qasia
Calculations for Storage.
635
lal auxiliary power required to maintain the same power after
li diversion.
x8* Effect of Maximum Storage. — As the head increases the
ntity of water needed to develop a given amount of power de-
ases» and storage becomes of much greater relative value. The
|age of comparatively small quantities of water also becomes
tore simple matter, but conditions which need little consideration
h larger flows and lower heads, then become more important- In
h cases, relatively, large reservoir capacity sometimes becomes
394. — Hydrograph Showiag Auxiliary Power Necei^ary to Maintain
4450 Ten 'hour Horse Power at Sterling, IlL
•«t^
395. — Hydrograpli Showing Auxiliary Power Needed to Maintain Ca^
paclty of Wheels and Prob&ble Increase Due to Dlvereien of Water
for Illinois and Mfssissippl CanaU
isible and only the questions of desirability and cost limit^ the
tent to which snch storage may be carried.
319. Calculations for Storage. — Rippl has owtlined a method of
imputing storage which may occasionally be used to advantage
ider high head conditions, when it is desired to utilize the average
w of a series of dry months or years hy extensive storage. This
^od consists in graphically representing the net yield of the
L.
636
Pondage and Storage.
stream during the period oi low flow and from the curve of the net
flow estimating the quantity of storage necssary for its full utilka*
tion.
The method suggested may be illustrated as follows:
From a study of the hydrographic conditions on the water shed
for a considerable term of year, the period of extreme low flow
is selected. For this period the observed or estimated flow of the
stream for each month is reduced by the loss due to evaporation,
1M0.0O0
T00.000
1D0.O00
Fig. 396. — Diagram Illustrating Rippl Method of Calculatfng Storige.
seepage, etc. The remainder represents the net quantity of mtter
available for power purposes, The summation of these monthlv
balances, added one to the other consecutively can be platted in a
rurye in which the abscissa of each point represents the total tinic
from the beginning of the period ; and the ordinate, the total quan*
tity of water available during the same interval* The scale niay
represent inches on the drainage areas, cubic feet, acre feet, or
such other unit as may be desired. Such a curve is represented iti
Fig. 396 by the irregular curve A-B-C-O-E-F. The inclination ^
the curve at any point indicates the rate of the net flow at lliatpaf*
L.
J
^P Calculations for Storage- 637
ticular time- When the curve is parallel to the horizontal axis^ the
flow at that time will just balance the losses caused by evapora-
tion, seepage, etc. A negative inclination of the supply line shows
that a loss from the reservoir is taking place.
In a similar manner the curve of consumption can be platted.
For most purposes this can be considered a straight line as the var-
iation in the use of power from season to season is a refinement not
usually warranted, unless the uses to which the power is to be put
at various times of the year arc well established. In Fig. 396 a
scries of straight lines of consumption arc drawn, representing the
use of water at rates of 100 to 600 acre feet per day. These rates
correspond essentially to rates of from 50 to 300 cubic feet per sec-
ond.
The ordinate between the supply and any demand line represents
the total surplus from the beginning of the period considered, and
when inclination of the supply line is less than that of the demand
line, the yield of the drainage area is less than the demand and a
reservoir is necessary.
The deficiency occurring during dry periods is fot^nd by drawing
lines parallel to the demand line, or lines, and tangent to the curve
at the various summits of the supply curve, as at B.
The maximum deficiency in the supply, and the necessary capac-
ity of the reservoir to maintain the demand during the period, is
shown by the maximum ordinate drawn from the tangent to the
curve itself. Tlie period during which the reservoir would be
drawn below the high water line is represented by the horizontal
distance between the tangent point and the first point of inter-
section of the curve. If the tangent from any summit parallel to
any demand line fails to intersect the curve, it indicates that, during
that period, the supply is inadequate for the demand. To insure a
full reservoir it is necessary that a parallel tangent drawn backward
from the low points on the supply curve shall intersect the curve at
some point below. For example: The line B-7, representing a daily
consumption of 700 acre feet, does not again intersect the curve
and is therefore beyond the capacity of the stream. The line B-S
intersects the curve at E and is the limit of the stream capacity.
Such a consumption will be provided by a storage of about 150,000
acre feet as represented by the length of the line 6-D, and such a
reservoir will be below the flow line for about twenty-two months
during the dry period illustrated in this diagram. That this reser-
voir will fill is shown by the intersection of the lower tangent D-A
d
Pondage and Storage,
with the curve near A. The conditions necessary to maiiiiam
capacities of 500, 400 and 300 second feet arc shown respectively by
the tangents E'5, B'4 and B'3, and the verticals 5-D, 4-C and 3*C
If the amount of storage is known, and it is desired to ascertain
the maxim urn demand, that can be satisfied by such fixed capacity.
I
Wl.
"^— (
KKIHI
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tAH
---4., J 1
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Fig. 397. — Diagram Showing Annua] Run-off from Tohickon CreeK,
the rate is determined by drawing various tangent lines from the
Summits, having the maximum ordinates equal to the fixed storage
the rate is det remined by drawing various tangent lines from the
summits, having the maximum ^rdinates equal to the fixed storage.
320. Me^od of Stara^^e Calculations, — The results of calcula-
tions, as outlined in See, 319 for various conditions of storage ou
Tohickon Creek, are shown in Table XXXIX and Fig. 398. To-
hickon Creek is one of the possible sources of water supply which
has been investigated by the City of Philadelphia for a constderabk
period. The observed monthly rainfalls and stream flows from the
drainage area of this stream (in inches on the drainage area) ik
given in Tables XL and XLL The five year period of tnipit«yi
flow is found by inspection to run from December, 1893, to Noveni'
her, 1898, as show-n by Fig. 397. Tlie approximate evaporatioo du^
ing the period is taken from Appendix F,
The calculations of the mass curves are based on the extrei^e
variations in reservoir area of o to 100 per cent ; that is, on the »s*
L.
Method of Storage Calculations.
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643
TABLE XL.
Tohiekon Creek^Monthly Rainfall in Inehes
Year.
OS
<
4J
*3
u
0
>
0
a
86
4.I0
6.01
4.763.42
7.14
4.53
5.47
1.08
1.30
2.59
5,16
3,83
49.45
m...
4.24
5.47
3.072.42
2.59
5,77
8.13 5.30
3. 36
1.93
1.42
6.63
50.22
m.->
5.31
4,34
5. 23.4. OS
3.03
1.69
3.20.8.07
8.32
4.06
3.66
4.35
55.. 34
89...
4.23
2. a?
3.67^4.90
5.4T
6.94
12,334.63
5.815.75
7.92
4.57,
8. 86
1.99
68. C^
90...
2.82
4.n
6.77 2.48
G.30
3.93
2.U8
6.31
1.07
2.75
51.60
91...
G.H
4.58'
4.791*97
2.83
3,88
7.498.90
1.87
3.81
1.97
5.09
52.32
.92...
5.49
1.23
4.131.95
5.66
3.20
4.27
3.76
2 91
.64
7.10
1.57
41.60
®3...
2.96
6. 88
2-464.96
4.98
4.05
2.10
8.97
3.20
3.72
4.37
3.17
60.52
m...
1.82
3JJ6
1.65 2.91
13.60
2.63
2.2a
2.03
9.44
5.18
3.01
4.60
53,01
[96...
4.19
.90
3.n'
5-50
2.99
4.49
3.53
4.43
.68
3.86
2.11
2.57
38.24
m...
I.IS
7.90
5,44
L48
3.18
4.07
8.06
1.63
5. S3
2.67
4.08
.94
46.46
m...
2,20
3.10
2.46
3.20
8.90
5.10
8.47
4.75
1.92
1.83
5.02
4.64
H^.69
ids...
4.19
3.38
2.S4
3.73
7.62
.76
4 Of J
^1.05
2.03
5.21,
3.56
3.49
46.92
m...
3.6S
4.75
6.60
2,19
2,23
2.74
3.29
5.05
6.70
1.39
2.65
2.34
43.61
Average..
3.64
4.08
4.04
3.33
4.74
3.95
5.42
4.93
4.16
3.71
3.33
3.78
4t).ll
TABLE XLI.
Tohiekon Creek — Monthly Discharge in Inches on Drainage Area,
frv V
Year.
i
c
m
K
<
OS
n
►-1
1^
<
0
0
i
1
^....,
4.36
9.19
4.28
4.75
3.43
1.41
.77
.69
.03
.05
1.91
2.38
32.66
^...
5.04
5.25
3.84
1.02
.93
1.21
1.63
1.96
.40
.25
.26
3.20
24.98
^...
6.38
6.72
6.27
4.28
,52
.15
.06
1.77
5.50
1,54
3.11
3.47
39.77
*89,,.
4.38
1.61
3 86
2.88
1.70
2,29
6.41
3.75
3.441
2.33
7.97
1.92
42.40
^..-
2.06
3,78
6.37
1,79
S.09
.75
.87
.92
1.2L'
3.54
.69
1.61
26.59
^1...
6.15
6,68
6,03
1.68
.28
.17
.90
8.92
.94
,46
.63
4.27
30.01
«2.,.
6.53
1.19
4.87
.84
2,05
.70
.51
.30
.19
.09,3.19
1.67
22.13
^...
2.22
6.64
4.64
3.22
3.79:
.45
.10
1.56
.83
.60
2.62
3.10
29.67
04...
.80
3 80
3.09
2.28
8.68
.53
.19
.12
3.37
2.10
2.67
3.57
31.10
^..-
3.95
1.70
5.37
4.65
M
.27
.80
37
.03
.09
.13
.67
IS. 69
%...
.54
1.59
6.48
.78
.30
.18
2.54
.19
1.12
i.oe
2.34
.80
19,87
97,,,
1.81
2.92
2.19
1.55
4,63
1.71
2.68
.73
.12
.07
1.79
4.Ck8
24,28
as...
3.70
4.05
1.83
2,50
6,04
.19
.07
.74
.08
.60
4.50
4.23
27.55
»»....
4.72
5.56
8.99
1.57
.25
.07
.08
1.02
2.26
.19
102
1.28
27,01
Average..,
3.69
4.26
4.70
2.50
2.08
.76
1.15
1.10
1.361.20
1.89
2 89
27.56
itnption that the reservoir may occupy from nothing to the en-
fe drainage area.
The conditions on the reservoir area are those due to the equal-
^tion of the rainfall with the evaporation, seepage and other
644
Pondage and Storage*
losses* The conditions on the balance of the water shed arc given
by the run-off and its summation.
Table XXXIX shows these calcniatiDtis in dttail and the mass
curves drawn from columns 6, lo, 14* 18 and 19 are platted in Fig
398. The maximum continuous power which could be matntamcd
throughout this period without storag« is shown by the lowest
slopes of the zero per cent, mass curve. The possible maximum de-
velopment of the stream with various percentages of reservoir ara
can be determined by an analysis of the lower curves similar to diit
described in Sec, 319,
321. Analjrtrcal Methods, — Graphical methods Oif computaltos
have been heretofore suggested as a means of investigating pondi^
and storage conditions. Such methods are believed to be advanti^
geous in most cases on account of presenting visible evidence whi
can usually be more clearly understood than an abstract analysis,
Analj^ical methods for the consideration of these questions iff
usually obvious after the graphical methods discussed are under-
stoodj and such methods should usually be used to check up tijf
graphical deductions. Such methods may be illustrated by the
lowing analysis of the effect of low water conditions on a pn
water power on a Western river on which the writer recently
nished a report
In this case daily guage readings were available for about
years, and the rainfall records were available for a considerabl
longer period.
Froin these records it appeared that the year 1905 was tlie d\
year on record, and that the power available during the low ^vat(
period of that year would have been equalled at least at all timo
during every year in the past twenty years, and with a probable liiit^
result in the future.
At the proposed plant eacli cubic foot per second, flawing durinf
a day of twenty-four hours, will, at So per cent, efficiency, ptoiv^,
3.63 continuous horse power. In order to develop 8,000 twenty-foarj
hour horse power, it would be necessary, therefore, to have
able a continuous flow of 2,200 second feet, while the minimiifp'
in 1905 was only 1240 second feet. An examination of the gaif]
ings shows that during the dry period erf 1905 the water was den*
lent in quantity for sixty-eight days. The average flow for this ^
riod was 1^700 second feet, causing an average deficiency of™
second feet. To impound sufficient water to maintain 2,200 secoco
feet would require, therefore, a storage capacity of about 1,000 acr*
Literature. 645
feet for each day of the dry period, or a total reservoir capacity of
about 68,000 acre feet. Above the proposed dam site is a lake hav-
ing an area of about 60 square miles or 38,400 acres. By raising the
level of this lake two feet a storage oi 76,800 acre feet would be at-
tainable which, with careful manipulation would be sufficient* to
maintain the desired power.
If no storage were possible, and auxiliary power was to be es-
tablished, the maximum capacity of the auxiliary plant would be
determined by the day of lowest flow. During this day there was a
deficiency of 960 second feet, equivalent to about 3,500 horse power
The average deficiency for the period was 500 second feet, rep-
resenting a necessary average of auxiliary power of 181 5 horse
power, or 43,560 horse power hours per day. The total auxiliary
power for this period (68 days) would therefore be about 3,000,000
horse power hours.
In the same manner the total amount of auxiliary power neces-
sary during each year could be estimated and the interest and de-
preciation on the cost of the plant, plus the average annual operating
expenses of the auxiliary plant, when considered in connection with
similar elements of the water power installation, would furnish
the basis for an estimate of the first cost and operating expenses of
the combined plant to develop the required power.
LITERATURE.
1. Rippl, W. The Capacity of Storage-Reservoirs for Water Supply. Insti-
tute of Civil Engineers, vol. 71. p. 270.
2. Fitzgerald, Desmond. Report on Capacity of the Sudbury River and
Lake Cochituate Water Sheds in Time of Drought. New Eng.
Water Works Asso.
3. Fitzgerald, Desmond. Methods Used to Determine the Best Capacity to
Give to Basin No. 5, Boston Water Works. Asso. of Eng. Soc.
Vol. X, p. 431.
^- Greenle«f, J. L. A Method for Determining the Supply from a Given
Water Shed. Eng. News, vol. S3, p 238.
5. Horton, Theodore. A Form of Mass Diagram for Studying the Yield of
Water Sheds. Eng. Rec. Vol. 36, p. 185.
^. Tumeaure and Russell. Public Water Supplies. Chapter XV. JohK.
Wiley ft Sons.
'^- Mead, Daniel W. Report on the Water Power of the Rock River at Ster-
ling and Rook Falls. HI. 1904.
CHAPTER XXVIL
COST, VALUE AND SALE OF POWER.
322. Financial Considerations. — Every engineer who is calW
upon to advise as to the commercial feasibility of a proposed water
power development must car ef ally consider all financial aspects oi
the project, for on its financial feasibility the entire commercial suc-
cess depends. It is not enough that the power be constant and suffi-
cient in quantity, that the plant be well designed, and that the cost
of the same be reasonable ; but there must also be a market in which
the power can be utilized to advantage and the price at which thf
power can be sold in competition with all other sources of power
must be sufficient to pay all expenses involved in the constrncticut
and operation of the plant and afford a fair return to those who a*^
sume the risk of the undertaking.
It is a common belief that any water power development imistk
profitable. Knowing that an undeveloped water power is a contin-
ual waste of energy, it is commonly assumed that the saving of this
waste is bound to result in a profit to those who acquire the prop-
erty and develop the power That many water powrs can not be de-
veloped at a profit under present conditions is a fact which in miny
instances is learned by its owner only after a large and unwarranted
expense is entailed,
323, Purpose of Development, — Any water power project mnit
be examined in the light of the purposes for which it is to be used
or the market it is to supply. The supply must be constant and con-
tinuous not only for every day in the year but for every year of its
operation unless its U5e will permit of the discontinuation of the
power during droughts, high water, or other contingencies that
will decrease or temporarily suspend the generation of powder by the
plant.
If its use or market will permit of such interruption, a temporarjf
power may sometimes be developed to advantage. Where the
power furnished must be continuous in order to avoid losses or
great inconvenience, precautions must be taken to so design Xht
plant with duplication of parts, extra units and suitable pondage or
Cost of Development. 647
storage or with such sufficient auxiliary sources of power that in-
terruptions shall be essentially obviated.
In some cases considerable losses have been entailed by hydraulic
developments constructed without sufficient study or consideration
of these questions. In such cases, the plants after completion, were
unable to maintain continuous power, without the installation of
auxiliary steam plants for use during the temporary interruptions
to which the plant was subject, and the income from the sale of
power would not warrant the extra expense and hence the plants
were commercial failures.
334. Cost of Water Power, — The cost of water power depends on :
First: The investment in real estate, water rights, power plant
and equipment, transmision lines, sub-stations, distribution system,
etc., and the interest which must be paid thereon.
Second : On the loss from the depreciation of the various elements
of the plant, the cost of maintenance and repairs, the cost of con-
tingent damages from floods or other accidents.
Third: The operating expenses, including labor, oil, waste, and
other station supplies and expenses, including also in, hydro-electic
plants, the patroling and maintenance of the transmission lines and
distribution system.
Fourth : The expenses for taxes, insurance, etc.
The total annual cost due to the above sources of expense is the
annual cost of the power to be furnished by the plant, be the quan-
tity of that power much or little.
The investment charge should be liberally estimated and should
include the entire expense of development including auxiliary power
plant, if needed. All contingencies should be carefully considered
and estimated. A serious error in the estimate of cost caused by
large and unexpected contingencies in construction may mean a
commercial failure of the enterprise. The same consideration
should be given to the estimate of contingent expenses, deprecia-
tion and operating expenses, and each other factor on which the
financial life of the plant depends.
325. Cost of Development. — ^The various conditions under which
water power is developed gjeatly affect the cost of development.
As a general rule, other things being comparatively equal, the larger
the power developed the smaller the cost of development per unit
capacity. This is particularly true when developments of various
capacities are considered on the same stream. Many of the features
^H 648 Cost, Value and Sale of Power. '
^M of th€ derelopmcnt must be essentially the same regardtess of tbc
^H ultimate capacity of the plant. This is especially true of dama
^H sod river protection work. The variation in cost per unit capidt]r
^H of various seized plants is well iHustrated by Table XLIX. ^^
^^H TABLE XLIL S
^^^^^^ Eitinutte of ths 6&$t of a Budro-EUctric Plant a^ Niagara FalU.* ^
^^^H Ituo.
24-Hous 1*0 wsB CAPAcrrr.
60>0O0 H. P.
Development.
75^000H. R
Developmetit.
leo.ooo ap,
DcTSlop^
meat.
^^1 Tiinpi^l tflili-rar* ,..,,,.,
11,260,000
450,000
500,000
300,000
1,080,000
760,000
350,000
100.000
75,000
11,260,000
450,000
700,000
460*000
1,440,000
910,000
525,000
100,000
75,000
|l,25O.fl00
7Q0,W}
1,40^ r»^
^^M f lead works and can&l t..<4..>.«
^m wh^i pi*
^^B pr\|^<Af> ^i\t|f^fl , ,
^^H Hydraulic equipment * .**.^-,
^H Efectric eqtiLpitient .,..
^H TraDiformer etation and equipment. .
^H Office building and machine shop. . ,
^^B Mifl'i*'Hlflr'fHf>Tii'. , ,,,...
^H Enfpneenng and contingeudeB 10 per
^^1 T!pnti . . # p i< . t * t , ,. .
$4,865,000
485,000
$5,900,000
500,000
^H Interest, 2 yearB at 4 per cent*
15.3.50,000
430,560
$0,49(1,000 1
&29«584
$7,m(mJ
15,786,560
$7,019,584
$S,«31,l«l^
^^^^^^^ Pf* 1" hi>rFfi-p^'\vpr 1
$114
$m
^ 1
^H * First report of tl yd ro- Electric Fuwer Commission of tha Province of Oatin^^B
^H page 15. ^M
^M Other things being comparatively equal, the cost of developmeotH
^m varies inversely, although not in the same ratio, as the head. Be^^B
^1 reason of this is evident from the fact that while the pc^er of ^^M
^M stream is directly proportional to the head, the capacity of 3 tu]tme^|
^P increases as the three-halves power of the head. With double t^^B
^1 head the power of a wheel is increased almost three times, ^M
^B For moderate changes in head, the cost of the turbines will van^^B
^B in proportion to their size and not their capacity; so that the co««^H
^B per unit of capacity will usually decrease considerably with tbf^B
^B head. The cost per unit of capacity of other features of w^terpowe ^B
^B plants will also frequently decrease as the head increases. Thisi^^
Cost of Development.
649
particularly true of pondage capacity which increases in value
directly as the head increases, although the cost per unit of land
overflowed may remain constant. The relative cost of high and
low head developments may be illustrated by the comparative cost
of two plants recently designed by the writer which were of ap-
proximately the same capacity but working imder diflFerent heads.
The comparison is as follows:
TABLE XLIII
Oomparatim Cost of Water Povoer Plants,
Head.
Coot of Water Poweb Development.
Capacity.
Without
dam.
With
dam.
With dam
and electrical
equipment.
With dam, electrical
equipment and
transmission line.
8,000
8,000
18
80
68.60
21
86
39
115
60
150
90
TABLE XHV.
Estimates of the 0ost of developing various Comachian power from Reports of
Ontario Hydro'Bleetrie Power Commission.
LootlSoii of PropoMd DeTolopment
Natur-
al
head.
Avafl.
able
head.
Power
develop-
ed, H. P.
Estimated
capital
cost.
C!oBt
Coet per
H. P. per
ft. head.
<1) Bealar's Fklto, Lower Trent River. .
no
ao
8S
18
18
80(5,
420
12
78(7)
78
27
810
40
8000
5<!00
QOOi
3200
3200
1600
1383
2287
4000
750
1200
8400
1100
2400
1867B
8S40
16350
88-»0
8086
1848
1675000
47.V)00
425000
3500 0
870000
325000
2.70000
291000
3600JO
115000
1T9000
l»i000
124000
214000
83SO0O
619700
815000
600000
857600
2C00.0
$84.38
91.37
69.67
109.88
115.63
203.12
187.58
87.50
153.88
149 16
81.25
181.82
89.16
61.00
91 .00
50.00
73.00
97.00
141.00
nVI4^ V^ll*. T^«4>r Tiwnt River. . r t
Rauney's Fftll
BApid8abov«Ol6ii Miller
Baplds above Traaton.
<t) MaMaml RfTor.
•••••••*
Itoaver RlTer (Eosenla Falls)
Sevetn Rlrer (BiE Cliota)
sooA^ittJSn.J?!:.:".!!^
^i| BL Lawrenca River. Iroqnola, Ont.
Mtaitefpiil River, Hbrh FalliTonC. A
847
847
89
89
81
81
Miaitaiippi River, High nUie. One. B
_
va. (6)
noladlnj
Head we
5Sj00fe<
>rksand 0
9t of head
anal less ex
water tunn(
pensive tt
lan ordin-
6SQ
Cost, Value and Sale of Power,
I
S
0
04
(S
el <d^ qa S et ^ ^ eg « e}
00 SSSSqq^SSSmSS
3
to ^o ^
8
■g
S SSS^SiSSSg :g
52 *CT o
1^
O CI
0-
I
o
I
J- .> ^ *
o u ^ h !*
m
pH p-o *-4 p4
Cost of Development.
6Si
II
So
I
S
a
o^'O^'d'c «* e^ g
9i
08
O P4 0*»<
S gSSSSSSSSS 8 888SS
00 ^ ^ 00 lO CO 00 ^ O ^^ 00 OO O CO QQ 00
rH i-(f-l r-i rH i-i C«i rH i-i « rH Cl rH
a -"
58
i
n ooooi-ii5o
8 S«»*-
8
i88S^
r-l O 0)lO CI CDOCO
ssa
o
28S§*S
111
00 00^
rHrHCO
525S
'co»ooo
»98
S » <ri
■feS
^»*' m fli rt '^
• ^ « « 4
•tit o •«
>-^ i
QQ g S
li|
Jit
: OS
• a
o g sfc 2
o-^ffi^S^J
J It!
S" 111
I
HI III It
lis sis 1^
m 111 It
III sU il
llifitl Iff
1^! ! I Tl
6$2 Cost, Value and Sale of Power. V
The estimates of The Ontario Hydro-Electric Power CommisiIi^J
of the cost of various hydro-electric plants proposed hi Ontarifl
furnish a good example of the variations in the cost, per umtil
power, of various plants under various conditions. These cstimitdj
are shown in Table XLIV. 1
Tlie actual costs per horse power capacity of various complete
American and foreigpi plants are shown in Tables XLV and XLVl,
respectively.
326* Depreciation. — ^In every operating plant there is in the
course of time a certain deterioration or reduction in value due to
ordinary operation and the effect of the elements. In the considers
tion of any power plant as an investment, allowance must be made
in the annual charges for a sum sufificient to keep the original in-
vestment uitact. In order to accomplish this an allowance should
be made on each feature of the plant for the annual redaction ia
value or deterioration. The amount of depreciation will v^ary witi
the character and use of the machinery or structure and shoojd be
estimated with the best possible knoweldge of the conditions utidex
wliich the plant will be operated, fully in mind. Such estimate*
should be sufficiently large to fully cover this item in order that the_
feasibility of the project may be correctly estimated.
The allowance for depreciation in an operating plant should
placed in a sinking fund which should be used to replace the vari-_
ous portions of the plant at the expiration of their useful life.
33 7, Annual Cost of Developed Powen — As already pointed oof
the annual cost of operating a plant includes:
a. Administration and operating expense,
b. Mamtenance and repairs.
c. Depreciation.
d. Interest, insurance and taxes.
Each of these items will vary with the duration and the condi*^
tions under which the power plant is installed and operated, The_
method of estimating these charges in shown in the following esti-
mates of the cost of operation of the Chicago Sanitary District'
Hydro-Electric Plant (see Electric World. Feb. 28, 1906),
Total coat of development and trariemisaioii •••.., f3»fi0O,OOO.tO ^
K8TIWATB OF COST.
Interest on in veatment at 4 per cent . » ,,,..,,.*, $1 40, 000. 00
Taxes on real estate baildingi, etc 7, 2)60 00
Depreciation on buildiiigs at 1 per cent S»650.0(?
Cost of Distribution. 653
Depreciation on water wheels at 2 per cent 2, 027.82
Depreciation on generators at 2 per cent. 1, 824.60
Depreciation on pole line at 8 per cent 2,020.50
Depreciation on other electrical appliances at 8 per ct. 8,905.52
ToUl fixed charges $161,137.94
OPERATING EXPENSES.
Power and snb-station labor. 63,240.00
Repairs to machinery and buildings 8, 700.00
Incidental expenses. 1, 200.00
Operating Lawrence avenne pumping station 43, 960.00
Operating 39th avenue pumping station 120, 380.00
Interest on investment 89th avenue pumping station. . 15, 599 . 76
248,079.76
Total cost to saniUry district $409,217.70
G^Mcity 15,500 H. P. Gostper H. P. per annum $26.40
An interesting comparison of the estimated yearly cost of various
Hydro-Electric generating plants is given in the various reports of
the Ontario Hydro-Electric Power Commission which are repro-
duced in Table XLVII-
328. Cost of Distribution. — ^Having estimated the annual cost of
the development of power at the plant, the cost of distributing the
power to the customer must also be considered. In many power
plants the power is generated at or near the point where it is to
be used and the transmission losses and costs will include its trans-
mission through shafting, cables, and belts, or by electrical means,
to the machine or appliances in which it is to be utilized. In other
cases the power has to be transmitted for miles by high voltage
electric currents. The units of power for which the power com-
pany will receive compensation may or may not include these
various transmission losses. Where the power is distributed to a
factory, the losses in transmission though shafting, belting, etc., is
usually at the consumer's expense; but the transmission loss in
long distance lines is ordinarily assumed by the power company
and must be taken into account in the determination of the cost of
furnishing power to the consumer The losses in any system of
distribution are a considerable element of the cost of the delivered
power and must be carefully estimated. (Sec. 20, page 24, et seq.)
The losses in the distribution of power in various mills, factories,
etc, as determined by Prof. C. H. Benjamin, are given in Table
XLVIII. The reports oi The Ontario Hydro-Electric Power Com-
mission, to which references have already been made, furnish nu-
nierous clear analyses of the cost of electrical distribution. Table
«554
Cost, Value and Sak of Power.
XLTX shows such an estimate for the delivery of power from a
proposed Niagara plant to a proposed sub-station at Hamiltoti,
Ontario. Table L shows the estimate of the Commission on the
cost of distributing power from a sub-station to an individual cm-
sutmer not within the local distribution. Tlie variations in the
cost of power from the generating plant to the consumer is also
well shown by Table LT, taken from the same source.
TABLE XLVn.
Estimated yearly operating expenses of generating plant from JUpmit 4
Ontario Hydro-Electric Power Commtssiom
LocatjoQ of PloQlh
V
hi
m
III
III
til
it
EE
II
1
1
1
1
nf
n^
P
(tl K[A£&)fft Dluit*.. *«•«**««
mm
75000
100000
5^;oo
SHOD
isoo
1333
4000
ftS07
mm
STSOO
49(KI
7«80
VX70
L300
£400
noo
»400
lasTS
6840
35:^50
|fi7900
Toaoo
80300
11HT5
10075
484^
411111
17483
£3713
6864
mi
6380
O^fiO
13760
l(Si75
]43^^
nono
6000
172GD0
%oa
1S500
saooo'
STM
mil
BSTi
&iig
SH40
fl€91
wm
104^7
lOtta^'
1T1J27
11478
11034
3868
106900
U95O0
950G
«7fia
SS4T
8671
14000
88il
»491
431621
lactr
im^
1O078
(1S34
tl$1400
saoaoo
19000
400QU
S0&4
4534
14000
£5940
n&i
TT7T
AW
S539
ffl4T87
s^mei
K4006
1430S
10*00
05000
^44S30
SlllflO
ustva
£4171
di II
<f) Middle FaUa,.. ,»
I0J1
HcaJe'y^i Falb^..,,.^....
Via
Two a^Qve combiBed. . . «
<9) Maitlaud Blf or,.. **♦,*..
9H
SauiTdea Bl^r.. ..•.«....
Ekmlh tElver » . * . . . ^ * * . . < j
l^*
4^;«......
Severn H4fer(BSg Chai&)
Sj9vorn and Bdarer RlYArt
Ci) St. tJkwrBiice RJver « * > * *
41114
SeMT
aiUM
MlsalSAlptii ELT^r High
Falls .»»*,.*, .,,
MUial^Jppl Mrer HJ^b
Ildutreal HItot Fuiitit-
lain FAill>««***4< * '
1h\ DnOf T^kll......
Canief"^ Rnpldfl. ■ 1 1 1 1 f r t
»..
Slate Fallt **..*•.
Jtter
Z,
'IjicLudiQiT lO-jear aluttlng f utid.
To make the delivered current available for power, a motor
must be installed. This is commonly furnished by the consumer.
Table LI I shows the estimated cost of induction motor service per '
horse power per year.
339, Effect of Partial Load on Cost of Power, — The majdmuni
amount of work that any plant can accomplish will be done only
when the plant works to its full capacity for twenty-four hours per
b.
Cost of Distribution.
655
19 AOa d«40H
s
3 S
sags ^isissig
-jaitmoo jad
I-* ^-tpH M ^4
s
s
ij -b^ oat 1*1
^ 11^ I i
^ ^ *, ©
o Is I
— * o ,
S 3 3 S
00 000
01 e^wiQJDj\i
*5 t*«
1/5 id
C^ 00 CO Ob t^
:g
.s
JO jaqtuHK
s s
0000 ^ a>
r-4 IQ l,'3 t-m,
S§
SiiiS
JO js<)ainj;
S l:;
3SS
s 3
ep M O ^
^ ^ .-* -H
u? ■— •
8-S
i-i O i-r
lA LA r^ LO r^ O P
jA*-i c^ M pi
e^ e^ -r coc^-*
i^C0O^*-«COW tHVi
ipM»C^^Ol04^CqM
^oOqsje^C*
s s g
ii5 ** iM
!S ?i
CSi r^ FN
^ OC iQiO
3
I
656
Cost) Value and Sale of Power*
TABLE XLIX.
Showing investments, annuul chargeB, and cost of low tension power at itjft^
station. {Sub-station included.)
Full bid.
U load.
Mlo«L
Total boraepower distributed ..,,..,,...
Total investment, including step -down
stations ftnd inteTGwitehing * *
Invesetment per H- P* delivered , . - -
Total annual retmim, depreciation, pa-
trolling and operation, ,....,. p
Administration, 10 percent of repairs, etc.
Annual interestj 4 per cent of investment
Total annual charges , «... p «•..,,, .
Coat of 24>hour power, including !iue aud
step*down sun-station kjaaee. .»,,.,*.♦.,
Coflt of transmitting and traaafomiing
Total coat of power.
1*3,000
$450,879
28 IS
22,496
2,250
18,035
12,000
f404,879
33 73
19,092
1,&09
16,195
8,000
|35S,S79
41 Sa
1,565 m
142,781
112 69
2 67
137, 196
112 49
3 10
|31,55t
$12 0^
115 36
|15 59
|ia2»
The above casta of power are billed on an assumed mt6 of fl2,00 per 24*^001
horse-pciwer per annum lor high-tension power at Niagara Falia.
TABLE L,
ShotMng aofff of distribution from municipal substation to an indindmt
corutuTneTt not cotk?r6d bj^ locul distributioTi.
Distance in
miles from
municipal
lub-station.
Cost pek Hohsb Poweh pkk Annum fob tub DixrrEKV
OF Various Amouxtsof Foweb.
50 H, P. 76 H. R 100 H.P. 150 H.P, 200 H.P,
2
a
I
5
8
10
12
15
$3 5S
6 89
7 92
8 87
10 20
14 10
16 12
18 76
22 74
f4 20
5 20
6 18
7 18
a 24
10 14
12 13
14 03
17 08
13 53
4 41
5 20
5 98
6 77
8 40
9 54
11 12
IS 48
$2 92
3 60
4 27
4 96
6 38
6 97
8 31
10 12
10 39
Cost of DIstributioQ.
657
TABLE LI.
Al*0tn3T OF POWZB DSLTTERED.
FtiUload, 2,0OOH. P.
MJoad, 1,500 H.P,,.
Hload, 1,000H. P...
CoiT OP 24^ Hoc & PowEM pia H* P,
PER Ann DM,
At Niagara
Fails iticlud-
iDg line and
etep'down
Bub station
losses.
At
aub-fitatton.
IIS 54
13 IS
12 85
121 SO
23 54
27 21
At
customer.
$20 03
29 06
34 48
TABLE LTL
Capital oaH and annuai charges on motor inataUations.
FOljpbafle SS-cjde, inducUoa motora.
Capacity H. P,
5
10
15
25
85
50
75
100
150
200
Capital
cost per
inatalled.
$41 00
39 00
35 00
28 00
25 00
24 00
21 00
20 00
17 00
16 00
Annual Chaboes,
Intereat
5 per cent.
12 05
95
75
40
26
20
05
00
85
SO
Deprecia-
tion and
repairs,
6 per cent.
Oil, care
and
operation.
Total per
H, P, per
aunnm.
|2 46
$4 00
2 34
3 00
2 10
2 60
1 88
200
1 50
1 75
1 44
1 50
1 26
1 25
1 20
1 00
1 02
80
96
70
f8 51
7 29
6 35
6 28
4 50
4 H
a 56
3 m
2 67
2 46
day. Thus, if a plant has a capacity of one thousand horse power
and IS operated continuously during the twenty-four hours, the
total output will be twenty-four thousand horse power hours of
work. Under such conditions the plant can be built at a minimum
expense per unit of output and the cost of operation, fixed charges,
interest, etc., will be less per unit of work done than under atiy
I other condition of operation.
€58 Cost, Value and Sale of- Power I
For example: If a plant of one thousand horse power be installed |
at a cost of one hundred thousand dolars^ the annual cost of opera-
tion, including fixed charges and all other legitimate expenses, may
be estimated as follows: ' J
Interest on |100»000at6 per cenL*, ,...., f C,Ot(U
Ke pairs and depreciation. p..,. 5|3D0
Operating ©xpenaas - .,-,,,.,, 10,000
MLicgI laueoiis and contingent expensea , . ^ **,.,,,..,. 4 , 250
^p Total anntml cost of power , ,,,, $Jo,650
On the above basis the annual cost for each horse power of maxi-
mum load will be $25,55. If the plant works at its maximum capac-
ity for twenty-four hours per day, the cost per horse power hour
will be .292 cts* If, however, the plant is operated to its full capac-
ity for 12 hours per day only^ the total cost of power may be reduced
to say $23,000 per annum* In this case the cost per horse power
of maximum load will be reduced to $23.00 per year, but the cost
per horse pow^r hour of energy generated will be increased to
.526 cts» In many cases the plant will be used for ten hours per
day and for six days per week* Its maximum capacity may be
utilized only occasionally^ and the demand for power will vafy
greatly from hooir to hour resulting in a load factor of perhaps 50
per cent, or less. In this case the annual cost per maximum horse
power will still not exceed twenty- three dollars {$23)) per year,
but the annual cost of average ten hour power will be forty-stx
dollars ($46), and the cost per horse power hour of useful work will
be increased approximately to 1.5 cents. The cost of each unit of
powder under the last condition is over five times as great as in the
first case mentioned, and about three times as great as in the second
case discussed. It is therefore obvious that unless the conditions
of use are carefully studied and conservatively estimated, they may
lead to unfortunate investments and financial losses,
330. Cost of Auxiliary Power, or Power Generated From Other
than Water Power Sources* — It frequently becomes necessary to cs*
timate the cost of power plants and of power developed from other
than water power sources* This is necessary in order to determine
the probable cost of auxiliary power plants and such auxiliaf^ri
power as may be needed to assist a water power plant at tini«^l
when the hydraulic power is deficient. It is also necessary to deter*
mine the cost of power with which the hydraulic plant may be
called upon to compete*
Cost of Auxiliary Power.
659
For a correct estimate of such cost, it is necessary to determine
:he efficiency of the various parts of the plant (see page 31) under
ill conditions of operation in order to correctly determine the actual
:ost of power due to the conditions of operation. The conditions for
naximum efficiencies are seldom met in actual operation, and the
:ost of generating the power is increased by the irregularities of
>perating conditions. In all power plants the effect of partial or
rregular load affects the cost of power in the same manner as al-
eady described in Section 328.
IWit
nw^ — 1
_ J"
|r
I
IffOl
1 ~l~
1
I]
t^J 1 1 j_
im -- --
i ™ Ti
M Tl
rt II
ir\m
a_l_
fr t
....... ^,
"Ba^
Of
_ ■ ^ 2
m. n. \.
II Itt^^S^^-
fillx £^^
'*E5±^-^.J
Ztz^^~^U%mQ^- -
'h:?::::'$
j:- = -5:;:|S3]^gyg^
[-^-^
'^1 1 r
= ^*--
«i-^^bJ^y^
j^ ?^m^ :^'PJ^^4^r[- i z 7
•'3r =. ,
:4dri.r:^
- — r, -
I ' ' -' i 'X
1 i 1 ; 1 1 1 1
,, 1 i
^ rr_ Ijik
_ ^ .^ im
t»o
Jm
ISO
Fig. 399. C!oBt of Steam Power per Horse Power per Annum in VariooB
Plants.
By far the largest amount of power generated is from fuel and
by steam plants. The cost of the development of steam power is
modified by the cost and character of coal used ; the size and char-
acter of the machinery operated; the character of the load (that is,
the load factorj ; the number of hours during which the plant is used
per year ; and the skill and ability of the engineer and fireman who
have charge of the plant. Observations of the actual cost of de-
66o
Cost, Value and Sale of Power,
veloping power must therefore form the basis of any accurate e^ti-
mate of the cost of power production.
Mr. H, A. Foster* made actual tests of twenty-two dififereni
power plants, including manufacturing establishments, electric
light stations, pumping plants, etc, and deternrined for each phtit
the power consumption per annum and its cost, ir.cluding not cmij
running expenses but fixed charges. The cost per horse power pci
annum varied from a minimum of $15.69 to a maximum of $233.95,
TABLE LIU.
Showing average powm' developed and its cost per HP, in ff Mteam pcKvf
Output.
Opera ling ex-
Fixed
Total cost.
HP. it,
cts.
Average HP.
deveUiped,
No, of
days per
atmum.
penseH, per
HP.
charges, per
IL P.
HK per
annnm.
]2.4
361
1147,93
f25,40
1173.33
5.m
20.9
365
123.12
28,43
151 54
LW>s
21.5
361
90.47
17.80
rr»^ .'^7
2m
S2.9
330
22.66
6.83
Ml
86.7
365
137.25
96.70
.. ■
f.Sli
42.4
365
86.3a
63.20
W^,o^
L708
63.
309
56.94
19.51
76,45
1J«
53. S
365
97.30
33.82
131.12
IM
70.4
366
101 69
20.78
122.45
IM\
121».3
365
30.14
9 41
39,55
.g7l
Kir; 7
mii
15 19
4.47
19.66
.639
173,
313
22.66
6,83
28.39
3.3SS
210,9 1
290
40.33
7.86
48.19
m
296.7
297
45.56
7.81
63.37
w
926.
307
11.73
8.77
20 50
M
1,010.8
306
15.70
7^74
23.44
.7'A
1,174.8
306
10.19
5.50
15 69
.:^il
1,278,7
293
10.49
6.23
16.72
,m
1,345.6
365
23 28
9.42
32.70
mj
1,352.
365
3;^.03
29.41
62.44
.nsJ
1.909.7
306
13,40
6.63
20.03
.OVffl
2,422.
306
15.67
6 73
22 40
,757B
.\ summation of the results of these observations is shown in T^^
LIII and the plotted results of the table are shown in Fig. 399,
Mr. R. W, Conant** determined the operating expenses of wotii
street railway power stations and compiled a table (see Tabic U\
which gives important information bearing on this question.
• See Trans, Am. Inst E. E, Vol. 14, p. 385.
•* See Engineering News, VoL 40, p 181
^
.2
I
I
*MXivq9 pazf j
Cost of Auxiliarj' Power.
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^^L 662 Cost» Value and Sale of Power. '
^^^"^ An important discussion o£ the effect of the load factor on the ^'
^H cost of power was recently made by Mn E, M. Archibald.f Tlits
^H discussion was accompanied by various diagrams which Olii*- ^'
^H trate clearly the principles involved. Two of these diagrams art -
^m reproduced in Figs 400 and 401, The diagrams are so complcie <
^H as to need no further description. The additional diagrams and ^
■ ^
/[/ L
2.
7 J
'V
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the de
in this
Tab
toys c
as est
fBee
i^. 400,— Operftting Eicpense r>f
with a 75
scriptive matter in the paf
i connection,
le LV shows the capital <
opacities and the annual c
i mated by nie Ontario I
Electrietl AgB, Kov., 190a
^ 4
a 90(1 K. W. C<i
0 IC W, Peak.
jer itself shoi
:osts of steal
ost of power
lydro-Electr
ndensinj^ Slf^m ?
lid be carefully
n power plants
per brake horse
ic Po»wer Comr
II nt
iStU
oi
Ilk*
Market Price of Water Power.
66^
imilar costs for producer gas power are shown in Table LVI from
le same source, and the Commission's estimate of the effect on
le cost of power of variations in the price of coal, is shown in
able LVII.
331. Market Price of Water Power. — ^The market price of water
ower must be predicated on two considerations: First: The
rice at which the Power Company can afford to furnish power and
isure a fair return of its investment, and. Second : The price that
le consumer can afford to pay for the power. The latter amount
so
-w
50
fO
y
/"
^-<,
y
H^
y
'^
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^y
^^
^
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^y^
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\
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\
-\-
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^^Ofipi
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Fig. 401.— T^atio of individual Items of Expense to Total Operating? Expense
of a 900 K. W. Condensing Steam Plant With a 750 K. W. Peak.
1 commonly fixed by what it will cost to produce the power by
>me other means.
If, in the preliminary investigation of a water power project,' it
found that the cost to the Power Company of generating power
ill be greater than the price at which the power can be sold, it is, of
Dursc, evident that the plant will be a financial failure, and the
:hcmc should at once be abandoned. In introducing a new
66^
Cost^ Value and Sale of Power,
TABLE LV.
Showing capital costs of steam plants inntaU&i ajtd annual cost* of psmr
per brake horse-power.
BiZE OF Plant?
Uafital CJofiT OP Plikt prr H, p.
Installsd,
Engines,
boilers, ate.,
inetatJed,
Buildings*
Total.
AnnD&l coet
of lO^hour
power p©r
B< H.. P*
of ^bov
GtABaL—EDginee; simple, aUde- valve, non-eondeneing*
tubular^
Boilftfe: retnm
10-
20.
60.
166 00
56 00
48 70
44 75
43 00
140 00
37 00
35 00
as 50
31 00
fiod 00
93 00
83 70
78 25
74 00
101 16
n 31
66 m
59 46
63 95
1180 7e
lfil4l
m m
117 H
106 16
CtAss IL^EEigines: Simple, Corlisii non-condensing. Boilers: EettLfn lobular.
30,
170 70
62 85
69 00
56 00
60 00
44 60
(35 00
33 50
31 00
30 00
27 60
25 00
1105 70
96 35
90 00
86 70
77 60
39 60
|61 14
55 50
60 70
47 43
43 96
40 a&
ItlT 70
40
60*...
m w
97 7t
60 ,,p_
91 U
80.*.
mc
100
79 16
<?LA3s IIL —Engines:
Compound, Corliss, condensing.
with reserve capacity.
Boilers: Eeto^rn tabulir,
100 ,.
163 40
53 70
60 10
45 m
43 65
41 25
40 60
39 00
|2g 00
24 00
20 OO
18 00
16 00
14 00
13 00
12 00
$91 40
77 70
70 10
63 90
69 55
55 25
63 50
51 00
$33 13
29 83
28 14
m 27
24 84
S3 73
23 56
23 26
160 06
150 ,-
M m
200,.,,*.....
51 Tl
300 „
4SS9
400...
500 *
4611
44 21
750,...-
44 ce
1,0(K)
43 71
Clam IV, — En gines : Co mpound , Co rl ias, co ndensing,
with reserve capacity.
Boilers: Water-la be,
300...,
156 20
61 50
49 40
4B 80
44 30
lia 00
16 00
14 00
13 00
12 00
173 20
67 50
63 40
59 70
66 80
«2& 77
24 18
23 19
22 m
22 47
f#S2
400.,..
500....
750...
43 51
41 £6
1,000 p.
41 11
NoxB.— Animal eosta include intareiFt at 6 per cent, dfprecjation and repaints
pl&nti oil and waste, labor and fuel, (coal at|4 00 per ton).
Brake hotae'paffer is tbe mechanical power at engine shall.
Cost of Auxiliary Power.
665
TABLE LVI.
tpUal easts of produoer gas plants installed and anmuU costs of
povoer per brake horse-potoer.
Plakt, H. p.
Capital Cost of Plant peb
H. P. Installsd.
Annual
cost of
10-hour
Annual
coetof
24-hour
Macbine'y
etc.
Buildings.
Total.
XK)wer
per
B. H. P.
1137 00
110 00
98 00
84 50
80 00
79 00
78 20
77 50
76 00
74 00
73 00
71 50
70 00
67 50
65 00
»40 00
36 00
83 00
29 00
26 00
24 00
22 00
20 00
19 00
17 00
16 00
14 00
12 00
10 00
8 00
1177 00
146 00
126 00
113 50
106 00
103 00
100 20
97 50
95 00
91 00
89 00
85 50
82 00
77 50
73 00
153 48
44 47
38 73
85 05
32 27
30 49
28 70
27 05
25 87
24 95
24 24
23 41
22 54
21 55
20 46
190 02
75 22
65 99
59 85
55 22
52 03
48 95
45 40
43 17
41 78
40 40
39 03
•
37 54
35 99
34 66
jinual costs include: interest at 5 per cent, depreciation and repairs
il and waste, labor and fuel (Bituminous coal at $4.00 and Anthra-
$5.00 per ton).
TABLE. LVII.
ie effexA on the cost of power of a variation in the price of coal of
onc'half dollar per ton.
ce of Plant.
Suction
Pkoduceb Gas.
10
Hour.
24
Hour.
Steam.
10 Hour.
24
Hour.
15
13
10
07
04
01
98
96
94
92
90
88
86
82
76
92 53
2 46
2 40
2 33
2 29
2 24
2 18
2 12
207
202
1 98
1 94
1 89
1 81
1 72
Simple slide
valve
Simple autoniat
ic non-condes--
ing
Compound con-
denaing
ComxK)und con-
densing water-
tube boilers. . .
%^ 14
5 25
4 71
3 56
3 37
3 26
3 15
3 12
1 75
1
X 62
1 56
1 39
1 39
1 39
113 47
11 56
10 35
7 84
7 41
7 16
6 97
6 87
3 85
3 71
3 60
844
305
3 05
3 05
666 Cost^ Value and Sale of Powers
source of power into any community where the power introduced
will be obliged to compete with other sources, it can seldom be
expected that the power to be so furnished can be sold at the same
price as the power already on the market. It is at least only safe
to estimate that the power must be sold at a somewhat lower figure.
If the power already in use is sold or generated at a profit, a cut
in price may be anticipated from the competing company; and, in
the second place, as a considerable expense is necessarily involved
in the change of apparatus, ctc,> necessaiy to utilize a new source of
power, consumers will be slow to make such changes unless they
can do so to a considerable financial advantage.
In calculating the cost of power to a consumer, if he undertakes
to generate it himself, the fair cost should be based upon interest,
depreciation, operation, etc., of the plant which is necessary to be
installed. If, however, the consumer has such a plant already in*
stalled, no further investment is necessary, and as the machinery
installed can not be sold to advantage, the investment charges or
the fixed charges on such a plant can not he considered, and iht
consumer will make a change in power only provided the power
can be fitrnislied from the new source at or below the actual cost
of generation in his own plant, or at such additional cost as the
convenient reliability of other desirable features of the new sourcf?
of power will warrant.
In estimating the price at whTch the consumer can afford to pur-
chase power, not only the price at which power is now sold btii
any possible decrease in the sale price, due to competition or t^'
other and more economical developments, must be considered
Better and more economical machinery in local plants, or water
powers that are nearer the market and that can be developed or
operated at less expense, may so rednce the market price as to scf^
iously affect the value of power, and hence the probability t^l
the development.
332. Sale of Power, — Attention has already been called to tk
fact that if the capacity of a plant can be used for only a portion of
the time, the cost of the development per unit of power, and xhtn-
fore the cost per unit, is very greatly increased. This is a mancr
of the greatest importance which should be kept clearly in miniJ tn
the sale power* The load factor of many users is comparait vdy
low. Most companies organized for the general sale of elccirictJ
power in municipalities have a load factor of 35% or les*?, A sale
of power to such consumerSp to be used under such condition^, i'
i^Mkri
Sale of Power. C67
liable to very greatly increase the cost of power to the power com-
pany, especially if the maximum power to be furnished is large as
compared with the total capacity of the plant. For example: If,
in a 3,000 horse power plant, power is sold on a horse power hour
basis, with a peak load of 1,000 horse power and a load factor of
30%, the average twenty-four hour power furnished to the con-
sumer will be only 300 horse power, while the total peak that the
power plant will be called upon to carry at any time will be 1,000
horse power or one-third of the total capacity of the power plant.
With such sale of power the power plant is likely to be seriously
handicapped. With power sold in such large blocks, the overlap-
pings of the peak loads can not reasonably be expected to compen-
sate for each other. The net results of such a sale will be that the
company has tied up one-third of the capacity of its plant but will
receive payment for only one-tenth of its capacity. It is evident
that unless such ccmditions are realized and such a charge is made
for power as will compensate the power company for the same,
the power company may readily tie up its entire out-put and yet
not receive 50% of the income that should be reasonably antici-
pated. If, on the other hand, the sale of power is made in small
blocks, or to small consumers, it is frequently possible to greatly
over-sell the total capacity of the plant and yet take care of the
consumers in a satisfactory manner. That is, on account of the
overlapping of the peak loads and the equalization of the load car-
ried throughout the twenty-four hours, the total connected load
sold may often considerably exceed the capacity of the plant. For
example: In one water power plant, having a total capacity of
about 4,000 horse power, the actual connected load is over 10,000
horse power. In many power plants the actual comnected load is
two or three times the plant's capacity. It is evident, however,
that such a condition can exist only with small consumers, and that
where a single consumer's load is a large fraction of the plant's
capacity, it will not only be impossible to overload the power plant,
but in addition extra machinery must always be installed to supply
the demand should any accident happen to the regular installation.
Mr. E. W. Lloyd has compiled some valuable data concerning
the power loads on various central states from various classes of
consumers. This data is given in Table LVIII.
The increase in the charges for power to consumers on account
of the variation in power factor is well illustrated by Fig. 402 taken
from the paper of Mr. Archibald before referred to.
663
Cost, Value and Sale of Power.
TABLE LVIIL
Actual coriditiong under which potr^r tit furnUMd to conmimer^ from Cmtrm
StatioHs,
CiKrActer of IiLstaJ]aticjEi«.
M a
<
JS
li
mi
h
|l
BiikedMi.**^....
Hitflerthopt.t****! «>*•
Boiler ahofm b— . .
BoQU and aboei.,,,,,,,.,,,*.
Box m&k^Dff .#.... ^« . .
BlAJckamlLbs...., *.,.>,.......
BrASi 0n|«hlft(r . ^ »**,«*,,«»** «
Butehen and pftciren. . ......
Bulchers and pAckerv »,,**..,
Breweries ■..........*...*....
Cftrpet cleontDK
Cetn^tit mlxinjt .«,*»».,,,»., <.
Ciiiid7 nianufnftorj^..
Ca nd jr man u factory ,^ » * » * * * * *
CdUod inillii ., ^ «..*,,<....... 4
Gnrrlage worka, »>....
Oi#tiJlc*i workH. . * . , „ . ,
Claiiiliig m&nu rapturing . . < < .
Featlier cJeonera . . ..«.....*..
Oeaeral mati ii facturfn;^* ^ * < . .
Enf rartng 6nd eiecU'oCyplDjf
Enfcmvlnjc nod eleistratjpJDg
OUm j^dndiiie. ...,..,
FoundrieB « ^ *.......
Foundries ...,.,«.«,,...»..*.,
Furn i i tircr manuf aoturl ng* . * «
Flour DiMla. * . ^ , . . ^ . * . ^ * ^ ^ . . . .
HoietliM; «^nd coE^^reyltig. .... *
HofMting and convey Ui^. .....
I^ ctt»»m ...,,.,........**..«.
Hefrte^ratlon. ............... ^
jBvevtTf ftfiajmr&oiurloK. . . . ,«
Laitndrtes . ^ >«....«......... ,.
Mflirhle tlD (shinjc.
H<4chln«» atiopa ...,...«< * * ..« «^
IS ewitpaperft.
>fl wspApera. . ....,>,......*..
Orn&uieatoJ Iron works^ . . . « .
Fttini miuiuraururjiii?. ........
Pr)Bt«n and bookbliidvrv. » , . .
prtoten »ixd boctkbindfrB*^....
HI u mbInK, mflfl ufact ti ring^ . . . .
Bubb«r tiiAJiu roiCty nni; ^ ..... .
bheet metal inAiiijfinjturiDg,.
HtoAD maaufacturln^..*....!*.
^ceaa.,. — --■
i^l rucjCurjil fltevl , . . . * ^ « . . . '.^^ .
Structtiral steol
Sloii« cutting:. ..«*.«««,....,...
T«DO«rft.^ ...............«*.. t .
ToImcco worklnjc ^ * * - ■ " ■
Wbolotale (Erocerie* ,..*.....
Wood workiDf^..... -.,
Woolen n> UU. . .,.»«,..........
AvprAff««.. .......... *.
158S
705.8
3».7
1179
306O
1565
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An Equitable Basis for the Sale of Power.
669
333. An Equitable Basis for The Sale of Power. — It is there-
ore essential, in order to establish an equitable basis for the sale
)f power, that some additional factor besides the units of power
urnished be considered in determining the basis for the prices
:harged. One of the most equitable bases for the sale of power
7P| , 1 1 1 1 ^ 1 1 1 -; >- 1 1 T^ 1-1 ■ 1 1 1 1 1 L fl ■ ■ 1
Z -it
\1 tit
rt
« ^ i
. ^ it 7 T
^ t t
-J- ^h-,
i -i
' f i
'-\- 2 t jj'
% -, L ^41
1 111
t -/ t t
%40 Z 4 -t
^ _ J. L 2
^ / J- t
% / J^ 4
^ y t t
^ ..«^^' / J
>t - ' ^c^V-" v . ./
1^ s^F' "
2J0 ^-^"^ \ ^-u^-*^. r-^ 1 ^rf^ y
^ ^ -- "^ j^t;;;^^ "" ^
_^— =="" ed'^ ^^
,— — ^"^"^ ^-^"^
w~ J^^^'t'^^^
1 ! ,..-,. , , 1., 1 1 i,
Fig. 402.— Cost of Steam-Generated Electric Power to the Consumer.
s apparently : First : A service charge to the consumer of a fixed
►rice, based on the peak load carried; Second: To this should be
dded a price for the units of power actually furnished. The fixed
•rice should equal the interest, depreciation, etc., on the capacity
hat is to be provided or set aside to carry the peak load of the
ustomer. The unit price for power should be an equitable charge
3r the quantity of power which will actually be sold. Where both
670
Cost, Value and Sale of Power*
of these quantities are fixed» a net price per horse power per year,
or a total price per annum for the power to be furnished, can, of
course, be arranged equitably, llie main idea in establishing a
price for power is to keep clearly in mind the factors that enter
into the sale of power, so that in making a contract for the use oi
power the rights of both power company and consumer shall k
duly considered. The sale of power at a pro6t is one of the mo5^t
essential features in the management of the power plant, and many
plants have been wholly or partially financial failures on acconni
of the ignorance of the basic principle on which power should bf
sold.
Tlie method of charging for power outlined above is illustrated by
the charges for Electric Current furnished from Niagara Falls, by
the Cataract Power & Conduit Co, of Buffalo, as given in the En*
gineering New^s (May 26th, 1898) as follows:—
'*An payments for power are to be made monthly and tJie amount
of each monthly payment will consist of a charge for service, and
in addition thereto, a charge for power. The chargje for service
is $1 per kilowatt per month, and this charge will depend only
upon the amount of power which the user may require the Catar-
act Power & Conduit Company to keep available and ready for bis
use. The monthly charge for power will depend upon the aggre-
gate amount used, as determined by integrating meters installed
by the Conduit Company upon the premises of the consumer* The
charge for power will be determined from the following schedule:-^
U7iitB{K~W. hTA.) used
per mtmth.
Up to 1,0U0
l,000to 2,000
2|000ta 3,000
3,0C0ta 5,000
5»000 to 10,000
10,000 to 20,000
20,000 to 40,000
40,000 to 80,000
Over 80, 000
Charge per
unU
For current up to
For (he cat
1,000 unitj*, 2.0 cte*
2.0 eU.
1,000 units, 2,0 cte,
1.5 cti;
2,000 unitB. 1.5 eta.
1.2 cti.
3 J 000 iitiitfi, 1.2 ctB*
1.0 cfce.
5,000 uniti», 1.0 cia
0,S cte.
10,000 units, 0.8 ctB,
0.75 eta.
20,000 UTiit^, 0.75 cts.
0.70 eta.
40,000 unite, 0.70 cts.
0.66 cti.
80,000 units, O.BGct'-.
O.cHcls.
334. Value of Improvements Intended to Effect Economy* — Iff
many plants the first cost of an installation is an important matter
and must sometimes have a greater effect than the interest and d^
preciation charge would seem to warrant. In most cases the plan
should be studied in detail and improvements introduced or it-
Value of a Water Power Property. 671
jccted on the basis of their true financial value* Such considera-
tion should usually be made on the following basis:
Br.
Invest ment roquired to eflect improTements $. . . . . * . ^ , ,
Interest on investEnent ,..* |.,.. ».
Depreoiation on ini prove men ta , , < I - <
ExiTB expenae of operation and mainten-
ance*.... * I
Total annual eoet of improvement.,
Saving tn power (or m expenae) effected
by iajprovement t-
Annual value of eaving effected.
Net annual gain or losa due to im-
provement , • |.
Capitalised value of poiver (or expense)
effected by i rapro vement . , , , %*
Net capitalized Joss or gaiji ejected $
33S- Value of a Water Power Property, — It has frequently be-
come necessary in this country to condemn water power privileges
on account of the necessity of securing public water supplies or
for other public purposes. Under such conditions it frequently be-
coines necessary to estimate the value of the water power property.
When such matters are brought into court and various witnesses
are heard on the subject, it is cominonly found that very great dif-
ferences of opinion exist as to the value of power These differ-
ences of opinion are largely the result of entirely different points of
view.
To those who have carefully followed the discussion of the hy-
drography and the estimate of power based thereon, the great var-
iations that occur in the potential power of streams at various
times in the season, and in the various years, are obvious.
It is apparent that different engineers, even if they take carefully
into account these variations in power, may differ very greatly in-
deed as to the extent to which the power can be economically de-
veloped.
The question of pondage as discussed in Chap. XXVI also has
a very important bearing on this matter. It is only by a careful
study of the whole question and the consideration of the power
market that even an approximately correct answer to this question
cafl be given. The value of such a plant may be considered in a
67a Cost^ Value and Sale of Power,
variety of ways : First : Its value if intelligently aod recently d^
signed^ may be represented by the cost of its reproduction pins a
certain value for the water power ri|^hts; Second* Its value miy
be computed on the capitalized net income that the plant can or
does earn; or. Third: The value of the plant may be consideTed
equal to the capitalized valu€ of the most economical plant tliai
can be installed to furnish power at the point at which the power is
CO be used By the term "most economical" is meant not ncce^
sarily the one lowest in first cost, but the plant that, when consid-
ered in the broadest sense, will furnish power, all things consid*
ered, at a less cost than from any other source of power. The sub-
ject is a very broad one and one that needs careful consideration
and study* A number of references are given to discussions of
this subject before various engineering societies, to which the en-
gineer is referred for furtlier information on this important sub-
ject, n
LTTETRATUHS,
COST AND VALITi; OF WAT££ FOW1&.
1. Kimball, Geo. A, Water Power: Its Measurement and Value, Joaf
Asm. Eng. Soc. 1893.
2. Main, C, T. The Value of Water Power. Trans. Am. Soc. Mtth, Eufi-
ToL 13, p. 140, Eng. Rec VoL 60, p. 694.
a. Grant, W* H. Calculation ot Mean Horse Power of a Variable Bttm^
Trana. Am. Soc, C/E, Vol. 22, p. 38!>,
4. Rockwood. G. L On the Value of a Horfie Power. Trans. Am. Ef>e. E E
Vol. 21, p. 500.
&. Nagle, A. F. An Analysis of the Commercial Value of Water Power*
per Horse Power per Annum, Trana. ^m, Soc, M, K l^^
Eng, News, vol. 49. p. 83.
6, Parker, M. S. Cost of Steam and W^ater Power In Montana. Jmir. h^
Eng. Soc. Vol. 15, p. 26.
1. MaiOi C, T. Cost of Steam and Water Power. TrEUis. Am. So<x M. K
VoL 11, p. lOS.
8. Manning, C. H. Comparative Cost of Steam and Water Power. T)
Am. Soc, M. K Vol, 10. p. 499.
6. Webeft SamueL The Cost of Water Power. Cassier's MagEXtne, fol ^
p. 415.
10. WaJbank, W. M. Lachin© Haplde Plamt and the Coat of ProiucUH
Power Therefrom. West. Elec. July 9, 1S9S.
11. Cost of Niagara Power in Buffalo. Elec World, April 23, 1S9S.
'mm^
Lriterature.
673
COST or POWEB,
V2. Jones, a L. Electrical World, Feb. 18, 1905.
13. Emery, C. E. Cost of Steam Power. Am. Inst Elee. Eng. 1895. Trans.
Am. Soe, C. E. Vol 12, p, 425. Trans. Am. Inst. Elec, Ear
Vol. 10. p. 119. Eng. Mag. Vol. S, p. 796. Power, 1SD5.
14. Dean, R W. Reduction in Cost of -Steam Power from 1870 to lSt7. Am.
Soc. M. E. Vol 9. p. 301, Eng. News. Dec. 1897.
15. Arnold, B. J* Cost of Producing Electrical Energy. Power, Dec. 1894.
16. Gray, C. C. An Investigation ot tlie Coat of Power. The Engineer, 1902.
Vol. 39. p, 64.
17. Perry, N. W. Comparative Cost of Generating Electrical Power. Elec.
World, vol. 25, p. 274.
18. Hlce, C* W. Analysis of the Cost of the Generation and Distribution of
a Unit of Electricity. West. Elec. June 25, 1898.
It- Dreyfus, E. D. Method of Invest Igatjng the Cost of pToduclng Electrical
Energy. Electrical World, vol. 52. p. 19.
2a. Archibald, E. M. The Effect of Load Factor on Coat of Power. Elec-
trical Age. Nov. 1906.
21. Forest, H. V. Cost of Electrical Power in Small Central Stations. Elec-
trical World, vol. 48, p. 1246.
22. Economy of Electric Stations. Report of Committee on Data of the Na-
tional Electric Light Asso. Eng. Rec. Vol. 36, p. 74. Elec.
Eng. Vol. 21, p. 522.
23. Elecricity — Costs and Revenues. Power, May, 1903,
24. What Does a Steam Power Cost? The American Engineer, 1890,
25.
26,
27,
28
29
30
21.
32
53.
THE SALE OF POWEB,
Harvey, G. A. Contracting for Use of Hydro-Electrlc Power on Ballws^
Systems. Electrical Age, Sept. 1906.
Storer, S. B, The Sale and Measurement of Electrical Power, Electrl*
ca! World, vol. 47, p. 069. ElectricAl Age, Aug. 1906, Engioeering
Record, Nov. 3, 1906.
Parsons, C. E. Sale of Water Power trom the Power Company's Point of
View. Engineering Record, vol. 54, p. 161,
The Principles of Modern Rate Making for Electric Light and Power.
Electrical World, vol. 49, p. 10S6,
Fowler. C. P* Some Fundamental Principlea Underlying the Sale of
Electrical Energy. Electrical World, vol. 50. p. 456.
Burnett, H, E. The Coats of Electricity, Supply, and Their Relation to
Scale of Charges. Electrical Review, vol, 51, p. 172.
POWEE TRAh'SMISSION,
Donaldson, Wm. Transmission of Power by Fluid Pressure, E. ft F. N,
Spon, London, 18S3.
Unwln, W. C, On the Development and Transmission! of Power. Long-
in an » Green A Co., Londun^ 1894.
Kern, E. W. Power and Power Transmission. John Wile?y & Son New
York, 1902.
41
674 Cost, Value and Sale of Power.
34. Mead, Daniel W. Commercial Transformation of Energj. IlL Soc Ebg.
& Sur. 1901. Vol. 14, p. 38.
DEPRECIATION.
35. Matheson, Ewing. The Depreciation of Factories. E. ft F. N. Spon.
London, 1903.
36. Mogerisen, Peter. A table for Depreciation or Sinking Fund Paymenti
with Annual Compounding. Eng. News, vol. 53, p. 226.
37. Alvord, J. W. Depreciation Proceedings. Am. W. W. Abso. 1903.
38. Bolton, R. P. Depreciation, Maintenance and Interest Charges. Ens-
Reyiew. Jan. 1902.
39. Brayan, W. H. The Appraisal and Depreciation of Water Works. Jour.
Asso. Eng. Soc. Dec. 1907.
40. Depreciation of Electrical Apparatus. Elec. World and Eng. Aug. 9,
1902. Iowa Engineer. July. 1902.
CHAPTER XXVllK
THE INVESTIGATION OF WATER POWER PROJECTS.
336. The Extent of the Investigation. — The investigation of any
water power project should include a careful study of all available
data relating to the physical and meteorological factors that affect
the water supply and that obtain on the drainage area of the
stream on which the water power development is projected. The
present condition of these factors is readily obtainable by careful
•observations and surveys but the ntost difficult and yet the most
important information needed for the correct understanding of the
project is the variations from present conditions that have occurred
in the past and that are therefore liable to re-occur in the future.
On the correct interpretation of the available data the success of
the project or at least the economy of the installation depends, es-
pecially if, as is usually the case, it is desired to develop the plant
to its economical maximum.
The extent of the investigation' must be governed by the import-
ance of the project, and will also depend on whether the investiga-
tion and report are to be of a preliminary character, or are to be
the basis of a final report on which the feasibility of the project
may be decided.
337. Preliminary Investigation and Report — An examination ot
the data available in any first class engineering library will gener-
ally give the information necessary to form an approximate judg-
ment of the probable feasibility of the project in so far as it depends
on the flow of the stream. The approximate area drained by the
stream can be determined by reference to such maps as may be
ivailable and the probable flow and the variations in the same that
will occur from day to day and from month to month, can usually be
determined by the construction of comparative hydrographs made
from either the measured flow of the stream, if such information is
available, (see Literature page 194) or otherwise on the compara-
tive fl*>w of similar and adjacent streams as described in Sec, 51^
page 83, and Sec. 100, page 184.
k
\jj6
The Invesiigation of Water Power Projecis,
k.
From such an investigation together with an appropriate know]
edge of the available head, an estimate of the probable power of
stream can be made, and from such information an opinion can
formed as to whether it is desirable to carry the investigation kf
then Frequently such an investigation will show beyond qoestion
the fntitity of the project, and even an examination of the lociHty
becomes unnecessary. If the preliminary investigation shows that
sufficient power is probably available on the stream in question tk
investigation can be carried into stcflicient detail to warrant an
opinion as to whether or not the project is feasible in all of its
phases,
338. Study of Run-off, — The information of primary importaiicc
in a water power project is the amount and variation in the ran-
off of the stream itself. If this is not available the run-off of neigh-
boring streams that have similar physical and meteorological condf-
tions prevailing on their drainage area is next in importance
As already pointed out, (see Sec. 99, page i8i), the hydrograph oi'
the actual ilow of the stream itself is the best information for study^
jng its variations in flow* Such hydrographs must be available for
a considerable term of years, and it is desirable that they shoM
cover all extremes of rain- fall and drought, and other physical and
meteorological conditions that influence run-off-
In the investigation of the liydrographical conditidn of am
stream, a single gauging of the stream is of little or no value. It is
however, desirabble to establish a guaging station as early as possi-
ble and to take daily gauge readings. It is also important, both for
the purpose of an imderstanding of the goage reading and for the
purpose of the study of head, to make stream flow measaremeuts
(see Chap, XI) under all large variations in flow, as e^rly as possi-
ble in order that a rating curve may be established.
When no local hydrographs are available, or w^hen such availabli
hydrographs are limited to a few years, it becomes desirable t<>^
gather together die flow data of all adjacent and similar streams and
to construct comparative hydrographs therefrom, as described in
Sec, 100, page 1S4* A long continued series of hydrographs of a
neighboring stream where similar conditions prevail is importani
and should usually be utilized even if local obser\"^ations have been
made for a few years. The value of comparative hydrographs i^
dependent on the similarity of conditions, a question that demands
careful consideration and a considerable amount of data to deter-
mine, and even then can be regarded only as indicative* It is alsa
^V Study of Rain-FaU. 677 H
^Ssential to make careful comparisons of the relations that exist ^M
between the hydrograph of the river under discussion and those of ^M
adjoining rivers, for such period as such data may be mutually ^M
available on both streams, in order that variations between the ^M
areas compared may be determined, ^M
339> Study of Rain-Fall — ^The rainfall records of the United ^M
States Weather Bureau and, previous to these, the records of the ^M
observations of the United States Signal Service (see Literature, ^M
page 130) are available from various stations throughout the United ^M
States for a long term of years. It is desirable to collect the rain- ^
fall data for the drainage area of the stream under consideration,
and also on such other drainage areas as may be used for compara-
tive purposes. Tliis information should be classified and studied
as outlined in Chapter VL In investigating rain-fall it is usually
especially desirable to make a study of both the annual rain*fall and
the periodical rain-fall of the divisions of the water year. (See Sec,
77, page 126.) The distribution of the rain-fall of these periods
lias a greater effect on the low water flow than the total rain-fall
for the year.
The relations between rain-fall and run-off for the period for
! which complete data is available should be investigated and such
relations established as clearly as possible for the drainage areas
under conideration. (See Chapter VTIL) With the information
concerning run-oflf commonly available and the rainfall records for
a considerable term of years, it will be possible to draw fairly accu-
rate conclusions as to the probable variation and average flow of
the stream. The probability of a larger maximum or a smaller min-
imum than the stream flow observations themselves indicate can
also be determined from such an investifj^a^tion,
I 340. Sttidy of Topographical and Geological Conditions. — The
topographical and geological conditions may ordinarily be inves-
tigated from data available in the publications of the United States
j Geological Survey, or of the Geolog^ical Surveys of the state in
which the drainage area may lie. The information sought from this
investigation is a kno^vlcdge of the conditions that will effect run-
' oflf, consequently, such a study is not of particular importance pro-
vided sufficient rain-fall and run-off data is available for the purpose
of the investigation.
If. however, the hydrographical Condition of the areas under
consideration, or of other adjacent and similarly located areas have
I not been previously investigated, and if few or no local ob ^m
67 S The Investigation cf Water Power Projects.
tions of stream flow have been made, the topographical and geolog-
ical data may form the basis of a more intelligent opinion in regard
to the probable run -off than can be obtained without such cunsiden-
tion. In any events this source of information should be utihzedto
the full extent war ran ted ^ as should all other sources of informatiod
that will in any way assist the engineer in an intelligent understand^
ing of the problem before bim, and the formation o-f a correct opin-
ion as to the possibilities and probabilities of the case in question.
341. Study of Flood-Flow.^ — It is important to establish both fram
information that is usually available in the stream valley under cotj-
sideration, and from information which may be available ifDm
adjoining streams, the probable maximum flood-flow of tlie strtam.
This must be determined, or at least a safe approximate estimatf
must be made in order that the dam and other works for the control
of the flow can be intelligeivtiy designed. (See Sec. 93, page 163. 1
After the rating curve has been established the elevation of \ht
high water marks in the immediate vicinity and the relation of ibc
same to guage heights will usually give a safe basis for the estimate
of extreme flood-flows.
342. Study of the Back- Water Curve* — A topographical $u^^ey
of the proposed site of the dam and of the stream valley above the
dam site, to the probable practical limit of the back-water eftecu
should be carefully made. In order to investigate the probabfr
height of the back-water under all conditions of flow it will be ntcf^
sary to make cross-sections of the river at such intervals and under
such conditions as will permit of the division of the river into
lengths or divisions having comparatively uniform sections. Gage?
should then be established at the various stations and nhservatiom
should be made of the gage heights at each station during variop^
stages of flow (see Chapter X). From the quantity of water fio^*
ing at any stage, together with the cross sections of the river on the
various divisions, the value of the hydraulic elements and especial!}
of the friction coefficients for each division and their variations vtn*
der such condition of flow, can be calculated. (See Sees. 37 to 40.
page 44.) After this has been done it is possible to calculate tlie
back- water curve (see Sec. 42, page 58) and to establish the pro^*
able limit of the back-water flow line under any other conditions 1^1
flow in a fairly reliable manner.
Study of Head. — The consideration of these conditions, the Ueig'^^
of the water surface at the dam due to various sections and length
of the spill-way and the practicable limit to which flood height in
Study of Storage and Pondage, 679
the valley above must be restricted, will usually establish the limit
>£ the height to which the dam can or should be built and will in-
dicate whether it is necessary or desirable to construct flood gates
Dr to use an adjustable crest, flash boards, or means for regulating
ind hmiting the flood height. When these conditions are estab-
lished the variations in head under various conditions of flow can
be determined (see Chap. V, page 93) and the effect of such varia-
tions on the power which may be developed can be calculated. (See
Sec. 62, page 103.)
343. Study of Storage and Pondage. — ^The topographical survey
will also give information concerning the storage and pondage con-
dition immediately above the dam. In special cases, reservoirs be-
yond the limit of the back-water effect may be desirable and special
surveys under such conditions will be necessary. As the conditions
of pondage and storage materially effect the amount of power avail-
able, these questions frequently become of great importance and
should receive the attention of the engineer that their importance in
each particular case seems to warrant After definite information is
obtained concerning the extreme permissible limit of flood-flow, and
the possibilities of storage and pondage, an estimate of the power
of the stream under various conditions of use can be readily made.
(See Chap. XXVI.)
344. Study of Probable Load Curve. — It is important in consider-
ing the power of the stream and especially the desirable condition
of pondage, to ascertain as far as practicable the probable necessary
distribution of the demand for power throughout the day. The way
in which the power is to be used, whether on 10 hour, 12 hour, or
24 hour service, and its probable variation during the hours of use,
has a most important bearing on the design of the plant. (See Chap-
ters XVII and XXI.) If variations in the demand for power
throughout the year are also likely to occur, and such variations are
likely to effect the requirements for storage, they must also receive
consideration.
A census of the power used in the district, to be supplied from the
proposed water power development, is important and should be
made in as great detail and with as great care as practicable. An
accurate estimate of the amount of power used by a factory or man-
ufacturing plant is a matter of considerable difficulty. In some
plants where power is electrically distributed, the use of indicating,
and sometimes of recording instruments, make it very easy to deter-
mine the energy output of the power plant. In most manufacturing
^M 680 The Investigation of Water Power Projecis. 1
^M establishments where power is distributed by belts, shaftiiig, anj
^B other than electrical means, the amount of power actually developed
^M and utilized is seldom definitely known. The use of the steam engine
^B indicator, if opportunity for such use is offered, will give a knowl'
^M edge of the indicated power of the engine at the time observations
^M are made; and if the probable variations are investigated* a fairly
^m close estimate of power used can often be made by this means.
^H The annual quantity of coal used, and a careful study of the coo-
^M dition and character of the boiler service, requirements for heating,
^ft condition of the engine used, together with a careful examination
^m of the machinery operated, will form the basis of a fairly approxi-
^M mate estimate of power used. Even where the estimate of power
^M used is fairly accurate, it must be remembered that when sucb
^M power is used and transmitted through a multitude of shafts, belts.
H etc., that if the electric power is substituted and individual motors
|H used on the machine to be operated, the power then used will bf
H very greatly reduced in amount.
■ 345* Study of Power Development^Having established tk
^1 probable load curve, the head under all conditions of flow, and the
^m fiow as modified by the pondage or storage conditions, the extent of
^1 the power development can be determined. All of the questions that
^M have been previously discussed lead up to the consideration of the
^" question of the desirable capacity or extent of the proposed power
I development This capacity should always be estimated on a con-
» servative basis. If, as is usually the case, uncertainties exist as to
the probable demand and distribution of power, or the probable min-
imum flow of the stream, it is desirable to develop the project to a
point below the probable commercial maximum but to keep in mind
the probability of the desirability of future enlargements and to
consider the plans %vith the future in view. In this connection the
question of auxiliary power, and tlie capacity of the plant as modi-
1 fied by such powen should receive attention.
; 346. Study of Auxiliary Power. — Tlie necessity of auxiliary power
I in connection with the proposed water power development can be
determined by an intelligent study of the hydrograph and an inves-
tigation of the effects thereon of the storage and pondage available,
(See Sec, 317.) As a general principle, it may be stated that a
I stream can often be developed to CDmmercial advantage to the ex-
tent of the power which will be uniformily available for eight or
nine months of the dryest year, and that auxiliary power is usnalh'
warranted to furnish the power deeded for the remainder of the sc
Study of Plant Design,
68 1
soft Thi5 IS a general rule which must be applied with caution.
Every proposed development must be carefully investigated for it-
self, and no general conclusion should form the basis of a final re-
port on the feasibility of such a project* The greater the demand
for power, and the greater the cost of development from other than
v\ratcr power sources, the more expense is warranted for auxiliary
service, pondage, etc., and the greater the capacity to which the
water power should be ultimately developed,
347, Study of Site of Dam and Power Station. — In addition to
the topographical survey previously mentioned, it is necessary to
examine in considerable detail the bed and banks of the stream and
f^ak^ all necessary soundings to fully establish all conditions on
%vhich the character of the construction recommended must depend.
It is important that all conditions be carefully investigated and the
type ot zonstruction to be recommended carefully considered. The
storage of energy almost always involves a hazard which must be
met with economical but safe design and construction. The preven-
tion of haw under and around the structure requires a detailed
knowledgt of the local conditions and is one of the most uncertain
conditions which, unless carefully and correctly estimated, is apt
to result ii. considerable extra expense. The flood flow is a condi-
tion which needs the most careful consideration for it is oiten the
condition ot greatest danger and, to assure safe construction during
the short period when such conditions obtain, requires special attcn-
tiom and intimate knowledge of the local conditions, and often in-
volves considerable expense.
348* Study of Plant Design. — The study of plant design requires
an extensive study of the various types of development that are in
practical use and the adaptability of such designs to the conditions
of the particular locality under consideration. It is seldom that
plans, no matter how successfully carried out in one place, can be
duplicated to advantage in another. Each plant should be built to
meet the particular conditions under which it is to be installed and
operated, and the best ideas from all sources that will apply to the
local conditions should be correlated and embodied in the proposed
plant. Extensive experience, observation, and study are each desir-
able and each essential for the best results. For his own, as well as
for his client's good, the engineer should endeavor to secure the very
best results possible when all things are carefully weighed and con-
sidered. No reasonable amount of conscientious work, painstaking
thought, study, labor or expense should stand in the way of such
682 The lnvcsti|^ation of Water Power Projects. _^J
results ; and anything less than this is a detriment to future pro-
fessional attainments which no engineer, young or old, can afford.
In the previous chapters the general principles underlying tbe
design of the varions elements of the plant have been considered
The consi tie ration of these matters has been very brief and the en-
gineer must extend his study in all cases to the extensive literature
on each subject, reference to some of which has been given at die
end of most chapters. Additional references can be found in the En*
gineering Index and in the indexes to the various technical publica-
tions and the publications of the various engineering societies. A
personal visit to and a detailed examination of successful plants is
a method for the acquisition of exact knowledge which should not
be neglected. New novel and untried designs are frequently d^
scribed in engineering publications, If they are successful their suc-
cess is often heralded in a similar manner. Their failure is seldom
mentioned by the technical press and the only method of ascertain-
ing their true value is by personal and confidential inquiry on the
ground,
34g, The Estimate of Cost* — In order that the preliminary esli-
mate shall be made on a safe basis, reasonable allowances should be
made for unforeseen and possible contingencies. This is especially
desirable in preliminary estimates on which the feasibility of the en-
tire project may be based. If a safe estimate of the actual cost ol
construction, — that is an estimate which will surely not be exceeded
and will undoubtedly be reduced in construction, — makes the feasi-
hility of the project doubtful, then, as a general proposition, tht
project is not worthy of further consideration. If the project h
predicated on the basis of an estimate that is known to be safe, it
can lead to no unfortunate investments. The owners of a develop*
ment are always satisfied if the cost of development is less than the
engineer's estimate ; but an increase in cost is often a serious matter
The desire to develop a project is sometimes apt to give an opti-
mistic coloring to the engineer's report. This is a tendency wbicli.
both on account of the interest of his client and his own future repu-
tation, he should carefuly guard against.
If the feasibility of the project is reasonat)ly well established bf I
the preliminary examination^ the examination should be still further j
extended and made fairly complete. Preliminary plans should be
outlined in order that a safe detailed estimate may be made. Th^
expense involved in such preliminary work is well warranted by th^
results obtained. In many cases plants have been recommended *
The Report. 683:
insufficient examination, and the estimates made with too optimistic
a view of the conditions to be met. The latter development of the
necessity of increased expense, has made the project less attractive
and has resulted in great disappointment botth to the owners and ta
the engineer on whose opinion the work has gone forward.
350. The Report. — As far as practicable the engineer, in making
a report on a water power project, should furnish his client with all
of the data on which his deductions are based. He should discuss
this data and its bearing on the project and point out as clearly
as possible the reasons for the opinions he expresses. In a well
drawn report the engineer can usually so illustrate and describe the
conditions by which a project is modified and controlled, that any
good business man will understand the basis on which his opinion
rests and the degree of probability of any departure from the ex-
pected result. While this is not true in regard to the technical de-
tails, it is entirely true with the general consideration on which the
feasibility of a project rests. If a report can not be so drawn it is
due either to insufficient data or to the fact that the engineer him-
self does not fully understand and appreciate the logic of the situa-
tion.
In general, a complete report on a water power project should
include a careful consideration and discussion of the following :
First: A general description of the drainage area, including the
size and the topographical, geological, and other physical conditions
that may have a direct bearing on the feasibility of the project.
Second : The run-off data available on the streams in question, if
any such data exists.
Third : If local run-off data is available, but only for a brief term
of years, the rainfall of the district for as long a period as possible
should be collected, and its relations to the available run-off data
established. From this the probable modification of the run-oflf
during other years during which the rainfall is found to vary, should
be carefully and fully discussed.
Fourth : The run-oflF data on adjoining streams, having drainage
areas with similar physical, topographical and geological condi-
tions, and where the hydrographical conditions of the rainfall and
run-off are apparently similar, when the difference therein can be
determined and estimated, should be graphically presented and dis-
cussed.
Fifth : The relations of the rainfall and of other conditions on the
I
I
68^ The Investigation of Water Power Projects. ^H
comparative areas considered, and their variations from the par-
ticular location under consideration, should be fully illustratei
Sixth ; The conclusion in regard to the probable flow from thf
drainage area, considered on the basis of its run-off, and the mn~o€
of comparative areas should be fully considered.
Seventh : A general description ol the locality at which the dam
and power stations are to be constructed* and the physical contri-
tions there existing, also the effect of such conditions upon the con-
struction of the plant, should be described and the methods of meet-
ing them should be carefully and fully outlined.
Eighth : The head available and the variations under various con-
ditions of flow should receive careful consideration.
Ninth: The probable power available with and without pondagCi
or with the pondage found by the preliminary survey to be avail-
able, should be carefully and futly treated, as this isoneof theesscn-^
tial features of the report. ■
Tenth : The auxiliary power, if any* necessary to maintain the
plant at all times to the capacity recommended, often needs specific
discussion.
Eleventh : An estimate should be made of the probable cost of die
development, the probable operating expenses, and the probable
cost of maintenance* ■
Twelfth : The probable market for the power to be generated, and
the probable distribution of the demand for the power through iHe
day and year, and the basis on which such estimates are made,
should be given.
Tliirteenth : The sources of power used in the territory which it is
proposed to supply, the cost of developing the same, and tlie prob-
able price at which power can be sold, are of primary importance.
Fourteenth: The report should be accompanied by hydrograpli?*
preliminary plans, and such other drawings as will, with the data
furnished, show conclusively that the facts are as the report sets
forth.
Fifteenth : In general it is advisable that the report itself should
be clear, concise and definite in its statements and recommends*
tlons. Any elaborate discussion of voluminous data should he hir-
nished in the form of an appendix to which the main report should
refer for confirmation of its findings and recommendations
I
APPENDIX— A.
WATER HAMMER.
In Chapter XVIII, Section 213, it is shown that the pressure head
due to a change of velocity in a water column is expressed by the
formula
It is evident that the water hammer head produced by the rapid
closing of a gate at the end of a pipe line will be maximum for the
dv
maximum possible value of-;^f or that obtained by closing the gate
instantly. Were it not for the elasticity of water and pipe, instan-
taneous gate closure would produce an infinite rate of retardation.
dv
■jp and hence infinite pressure. In reality the water near the gate
first compresses and the surrounding pipe expands, due to the water
hammer pressure, the flow meanwhile continuing undiminished in
the remainder of the pipe in order to fill the additional space thus
obtained. The point up to which this compression of the water has
taken place, as shown by Joukowsky * travels along the pipe from
gate to reservoir as a wave with a velocity, A,t equal to that of
^ See the "Memoires of the Imperial Acadamemy of Sciences of St Peters-
burg," vol. IX, No. 6. Ueber den Hydraulischen Stoss in Wasserleitunjrerohren,
by N. Joukowsky; published In German and Ru&sian. See also the synopsis
of same by O. Simin in The Trans, of the American W. W. Ass'n, 1904.
t A. varies from about 4,500 to 3,000 feet per second as the size of the pipe
increases, and can always be obtained by the formula (due to Joukowsky) :
wberM
X = velocity of the wave in feet per second.
K = volumnar modulus of elasticity of the water = 294, OCO
pounds per square inch,
e = thickness of the pipe walls in inches.
E ^ modulus of elasticity of the material of the pipe.
w, g, and d = as previously defined in Chapter XVIIT.
-686
Water Hammer.
tsound in the same column of water. The water has not all beeti
brought to rest until the wave reaches the reservoir, which evi-
dently requires a timey. Although only an elementary length of
the water column is brought to rest at a time, the effect upon tk
pressure is the same as would result frcmi retarding the whole col-
umn as a unit in a time-;^- The maximum possible rate of retar-
dation is hence
Mas
dv
V H-
1
From
Equation
CO
(2)
Hin —
: maxitniim
h.=
T '
Av ♦
Tlie pressure-head given by this formula varies from about T40
to 100 feet per foot of extinguished velocity as the pipe increases
in si^e from 2" upwards. If the gate is only partially closed by tb^^
instantaneous motion, the pressure head is given by the same for-
mula in which case v represents the amount of the velocity which \^
instan taneously extingu ish ed .
Thus, in the case of instantaneous gate movement, the pressure is
not produced at the same instant along the entire pipe, but tra^xls
us a wave with a velocity A from the gate to the origin of the pipe
and back again to the gate. It then reverses and becomes a wavt^
of rarefaction which travels twice the length of the pipe in the same
inannen This continues until the energy of the moving column ot
water has been dissipated by friction, and the wave gradually sul>
sides. This phenomenon is identical with that of the vibrating
sound wave in an organ pipe.
Although equation (2) gives the maximum possible pressure
head which can result from the extinction of a given velocity v in
a pipe it does not, however, represent the maximum pressure which
could be obtained as the result of several successive gate move-
ments; in fact, no limit can be assigned to the pressure which mi^ht
result in case several water hammer waves were to be produced at
intervals differing approximately by multiples of the vibraiion
* This formula Is the same as that obtajoed hy Joukowsky hj two dtber
methods of analysis. His discussion of water hsimmer phenomena includes
all that ia known iipim the subject, ami k> or Siniifi> spnopiw^ should beretil e?~
pecislly by every en^neer interei!ited in high head deveiopmenta aa Ihe anbieci
can only briedy he touched in thie book.
Water Hammer. 687
period of the water column, in which case they are known to "pile
up" to enormous indeterminable pressures.
When the flow in a pipe is shut off by the gradual closure of a
^ate then equation (i) and also the. following equation
'« Ir-^O-^)
from Chapter XIX, sections 213 and 217, apply as before except that
in this case not only v but also V is a variable, its value being differ-
ent for each successive position of the gate, and its law of variation
depending upon the law and rate of gate movement- The integra-
tion of equation (3) in its general form, to obtain the velocity curve
is then very difficult if not impossible.
An approximate curve of v, and hence also of h can be plotted by
assuming the gate closure to take place by means of a great many
small instantaneous movements, according to any law which may
be chosen. The value of V for each of the many gate positions can
then be computed from the known hydraulic data of the wheels
and penstock.
Now, in equation (3), substitute for v the initial velocity in the
pipe, and for V the normal velocity (above determined), after the
gate has received its first small instantaneous movement. The re-
dv
suit will be the initial slope of the v-t curve = jj-. Assume this
rate of decrease in velocity to continue constant for the short in-
terval between successive gate movements ; then the actual velocity,
v, at the instant of the next gate movement will be
where 1 is the interval between the two movements.
Assume this new value of v, to be v^ and using the value of V for
the corresponding (or second) gate position, again apply equations
(3) and (4), until the gate is completely shut.
Having thus determined the v-t curve, the head curve can be
readily found from equation (i), which gives the excess of head
above static or so called water hammer head.
Substituting the value of -^ from (3) in (1) give
(4) ^=^o-i5^
(5) b.= H(l-^)
Church has investigated this problem by a method described in
the Journal of the Franklin Institute for April and May, 1890.
APPENDIX— B.
SPEED REGULATION, A MORE DETAILED ANALYSE
THAN IN CHAPTER XVIII.
In Chapter XVIII,. Section 217, the following equation was sho^
to express the rate of acceleration of water in the penstock subs
quent to an instantaneous change in gate opening of the wheel.
<•) w-»r('-^)
Separating the variables v and t, gives
,, IV dv
Integrating we have:
(a) t-^iog.7-''
To determine the constant of integration, C, assume that r =
when t = 0, hence
IV , V-vo
0 = - 0-T3 log.
Let
(3)
k-%fa„dk
(4)
T, _ V 4 V.
^- V-v.
2gH '^^ V + Vf
2gH
2.3 VI
Substituting these values of C, B and k in (2), gives,
(6) * = IT ^og«
F^"^*B V+1?
From the definition of a logarithm: if X = log^ N, then e* =
hence
^^' « -B V+v
Solving for v we obtain:
(7) y=V?« -1
Be"+1
From the principles of logarithms we have:
kt ^ ^'^
= 102.3 = 10
Change of Penstock Velocity.
689
nee
(8)
v = V
BXantilogkH — 1
B X antiiog k'l + 1
Equation (8) is very readily applied to finding the curve of
locity increase cm* decrease in any pipe line subsequent to a sudden
lange of gate opening. It has been experimentally demonstrated
m
«
>
iJ
• «
/f
•
#•-
u
a
A
V
z
/
>
h
0
J
■/■
- J
r ■
>
•/
/•
1
.7
p"
-/
C
/
2 3 4
TIMC - 8CC0N08
Fig. 403.— Curve Showing the Acceleration of Water in a Pipe Line After
a Sudden Opening of the Gate.
r the acceleration of water in the drive pipe of an hydraulic ram,
shown by Fig. 403 which is taken from Bulletin No. 205, Uni-
rsity of Wisconsin, Engineering Series, Vol. 4, No. 3, "An Investi-
tion of the Hydraulic Ram," by the writer.
The curve is the plot of equation ('8) and the experimental points
ere determined by an especially designed instrument. The fact
at they fall commonly below the theoretical curve is due to a
stematic friction error in the instrument. The agreement is suf-
nently close, however, to entirely verify the form of equation (8).
Fig. 404 shows the curves determined from equation (8) for
42
690
Speed Regulation.
the wheel used for illustrative problems in Chap. XVIII, Section
228. Acceleration curves are shown for changes from 0 to the ve-
locities of t, i, .9 and full loads; retardation curves from an initial
velocity of 5' per sec. to the above velocities. It will be observed
that in each case the actual velocity approaches, but theoretically
never equals, the normal value, V, for the given gate position.
The values of the constants used in computing these v-t curves
are given below. B, for the accelerating from an initial velocity of
zero, is:
V -f vo _V _
V - vo "V"^
B =
I ^^^
.
.__
Cytij4.a«j^
vti^O^
T*~
O"""
^ — ^
—
— ^
^ fl J^QAD VCL4t
lT¥_|
\\
^
^
\
\
-<ii
H
-^
\
^
^,.,
^
/
WOAD
wctpi
I'ln
V
" — '"
VZ
pfL^
■"""* *
7^-
:=^
=*
'^
^
^
^
- &A9
wq*fl
vrt&
S1-:
_.
^
ZZ^
^~
1
^
/
f~
/
* TiriC m *CC0NO«
Fig. 404.— Curves of Acceleration and Retardation of Water in Penstock for
Various Gate Movements.
The other constants are: H = 50', 1 = 500 , and Vp = ? for re-
tardation curves ; also for the retardation curves B is negative, since
Vo is greater than V. If wc always use the positive value of
B = ^ ^ ^0
^ V V
we will obtain two equations:
For increasing velocities or acceleration
r antiloK k't — 1
(0)
v= V-
antilog k't + 1
For decreasing or retarding velocities,
Bantilog k't+1
B antil(»gk't — 1
(10)
v = V
Change of Penstock Velocity,
"rom equations (3) and (4) we obtain the tables
691
Lo«d.
V.
B
k^
1.0
4,77
41<S
.685
.9
4M
19-1
•623
.§
8.Sg
8.71
.076
M
un
2.27
1.444
i
^The computations of v, by equations (9) and Ci^)j for*variou»
assumed values of t is Y^ry simple if tabulated as below. The
computation of the curve of acceleration and retardation of water
in the penstock from 0, and from S feet per second, respectively, to
its value 2.88 ft. per sec, for 1^ load is shown. It is assumed that
the gate opens instantly from 0 to its position at % load, and closes
to this position instantly when the velocity is 5' per see, giving
the values of velocity in columns v and v', (4) and (6), respectively.
Compuiaticm of v-t eurtne.*
H =^ 6(y, 1 = 600S d = 8 , k / = .976, B = S.71, v, = 0 and B\ V ?= 2 J
(1)
m -
(3)
(4) - V
(5)
(6)=T'
t.
k't
untilog of
k't
C3) + l^'^
t3)X3,71
f^) + ^2B8
,0
.0
1.
.0
3.71
5.0
• .1
.0f*73
1,251
.321
4,64
4.17
-2
,1?™
1.565
,635
5.81
4,077
.4
,asti2
2-45
1.210
9,10
3.59
.li
.5838
3.835
1.690
14.23
3,31
.8
;77W
6,003
2.055
22,27
3.15
1*0
.973
9.S97
2.327
34.85
3.05
K2
1.168
14,72
2.513
54.70
2.99
K4
1.362
23.01
2.64
H5.5
2,95
1.7
1,654
45.08
2.753
167.3
2,91
2.0
1.946
88.31
2,81
328,0
2,897
* A number encloeed in parentheeia refers to the ralue given in the colutnn of
thai number
Referring again ro Figure 404 we see that the acceleration curves
thus computed all have a comnnon tangent at the origin showing an
initial rate of acceleration in each case of,
dT _ gH
The initial rate of retardation, however, depends upon the gate
opening.
6g2 Speed Regulation.
As shown by equations (9), (10) and the curves in Figure 404 the
velocity never equals, but approaches indefinitely near, to its normal
value, V, for a given gate opening.
To show the application of the foregoing discussion to the change
of penstock velocity, power, speed, etc., at a change of load, refer to
Figure 405. Here the line A B represents t load, line C C repre-
sents full load, line D D .8 load and line H H 45 per cent, load for
the same wheel discussed above. Lines A' B', C C^ and Jy U
represent the corresponding hydraulic power input lines. Line
abccba represents the line of gate movement from its initial position
at l^ to its position at full load and back again to 14 load. Line 0
C^ C is copied from Figure(404) and represents the curve of velocity
increase which would result from a sudden complete opening of the
gate. At b the gate begins to open, and the velocity to increase
along an estimated curve B^ Cy, This curve could be more accu-
rately determined by the process outlined in Appendix A, but was
not so determined here. In the same way curve F B% A^ was taken
from Figure 404 and the velocity curve during gate movement, C\B';
was estimated.
Having thus obtained the velocity curve A^ B^ C^ C C\ B\ A^.
the curve of effective head at the wheel can be readily determined
from equation (11) Chapter XVHI, or
V
(11) h = -^^^ IV
While the gate is in motion from b to c the valve of V changes,
but can be readily estimated by interpolation from the values at
14 and full gates. From c to c (gate curve) V is constant, and
equal to 4.77 ft. per second. Since the friction loss in the pen-
stock is slight in the problem under discussion H' is assumed to
equal H = SO'. The resulting: curve for h is A^ BjjChChC'hB'hAt
The curve of hydraulic horse power or input was then determined
by applying the equation below to several points along the v and ^
curves obtaining curve A' B' Ci Y' X'
P -^ _ Avh
*~ 8.8 " 8.8
The output power curve A B C© Y X was then computed by
P_ qhE
"^ " 8.8
E or efficiency for each point was obtained, from the characteristic
curve of the wheel, Figure 245, by first computing from the known
Graphical Analysis. 69
'■^ values of q» h, and S {= 180) at each point the values of the dis
* charge under one foot head and tf>.
Many interesting facts can now be seen from a study of Figure 40
*' It will be seen that the opening or closing of the gate in order to in
'^ crease, or decrease, the power of the wheel has an immediate effec
M directly opposite to that intended and that in the output curvx th
r:
1
'^ ■
•r -^
IS=
t^
-*—
—
CZi
; r:
H
r-
^
^
^
^
_
^
^
.^
=
—
:4_
,
t^^
^
r
—
—
—
—
—
—
—
—
■ —
—
—
-«*
-y
z
—
--
— -
—
\ *"
f
\
■^
^
—
—
—
—
^
^
^
—
^
?*5*
—
id
■
l~
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--
—
—
—
1-
~t
—
' —
—
—
y
^
^
Zl
^
' —
^
—
B
^
^
' —
—
" —
1-
5r
F
—
—
/■
^
F^
—
—
—
—
—
-
lt_
^
^
^
^
T»
—
1
&^
\
^
IT
/
—
—
—
r
—
—
»-
zz
^
^
M
4'
fl
^ii
I^TI
^
1*2
j^
^
'
'
""■-»
^
_
_
ji^
d^
_t
■ I^
A''
WtZ
'\
/
3"
/
V
■i
K
^
--
—
—
-
_.
-
^_
^
<^
^
&
n
"^
"^
^ e
>
i:
1;
po\
sec
anc
mo
hea
it h
to 1
•^
^
' —
I-—
^^
—
—
_.
—
■ ~
—
1- '
~_^
r ~"-
^
^
*"
~"
^
F-8
V "*>,
r
"~
.»
._
'■"
""■
" "
i>^
^
\
<■
V.
s:
K
1
s;'
e
^*
■ 1 1
Fg.405.-
ver reduces to pt
ond. The effecti
i rises during re
vement here use<
d rises to about
4ow, since the pr
% evident that the
the various load
3
-Graphic*
■acticaliy
ve head
tardatior
1 (Vs sec
165 feet
oduct of
areas oi
curves a
1 Anah'sia of Speed 1
, if not quite, ze
drops very greatl
. It is evident
:ond) is too fast
over three time
power and time
the figures gene
re proportional t
1
Etegulation
to for n(
y during
that the
for clos
5 its nor
gives en
rated by
0 the de
t hF
•
early one-hat
acceleration
rate of gat
ure, since thi
mal value*
ergy or work
the ordinate
mand for en
f
e
e
s
694 speed Regulation* ^^^^^^^^^
ergy and the areas of the autput curves are proporttonal to thf
supply. The area between the two curves, therefore, represents 3
deficiency or excess of work accomplished by the wheel, and can
be measured by means of a planimeter or otherwise. The ^^lucof
one square is ^X 2001^^ 50 horse power seconds ^=50X550^
27,500 foot pounds.
It was found in this way that the deficient hydraulic energy sup*
plied to the wheel, assuming the load demand to increase frofn %
to full i3
27,600 X area B' Ct Y' X C B'
= 27,500 X 36
= mWtOOO loot poundi.
The deficient load output is
27,5(J0 X area B C^ Y X C B
= 27,500 X 35 = 963,000 foot pounds.
This deficiency of input over output must be supplied from the
energy stored in the rotating parts, or from the fly-wheel efFccL
and can be accomplished only by a drop in speed of the power unit
Furthermore, in the case considered, the speed can never return to
normal as long as the load remains at full value, but suffers a per-
manent drop due to the fact that v, q, h and power theoretically
approach, but never equal the normal values for the new gate
opening.
The excess energy, when the load again drops to its ^^4 value is,
27,500 X area C E F A B C or
27,500 X 18 = 495,000 foot|M^undH.
It is evident that this excess energy at decreasing load will al-
ways be less than the deficient energy at time of increasing loai
since the low efficiency of the wheel during the velocity-chaitg?
tends to decrease the former and increa*?e the latter.
It is also possible to dissipate the exce^? energy through a by-
pass or relief valve, while no method is available for supplying the
deficiency during load increase except at a ^^acrtfice of the kinetic
energy of the rotating parts and conseque^it reduction of spec^.
In Section 226, Chap, XVIII, it was shown that the percentage
departure of the speed from normal is
S = 294.000 ^^^{^^
Since the deficient energy AK is actually measured in this cast
the estimated co-efficient R becomes unity. The normal speed, 5.
of the wheel is 180, and I will be assumed as 1,000,000 ft.* lbs., or
1,000,000 pounds at one foot radiu*;, then
Numerical Example. 695
J -201 OOP ^^^^
ff-^.OOO 1^000,000 X180«
= 8.7 per cent.
This is a permanent drop in speed.
In order for the speed to pick up again to normal, the gate must
therefore overrun. The condition then is best illustrated by assum-
ing in Figure 405 that the load increases only to 0.8 of full load
value, following the line A B D D, while the gate movement follows
the same line as before. In this case the v, h, wheel imput, and
wheel output curves will be unchanged.
The deficiency of input or of energy in the delivered water is then
(by means of planimeter) represented by area B' D' Y' Q B' or
= 27,500 X 21.8 = 600,000 foot pounds.
The deficiency of output, represented by area B D Y C© B, is
27,500 X 21.3 = 586,000 foot pounds,
giving a speed regulation of
= 2^'«\oS^T805=^-^2percent
The two quantities will .probably always agree as closely as the
accuracy of the problem demands, and much labor, can be saved in
an analysis if hydraulic horse power, or input, only is considered.
At Y the power curve crosses the demand line, D D, and the
speed begins to pick up, due to an excess of developed power. The
time required for return to normal can be obtained by continuing
the two curves until the excess area equals the former deficiency.
In this case 8% seconds is required.
By the successive application of equation (41) Chapter XVIII to
narrow vertical strips of the excess or deficient energy area, we
may plat the speed curve of the unit. In this way curve MSSj..
Figure 405, for increase from 14 to ^"^1 load; curve MSSj for in-
crease from ^ to .8 load but simultaneous full gate opening ; curve
S' Si, for decrease from full to ^4 load, and curve S' Sj for decrease
from full to 45 per cent, load, were platted. Curves MSSi and
S' Sj never returned to normal (180 R. P. M.), but curve MSS, re-
turns in Sy2 seconds, and curve S' Sj in 4 seconds-
It is the belief of the writer that this method of analysis is not too
long for a problem in practice and, if not, is therefore better than
the method given in Chapter XVIII since the conditions before
and during gate movement can be readily included.
APPENDIX— C.
>
THE STAND-PIPE.
It was shown in Section 223, Chapter XVIII that the following
equations apply to the operation of a plant with standpipe:
(1)
dv tt St
_ =^ (accelerating head) = -p b^
dt ~ dt ^ F
(2)
The value of h^ in a plant with penstock, is
= y _ (1 + f _ 4. euij _ := y _ e^i
Equation (2) gives the instantaneous rate of fluctuations of water
level in the stand- pipe.
Equation (3) g^ves the rate of increase of penstock velocity in
terms of the then existing values of y and v.
The quantity, q, in equation (2), represents the water used by the
wheel. This may remain practically constant if the head fluctua-
tion is not too large, in which case the speed of the wheel will suffer;
or, by means of an ideal action of the governor^ it may be made to
fluctuate inversely as the head h, thus maintaining a constant value
of the product, qh^ and hence of the power input of the wheel. In
case this latter assumption is made, then;
qh =qi hi
or q(H -y)=AviCH-cv,«)
Substituting this value of q in equation (2) gives:
i
(4)
dj^A_r V, (H — cv,')1
dt K L^ (H-y) J
The solution of the two simultaneous differential equations 2 atid
3, or 3 and 4, depending upon which assumption is made, is nee*
essary in order to determine the exact curve of variation of head
and velocity. Their general solution is however, very difficult if not ^
impossible in this form. The equations may be applied successively
to short portions of the arc by considering the curves to consist of
Graphical Analysis.
697
great many short straight lines. This method is not too long for
Ipplication to a problem in practice, and will assist in obtaining ap-
proximate formulas which will be seen to coincide very closely with
lllie true curves.
Assume an installation where d==8', 1^500^ H^SO, F^8A.
[Let the velocities on the penstock at fractional loads be the same as
fivcn in the problem considered in Section 228, Chapter XVIIL It
the load suddenly increases from % to full^ the velocity in the pen-
It ock must accelerate from 1,94 to 4,77 feet per secondj or q from
^8 to 240 cu. ft per sec.
Estimating f = .018, equation (3) gives
dv 32.15 r ,,.«,« 500, v« 1
dt
(5) ^=.0643(y-.0S31v<)
01
ind equation (4) gives:
^ = — ^y 4.77X49.2r^
dt ~ dt " ' "'
8 a(H — y)
29.4
or
^
dt 8 H — y
Curves Ay and Ai^ ^Figure 406, show the curves of velocity, v^ and
head, h, respectively, obtained by applying equations (s) and (6)
alternating to the two curves, considering them to remain straight
for the time interval between consecutive points which were taken
from 14 to one second apart depending upon the curvature* The
closer these points are taken the more accurate would be the result*
ing curv^es.
If friction in the penstock, and the action of the governor, in
compensating for the fluctuations of h, be neglected then equations
(1) and (2) become
(7) *^^ - ^ ""
(8)
Dividing (8) by (7):
dt ~ 1 ^
dy A ,
Integrating;
(9)
dv
— T
y* Al / V* \ . r,
To determine the constant of integration, C; let v = v^ when
ys=^o, whence:
«'^ (¥-.'.)
698 The Stand-pipe.
Substituting this value in (9) gives :
(10) y = -^ b^ - ^•)" - <^i - ^)']
Substituting this value of y in (7) and solving for dt gives:
W ^»=A^-V(v.-v.)^-(v.-v,.
The integral of (11) is:
(12) t = -^dn-'^^+0
When t = o, V = Vo, hence
after which (12) becomes:
4 /IF r . — 1 Vj — V I «^ 1
^^ Ag Vi — V,
Solving this equation for v gives:
(13) V = V, - (vi - Vo) cos -^M- 1
If this value of v be now substituted in equation (8) the equatio;
for y in terms of t can be obtained as follows :
y = |.(v.-v.).^sin^t + C
When y = o, t = o, hence C = o and
Since this equation is that of a true sine curve it will be readily
seen that the maximum ordinate and hence the maximum de*
parture of the head from normal is
(15) Y = ±.^(v,-Vo),
and return to normal head occurs when
IF \ IF
Whence
(10) T = .^
Fluctuations of Head and Velocity.
699
Equations 13 and 14 may now be revised to read
(17)
(18)
v = Vj— (Vl-
y == Y sin ^ t
Vo)cofl~t and
These equations, (17) and (18), are shown for a particular prob-
lem, by the dotted lines B^ and Bi, in Figure 406. The closeness of
their agreement with the curves A^ and A^ which involve the
effect of both friction and governor action shows that the values
g B
— r — 1 — r-1 — [ — 1 — 1 — r^
— 1 — r
— 1 — 1 —
■ -( — 1 — r.
"^
—
—
^
^
-^
^
^
L 1
1 1
«'
L^
^
^
^
N,
^y^"
"k
go
.^.^V*"
\
\
1
r
ar/:^:^
^
r'
^1
s
H
OF
l¥'
kL _
VEH
3CFT
^
1 i
_R_ H
irw|
LQ
A0_
_■
kN
a_
J
^X
s_
^
^
If
\i 1
M^
IE
_C
UF
lyi
■_'
a-
/'
r
'N
s
y
"*
s
e 3
^^'
"*
■v
>^
^ 1
'''*
^
■
^
>
■^
/1
Ntin
m.
L^_V
P^DCITY
rjifl
-'■
W
ei
PW
J, LOAD
!"'
"'"'
'"^
1
^
fy
f
s! 0
!
♦a
Jt
'
^ .
n
-=
-
'^-
^
^
'-
-J— tT-
^^^
_^^
|*^,'1
-
*"
039
<
■"
i ! t
tf
>^
'
j.
V
~
=^
^
*%
NOf^MAL HEAD AND
^'f
.
w
^XI5 or e^NE CURVE
~-
H
S.
"a
s
.'
'i
^^B
X
\
-'
^
n
3
•^5
^4D
"^^^
^^^
y
[
^ -
,-
^-j
i
^ j
^,_,,-
"T
<
— — fl
'
/
j.>i '
•B
TIME 8INCE
30
OPENING
40
or GATE
50 fia
IN SCCONOS
Fig. 406.— Carves Showing Fl actuations of Head and Penetock-Velocity
in a Plant with Standpipe.
T and Y would commonly be as close to the truth as the estimate
::ould be made of the probable load change (vj — Vq), for which the
stand pipe should be designed.
More exact formulas can be derived, however, from the stand
point of energy as follows :
Let the time lequired to reach D' and hence to approximately
reach the valve v^, under exact conditions, be —•
700
The Stand-Pipe,
I
k
The time^ will be slightly greater thani^* when friction and
governor action are involved, and the method of dcternuaing it will
be given later (equation 30),
It is evident that the number of foot pounds of energy whidi
must be supplied by the standpipe in this time ^ Is equal to the en-
ergy required by the wheel plus that required to accelerate the water
in the penstock plus that necessary to overcome the friction of tht
penstock minus that supplied through the penstock,
(19) Or E,-Ew+E, + l4 — Ep
Now,
(20) E. = wFD' (h — cV — y)
where D* is the maximum surge below the initial friction gradient
for Vo, and is used in place of Y to distinguish it from the value
obtained by the other formula;
Also,
of thc^
m
(21)
(22)
Ew = A Vj Y^ (H — evj*) and
E.=-^ Al(vi* — Vi«)
To obtain E, we have
(23) d Ei = A V w X cv* at
where c is the friction coefficient and v is obtained from equation (17).
The integration of (23) between the limits t s= y and 0, gives,
m)
vi» C VI — v») + ai T' VI (f 1 - nl*
T 1
-■g^Cvi-vo)' ]
Also to find Ep we have
d Ep ^ HAwT dfc,
ivhere v is obtained from equation (17) as before,
tween the limitsy and 0, gives
(25) E,= HAwT(^-:^i^)
Combining and simplifying:
Integrating be-
tr
(26) D'- -2 (H - cvftM IK = - -|r I -~ (vi* - va') + C [- —
vi« f VI — V0) + 5C T' VI ( VI — ve>* - ij- Cvi — To)»l + —^^— (VI - T.) }
(27) Dii = iy + cV
i
Maximum Drop in Head. 701
The upward surge can be found by the same equation by a proper
change of signs, but is unimportant since it is always less than the
downward surge D^ for the same change of velocities.
If friction be omitted and T' be changed to T for reasons men-
tioned later, equation (26) reduces to
(28)
D« -2HD = --|r {^ (vi« - voM + — (vi - vo) \
To derive an equation for the maximum upward surge D|^, when
full load is rejected, we may e'quate the original kinetic energy in
the penstock to that expended in friction plus that used in raising
water in the standpipe.. The energy lost in friction is found from
equation (24) by putting v^ = o
or E, = g
The other quantities are evident. This gives :
W A L _ , _ A w c T vo» , w F Da«
^^^^•• = 6 +-^— ^'
Equations (21), (24), (25) and (26) are all theoretically exact
except for the assumption that the velocity change takes place along
a simple harmonic in time-^-. The true curve for a half cycle, as
used, is scarcely distinguishable from a simple harmonic but its
period T^ or time for return of water in standpipe to normal level is
greater than the value T, given by equation (7). In three cases
which the writer has solved by successively applying the differen-
tial equations to short positions of the arc he has found that the
true value T may be closely approximated by the following for-
mula:
(80) T^ = Y T
where T is found from equation (16),
Y from equation (15), and
D from equation (28).
The quantity T' is useful in itself as the true time for return to
normal head, but its use in formula (26) for determining D' is not
advisable, as the writer has found by solving a number of problems
that the value of Jy, thus found, agrees almost exactly with the
value of D found from equation (28), in which equation the value of
T from equation (16) is used. Equation (28) is therefore offered as
702
The Stand-Pipe.
a much simpler substitute far equation (26) ind equation (27]
becomes :
(31) Dfc^D + cvo' *
Like all wave motions, these surge waves are liable to pile up, one
upon another, in case several gate movements occur at proper imcr-
vals and, in fact, no limit can be placed upon the possible amplitude
of the surge which can occur in this way. In a plant where large
frequent load changes are anticipated the danger from Hi is source
should receive careful attention. Some means should be adopted
for causing the wave, due to a given gate movement, to rapidly
subside in order to lessen the probability of its combination with
another wave. One method of accomplishing this result is by ar-
ranging the standpipe to overflow at a definite elevation above the
forebay. This limits the upward surge and thereby the maximum
possible downward surge which could occur under any assumption
of gate movements. This method necessitates a waste of water.
Another methodf is that of imposing a resistance between pen-
stock and standpipe. This not only causes the waves to subside
more rapidly but alsOi if properly designed, reduces the amplitude
of a single wave. This is of greatest advantage near full load where
the downward surge is apt to lower the head sufficiently to make
it impossible for the unit to deliver the required power. Anot^ier
effect of the resistance, however, is to change the form of the cun-e
of effective head so that, instead of a slow sinuous pressure drop
after an increase of load, a sudden drop is obtained, Tliis is evi-
dently opposed to good speed regulation as it adds to the effective
sudden load for which the governor must compensate by requiring
a greater q to make up, not only for the increased load, but also for
the suddenly decreased head.'*°*^
Boc. M. E. 190S ha$> derived an ei|tiiiioQ tor
Vi)*+ c* {vi« — Vp»)»
*Mr. Rftymond D* John son in Am
D tie follows:
The results obt ained by this equation agree quite closely with tho^ oblsiaed
by the writer's method and the two eutirely irtdepetidenl ana) yeea oi the problem
Are tDutuaHy corroborative.
f See paper on "Surge Tanke for Water Power Plaeta** b^ R, D. Jotrsicti
with (iiscuesiona by the writer an<! others in the Trans. Am. Soc_ of M. E. I^QS
^*For further dlEcuEf Jon of this auhject and a mathematleal aoaJjils of tb«
problem Fee Mr. R. D. Johaaoa'e paper with discussions aa previoCisly tt*
ferred to*
1
APPENDIX-D.
^
n
TEST DATA OF TURBINE WATER WHEELS.
•
^
TABLE LIX-
1
T£»t of a nS4nch Emit Center Vent Turbine. BuUt
in 180 far the BoM ^
Cottwi Mith,
Lifwdl, Masii,^ after desit/ns by Jame^ B, FranciM,
■
Number
m«Dt.
Oate
opening
ipropor-
Proportlgmil
(dlschafjfe
at full icat*
with Uighest
efficieiiay = l).
Hull
feet.
Duration
of tut Id
minutea.
tkiiji per
mtnut«.
charge
loiec-
ood-
ff«t.
power
devel-
oped.
Fenwit^ V
1
ft
S
4
5
6
7
8
»
I .^,
0,85
o,a
0,35
0.%
0.86
0.15
0,600
o.ew
o.wt
O.Mffi
0.fiW
0,5fiS
0.M4
ueo
14.07
14.87
14,10
14.20
1*,14
UM
14JW
17
85.S
43.4
32.7
ioo
sflO
S&.25
noa
57,53
€6.43
6tf,51
57,iJe
57.87
01.09
4S,£
t1,M
JS:J
41.1
4C»,0
K9.a
0.0 '
87,7
90.3
33.3
35,2
33^.1
37,3
17.0
0.0
S,,, ****,.,
J ».,,.
4.
5. .*
a,
T ••-.
B .-<*
f.,**
10.,.,.
11 ,,
0,SO
a.fio
0.60
0,50
0,50
0,fiO
0.liO
o,eo
0,?M
0.717
0,TT5
0.7«I
0,785
o.aoa
0.815
o,«a5
14,^8
14.30
11 19
U.itt
ia.7S
18,61
13.06
11
10
10
14
li
11
57.0
55,0
54,1
51.4
41.5
&^.»
70-fl
85.0
t»ft.85
a7.06
«J.l7
»f,70
77,11
41.T
Si
58,6
54.4
0.0
TO. a
37.0
*1.5
44.4
43.0
53,8
3».5
0.0
)^ ^. ,
19.. „*«....
J4
15 ,,
W .,.*.
IT
0,75
O.TS
0.7&
0.75
0.75
0.7i^
u,7a
0 7a
0.76
1 00
I,W
1.00
],00
1.0(1
1.0(1
1,00
l.OO
1 00
r,oo
1.00
1 00
o.efis
0,S7i
oe«i
o.oio
o.ots
0.930
0.1H»
O.Kl
0 tna
0.S18
1.000
1.005
i,aw
i,oa>
i,ooe
1,007
1.006
1,010
1.017
1.013
O.aai
0.900
O.Wf
13,53
ia,a7
13.87
lil.4U
13. sa
n.^
18.70
13.40
13.43
IB. 33
iS.itei
13.30
ia.8W
1B,W
la.as
ia.4o
l3.fJ3
13,54
issr
2.5
IS
10
511,0
A4 1
40,5
47.1!
44,8
4a.5
42.a
41 .B
75,2
49.5
41.9
40,7
40.3
30,5
^.0
3»,1
«74
llQ.fi
53.5
0.0
0.0
77,0
95.70
Oi4«
imA2
Hit At
im.5*i
HJ3.77
lo;i.*!fl
H£,A3
112W
mM
113.00
lt3aT7
in.16
1 13, ou
113.07
1H.»
lia.07
110.45
110,32
36.0
»,«
87,5
108,3
107,7
III.S
U3.0
114.0
114. 0
0.0
130.4
137.0
133.5
138.5
135,3
135.9
135.5
135.5
135.7
134 6
0.0
0.0
00
41,7
57,0
05,7
H
7S.B
71,1
0.0
70,7
70 3
70,7
70.7
?».7
n>.7
79,!*
19.2
73.7
73.1
0,0
0,0
OO
IS
IB,..,.,,*,,
■0.. .,,
Si ........
^
21., **
Ifi ^,,
JIO
ST -,.
29.,
80.,,.,
31
13.,
^■M..,.it,,,,
as .
»
3J ,,„
B« ""
J» -...
H
704
Turbine Test Data.
i
I
§
6S^3i3"
• Isll ill
O to -tj
I
3|i
I
to g
1
fc
IS
d1
7^
^ III
lis
lis.
Is
IS
2i
B
!M
1^ B
ei
^ 3 § 4i t Si£
af
■ n r~' 1^ ti^ ^ o^ gif g^ ^ ^ ^ p^ qe ej
^iiiiBllillllil ! ipiilliiji
:iliiHiisgiiil ! igisiiiiit'
§p^S|§mi§liP ^P,l§i.PJl^
liiiliiiiiiiiiiilliiiliii;
Jii^i^g^s^ii^is 1 sl^§igHl il
s.
^;s::si^i ^*r l • z : > i ; i :
*»t«ainij!
i^il§'i^§gi§m§0 §SMSI§8il^S
Victor Turbine. 705
Mimss^si ss8i;2^!es 8ssi;i!89f!B8 s:;sssas ssssRsasx
8sgi^§ss§ i^si^issisfse :i^ii!p!istt^t tUstit iifi44ih94
mmm tmrnt. mum ii mm% mmm
mmim umm mnm \ \ iiisiii mmm
tf o o » o o
mmn mmu liiiiiiiii liiiiii mmm
siiiiisif s«§sa§§8 ssass^iizs mii%t iinsss^ii
ssis^ssss? 9S8s8ssac sassssstsfi^ 8s:9Sf!88 ssissasaisB
^^st'is-s^'s \siisiitt :iriRtiii!iii!is itsiisiit 4^*4944444
mnmn mfifim iip^ssssi m^m mmm
8S8SS88S8 9;8S|e9S8« SSSSSS^^SS ! ! «;^9^8S;S SI^SSS^'S^
g!Ss^)$^:(M^ U4i4i44i ^i^fifsssseii i ; 9«i88!^i5i$ i89(Ktifts8;(
mmm mmu iiiiijiiiiiiiiiii mmt
mmm utmm ummii ^mm m^^^^^^
lumm issssasa w^nnm i^^s^^^ m^mn
i^
iihiM milM ihitmii Bhiii tiihhu
•fm> "i^ 1^ »g 1^
mmm mmu mmmt mmt mmm
43
H 706
^V Test of a 984n€h
^H Lowell^ MouL,
Turbine Test Data*
TABLE T-XT.
Fourneu^^on Turbine BuUt in 1S61
after dmgn^ by Jainc* B, Francis.
^
for the
TVemoHi IfiQl 1
^^m «xp«rU
QAte
opeukij;
(propor*
part.
Proportional
di:iciiarge
at full gatf?
Willi bi*thMt
efficlencj=^l>.
head m
Duration
of t«6t Id
minutea
Reirolll-
tioD* per
minute.
ch&qge
lD»eo-
ood*
f^t.
povrer
oped*
^H
»
3
4
It
ti
T
«
1
^1
^H s.
^H 3
^B 4
1.0
1.0
1.0
1.0
l.O
l.O
1.0
1.0
10
1.0
1 0
1.0
10
1.0
1.0
1.0
1.0 1
1.0
1.0
1.0
1.0
1.0
l.U
1.0
1.0
1.0
1.0
1.0
1.0
1.0
1.0 ,
1.0 ,
1.0
1.0
1.0
1.0
t.o
1.0
1.0
1.0
1.0
1.0
1-0
1.0
1.0
1.0
1.0
1.0
1.0
1.0
0.75
0.7fi
O.Tfi
075
0.7s
0.73
0.75
0.75
0.7.^
0.7S
0.75
1.01
1.01
J. 01
1.18
1.10
l.OH
l.i/I
IM
1.05
1,04
i.ie"
LOS
1.08
1.03
l.Oi
1.0»
1,01
I.OL
l.Ol
LOl
1.17
1,01
1.01
1,0
1.0
1.0
1.0
1.0
1.17
10
1.0
1.0
1.0
O.90
0.U8
L17
0.63
0.07
0,07
O.tiT
0.08
o.aa
1,17
1.00
1.00
1.00
1 00
1.00
IM
1.01
1.00
1.00
0.0»
o.oe
0.S8
0,»7
O.BQ
0.%
Q @5
U.S6
ld.8<$
lg.«7
13.S5
lU 51
IS.flfl
18.70
nM
IS. BO
m.m
"'is'fii"
n.m
it.m
111.8^
IS. 00
12.83
1:2.83
18,87
18.00
12,00
18.43
12. BO
18. go
18. bS
la.tMl
ttf.t»l
38.91
J £.80
1^.54
18.81
18 8il
12. &4
18.94
1S,9S
18.94
U.6
12.96
12.VI
litJlS
i;£.gd
la.flo
18.77
32.47
18.90
18,93
18^95
18 95
lt.V5
12.7a
nM
18 S3
TJ 94
1^.95
18,8^
18.99
18.03
13 00
13.01
13 03
3
10
10
5
a
7
7
5
6
3
8
0
8
8
9
3
B
T
10
0
10
H
9
9
13
5
14
13
It
18
8
6
10
11
11
11
10
a
IS
B
a
8
l.ft
8.5
9
U
10
u
IS
It
7
8
8
i
8
a
9
9
9
9
53 08
53.5
58,5
95,3
ill .9
ST. 7
m,Q
73.5
77.4
71 0
a?.&
lOT.O
1U7.0
04.0
03.4
60.0
58.8
56.7
55.4
64.7
64.1
&3.B
loa.i
68.6
m.i
£8.5
58.3
68.4
68.0
61.1
ma
£0.8
48.8
47.1
14,5
41. T
38.7
107 I
an 3
38.0
SI. 9
r.»
00
0.0
106.8
499
490
47 4
46 8
890
76.1
m^.5
64.7
61.4
37.9
60.3
540
51.9
50.1
4^1 a
339 4;%
13:».4^
389.47
136 69
154 3U
liyj.27
148.46
147.29
146. 0@
144. 8r
143.1*1
"ifiiiia'
148. «S
14S.04
1|K9(B
141.8S
140.47
140. OB
1^0.01
139.90
139. U7
161,60
189. ri
139. (A
138.70
138. S6
138,37
138 61
13B.19
lOij 38
]mM
1HS.23
899. U»
137.71
136.49
r.ir, U
101 tiO
13^34
134 >^
133.75
1^.49
1^ 05
las.tJS
I3«.6»
lasAo
138,47
133.37
138.16
143.^
13AS1
137 75
137. to
137.00
135.54
136 10
134 S3
133. 3U
138. OU
181.4
169.4
150.6
60.0
77.9
940
309,9
1^1.5
131,7
U0.8
147 9
00
0.0
1GS.8
155.8
157.0
153.3
158 J
159 6
169.7
lOO.O
lao.i
0,0
:«o.5
160.4
150.5
1006
160.:^
160.6
160.6
00
100. a
100. 6
160.0
153.4
Jie.i
16!'.6
U 0
153.0
119,8
1^.0
0.0
0.0
0.0
IftI 1
ItiO.?
160. ■
159 J
71.7
1W.6
I9«t.l
14i8
14.^.9
143,3
349.0
3496
149.6
149.3
14S.7
114
HI
;!«
t J
fii
ml
r,A
«u
m'
tni
OJ
Q.<
Iti
mi
75i
^«
U.i
n.9
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mi
m4
Of
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ni
nA
tt
i»J
T9i
ni
TTt
9.«
»>
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ri 1
0*
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mi
ml
ffi.1
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Ui
r»
IS::
IS!
n.i
Tit
^H If ,.
^H 7 ,*
^H i^..^ ,
^H e.»,^,*,..*
^H io..i»*i..*«
^H 11
^m 13 ...
^H 14. ,.*..«<.
^H
^H ]3,,„,«,p,.
^H
^B to.....
^^ ^l..i««#.f«>
21 ,,,^,
^«.«.«i«p.»
M. .!,«
85,.
M..«^..i,^.
i7„„.
^3... ..,...*
£B.«
SO.....
31 .„
m
1 w.,,.,
at.,. »*
85
35,
ST.,,.p.«i..
m,.
sg
10
41 ,
4i. ..•*..•..
43..........
44 ..»♦,,,».
45. .........
45..,,
47....^,«..«,
43 .,,„
41),,,. »..,..
50
51
f (HI.. .,.
\ 53 ,.
54
fiS
5fl.. ........
57
5^
59.
' 4MJ....
, 51 ..,,,
Francis* Tremont Turbine.
70/
TABLE LXI.— Continued.
of a 96'inch Foumeyron Turbine BuUt w 1861 for the Tremont MiUe,
LoweUf Mass,, after designs by James B, Francis,
nbcr
0«te
(propor-
part).
PtoportloDAl
(dlseharg^i
at fulL g^ta
with hlffbwt
hemd In
f6dL
DttratJot)
of test JD
mJauLa.
ond-
Horse-
pow«r
d^vel-
»K* of
em-
1 cianey.
1
%
a
4
0
0
7
S
0
!««#">
0J5
0.75
0.T5
0.49
0.49
0.40
0.40
0.40
0,4«
0.49
0.49
0.49
0.49
0.87
0.87
0.87
o,e5 .
o.;2&
0.S5
o.«a
OflS
0.W
0.95
O.OBT
0.B5
D.9S
1 OS
o.m
^M
0.83
O.BS
0.81
0.79
0.78
0.78
0.7ti
0.75
o*7a
0.99
0.99
0.99
O.BS
0,&7
O.M
O.M
0.59
0.51
0.49
0.4T
044
0.44
o.»
9,17
15.04
ia.03
13.17
13.0a
la.is
18.91
is.ai
IS. 31
11.88
15.85
15.4t
l^.BS
lir.eu
]9.«1
18 .35
18.40
38.48
ia.43
13.5L
la.f^
13.55
13.69
18.58
18.98
14.00
14.09
11
11
11
48.5
€d.5
103.0
Si. 9
8U1
73.1
65.0
60.9
55.4
&0.8
40.5
46.5
4Li
38.9
^.4
51.8
49.8
47.4
74.9
e8.s
fir. 8
40. ^ 1
40.3
ftiO
97.7
18.0
0.0
0.0
871
41.8
93.8
180.99
]3U.d9
U9.55
191.97
115.55
110.1
114.^
115.94
111.63
109. 71
lQiJ.05
lOr.SD
106.58
100.85
100.54
1^.35
13a. 97
]3ei.65
80.45
78.54
UM
' 74.05
71.37
70,0 J
87.83
04.61
50 .:K
50.48
85.tt
38.57
87. !7
147.9
I15J
0,0
0.0
69.3
78.8
90. fi
103.8
iua.7
107.8
106.5
1U7.0
ica.i
9T.8
85.7 1
168.8
J57.0
166.8
0.0 ,
88.5
49.7
60.9
48.S
44.4
a«.7
00
0.0
9C0
o.aa
14.^
70.4
7^.0
0.0
0.0
30.0
45 3
506
90.9
51.7
86. V
65.5
6&.5
04.1
51.9
H.8
nA
78.4
73.3
0.0
14.1
38.9
44.0
40.3
46.5
49.7
38.0
o.u
^«*#-«
T
T
IT
0.0
18.0
lO.t
94.0
7o8
Turbine Test Data*
TABLE LXTI.
Te$i of a S7-inch Left Hand McCormick Turbine. BuUt b^ J, and IT. Mj,
Holifiike, Mass. Teeing Flume of the Holyoke Water Power Co. TeMtid cr
Uonical Draft Tube. Test No. 1156, Oct SI and Nov. I, 18B8.
With the niuDfl flmpt}- a itrftLa of 17 Iba. Applied S.Q f«<et from the cBDier of llie«han,
»ijf!^c«l to itATt the wh«el.
Numbflr
of
expert-
mem.
Gato
op«uiDf?
tpropor-
tional
part).
PrtyportlcinAl
di«chiLr^o
(dlst^hartfe
at full ^»ta
wUh hi^he«t
efficiency =1>.
Mean
head In
feet.
Dumtlon
of test io
mlotites.
RsTolu-
tloDi per
ch&rite
j£i sec-
ond-
feek
power
oped
fin
dfUCJ
1
S
3
4
ft
t
t
8
fl
40
i|9.,.
I ooa
1,01 -0
i.floa
1.000
l.OUO
l.OQU
0.770
0.770
o,m
0.770
0,770
0,770
orro
O.fi].^
0.016
0.615
o.ets
o.ei!s
0.016
o.eis
0.4.'S
0.41^
0.483
0.4g3
0.4^
0.483 1
0.4SS
0.483
0.488
o.saa
o.atto
o.aaQ
0.803
0.360
o,3ao
O.SdO
o.iieo
o,soo
uou
1,007
1 (104
Lo-a
0,iHM
O.U^
0.890
o.awi
0,£t^
O.BSl
O.STfl
0.8OH
0.857
0.817
0.702
0.701
0.757
0,7M
0.744
0,7»l
0.789
OTia
O.OilO
0.020
O.Sil
0.6L&
0.609
O.«0.'l
0.K08
0,500
0,4W
04fld
O.40S
0.408
0.4^7
o*4ai
0.479
0.474
18.77
IB. 03
14. €9
14 JO
11 09
14,73
14,73
14 70
14. IM
15.30
15 HO
iA.a»
15.45
1ft, 47
lfi.63
15. »7
15.85
15. Bl
15. Bl
15.74
I5.T5
15.7»
15.70
10.^
10.^
10.43 1
10.41
^0.43
10.42
1^.45
16.64
10 69
A
7D8:
^.n
8C.75
SO.flS
H.ilS
09.i7
8a.B7
fl5 7C
88,;6
gs.oo
95.50
98,00
101.50
77 75
i0.20
By. we
OU 37
oe.7S
102;S5
7S,13
8»,Ji7
«I3.87
89.50
OS.QO
06,00
09.^
102. «7
105. 5Q
74.75
87. la
D0.»7
09,75
oe.Oii
100.25
lOi.37
244.!^
B44 84
S44.10
«iS.5^
sMo.eo
2^.19
tll.41
sao.si
ftl9,17
>17*03
ilG.S
£13,41
104. £0
IM.Ei
19-1 .nS
193 50
JOQ.fte
lefi.OJ
187.15
185.14
1^.25
ltK>.80
15.1.31
167.40
16^.03
\MM
153.45
18L.5S
lai.ai
130, Oii
m.75
127 90
1«7.21
106. S:)
1^.70
aQG.ao
aoo.it
sn.4g
31K73
813. Od
£99.00
an.os
803.«4
aoo.aA
arnjo
»8.75
»8,00
iftt 71
mt,m
m^M
8^.57
257.51
851 16
£18.37
215 (i»
n'M
aOSTl
S01.38
19^.74
187.07
L1V,30
101.T4
loa.&j
103.46
101.15
mM
149 15
143 )7
U4.M
mil
IBA
(««
37,«,...»««^
«3 If
JK.,^,
MA
a5.»,,.
n«
34„p
SOJl
as .,,,.
fi.et
9^. ........ .
MM
3L,,.,,..*,
MM
aa*,.
tt>
go ,,
81 •
87,., .,
PC
Its
26,.
85,,,,
IT*
»4.»,
TfJi
^., «..«.«..
7BJI
2}
ni
ij
17 i<
ao,
nM
10..,
an
18
tin
IT *..
le p..
]&
:>«
14,,.
n.c
13* ,
n .,...
11
10.,,,..,,,,
7**
lit
<»4l
g
».41,
8
s^^yJ
7..—
e .„,
17 ji
fi.«
4, ..»....,.
mm
8-,
l&^*mM**.**.
1^^^,
^K Samson Turbine. 709 ^M
^^ TABLE LXIIL ^M
Test of Se^nch Mght Hand Salmon Turbine, built by James Leffel Co., Spring* ^M
fields a TeMng Flume of the Holyoke Water Power Co. T§«t iVa I2S7. ^M
June 20, 2900, Tested on Conical Cylinder . ^^^H
With (b« flum« eraptj ft fXttkin oI^Wa. applied a .0 fwt from th« oetieer of the tbftfl, ^^^H
mimcmd to atart tb6 wbeel. ^^^H
Kumber
of
«iperl-
Gate
opening
part).
ProportJonal
d|acb*rge
&t full gttttf
with hiKb<?at
bcadJn
feet.
Du ration
of test (Ti
ReTolu-
tioiiB per
mlnutij;.
Infleo-
Olid*
feet.
powpr
devel-
oped.
Fereefitr ^H
I
%
3
4
S
«
7
8
1
it::::::::::
t.ooo
3,000
1000
IJJOU
uooa
O.«10
OBJB
o,ai))
o.msi
0.9LS»
O.ilfl
0.N6
O.IHS
o.&je
0.M6
O.MO
0.771
0.7TI
0.771
0.771
0 771
0.771
o,aM
0 l»Nt
OSM
U.Agtt
o.<m
o.flao
0.«MS
0.564
0.664
0.504
0564
OSiH
0 561
O.W
0.4i*7
0.4tt7
0,497
0,»95
o.ywi
KOOl
O.MO
0.tH>S
o.wo
owa
0.W7
0.1«!i
O.Wlfl
0.^85
o.B»a
OB®
OJfTO
0.*Ci.>
0^43
0.flS|
o.sia
o>8oa
0-71H
0,7«6
0.7811
0.737
0.785
0.717
0.716
O.OflS
0.060
0.BS5
0.451
0.li47
0JH13
O.fiOl) 1
0.5^3
0587
0.581
o.r*-^
0M2
o,6irr
o.fifia
o.oao
0.517
18,37
l;j.:i7
13. CU
]».5t
la. 50
ia.r,fl
la.ea
ja.u
I8,fl0
lS-79
13.80
13 01
14.0ft
14. U
14.15
14. IS
14.21
14.i?4
H.Sf7
UM
U.63
14 JO
H,70
14,75
W.I31
15.U
15.13
15. Ifi
15,13
15.17
15.45
15 44
15. 4«
15.40
15.51
15.5fi
1&.0I
15.^5
16lhi
16.04
16.04
16.07
4
«^«7
104 00
lOH.oa
111.75
US.50
117.00
99.37
104 85
Wn 75
1 10.114
112 37
iiaja
101.00
103 n
105.00
107. W)
no.*^r
113.50
101*. 12
1(4,00
10fi.S5
100 67
97fif>
100,37
II a. 75
106 »7
no.5o
Ifia.OO
105,00
107 37
U0 76
05.50
10*35
105.75
ioy.87
114.00
101.85
H15.ia
101*. 330
U3.37
117.50
1«5,75
a*5 41
245 75
i^40.HJ
845.i»
a43,ai
SS5 4S
235,56
^.Ht>
S13 37
22».77
ZJl.80
23047
^*j9.a6
517.31
m.58
sio.oa
2OB.0&
007 29
JfOS.Ol
aw.oa
SDi.ai
190,73
188.70
1«8.^
18« 57 ;
lt6,3B
174.50
178.^
17S.S35
m.55
170.7IJ
160.63
159,54
150.11
157. 7S
156,65
156.30
145,14
I4ia.rt7
141.70
140,BI
1I0.S7
316 23
aj7 V7
aor.4o
3aa 19
aw.03
ani C0
304.47
SOLA;:
295 43
381.**
aoa.a*
£96.35
£13 06
S7i<.«J
2.9 bl
8ffi 77
2K0 IS
374. e«
2tt9 i:i
2tt4 JL*
260.71
254,96
254 26
S&J.6S
8!Hn43
24;. 67
ssseo
2a!»0t
336 77
231 17
1235.00
210.89
218.80
417.37
214 Ot
BOi^.'^
201.81
105 ft0
19^. n
iHi.ia
184. ft>
179.56
170.82
ss %
83.5^ '
82.71*
81,64
78.SW
P3.TS
84.60
82 .W
80.63
TS.Ol
81.84
aa.t4
84.10
8041
78.75
84.08
0.5U
m.m
81 45
80.60
70. IS
80,74
80.81
Ttl.fi
80.06
80.86
79,WI
7H7i>
n 01
71*39
7W.S3
7».0'J
77.401
75.WI
n.m
75 01
74. 2D
73.11
71.85
TO. 20
66.06
It,.
J5 ^,„
14
Ifi
S:::;:;;":
a.
St ,..
«o
_M. ,
ik:
fB;!"";;"
»^ ,
»
■7. ........ .
10.-*....*..
114. >.,......
Kl
M,
51.
iO^, „,
!§.,
48
47, „
4» ^^ 1
#4--,
4S.. ««..,...
dS
il«.. *...*.,
40...
»::::::::::
>8.,,,.
S8
» .»,
S;;;;";;;:
ji^.. ........
0...^..*,*.
S...... 1
4*.
t.
f
I ..**
^^^^^^ .^^^^^^^^L^
H 710 Turbine Test Data. ^^^^^^H
^^^ TABLE LXIV, 1
^^^^ Test <if a S4-ineh Might Band Special Hercules Turbine. Buiii b^ ths Ed^ 1
^^^K Machitie C(K, Holyoke, Mass. Testing Flvme of the Holyoke Wut& fmxr 1
^^^r C<k No, 105L Date Nov. IS, 18^7, 1
^H Number
^H experl-
<propor» '
FroporElonml
diftchai<4£i«
mt full »t«
witli hlfiWiit
Mvmxt
head In
feet.
Dumtiou
of tMt is
nalntiMwa.
Re vol u-
Uo&s per
Dim-
ch*rg«
teeu
pow«r
devel-
oped-
•a-
^1
3
8
4
5
e
7
a
e
^^m 4i»., «,,,**..
l.CBO
l.OOtt
i.tkjy
l.UQO
1.000
hOOO
1.000
.rao
.800
.eoo
.HOO
.BOO
.800
.mi\
.800
.660
.650
.050
.«&0
,650
.650
,650
.«50
.fi27
.627
.W7
.SW
.410
.410
.410
,410
.410
.410
.410
.410
l.OOt
.mi
.ii«l
.«74
.104
.lite
.fti4
Ml
.Bib
.im
Jia
.»44
.830
,«!»
.B^
.7^&
,746
,7»»
.734
,72?i
.714
.Tlia
.080
.018
.an
.000
.MT
.»a
.409
.4»4
.480
.483
.47S
.iTS
.467
.400
13,99
WW
14. la
U.^
14.^
u.m
14.38
14 mi
14.73
H:m
14. ^7
14.04
15.01
15. U7
Ifi.UQ
15.15
IbM
15.*>
15.4.i
ia.4«
l3.41>
15. *7
15.60
15. aa
I5.fi7
10.07
10.01
10. OP
10.13}
10.1ft
10. »»
10. £a
10.68
10.08
lfl.64
LO.Otf
iB.eo
iH.ba
10. 7a
1«.7U
5
f)0.40
54 1^
87.00
90 M
&1 00
98.00
101 CO
l(H.a7
go. DO
S3 ifO
^.00
03.70
iff. IS
101 QO
101.67
10^.40
rr,oo
81.00
M.m
SB.flO
>fe.so
10i£.4O
106.7»
74.00
70.87
87.25
91.6:3
9fi.37
90. S5
109,00
77.00
81.02
80.00
94.70
M.10
ioaj&
iw.a>
230.00
^bj 9fl
aiS,Tl
H&.a)
eea.io
1231. or.
:fi9,3jj
ifioo.oa
£00.72
£04.ea
£i£.ue
201.77
S0tL4l
isio.ue
197 afl
L«0.40
17^ M
171*, 0*
m 87
i7rt sa
175. m»
170.10
108. II
Ifi^.^T
10U47
ISi^.U
148. «0
140. H
14!^.<1U
140.98
14^.06
1^.5«1
123.44
123,20
131). SM
119,08
118.^4)
117 ft)
n5,53
aoosei
30e,9i
aoe c!
sw.oo
ajs.ii
285.00
S87.01
287. 1»
^.!«7.10
21^.38
S81.7d
f77.W
^1.48
IHU 96
S50.4S
ffiL7M
2a*. as
tiSOl
S12.10
204.43
m:u
waA9
m:M
m^M
19^.57
li§90
lOS^ftl
lOS.rii
102.07
100. IB»
l&t 51
148.14
H0.«»
IZi W7
»75
e>
n.s
mm
nm
mM
mm
mM
m^m
iiii
*ir»
».»
TT 1
aj*
7341
T4C
Till
lit:
Hit
ne
nM
mA\
mM
mx
43 Jl
^^m S)....i.«.^t
^H m^,,
^H
^H 8fl^-.»i*«.*«
^H 8a>...,
^H
^H
^H T^
^H 8h*
^H £9.. ..>...*.
^H si^* ...
W S6
ss..<
£4 »...
£8..........
££.....-*,.,
gl.,,,.
£0....i^..<.
IV' >....*...
lB...<i.*«i.
17,,
10.>*.......
16 .,,,.
14.*..»..i«*
13
iz
U..........
10
B,.i.«i.>.,
a
' 7...
e .,„
£.........^
4,...*#...«
a...
Si *....*.* *
1 „
1, J
r
McCormick Turbine^
711 ^M
r
TABLE LXV,
■
Tui ofaSI'inch Left Hav^ McCormi<^k Turbine. BuiU bu J. and W. JoUn, ^H
ffolmf^^ ^ass. Tenting Flume of the Holmke Water Fencer Co, Tesi No, ^M
iU4r Feb. 29 and BO, 1903, Tested on Conical Draft Tube.
^1
With th« Sume emptT & Btmlo of 37 lbs. ftppifed a. e feet frttm the otsntor of th« abaft. ^H
sufficed to atmjt tbe whe«L
■
PitiportloniLt
DlS'
■
Kumber
of
ezpBrJh
Gate
discharge
(discharge
Mean
Dura tl on
EftTOlu-
chttj^pe
ODd
fftBl
Horse-
dencj, ^
tpropor*
pa^t^
at full gAte
with highett
omclencj^l).
head in
feet.
of test la
miDiJtea,
tiODI pVT
mlDute.
devel*
op«d.
1
«
3
4
6
6
7
B
t»
•T,, ,,.,*,*.
1,000
LOOT
10.90
fie. 50
lOfl.SS
SOS, 00
86.111
W.. ........
i,cioa
1,001
H,71
101. IS
J03.aD
srw.ia
80.70
M.*..
1.000
0.090
H.70
1Q5.0O
101.00
277.38
86. S4
M....
1.000
0 MS
14. eB
no. 00
lOt.OS
£74. 3S
80.98-
Mi^
1 OOD
0 G80
14 05
113 75
1B9 56
»^ 40
85.91
81.40
S:::;;:::;:
l.OOO
0,H74
H.74
lti.35
187.80
^55] 10
«0.-..
l.OOO
0,»lf(
14.8G
m.25
1HS.09
B34.54
70,01
-••
1,000
O.I^
J5.0I
130.35
170.05
210.74
1^.00
•tt
1.000
0.807
15.10
ise.oo
174.70
1SS.87
51.06'
•n
0.700
0,fl70
]0.fl&
w.ao
174.38
259.30
83.85
n
Q.7m
0,!^
1&.65
90.60
173,55
gfl5.47
^6.54
74 ..*
0.700
0.871
15.07
101.75
i75r.n
204.00
86.04
^. ........
0.7«0
O.SOl
15.70
106.00
171,13
SflU.SI
85.^
«,. ..
0,T60
o.eso
15. 8S
110.7.'i
11 JO. 47
2^7,58
84.66
^-.*...,,,.
O.TW
0.B40
16.M
114.«5
I6ft.07
250. afl 1
K2,3B
TO
0,760
o.tg«
10,04
110,50
105.73
^mM
79.50
...........
O.TflO
O.SI»
Ifl.li
iaiJ7
163. as
2^28.&5
76.14
«*..*......
O.70O
0.795
10.»
129.00
100.65
918.73
70.32
i7.. «*.,....
0M4
0.778
0.707
16.74
15. oa
13S.S5
00.00
154.05
101.93
178.81
£18.42
54.59
81.11
M....
84,.*. -..«..
0.004
O.TW
15, ei
J5.04
04.75
100.®
151.14
140,67
ifl9.73
218.87
82.18
8^.43
a..........
H .,,.
' 0,^
0.74a
J5,II7
104.85
147.07
313.65
W.75
Bl «*,*
UOaM
o.?»
15.73
106.70
146.98
3U6.74
70. 4«
o.e^
0.?^
15. 7S
114.30
144.08
200.99
77.67
fi, «<<.i.f t>,.
o.eai
o.na
15.80
lltt.75
141,08
i8».n
74.20
IS-.. >....*.
0.6S4
0,I19H
15.90 '
337.50
130 75
171.91
67.96
97
O.SOO
0.0&6
lO.Iil
10. OS
134.75
F7.00
137.55
151.19
178.30
57.80
75 .«7
4r...,.*..t.
41.
0,600
0.053
15.90
91,63
13.1.01
170.53
75.04
4a..........
O.fiOO
0.0411
10.05
fr7.ia
130.U '
iai.05
70.03
4*
O.StiO
0.0 JO
15.14
101 M
138.70
178.19
75.61
«.*..
0.500
o.esa
ie,ifl
100.00
127.55
m,08
74.7^
«.
0MO
O.IKI
10. as
111.50
lJ«.Ot
100.13
73 M
41
o.aoo
0.S15
je,s7
118.90
194.^
* 150. S7
00.49
40. -
0,5iD
0,600
10. ao
rJ4.00
Iffl.SO
Hfi-Efl
64.73
m
O.MO
O.Sfll
10. ao
120. flO
1B0.B7
131.20
58.8;»
m
O.&DO
0.585
10.41
135.50
118 OS
114.18
61.71
^
!
711
Turbine Test Data.
TABLE LX\^
ffef* of a 45-imih Right Hand Victor Turbine, Built hy the Piatt Iron Wurh
Co., DayifffK OhU, Testing Fiume of the Bolyoke FTaler Potcer Ca Terf
JVb. 1177. Marth IS and 14, 1S$9, Tested on Conical I>raft Tube.
WlHi the flame emptj a ttrftlii of 10 lb«. applied 3.6 fe«t (ram tb« c«Qtor of lli« tfa^
Aufflced to itart the wlipeL
of
«xpeii*
Gmifl
opvoloft
(propor^
tidHAl
p*rtK
FrDporlioDAl
(dlBcbarfte
^ full f^Ate
with highe«t
b«ad in
feet.
BtimtJon
of test io
ReTolu-
tioni per
cliAj|:e
In sfro-
ond-
feelw
3
4«.
41«.
as..
Si..
»,.
10..
«!..
98,,
97..
SI.,
«.,
1».
ti.,
IT.
1«.
14.
ts..
1ft.,
11*,
10.,
I.,
a.,
7.
« ,
5»,
4.,
s.,
t.,
1.,
1.000
l.CftX)
l.fKW
KOOO
1,000
l.OQO
O.KN)
O.fiOO
0.300
O.SOD
Q.goo
O.BOO
0.800
OJKU
O.BOO
O.SOO
o.eoo
O.TtO
0«7tNl
0.700
O.TOO
0.7U0
0.700
0.700
O.«00
o.«oo
O.0OO
o.«o
0.000
O.flOO"
0.000
O.OCIO
0.503
o.ftoa
Q.C03
0.503
0.GCSI3
O.&QS
O.BOa
O.AOi
i.oie
1.000
1.004
0,W7
O.0T3
0.WV4
o«sai
O.^d
O.Mft
o.dii
o.gir
0.307
0.806
o.««u
p. sea
o.H^e
0.867
o.am
0.861
0h838
o.asfl
0.S03
0.T90
0.7M
0.78L
0.708
0.75S
0.747
O.TW
0.708
0.6M
o.e^
0.A76
0.669
0.66!*
O.QOO
O.flOT
0,eti6
O.MH
0580
0.6SO
0.67*
0.674
0.570
1ft. S8
15.21
15.90
15.^
15.31
15.^5
1A.80
16.il
16.33
15, as
15. S6
15. ao
15.50
15. M
15.68
15,73
15.73
15. DO
16,04
16.30
16,^4
I6.B0
16.34
m.m
16.30
16.16
16.16
16.17
16.113
16.16
16.10
16. SS
10.80
IO.»0
16.38
10.44
16. 4i
16.4iZ
10.43
16.44
16.60
16.60
16.01
10 Ji^
16.60
16.66
10,68
10.08
loft.ar
107.50
111.50
110.07
121.00
19a. r>
1%,«)
iai,&o
T0a.S7
107,^5
111.30
116.80
lltt.OO
lai.so
127.50
ias.50
07.186
106 .TO
111.00
lis. 00
118.07
101. 35
l£5.l2a
161.8?
fiO.OO
104.19
10».0I
114,50
] 18.430
la^.TS
IBOdI
P6.00
101.37
109. 75
111.03
116.50
]»4.50
100. osr
100.76
114.80
130.00
l%.fiO
IS1.60
180 .flO
1H0.S4
I7S.20
17S,2G
170,54
174.41
171. 1»
167.08
J71,7B
171.19
iro.ifi
100. S8
167.41
105.39
m%.m
1(^,76
]6t.5a
16^.45
161.79
11)0.41
1^8.91
167 J4
l&I.Bl
152. S4
147.50
147,04
14«.*1
141.60
14U43
ISO. 51
187.7^
tmm
130.0t
im.m
1HI.85
125.45
l<^4.oo
lai.f^i
isi.m
113.21
119.4^
110.91
103.33
lOg.itf
107.6«
1(17.30
100.50
iflo.a
ITilS
173 i«
170.SI
I6S 34
loa.oe
151.55
Samson Turbine
713
TABLE LXVIL
Test of a 4SAneh Right Hand Samson Turbine, Built by The Jamet Lejfd Co.,
Springfield, Ohio, Testing Flume of the Holyoke Water Power Ca 7M
No, 979. Jan. U and M6. 1897. Tested with Conioad Cylinder
With th<» flume trnptj a ■train of 16 lbs. applied 8.6 feet from the center of the aiiaflk
tufflced to Btart the wheeL
If amber
(propor-
tJocal
part}.
PropoPtlonftl
At full gWkKe
with hlffhEAt
e(Eclency=l).
Heon
bend la
feet*
BiiriLtt^m
of UAt In
RpTolu-
tJotift per
Dle-
charjES
ODd-
feet.
Horse-
power
<fet<l-
opeiL
a^eof
a.
4.
a.
t,
t.
IB.
le.
16.
14.
IS.
II-
10.
9.,
V.
WL
ft.
•6.
ST.
6S.
61.,
41.
«.,
M.I
H.,
«^,
1.000
1.000
1.000
1.000
l,€0O
1. 000
1 000
1.000
o.aas
0.8B
o.8aa
0 831
0.83S
0.83S
0.S8SS
0 684
0.6A4
G.mA
0.»H
06M
0 6^
0.6S4
0,606
0.&66
0.M8
0508
0.566
0.M8
0.4S4
o.«u
0.434
0.494
0.4«4
0.461
0.404
9.066
11.94
1.000
u.sa
o.Me
u.n
6.660
l&.OO
1.601
l&.OJJ
i.ooa
ISJ^
o.«»
IS.M
0.666
t!>.n
o.m
14.09
0.89a
16.03
0.806
iB.Ot
0.667
Ifi.O»
0.866
15.04
0.6S6
15.06
0.8§S
15JI0
o.«ei
15.16
o.m
15. SI
0-847
15.32
0.766
15.10
0.768
I5.1fl
O.Tffi
l!iA\
0.7«*
15 14
0.7M
15 30
0.74s
15,28
6.786
15.SS
0.7SM
laao
o.n9
15.46
6641
iB.es
0.1:33
16.H6
0.660
10 86
0.6SO
16.89
o.oaa
15.84
0.613
js.ao
0.BW
lO.rjO
O.4B0
lA.oa
0 460
16.49
04OT
IC,55
6 497
16.47
0.4M
10.66
0.407
16.50
0.476
lft.08
157.00
133.40
138.13
141. 00
H8.76
153. S3
157,75
100.83
112.60
119.75
1% 13
1£t:i 25
l»l IS
143 00
148 19
15L$6
155.00
160.50
113 B7
1^7.67
131 .£0
135.50
163 00
141.76
147 00
ISO. CO
126.80
181.50
136.76
160 75
14^. S6
148. S5
na.5o
m.je5
134.00
IliT 00
1«6.K7
181.76
136. ao
161.66
171.34
17B.W
iri.eo
173.33
ITS. 81
371.11
153^
lU 34
155.04
166.27
15.'}. (13
154.74
;5<H,m
156.16
35SI6
146,09
133 52
133.24
133*. 31
131.58
MO. 06
128.03
127.53
136. VO
113 t«B
112 (15
112 04
ju.iia
110.4A
109.02
00.70
90.69
60^
60.4^
fiO fl9
87.01
£36. »4
938.66
S40.9T
i40.»
696.86
618.65
£15 OS
219 52
^3. It
223. 61
£21.79
»i»e«
114 01
196.62
189.04
1^83
191.03
187 S5
165.27
1(^.40
178.39
I7fi.9»
169.70
les !^
ltS2 80
150. U8
157.81
152.99
146.23
1S8.[?
1^7.84
1E7 76
127. 73
126 47
121 57
113.18
66.41
81.H
^.61
81,61
81 18
80 0»
74 61
TV. 90
61 60
H3 16
81.80
81 .61
^n
6r»
79.ftS
76. «
80.14
83 »l
83.fl4
82 67
81 68
80.97
BO, 16
79.56
77.01
79.42
rO 26
70 78
78.71
77.11
74 66
73.05
75.28
"\,6I
7S.49
75. B6
74.56
73.60
59 J8
7^4
Turbine Test Data,
TABLE LXVm.
Teat of a 4jhinch Left Hand Improveti Neu? Aiiierican Turbine, BuQi hff ft*
Dayton Olobe Iron ^Vorks Do,, Day loth Ohio. Tmting Flume of the Boiyakt
Watf^ Power Co. Tent. Ko, MOB. Mar^ Bl^ IU04- Tested on Lang Conjed
Drnft Tube. Bah need Gate.
WLtJi the flam« emptf a itmJn of 7 lb A. applied S.5 fset from. Ibe denier of the ah&fl,
sufficed to ftJLrt tbe irbed.
Numb*r
of
eipeii-
opening
(propor-
tlouul
part. )
Proporttoa^l
rdlschar^e
lit full n^ixle
wftb lilijbevt
fltllGleuc J ^ ] ).
htojd in
feet
DumtloB
af («0t Ln
ntlnutei.
a.,
».,
10..
a..
1..
40..
IT
4&.
44.
ID..
IS..
3T.,
10.,
16..
14..
13..
IS.,
11..
8».,
SO.,
fit!.,
e4.,
9tt..
»7..
as..
M.,
^..
81..
43.,
41..
40 ,
1.000
1 000
1 €00
1000
l.OiX)
l.DOO
1,000
J.OfW
1.000
i.OCKI
0,907
OtOT
0 &07
O.W"
0.gl£l|
O.SiS
0 N!ii
0.hj:J
O.m:^
OJt-23
0 H23
oesa
o.eai
0.6&4
O.fl'i*
0.684
^M\
0.084
0 im
0.664
O.ftBl
O.fiftl
O.Nill
O.^Bl
O.lbSl
0,Ei8l
0.&»1
0.4.^
O.'l.'jfl
0.4fiQ
0.409
0.4»»
0.450
0.960
O/UQSI
1.001
1.014
1,011
O.fHIO
0,08J4
0.»7«
0.7T1I
0.944
0.944
0.94D
0.95SI
01>45
0.«S5
0.878
0,683
0.}<«4
0 jtao
0.871
o,««ea
0-S55
0.B48
0,BS8
O.hSI
O.Tim
OJ^
o.rao
0.74li
o.rafi
0.725
0-7O1
0 680
0.fiG£
0.638
0.633
0.M8
o.eH
0,580
0.&06
0,651
o.ids
0.408
0,-l«S
0,4^
OM0
0.441
15,34
is^se*
IFt.lft
t«.lS
ie,37
10.15
15.4a
15.4;8
15.39
15. 4T
15.r*S
15,61
la.MI
I8.5fi
15,Cir
tfi ei
15.07
15.7U
15.7.1
15.74
15. di
15 94
16. ai
10.«I
16.19
15.19
le.lO
ltt.17
16 94
16 35
1641
16,04
Id B5
Tfl 66
15.63
10.76
15.87
18, PT
17.09
i7.oa
17,04
17.10
17.11
17,08
^^^^^^^^^^^^^ Victor Turbine, 715 ^M
' TABLE LXIX, H
afV«* of a 4g-inch Eight Band Victor Turbine. BtiiH by the Pla't Iron Werka^ ^M
Co,, Day ton, Oftw, Teating Flume of the Hobjoke Water Power Ca Test ^^
JVo, 1707. TeMed on Conical Draft Tube. Siting Gate. Nov. iO, 1907, ^^H
with the fiume tmptj m Btr&ln of m IbA. applied B.6 fof^t from Ui« center ot the ihaft. ^^^^M
aumoed to stArC th« wheel. ^^^^|
Number
of
«xper(-
G»ee
opening
(propor^
liopai
part).
pFoporLloDal
diftcbAfpe
(djaeharfr«
at full i^te
with lifjche^t
effldencj=ll.
head lo
feel.
Duraffou
of it'flt la
HI in Kiefs,
HeTolu-
£ions per
minute.
eharre
Inaeo
crnd-
feet.
Horse-
power
^evpl-
oped.
I
2
3
4
jft
6
7
8
I
^;;;;;;;;;
I.OOft
i.mjo
IJIOO
i.ado
1.000
1.000
I oiJO
1,000
1 <xw
l.rxo
1 001
l.lm
I 000
0.900
U.IOI
0 tlOU
WJOU
0.^'0CJ
11,000
o,wo
OJ)00
o,eoo
0000
0.ft«
0.W3Q
0,«0
0,8(0
0 eoo
Q.»JO
o.eiio
o.aio
o.s«
0.800
O.IWO
0-800
0.700
0.700
0.700
O.M)
0.700
O.Ttl)
0.700
0.700
0.?D0
0.700
0.000
0.000
iieoo
O.eUi
0.000
oarii
O.6O0
o.aoQ
O.flOO
O.fiuO
0.t«2
CWflO
O.OHO
o.uee '
O.ilUB
i.one
1.000
1.006
S:S3
0,87»
0.80(*
O.TiSJ
0.P74
D.OOl
o.yoa
0.911
0.&18
o.Dia
0.B04
cm
OSes
0.i31»
OTfM
0.743
0.000
0.7SS
o.ea;
0.847
0.B47
O.Pa!4
HMT
0.773
a.Tio
o.«o
0.ttg7
0.717
o.r<t8
0,75*
0.75a
o.r.'ja
0.70B
O.BTi
0.650
0BI8
0508
O.C^l
0 C34
0.fM3
0.045
o.m
0.«01
0 .iKS
Ofieo
0.54a
O.SOl
10. 10
15J8
15. oa
J5.79
IfiTS
1&74
i3.ro
10.01
10.10
10.23
16 SO
10. ao
16 07
15.00
15.*8
15.90
15.84
is.m
15.81
15.8rt
15.&1
15.W4
lO.US
le.zi
16.38
16.AU
lO.SS
le 15
16.14
16.13
10.23
10. ao
16.W
Ifl.flT
losa
16.67
le.fii
16.43
10.38
16.44
16.53
lO.OIJ
16.70
17,08
10. M
16,8©
10.88
16.90
16.81
10. »0
16.B7
17,04
17.14
3
4
Still
lOU.ltt
i^m
148,00
161.83
lSft.67
105.00
171^.^5
m,75
178,7^
lftaJ»5
ISO. 07
214.35
224-00
i0,76
111.75
127.00
im.m
150.25
168.50
160.35
104 00
Itt8.fi0
174.00
184 2a
IM.OO
218,00
00.®
110,25
l»v60
140.00
148 00
161 76
161 .50
178.75
187,00
215.00
B9 33
110.07
liW.OO
IRJOO
142. as
150.50
160 00
17S.50
SOO.OO
04.BT
105.00
110.00
i&tso
120 50
1S4 r^
Ui.i:5
160,25
lh«.50
£Q4 00
I54.7S
m.n
174.68
IT6 80
mM
17S.7B
i;fl.2S
150 64
miy
176.80
m.sa
100.3a
lOO.aJ?
148.50
140,43
107 71
109 80
16^54
1(^.07
1*4 J6
lao.Ty
158,15
15531
151.08
146.14
I^.BO
ueo.si
142 88
151 Vtl
163 SO
15a 56
14y.»»
147.12
141.45
liisao
127.18
116.21
101,75
135,46
187. B5
187,41
I33.t»
l£^.98
ie4,uo
lsi0,02
in.43
105.73
115.74
117.60
110.03
110.28
11B74
111.47
ice. SO
m.44
101.40
04, Oi
■
!^8L46
BI7.0«
2nJ 22
254. a4
254.01
S2M.35
1.30.18
!W.77
137.01
7ii.5fl
05 69 ^m
Ta.35 ^M
78.08 ^
70.01
7*09
70.87
70.S
78.21.
73 57
61.85
26.05
S::::;:;:::
S
i
T
8.-.*
»...-
4, ,».......
3 ,
t..........
«l
183.44
**6.fr0
232 34
24434
241 M
2mM
20.^,51
1B8 64
IDOI^
101.13
fl3.fO
TH.ao
78.78
81.38
88.71)
^.00
TS.7*
76.79
73 19
5i.4a^
40.U7
S:::;;;;:;;
K.. .-
31.....
S::::::::::
n
ai.,...4— i*
130.31
218 10
234 m
3^,42
2385. W
IB6.97
104 P2
136.71
40.£a
78 40
84.61
Bim
79.3»
74.77
es.8H
63.6«
»7
m
^
9i. ..*.,,...
ta ,
^.*, ...>...
11 -**.
^ ,,,
ag,.,.
47.^......*.
157.87
1^ 7a
2<«.17
211.7a
2011.73
IWTT
17«.40
)OS.f*a
Ut.08
74.80
II
79,HT
75.75
71.53
66.7i
S;:;;:;::::
4& **.*.
4a..,.,
44 "
49 **
4a ,,.
I;e;;:;
M *•*..
5T ..*.<
W
6S,, ,,
147 04
109.00
172.08
178 40
171.43
104,04
150,ri8
ia5.7J
92.74
«fl.35
71.0?
70.11
78.51
77.00
TO 77
75.00
07 sa
47 01
1 a*.........,
58,
111..*....*..
»...
4A
7i6
Turbine Test Data.
TABLE LXIX. -Continued,
Test of a J^-inek Right Hand Victor Turbine, Built by the Hatt Iron Worfa
Co., Daf/ton, Ohio, Testing Flume of the Holyoke Water Power Co. Tai
No, 1707. Nov, to, 1907, Tested on Conical Draft Tube. Swing QcU
With the flume empty a strain of 80 lbs. applied 8.0 feet from the center of the shaft,
sufficed to start the wheel.
Number
experi-
ment.
Qat«
opeainn
tpropor-
tlonol
port^
FroportloD^
dlicbars^
(dLicliari^e
at full eate
with hJ^efll
Mefta
feet.
Duratl^^a
of te«t ja
mLautea,
R«v-o!u
tloEie per
mlnubiL
Dla-
oud--
feet.
Horse-
power
devel-
oped.
■£FOf
1
a
3
4
S
6
7
8
9
87 -•,».,..*
ee**.*
asm
0 ^n^
OfiOO
0.500
0.55S
o.asd
O.Gi5
0.49V
0.4Te
(K4A1
MM
17. M
17.25
17 88
ir.sa
17.31
17 .ao
n;60
04.:iS
100. 67
IIB.^
133.75
lfiO.50
1B4.^
lOL.ea
lOf.OO
m.oi
85.^
iaa.31
I4i«0
144.00
1^7.97
I5f7.47
ll0.4fi
«e40
0A.1I
71 jr
^..i. ......
0(....i.H,».*.
48
7^81
S£ , . . ,
flL.<.i.<...
00.. *»**....
jfiji
CO
Non— For experimenu 2. 10^ 88, 88^ 48, SOL Jacket Loose.
McCormtck Turbme.
TABLE LXX,
Tt^t of a S9*inch Left Hand McCormick Turbine BuUt by the S, Morgan
Smith Co., Yorkf Fenn. Testing Flume of the Hotyoke U'afer Power Co^
Tested on Conical Draft Tube. Test No, ll&l. May iB, 1899.
Witb the flume emptj m Btrein of fl Ibe, applied S.a feet fnim th» ceotor of Ihe iih&ft^
iiaffle«d to iiart tbe wbeeL
Humber
of
expert-
mei:it^
«.,
4.
I-
4S.
«».
Be.
38.,
87,,
opeoiiiff
{proper^
tiOELftl
part;
PrtiporttotDiil
(dlach&rEe
ei rul) KAte
with blfcbeal
6fflclei]cir=l).
ir..
f5.
jfi ,.*,
so..*
li
If....
15...
14..-
lU..
LOOO
l.QOO
roQj
i.uuo
1.000
LOttl
i.ou)
l.UQO
o,m
O.TBft
0 TUB
om
Q'm
0.796
o.Oii
ii.m
0.1921
(1,631
0.691
o.e^i
O.ttSl
o.4«e
0.41)IS
W.4B8
o.4&e
0.4S6
0.46S
0.406
0.390
0,S90
o.3ea
0.390
O.lfiO
0.890
QWO
0.300
i.ooa
l.DOl
o.ow
o.&go
0.977
o.oai
0.M5
o.goft
0,6W
O.SQQ
0.«>8«
0.S7A
o.m
O.BSS
0.813
0,760
0.7&4
a.74S
0.7*8
o.m
O.T2«
o.rm
o.Toa
0.615
O.MO
0.6^
0.62a
0.6i»
0.6J7
o.«no
o.&es
o.55i:
0.5;^
o.sw
0.&l£
O.fi0&
o.aoe
0.50!
0.405
0.4^
Me&D
bsiad In
feee.
1A.79
15.70
15.82
15.85
15.87
i5.yi
15. D6
15.QS
15.05
15.07
]5.*7
15.09
15.96
in .03
10.03
ifl.oa
15.11
16.20
10.J£9
lO.liO
15 84
10. aa
16.37
16.40
16.65
1&.5&
10.55
i6.M
10.50
15.00
16.69
15,71
15.79
16.73
IB. 73
16.7S
J6.T6
15.77
10 70
10.75
Ifl.TT
10.77
DurAtloti
of teat is
mjDutei.
ReTolu*
tioDs per
mtoube
iMt*
cbtfge
la sec-
ODd^
feet
126.00
131.75
138 00
143.00
150.00
154.00
150.^
185.75
118,23
12u.i5
133.0U
130.00
140.W
]45 DO
141100
i5;i.S5
128.75
m.m
130.WO
131.4)0
IM 35
14s:.Z5
147.75
350,25
115.00
123.50
127.75
181. 7.S
130.2^
U'J.OO
150.25
167.75
116.75
121.60
125.50
120.50
183.00
185.50
189.75
145.00
m.ao
Eoree-
power
d«Tel-
oped.
117.83
1L7.40
115.96
116.70
115.80
it4.5;i
110.99
105.86
105.51
loa.oa
104.44
103.0a
imjs
101.72
100.45
90.41
80.»r
80,41
8t}.78
87.fl4
67.16
85,51
65.00
83.55
77.10
76.4r
7.1.05
75.81
74.77
74. 1«
ra.ao
70.71
S3.2C
82.56
82.06
61.08
01.28
00.80
00.38
60.60
58.61
177.88
ITS. as
179.64
179.Sa
ITT. 03
171.06
152.53
I5ii.i0
160.91
101.17
16i0a
100. i^t
157.66
153.45
151.52
146 54
141.30
lao.fe!
Iif&,3^
185.4T
180,97
129.17
iao.79
13^.61
115 26
100.57
110.14
I0«.05
107.53
100.09
104. 6SI
101 09
87.27
83.97
82.91)
81 .rr
HD.IO
7B.48
70.83
73.88
:o 41
54,80
Perceoi-
Ageof
em-
oleaoj.
84.15
65.19
86.78
65.66
m.m
10.70
70.07
88.51
84.4»
85.82
64.70
64.11
31.78
60.19
77.tttf
82.63t
8t.U£
6t.5l
ao.oA
60.05
7iJ3
77.70
74.17
75.80
75.8^
76. ao
75.15
75.fiO
75.U
72.04
ei».77
54.03
70.09
oa.fti
09.44
^.50
€7M
05.32
-64.48
ea.io
56.00
'iS
Turbine Test Data.
TABLE LXXI.
T^st of a Sit- inch Bight Hand Bwain Turbine Bmli by the St&ain TuTbine and
Mfg, Co., LQwetl, MaMS. Testing Flume Qf the Holyoke Water Power Ca .Vft
S7% Date Jan. iO*£U J^'97*
Number
qf
Ottte
opeDlng
(propor-
parlK
FroparlloDal
discburf^e
at full i;ate
with hi^hi'it
efflt:leiit'y si).
Ueaa
bend Ja
DUTAtlOtl
of temi tn
mJnutoa
Clqns per
charge
III Mse-
Knad-
3
m...
m *..
01..
m
m
bA
67
tt.. .......
U
b8.
W
51 .,
fiO,.*.
40
•M.. ,.,..«.
41.........
46...
45. ........
4i ,
4»*.t ^
41
40
8ft..
M
m
m
tt.
«...
m,
ai.„
m*
m,
m
m,
3W
£4
^.. .......
32.........
*1....,..,,
8U.........
fl7,
10
la
IJ
16
1&
r*..
18.........
i»...
u...
10. .««<■.■■
1.000
1.000
l.OtX)
1.000
I.IIOO
1,000
1.000
1. 000
l.OQO
.^5
.«75
,»?«
.875
.7nO
.750
.760
.750
.760
;750
jm
.(^
.€£&
.500
.500
.«oa
.«»
.50l>
,S76
.»75
.8711
.375
.876
.375
.37B
.290
,m}
.flCO
.»0
.sso
.250
.250
.S50
.230
1.0114
.oas
.eg4
.054
.045
.9S4
.0^
.oia
.007
.857
.860
.aeP7
.849
.844
.8^
,J67
.7fiB
.749
.715
.676
.668
.044
.685
.MT
.AS?
.MO
.58S
M\
.021
.614
.&04
.420
.416
.412
.4xn
,401
.886
.se6
,878
.867
.3Sfl
15.16
15, 40
15.4i£
15.43
15.48
15,47
15.44
15.3a
16.16
15,16
16. a*
15.41
I6.fia
15.110
16.^
15,74
15.7a
15.70
15.54
15,(^
15.16
15.20
15.30
15.SS
15.43
15.47
15.61
15.58
16,05
15, 74
15.7S
15 .Si
15,65
I5.ei
15.65
is.fie
15.81
15.10
15,ftl
16. SI
15. ad
L5.21
15. ao
lA.ao
15.58
t&.54
15. S7
15.01
IS. 00
15 81
15 05
16,70
15.74
15.70
laa oo
L40.3»
144.00
140.50
150.75
1^.00
168 00
161.37
iUM
135.75
140.75
H7JJ0
153,50
laooo
IBB .00
141,00
U6,00
140.75
167 .as
156 .7!V
IM.fS
127,50
I4SJ2
140,50
154.50
162.75
160.50
mM
18 1.25
137.50
144.00
J 50.25
157.50
1B3.8a
120,37
13(7.50
123.50
139, ijO
145.07
15^,8^
1011.25
107 .30
113.50
120.25
116.50
]e.2S
1:10.50
146.25
165 75
IK3.&>
ni,7a
170.50
78.49
75.fta
74.74
74. l«
7a. 45
72.73
71. 7U
70.50
70.06
70.42
TO.Ol
07.75
67 03
6d52
65.08
65.41
64.64
04.00
82.38
&2.05
50.00
6tf.45
58.ao
57.70
55.62
55.3^
mM
51.54
51. Od
&L4£
50. H7
50.31
40.82
i^M
4^.06
4l.5t)
41,06
40.58
40,01
SO .96
38.57
8^.40
82.11
3LS3
SL.46
S1,00
80.50
30.91
mM
27.64
111.^
111.4T
lU.Ol
130.10
10».5l
10^.08
101. 7t
1U1.48
Ji7.07
102.56
ltd 20
102.54
laiM
9S.55
20:T»
2a.«r
11.80
«i.ii
SIM
i
Swain Turbine.
719
TABLE llXXI.— Continued.
Test of a SS-inch Right Hand Svxiin Turbine, Built hy the Swain Turbine and
Mfg. Co., LoujdU Maes, Testing Flume of the Holyoke Water Power Co, No,
977. Date Jan, to-tl, 1897.
Number
of
experi-
ment.
Gate
opening
(propor-
tional
I»rt)
discharge
(discharge
at full gate
with hignett
effldenojal).
Mean
head in
feet.
Duration
of test in
minutes.
Rerolu-
Uons per
minute.
Dis-
charge
inseo-
ond-
feet
Horse-
oped.
Percent-
age of
effi-
ciency.
1
2
8
4
6
6
7
8
9
0
0.185
.125
.125
.185
.185
.186
.185
.185
.007
0.857
.849
.847
.845
.848
.880
.181
16.03
16.01
16.07
ioiin
10.18
16.88
16.11
10.40
4
111.60
119.00
180.75
184.18
141.00
146.85
158.25
160.60
158.25
80.06
19.89
19.76
19.62
19.45
19.84
19.07
18.78
18.80
16.98
16.62
16.16
16.47
14.66
ii:S
0.08
46.41
8
46.01
7
44.88
e
48 00
6
40 65
4
87.78
8
84.26
8
88.80
1
H 720 Turbine Test Data. ^^^^^^|
H TABLK LXXIL ^^H
^M Test ef a 3€-in€h Right Hand Vietor Turbine* Built by the Piatt Iron Wm-h
^B Cft, Dayton, Ohio. Teifting Flume of the Holifoke Water Pcnt'er Co, Tat
^^^ No, 1Q81, December 14, ISB?, Tested on Coniml Draft Tube. Ciflittder Gait
^^^K With Uxe Aume empty a ttraln of S lbs. applietl 9,3 feet from th^ Oditer oC tb« •&&!(, ^
^^^H luMcMd to vtart the wl:i«eLp ^^
^H Nuiabvr
^H of
GftbB
opening
tloDal
pATW
FroportloEtal
dLacharge
(dliBCha^e
at full gAto
with hL^e«(
eflflcieacj^l).
Mean
head in
fert.
Dura tin a
of te«t iQ
miaiitea
KeTola-
Uiini per
ebAtKe
in aec-
ottd-
Hoi«&-
devel-
oped.
Eiency
^H
9
a
4
5
6
7
ft
•
^V 1Sr*.«^...l^
l.OtJO
1. 000
1.000
1.000
1.000
l.QQO
1.000
1.000
1.000
1.000
1.000
0.900
0.900
O.uuo
o.eoo
0.900
0.900
0.900
0.900
0.801
O.0D1
O.BDl
0.801
o.eoi
0.801
o.aot
o.aii
0.801
0.?101
0.701
O.TOI
0.701
0.701
0.701
(nTOl
0.701
O.COl
OflOl
Ofltri
0 UO]
0.001
0.601
o.doi
o.&oa
0.S09
o.tm
0.50tl
O.GJS
Ofi03i
0.503
1.010
1.009
1.009
i.ooa
0.9V7
0.9fiS
O.tKJJ
O.WB
0.9KS
0.963
0.941
0.tnj3
0.748
OOttT
0.965
0.95i»
0.9&B
0.947
o.^m
0.9^^
0.914
0.900
0.900
o.etm
O.BIKI
0.884
o.s?o
0.S63
o.sae
0.645
O.BU
0.S14
o.&ts
O.WT
0.7M
0.787
O.TTB
O.70d
D.m
e.7u
0.7oe
0.099
O.0S.>
0.67fl
0.«!»
0.flt7
0.000
0.6S8
0.5»!2
0.588
0 f^'^O
O.&Tfl
16. TD
Ifi.TQ
ie.T4
I4.7«
15. 80
16. Ke
1«.09
li.ss
Ifi.TO
17. sa
14.99
10.99
17.01
17 .04
17.IIB
17.04
17.05
17.0a
17.10
17.07
17 .Od
17.03
17. ft^
17. Od
lfl.97
je.9:j
le.HO
10.80
16.00
10.80
16.9^
17.00
17.0?
17. 16
17. IB
17.24
11 M
17.30
17.44
17.47
17. M
17.54
17 60
17 55
17 M
17.5a
17. SS
17 &e
17 r*
I7.5fi
a
4
133.33
139. 2&
144.^
150.75
IKV.OC)
156. riO
101.7G
162.75
167.00
17!^. S&
177.E5
ISi.OO
^O.qO
1S3.T5
ISO. 60
144, OJ
148.60
15^.00
1.'i7*00
104.00
170 00
132.33
137.75
142.120
147.00
161.25
156.05
159.25
ld3.JS0
108.25
1S6.<J7
lJti.75
144.35
14H.T5
16a. QO
15^.75
1*0.00
137,00
143 as
14H 00
J 5a 75
15»00
lete.oo
m S3
131 67
i»d on
U'i.OO
UO.iTS
166.37
101 60
170-25
lis. AS
116.88
iia,i7
115.08
115.01
iL4.ao
113,40
113.21
110.68
10^,31
108.09
Ki6.S^1
87.70
lis .(17
112.07
111.87
]10.7«
no 03
lOli.lO
107.02
im.m
104.70
104.67
101.32
103 61
102. OB
101.04
100.00
99.18
97.79
94.25
94.03
9S.47
91.54
89.62
8a,8T
83.65
aa.TT
61.91
80.02
7y.77
76.57
78.^
71.81
70.57
»9.Sff
69 .84
6S 44
67.61
175.90
176.99
177.91
177.78
176. ff?
172.97
178,81
169. »
194,07
158.65
15S.37
14l.;£3
mM
ft).T1
mM
79.0
7a.i«
77.H
746&
^ 11
^H s
^H
^H
^H 4
^H s,,,
^H
^m 1
^H 6B
1T2.47
174.74
174 19
I73.se
in .78
]&^.17
]61.«r
100*07
1 fit. 40
1^.40
HU ,67
150.74
157.29
154.60
IfiO.W
144.64
1*4 27
lad.oo
140. sti
]40.Sf
130.75
1*7.70
]84.5S
iao.81
117.85
19129
120 61
119. 05
116.12
112SS
107 .oa
SS.ftt
W.16
98 18
«063 ,
85. S4
78.40
m.vi
iijj
eo9i
80 .St
80.H4
«.it
ta.fl6
78.;»
«0fl4
m>
BOM
89.44
7741
T4r
70 if
78. M
77. :9
74,ft4
UM
7im
mM I
fil4l J
A|4i 1
mrj 1
^1 &!*.,,„.,..
^H S0.««.
^H #.,,„,,..,
^H 48
^H 4r
■ 40'
44 .«■•>•<■
4A.,.p.t^^-.
4:9,. *••<»•>.
41. ....if*.
4C^.. •••..<*»
W......i...
89., .iP,
S.
w::;;:::;;;
as
M.. «..««**«
89,
ai,***
ai,„
80...p,.„i*
M.*
S8*»,.i.,*.»
S6 ...^
fiS
94 *....
S3
sa
30.. ..^..>..
IS
10..........
n...
10...^....*.
lii.,„ ,
H
1 IS ,«
Fc^ experioietK 53
^ Ibo J&ckel wai
rdmoTod from the djoamometer,
i
Special Smith Turbine.
721
TABLE LXXIIL
a SS'ineh Special Left Hand Turbine. Built by the S. Morgan Smith
Yarkf Penn. Testing Flume of the Hohfoke Water Power Ca Test
1611. March 26 and 26, 1904. Tested on Conical Draft Tube. Bat-
tfd Gate.
flume empty a strain of 0 lbs. applied 8.8 feet from the center, sufBoedto start the wheel.
r
Gate 1
opening
Firoportiona]
4ia«harg:o
(discharge
at full gat9
wi%^ high eat
Mean
I>uratlon
Revolu-
, DltH
chATxe
Hone-
■KB of
em-
cJoncj.
Cpropor^
tlon^l
p*rt.
head in
feet.
Df umt lu
tions per
ond-
feet
oped.
fl
3
4
fi
fl
T
9
1,000
o.sq:^
n.oi
iw.oo
II2.S1 1
118.22
&Lid
,,
1.000
O.OSH
10. &9
^m.m
113,05 ;
ITBfia
mAi
«.
1.09Q
1.000
16 ge
;!0S.75
lis. ISO
170. a4
S3. 27
,,
l.OOU
l.ODS
ifi.^
214.60
US 53
179,40
ai.oo
,,
l.OOQ
1.001
16. oa
£30 00
113 .^>
177.97
81, 5:1
,,
l.OUO
0.006
16.04
tii.^y
1 13. ii:
u^.m
B0,2a
-
1 OQJ
o.oei
ir.Oo
»f3,50
111.46
169. IB
76.27
.,
O.OiB
0.«6t
IT.Ofi
194.7a
100.42
177. OB
S8.70
,4
O.MS
O.0G7
17 11
L'Ol.&U
109 00
iTO.ia
M.18
-»
O.IHH
o.Be9
17,08
£[H.7fi
ito,ota
170.75
84.^
»■
0.IM8
0.«6fl
17,14
1&^ 75
110.14
1*^.20
84,17
,,
O.IHS
0.05»
17.1^
9IL.T&
109.30
175.28
«i.26
,,
0.9411
O.fl-lii
17.17
211,00
100.45
mk97
fiO.96
^^
O.G4«
0.010
17,10
3!I4.75
106.11
168. 3a
79 87
"
O.BiS
Dueft
n.oo
210.40
106.60
16Sf.Sl
78.75
0,ffiS
0.000
17. 5»
lfiJ,T5
103.64
178.24
^1,5,08
,^
o.gga
o.eio
IT.tffi
186.75
10^,84
175 66
f^.U
aw
0 81^
(I.UU
n.sj
laaoo
104.^
175.49
86.10
Al
ti.&-^
0.0(10
17.24
197 00
lOa 71
172,95
b5.29
p»!
o.usa
OSOl
I7.l!a
199 ^^i
10^^.90
16S.09
«3.65
■1*1
o.e«8
O.a+3
17. ai
aoa.vio
lOi.OO
164.07
82.17
.*'
o.8aa
O.STO
I7.S0
203 60
100.34
156.110
70.42
0.8S1
O.BM
17.15
Ifll.OO
mM
170 0ft
88.07
*■
0.»&1
o.«%«
17. l«
1«8,&0
100.58
160,24
»4.78
^^
o.s&i
0,^5
17.90
190.50
00.77
162.65
Ki.m
mm
0.B51
o,«e»
n,S7
000.25
9g.0r7
150,48
83.10
,,
06&t
e.fiss
mm
908. S0
%,02
155.60
BO, 90
14
O.S5t
D.«&1
204.^
87:8*
152.6^
TO.ftJ
P*
o.sai
S:^-
nM
am. 25
96.50
150.:!0
79 03
jj
0.8&1
37. a?
:£i« 07
as. 74
146. TO
77.78
j_
0.»5L
082r
17. *s
315 so
D4^f^
141.90
75.75
*»
O.BQl
Q.Bia
17.4i
S18 25
08. &f
iso.aB
74.18
O.Tte
0.88ft
17. 3T
100.25
95.78
161.82
85.55
^,
0.765
0.8S8
17. Si
172 75
fi4.Sl
160 35
86.80
..
0 765
o.eitt
17.41
m.«o
, 08,70
150. £a
86.00
**'
0.765
o,eo6
17.45
im.75
g:S
163.86
».33
,,
0.T6S
o.m
17. 4S
1W.75
145.04
81.81
**
U.TQ&
o.m
17. to
800. as
Ei.rt
100.34
76,66
0.7D£
0.7M
17.38
15U00
87.89
144.67
84.17
,,
0.709
0.755
17^38
166.67
57.50
H7.aT
^S.60
,,
0,TlS
0.763
17,85
16,'*.60
K 3JS
liT.82
84 01
,,
0,702
OTca
17.37
J-S!.(X)
85Ji5
148.45
84.78
^^
O.TOI
0.780
n.ag
175.07
M.Ofl
30.00
83. H4
fli
0.702
0.7SO
17. 4£
4
IfiO.S-i
^.64)
i:i6.:7
82. i«
..
Qim
0.720
17.U
mi. 00
H9.57
133, 4L
81.09
,,'
o.im
0,707
17.4a
1^.(30
M,18
130.37
81.01
*.;
0 700
0.690
17.50
197.75
70,34
124.01
78.75
o.«3a
0.711
17.71
imM
m.u
187.57
83.28
,,
0.68a
o.7oa
17.09
100.26
81.51
U'i.fta
82. HH
^j
0.tS3ti
Q.em
17.71
170 60
00,48
188.66
Mi. 73
j^
0.080
QW9
17.00
173.58
70 68
181.05
82.46
,,
o.ois
0.680
17,70
ITS .DO
T8.80
199.80
89.06
,,
0.038
0.6:0
17.73
1B0.25
n.54
186. Ott
81. »l
^^
0.636
0.0r«
17.74
:S7.50
76.15
isa.40
80.58
..
o.sao
0.6^
17,78
309.50
709
1LS.24
77.IW
u
722
Turbine Test Data
TABLE LXXIII.— Continued.
Te8t of a SS-ineh Special Left Hand Turbine. BuUt hp the & Morgan Anitt
Co,, York, Penn. Teeting Flume of the Holfoke Water P&wer Ca Tad
No, 1611. March 25 and MS, 190^ Tuted on Conical Draft Tube Bal^
anced Oate,
With the flume emp^ a ttimia of 9 lbs. applied S.8 feet from the center, eiiilloed
to start the wheeL
Number
of
experi-
ment.
Oate
opening
part.
ProportioDal
discharge
(dlMharse
at full gate
with highest
efflcienojral).
Mean
head in
feet.
Duration
of test in
mtaiutes.
ReTolu-
Uons per
minute.
obftrga
inaeo-
ond-
feec
Hone-
powipr
« evel-
oped.
P»e(»
•ar-
dency.
1
2
8
4
6
6
7
8
9
a
0.568
0.6B8
0.668
0.668
0.668
0.668
0.658
0.818
0.836
0.666
0.810
0.806
0.580
0.684
iT.n
17.16
17.Ti
17.78
17.19
17.80
17.88
168.66
168.80
168.00
181.00
184.10
6U6.76
^.00
n.40
78.82
78.60
71.78
70.10
68.88
86.46
108.86
180.89
119.86
110.10
108.&S
78.88
TIJI
t9
81 .ft
81
81 M
90
a0.ir
1»
77 Tl
18
IT
74.«
1
Victor Turbine,
tn
TABLE LXXIV.
TeH of a SS-inch Bight HaTtd Vietor Turbin&. Bmlt by the Ptatt Iron WorkM
C(h^ Daytotu Ohio. Testing Flume of the Hot yoke Water Power Co. Test
No. liSOf May i9 and SI, 1900. Tested on Conical Cylinder, Wicket or Swing
Oate.
With the fiume empty a Btrain of 12 \h% applied 3.S feet from ihe c«oler o£ the ibaft,
flufflecd to Al&rt th« wheel
^L 7H
Turbine Teat D^isu
TABLE LXXV.
^1 Test of a SO^indh
SpeHal Chase Jonifai Turbine. Built % ffte ChoM^
Turhim
^M Mfg. Co., Ofa
Tige, Mass, Testing Flume of the Ho^yoke IVater FQiter Ca
^^^^ No. £Se* June 7, 1884*
^^^^P With tbe Rurnt
i empij 4 fitraln of 4 Iba. AppLlfd 3.4 ftot from the center of the thmlX
iufflced to start tiia wh^el
^H erp«H-
^H meat.
G&tQ
(proj>or-
part.
Proportlonai
(dUcharge
at full fcate
wStb hUhest
eflli:jaiicy"l}.
bead Ln
feet.
Dtjr&tlon
of teat tn
miiiuteii.
ttoiu per
mlfiiit«.
Dia-
cbari^e
in *Pi2-
otid>
feet.
HOTf©-
power
opod.
a<E*of
ckncy
^H
s
8
«
6
6
7
8
ff
^H
1 000
0 WSf}
14 73
Still.
as 74
^H e.* ,
1.000
1.U00
1.004
14. dl
H.4B
10&J17
1BLI17
41.43
41.18
4B.flA
60, OS
7S.31
^1 7..
^H e*«.
LOOO
l.OOi
14.61
3LH,75
41.42
41.10
51.60
?B.tf
^H fl..........
^B 4...>«»....
1,04*
LOOO
0.fiM»
1. 001
0.{K«
0.922
14.41
14.41
14.49
14. OS
!a44.i0
lS&.7fi
40 W
41.tJ3
40. dd
38J?
&1.13
&J.43
4ft.£7
75,J«
^H ^..ti«*.t..
^H s...,^.....
^H
^y
O.iiOU
o.t«o
O.tKiO
0.&30
0J37
09ie
o.tia
0.S3L
ll.72i
14. iH
14.87
14,^
1V4,17
£iia.75
sria.oo
2:^00
ISO. 00
Ji8.07
35.07
40.78
50 &^
50.6fi
60 .«a
44.10
7*.t'
m.fk
^ S3,»,...«...
*4.*, ,.
W**w*Mm,*,*
ITi.*
li,, ,,,
0.837
0837
0.847
0.107
0.83?
0.fl74
0.fl74
il.HTi
0.828
o.a^
o.eis
o.eoa
0.t$&3
O.'Ol
IS, 4a
15.3-i
15.^
le.H
lfl.fl7
m.oo
£07 00
siooa
103. fjO
174.25
35.03
$5.00
84. 7o
S4.05
34.40
47.17
47. 4S
47.;$l
47.30
44W
86.15
86.S0
86.46
77 11
77 71
n.n
61 :q
19.61
]G
18*. ...>*.*»
19
i!0.»»..*ti».
14. „.,
IS.«*»*,*«*,
IS....*.....
11
«.674
o.fltty
IIJ.M
hid. 5*1
22i53
BG.M
IB.*
io...„
0.874
O.BT«
0.(15^
10.14
la.ao
SIT.UO
28.40
2».£5
86.^
36.71
19M
»,*,,»,..
30
o.4sa
0,468
{i,4ai]
0,4£fl
17. lt>
17. IL
I7.t«8
14^.»
1&8.A0
I74.a3 1
iSO.n
3S0.a&
1W.43
16*26
16.87
16.74
40.74
4116
£9.*..^«ii.4
2S ..,..
27. ,,,,
0 4^
0.451}
17.m
lag.fiU
ftt.43
iS.4S
SQ 87
le.oo
4^.«
! ^...i...**.
0,4^
0 458
0.457
1
iT.tT
17.09
16.67
16.(4
4LII
i 91. ..,,.••*.
Chase Jonval Turbine,
TABLE LXXVT.
Tett of a SO-imh Eegutar Chase Jonval Turbine, BuVt by the Chase T^irhin^
Mfg. Oo^ Orange Mass, Testing Flume of the Hdlycke Watm" i\jt/vr Co.
June 10, 1884-
WlLb tha flume omptj m stritla tit t^ Ibt. Applied 2.4 feet fram tbe cettt«r of ^ae itMift,
■iiin.ced to sUirt the wheeL
Number
expeii-
menl.
G«te
OpPfliilir
(pp^por-
tlonul
I'ToportfoDvl
Cdisehar^a
at fui] gfite
with bjgbaat
affloi©ttc>=l).
Mom
beodln
ftet.
Duration
of u^flt Id
inlnutea.
Rj^TOlU-
tlonA per
niliiutfs
chflixo
In m&d-
ond-
f««t.
Horwe
powar
OiHid,
.1
9
3
4
6
6
7
s
e
1.
B
KOUO
1.000
LOQO
l.UOO
0880
O.BSB
0.^
0.P89
0,S§B
0.733 !
O.Tte
0.T83
08!!
0,flU
o.eiL
0 611
O.ftll
O.flll
0.411
0411
0.411
O.Ul
0.411
0.»3S
o.vea
O.flttS
owe
i.aji
l.OOT
0.854
0.S97
0.B97
0,80S
O.fiOl
O.WS
0,007
0.7M
0.757
0.75«
0.756
0 707
0044
0044
O.tML
0 t(44
0.0-M
0.W7
0.109
0 w
o.«»
0.4bU
0.471
i5.af
ISJifl
is.ao
16.CT
l5>Sfl
in.7a
15.77
1S.75.
IB W
15.77
15,74
15.718
111.30
10.27
ta.as
ifl.ea
10.05
10,08
16,77
10.87
10.01
17.14
n.ao
17.17
17-13
17.1)0
BtlU.
m.nn
301 .«T
£11.14
237.00
174. 7B
m».25
COiJ ;S
fiL.aa
as(l.07
2£Z (JO
38431.67
1^.50
lfci,25
£o; 00
aiii.OT
Bio.eo
175.80
lt<«.7fi
2112 Oil
lao.aa
111 S3
157.00
100.00
1S4 IIJ
LOO. DO
aa.aa
oi.fla
B2 01
8^.01
Bg.lO
&A7
UW
27,4.1
'27.il
£7,47
n.4a
i7.4T
».08
21.00
£a,0d
j&.a4
«a.Ti
17.47
17.47
JT.46
I7.*a
17.53
49.4B
46,35
46.40
S;3
4LfiO
4«.04
43 06
4^48
43.40 1
48,50
4AM
8«.2ft
00.01
8rt.i>3
S7.00
ao.w
S:8
27 70
ar.os
ii.m
mm
ia.»i
lJ.Oi
71 70
£
71.58
4........PP
71. OX
fl,
71 .M
^.*..»,...
TO.M
M... .......
7S BO
g::::::::::
20 *
74,511
76.M
m
fti.-
7&.70
«...,
Bt .J
75.17
71. «i
*l.....
»
1»*
14*...«.. t ..
11 ."<*
IS.
15 .......
W,. ...... .
17-....,....
T. "
1.—
1.,. .
%
1
7i.W
S:S
Ot.lfl
0X21
01 x\
00.66
38.10
3T.M
34 60
APPENDIX E,
EFFECT OF AN "UMBRELLA** UPON THE FORMATION
OF VORTICES.
Report of Test Made on Sfi-Jnch Horizontal Wheel With '^Umbretlar at tht
Holyoke Water Power Company's Flume, April tofh to 27 ih, J5fl7, by
F. Moeiler, E^igineer Power and Mininit Department of the Wcllw^sn,
Seaver, Morgan Co. for The Southern Wisconsin Povm^ C&mpanf,
The general arrangement of the wlieel and lesling apparatus is sliowi) hj
Fig. 407.
Before beginning the test it was desired to note the action of the watef
without umbrella in place. The penstock was filled, the level of the wawr
being 8' above the center of the shaft, making the total head of water llf.
Under this condition, xv*ith the head stationary and the wicket gates wide
open, a large vortex was formed immediately above tie wheel.
rPWITffflTfFti «
Fig. 407.
Formation of Vortices.
727
Tlie umbrella which was first made T in diameter and dished ll"", was
lowered into the penstock until the edge was Z.V above the center of the
shaft, with the level of the water the same as before. With this arrangement
no vortex was formed immediately above the wheel, but there were vortiees
near the edge of the umbrella, (see Fig. 408). The umbrella was then re-
moved and a raft 8' square was built of matched pine about IW' thick*
tongued and grooved and placed as nearly as possible over the center of the
wheel on the surface of the water. This did not prevent the formation of
vortices. The raft waa then Increased from 8'x8' to 8'xl2^ and placed in po-
sition as shown in Figure 409. This entirely prevented the formation of
vortices under the same condition of head as before and under all the run-
ning conditions of the wheel.
Regarding these vortices it was observed that all of them were formed at
the right hand side of the wheel (standing at the point marked "A," Fig. 408)
and towards the upper face of the penstock. The water enters the penstock
from the left hand side, flows through the wheel and draft tube and oft at
the right hand side. The most reasonable explanation of this tendency for
tiM vortices to form at the place mentioned was that the wheel, being right
haod, the gates at the right hand side of the wheel pointed upward (see Fig-
ure 410) and formed a comparatively direct path for the vortex into the
wheal, while the gates on the right hand side pointing downward, formed an
effectnal barrier. An examination of Figure 409 shows that the left hand
edge of the large raft doe^ not project beyond the gates so that there wae every
chance for the vortices to form at this point, yet none formed on this side in
aB7 of the experiments.
As a result of these preliminary trials it was decided to increase the urn-
bMla. to 10^' in diameter, and meanwhile a test was run off at full gate
aod three-quarter gate opening, with the large raft in place, to determine the
sfllcieBcy of the wheel under this condition. These efficiencies are shown on
the report of the Holyoke Water Power Company and are numbered 1 to 18.
It may be here noted that the Holyoke Water Power Company finds it
necessary to use a raft on practically all of the horizontal tests made by
728
Effect of "Umbrella** Upon Vortices.
thenif the exceptions being onlsr In tlie case of the smaltest wbeeLa, md It U
the opinion of tbe Hydraulic En^neer of that Company; ag a result of Mt
obserratlona on the Tarloua tests, that the etnploytnent of rafts to prsTeiit tlid
fonuation of vortices does not aHect the efficiency of the wheels. This is
Yarified In at least one iDstance, In the test made of two 33"^ runners buUt
for the '^Soo,'* the maximum efficiency obtained was S4%» It being necsefisarr
ta making this test to use a raft, and this efficiency has not been exce^fd
by the same wheels when tested In a vertical getting when no raft was mtL
The next test was made on the wheel with the enlarged umbrfiUa In placi,
the edge of the uttibrelJa being 2' 2* above the center of the shaft, the cexitj^
of the umbrella being In the vertical plane of the shaft The head of lie
water was 16.2'. With the wheel standing stUl fwith gate wide open). Tor*
tices formed ocwaialonally, but only for an Instant, Immediately dlsappearliag
With the wheel allowed to run under the brake, no vortices formed, but Uii
Fig. 410.
surface of the water was disturbed by the formation of whirls, which, how-
ever, disappeared without becoming vortices. This action took place &i aJi
speeds of full gate opening. The same peculiar It iea of the action of tk>*
water were noticed under three-Quarter gate opening^ but at no time ^ere
any actual vortices formed,
A test was then made of the wheel with the umbrella in the last xuni^d
position, and the results of this test are noted under Nos, 19 to ^^ In the ^
port of the Hoi yoke Water Power Company,
It was then decided to suspend the umbrella towards the right side of tH«
wheel. With the umbella In this position there were no whirls or vortices
at any gate opening, and the level of tiie water was entirely smoolh "
cept 0ueh disturbances as were created by the current of the water flo^lni
in. With the umbrella In thli position it waa decided to make a few tfsts
to determine whether or not there was any difference in the eSldenctes ht
tween the two positions of the umbrella.
A test was then made with the bead lowered about 2' and it was d
to conBne the test to only full gate. Tbe action of the water during tb
Comparison of Results. 729
«howed the formation of irregular whirls, but no actual yortlces resulted.
The results of this test are numbered 38 to 43.
The head was then lowered about 1\ Under this condition the level of the
water was about 15^ above the umbrella. No whirls or vortices were formed
and there was less disturbance to the water than in previous tests, but owing
to the method used for changing the level of the water in the penstock* it
was necessary with the water at this head, to allow the incoming water to
fall over the gate so that the water when flowing into the wheel was rather
full of air bubbles. The results of this test are numbered 44 to 49.
The level of the water was then reduced 2' more so that the top of the
^Lmbrella projected 11^ above the level of the water. Under this condition
there were absolutely no disturbances of the water, except that it was full of
air bubbles in the head race, and upon examining the water in the tail race it
was found that the water there was also full of air bubbles. This condition
•of the water probably accounts for the lower efficiencies obtained under these
conditions. The results of the tests are given in numbers 60 to 56.
A final test was made with the umbrella raised so that the top was about
fiush with the level of the water. Under these conditions there were small
whirls forming around the edge of the umbrella, but no vortices occurred.
The surface of the water on the whole was quieter than with the umbrella
placed immediately above the wheel. The results of this test are numbered
57 to 65.
COMPABISON OF RESULTS.
It must be noted from an examination of all of the tests that the best effi-
ciency obtained on this wheel was practically at about .8 gate, so that in
making comparisons for similar speeds under different gate openings, this
•must be allowed for.
ONE — Comparing the results obtained with the raft, numbered 1 to 18,
with the results obtained with the umbrella placed immediately above the
-wheels, numbered 18 to 33: —
Take No. 5 Head 16.09 Revolutions 163 Efficiency 76.18
No. 24 Head 16.16 Revolutions 161.25 Efficiency 76.51
Also No. 25 Head 16.19 • Revolutions 164.20 Efficiency 76.05
These show that the umbrella, if anything, is better.
Take No. 16 Head 16.95 Revolutions 142.25 Efficiency 78.99
No. 17 Head 16.93 Revolutions 187.5 Efficiency 79.11
and compare with
No. 33 Head 16.84 Revolutions 140.5 Efficiency 79.07
This also indicates that the umbrella is a little better than the rafL
TWO — Comparing the umbrella at the surface with the umbrella immedi-
ately above the wheel: —
Take No. 61 Head 16.48 Revolutions 158.25 Efficiency 78.7
No. 26 Head 16.16 Revolutions 157. Efficiency 76.19
No. 29 Head 16.8 Revolutions 159.75 Efficiency 74.08
-show that the umbrella should be placed near the surface of the water.
73°
Effect o£ "Umbrella" Upon Vortices.
I
Take No. 5S Head 16.53
No. 22 Head 16.24
which Indfcates the same.
Revolutions 168.
Revolutions 168.75
EflSdeney 74,S1
TH FiEE— Comparing the resulti obtained in tests numbered SS to 43 wllb
those obtained in tests 1 to IS: —
Take No. 43 Head 14.58 Revolutions 129.75 EJfllciency 77.36 with
No. 17 Head 16.93 Hevolutlona 137.50 Efficiency 79.11
(Giving 137 Vfe revolutions at 16.95 head.)
This shows a falling off In the efficiency » but as specified above, the polM
of gate opening for Na IT is at the poiat of maximum efflcfency of On
wheel, whereas the point of gat6 opeulng under No. 43 is consi derail}
larger and therefore of Itself would be less etSclent.
Compare No. 40 Head 14,62 Revolutions 148.5 Efficiency 77,14
(Giving 156 revolutions at 16.07 head) with
No. @ Head 16.07 Revolutions 154.5 E^flkieney 75.9a
No. S Head 16.06 Revolutions 157.6 Emciencj 76.03
AlBo No. 40 (Giving 160 He volutions at 16.99 Head) with
No. 13 Head 16.99 Revolutions 159.75 EfBciency 75.09
The result of these comparisons would show no loss In efficiency*
F0£7;f— Comparing numhere 44 to 49 with 1 to 18 testa:—-
No. 47 Head 13.54 Revolutions 138. Efficiency 77.41
(Giving 151 Revolutions at 16.08 Head) with
No. 7 Head 16.08 Revolutions 150. Efficiency 75,63
Also No. 47 (Giving 165 RevoIutlonB at 16.99 Head) with
No. 13 Head 15.99 Kevolutions 156.& Efficiency 75.09
This shows no loss.
f/y^^-Compartng teats Nos. 60 to 56 with 1 to IS: —
TakeNo. 54 Head 11.5 Revolutions 136. Efficiency 74.93
(Giving 161 Revolutions at 16.09 Head) with
No. 5 Head 16.09 Revolutions 163. Efficiency 7 6. IS
This shows a loss, as was to be expected from the oondition of the wtter,
as stated above.
As a result of our calculations from the tests we should say as follotps:^
(A) That the use of an umbrella or bood does not reduce the efflcliiief of
the wheel.
(B) That the hood should he Kept as close to the surface of the water ii
possibla.
(Signed) F* MofiLiA
I
r
APPENDIX^R ^™
p
EVAPORATION TABLES. ■
^DifpeJi of etwpomfwM. in inches, at signal sernice stations, in therfnometer shett- ^M
^P ers, computed from the meam of th^ tri<laiip determimiiioti (^ dew-point and ^H
^^ wet-biiib od^rmli0n&* ^^
Stations and
Diatricta,
.egg
If
11
ii
B
Ii
JVeif' England:
Easiport .
Portlajid • . . * ,
.,,. 0 &
1.4
1.6
24
2.5
2.7
2 2
2.9
2^5
26
2,2
14
25 2
.... 1.0
1.2
1.8
2.6
1.8
3.3
is
3.0
34
3.0
2.5
14
29. 7
Mancheet-er . . .
... 0.9
1.6
2-2
3 3
3.8
5.0
4.1
33
2 5
2.8
2.4
1.4
33.3
Konh field .,.
... 0.8
1.0
1.5
2.3
2.5
3.4
3.6
2.7
2 3
1.8
M
1.0
23.9
Boston
... 1.2
1.6
2.2
3.4
3.1
4.7
4.4
4.0
3.5
2 r
2,2
1.4
MA
Natitocket ...
... 1.1
1.1
1.2
1.5
l.»
2.1
3.3
3.S
3.4
2.7
1.8
1,8
3^.6
Wcwd's Holl .
... 0.5
0.8
1.8
2,4
1.8
2.7
2.7
2-4
2 7
12
0.8
0 5
20.3
Block Island .
.... IJ
1.1
1.2
2.0
LS
2.6
2.6
31
2.8
2.6
1 8
1 4
24.0
New Haveu..
... 1.1
1-6
1.8
27
2.7
4.1
3.7
3-8
3.1
3.2
2.4
1.6
31.8
Kew London.
... 1.5
1.3
1.5
2.6
2.8
4.0
3.4
3-9
3-2
3 1
2.4
2.1
il.8 ^
Mid^AtJantic Sta
ties:
Albany ......
0.9
1.2
1.6
3.3
3.9
4.5
5.0
4.7
3.2
ZM
2.1
1.4
34.8
New York Cit^
r... 1.8
1.4
20
3.4
S-3
4.6
5.0
6.2
4.3
4.1
3.3
2.2
40 6
Philfldelphm/
.... 1.6
2.]
2.5
4.4
4.0
5.7
6.7
6.2
4 3
4,0
3 3
2.2
45 0
A 1 1ft n tic City.
.... 1.2
1.6
1.5
2.4
l.S
3.6
2.9
3 3
2.4
1 8
1.2
1.5
26 2
Baltimore
. .. 2.0
2.2
2.8
5J
47
5.6
6.0
5 0
4.4
4 3
3.6
2-4
48.1
Wellington C
hy. 1.8
1.7
2 5
4.2
3-8
6.0
64
4 9
4.1
42
4.5
25
45.6
Norfolk
.... 2.6
2.1
3.4
5,2
4.5
5.6
4,7
4.3
3.3
3.4
3,2
2.6
45. 6
... 1.8
1.6
2.3
3.5
3.2
4.2
4.6
3-7
3.7
2 9
23
IS
35.6
So. Atlantic Stc
ties:
Charlivtie ,..♦
.... 2.6
2.6
4.3
6 4
4.5
5.8
4.0
4.0
4.6
4.0
3.6
2.6
49.0
Haiteras
... 1.8
l.^.
1.6
2.5
2-2
3.0
3.3
4.1
3.8
3.2
2.6
1,6
31 3
Raleij^h
.... 2.0
1 a
2.6
3-8
4.)
5.4
4.2
3 2
3-0
2.7
2.4
1 &
37.0
Wifmin^ton..
.... 2.4
2.2
2 7
3.3
3.3
4.3
4.3
3.1
3-9
3-4
2 8
2.7
38.4
Charleston * * *
.... 2.5
2.5
3.5
3.7
3.[l
4.4
4,5
4.8
42
4.0
3,2
2.5
43.7
Olumbia , - , -
.... 2.2
2.3
2.6
4-8
4.3
5.4
4.2
3-8
4-2
3.4
3.*>
2.4
43-2
Augusta * . • -
.... SO
2.6
3.4
5.3
4.8
6.0
4.8
45
5,1
4.1
3 6
3,1
49,3
Bavannah .,*«
.... 3.3
2.8
4.1
4.7
4.3
4.6
4.2
4-7
3.4
3.6
3.5
28
46,0
Jacksonville .
.... 2.9
2,6
3.8
4.3
4.6
6.3
6.0
4.7
3.8
3,6
30
2.1
45.7
Fl&rida Pminm
la:
t
TituBville....
.... 3.5
2,6
S.3
3.8
3.8
4.8
3.8
4.3
4.0
4.1
S.6
3,1
44 2
Cedar Kevi ,.
.... 3^3
2 8
4 0
4 6
4 5
5.1
5.0
5.e
4.5
4.1
35
2 6
49 5
Key West....
.... ii.!i' 3.7' 3,8
4.5
4.4' 4,8' 5.!' 5.1' 4.7' 4.3' 3.8' 3.6
51 a
•From MoDth
ly Weather R«vie#, Septwobar, 1888.
^
^l^ 732
Evaporation Tables. 1
^^^^^ Depfh of evaporation^ in incbest mt signal ^ert^jW t(^ftoi« jf^^Co&tinned* 1
^^^^L Statione and
1^
|i
m
H Eastern Gidf States:
1
^H Atlfintic *.....>..
2.7
2.6
4.0
6 2
4.7
5.C
4.6
4,7
5.8
4.G
4.2
■■
^H PaDeacola
3.g
2.S
4.1
4.0
4.3
4.6
5.0
5,4
5.2
4.5
3.6} :
^B Mobile ..-..
2.6
2.5
2.8
3.5
3.7
4,C
4.1
4.6
4.6
4 1
3.41 2-2^M
^H Montgomery
3 6
3.3
5.1
6,5
6.9
5.8
4.3
4.S
6.7
4.6
4.^
I a VHf^
2J
2.5
3.6
5.1
5.7
4.8
4.0
6.0
4.7
3-4
4,01 2 -
^H New Orleans « . ^ * .
2.8
2.8
4,1
3 S
4.2
4.1
4.1
4-3
4.4
4.6
3."!
' _
^m West. Qulf States:
^H Shrevepiort^ . . ^ * * .
1.0
2.1
3.0
4,8
4.9
4>2
4.9
6.2
6.0
4.1
B 4
I' 2 44VI
^B Fort3mith.....«>
2.2
2.7
3.5
6.3
4.4
4.6
5.6
4 6
4^7
5.9
3.9' 2 2iDo
^1 Little Hock ..*,.,
2.1
2.8
3.5
6.5
4,8
4.1
5 4
5.9
5.S
5.2
4,:j
2.33L.:
^H Corpui Cliristie . .
1.4
1.6
3.3
3.0
3.2
3,0
4.4
4.3
4.3
4.1
3 C
2s:is.i
^H Gal vegton
1.6
2.8
3.2
2.0
4.3
4.2
6.3
5.2
6.2
4.7
4 2
2J4IJ.0
1
^m FfV^f, Gulf States—
^H Gontinaed.
^H FalePtine *«*.•.*.
2.1
3.0
3.3
4.2
4.3
4.6
5. ft
4-6
4.8
4.4
4.0
2.1 '47 1
^H San Aiitonio . ** . .
2.4
3.3
4.1
3.8
4.0
4.5
6.6
5.8
5,2
6.4
4.2
3.1614
^m Eio Grande YaUey;
^H Eio Grande City« .
2.7
3.5
3,5
3.6
4.6
4.3
e.9
7.0
6.2
4.9
3,6
3.153-1
^H Brownevillet,/. ..
1.8
2.6
2.9
3,0
3.5
3.9
4.0
4.1
3.3
3.0
2.6
2.S
37.0^
^B ^io Valley and
I
^^ Tennessee:
■
r Chattanoogo. , . < . .
2.0
3.3
3.3
5.3i
3.7
4.3
4.3
5.0
5.4
4.0
3.9
L1/I6J
Kuoxvilie
2.4
2.6,
3.4
5,0
3.5
4.2
4.9
6.0
4.9
4.1
3.8
2.H5.y
Memphis ......p.
2.1
2.3
3.1
5.^^
5.3
4.8
4,9
6.4
5.5
4.2
4.1
2AmM
Noshvilla ,..
1.9
2.1
3.2
5.9
6,0
5.1
5.5
6.3
5.1)
4.0
3.3
1.950.1
Louisville
1.7
2.1
2.8
5.6
5.4
5.8
6.8
7.4
6.4
4.9
3.8
LMi.ii.S
Indian a pal la
1.3
1.4
2.2
4.6
4.8
5.7
7.7
6.9
6.2
4.1
3.1
1,6'llfi
Cincinnati.......
1.8
1.8
2.6
4.9
5.2
6.4
6.5
6.6
6.1
4.7
3.3
ZA^U
Coiumbua
1.6
2.0
2.3
4.5
4.8
5.8
6.9
6.4
5.1
4.0
2.6
i.8|4r.8
Pittaburg
1.4
1.9
2.2
3.6
4.2
5.4
6.6
5.6
4.9
3.4
2.8
2.3 14 J
Lower Lake Begion:
Buffalo .,......*,
0,8
1.1
1.3
S.2
3.3
3.9
4.9
5.2
3.9
2.8
1.9
i.ess.a
Oswego ..........
O.fl
1.0
1.1
2.2
2.8
3.8
3.9
4.0
3.6
2.7
2.2
i-o«.t
Bochet^ter
0.5
1.1
0.9
2.6
3.8
4.9
4.6
4.1
3.8
2.6
2.2
1. 3 32 4
Erie
1.0
1.4
1.4
2.7
3,7
4.6
6.5
4.8
3,]
2.5
1.9
i.aiss.n
Cleveland . « * , ....
IJ
1.4
1.6
2.9
3.S
4.4
6,2
4.9
3.8
3.4
2.4
1 ^'"^ '
Sandueky
0.8
1.4
1.5
3.2;
3.7
4.6
5.4
5.4
3.7
3.4:
2.2
1
Toledo..
O.fl
1.1
1.5
3.5
3.3
4,6
6.0
6.4
3.7
3.4
2.4
1.;: -
Detroit
0.8
1,1
1,6
3.0
4.1
4.8
5.9
5.2
3.4
2,8
2.0
1.3
36.\J
Upper Lake Region:
Alpena ...... —
0.7
0.6
0.9
1.6
2,1
3.6
3.8
3.7
2.8
2.2
1.6
0.8
m
1 Grand Haven ....
0.5
0.7
1.3
2-6
3,1
3.8
4.7
3,8
2,7
2,6
1.7
ijyr ■
Lansing..*..
0.6
1.2
1.4
2.7
2.8
4.0
4.3
3,0
2.4
1.9
1.4
1." J- ■
Marquetta .......
0.8
0.8
0.9
1.7,
2.4
3.3
3.4
3.3
3.1
2,2
1.3
l.;i:i.'j 1
Port Huron ......
O.G
1.0
1.1
2.6
3.0
3.8
4.6
4.2
3.2
2,5
1,7
1.0
5j
Chicago ..,,.•*...
i.O
1.2
1.8
3,2
3.3
4.8
6.4
5.3
4.1
3.2
2.3
1.2
m
Milwaukee
0.5
1.0
1.1
2M
2.6
3.81
4.8
3.7
3.4
2.9
1.9
0.9
m
Green Bav
0,5
0.6
0,8 1.7
2.5 4.1
5.6
4,2
3,0
2 4
K9
0.9
28,3
Duluth ..".
0.5
0.6
0.6 1.6
2.4 2.5
3.9
BA
3,0
2.51
1.2
1.0
J
^.0
■
Evaporation Tables.
733
Depth of evaporation^ in inches, at signal i
iervice «/af tow*— Continued,
Stations and
Distdcti.
'CO
^ i-.
a) s?
1^
2 CO
li
t'
s
>
Extreme Northwest:
Moorhead .... —
0,2
1.4
0.5
2,1
S.G
3.S
3.7
3.3
3.5
2.4
1.3
0.5
26. a
Bsint Vincent
0.3
0.3
0.5
i.a
3.8
3.9
3.1
2.6
2.6
2.0
0.9
0.3
22.1
Biainarck
0.4
0.6
0,6
3.0
4.3
4,1
5.6
4.2
4.0
2.6
1.2
0.4
31. D
Port Buford
1,4
0.7
0.6
3.0
4.7
5.0
6.2
4.9
4.8
3 0
1.7
0,5
35,6
Fort Tottea ......
0.2
O.S
0.4
2.2
4*6
3.8
4.2
3.7
3.7
2,3
1.4
0.4
27.2
Upp^r MUsiMsippi
Vaiie^f:
St, Paul
0.7
0.7
2,2
2.0
2.3
4.1
6.0
3.7
2.8
2.4
1.5
0.7
28.1
I^CroBse ,>»..».,.
0.4
1.2
1.4
3.3
3.5
4.4
5.4
4.7
3.0
3.0
l.S
0.8
32.9
Duv^np^rt .....^ ..
0.5
1.0
1.8
3.8
3.4
4.0
6.9
6.2
4.4
3,0
2.3
1.1
39.0
Def^Moiiiee
0.6
1.0
1,5
3.7
3.1
4,2
6.6
4.7
4a
3.3
2,3
0.9
36.0
Dubuque. ., .^ , . . .
0.7
1.0
1.4
2.2
2.9
4.2
6.2
4,8
3.3
2.8
1.8
0.9
33.2
Keokuk....
0.8
1,1
2.1
4.2
3.7
4.3
7.0
6.g
6.0
3.8
2.9
1,2
42.9
Cairo
1,6
2.1
2.9
5.8
4.4
4.3
6.6
6.6
5.1
4,5
3.8
2.3
4S.9
Springfield, III...
O.S
1.1
2.0
4.6
3.8
4.3
6,4
6.6
4.5
3.5
2.9
1.4
40,8
St. Louis
1.3
1.6
2.5
6.5
4.7
5.0
7.5
8.0
5.9
4,9
3.9
1.4
52.2
Missouri Valley:
I^umr
1.1
1.6
2,4
4.4
3.8
4.0
6,0
4.6
a. 7
3.6
2.9
1.5
39. e
6 print? field, Mo^..
1.1
1.7
2.4
5.0
4.3
4.0
5.0
3.4
3.4
3.5
3.1
1,4
33.3
Leaves) worth
0.9
1.5
2.3
4.6
4.5
5.0
0.3
4.6
4,0
3.9
2.7
1.4
41.6
Topeka
1,1
1.2
2.0
4.0
4.1
4.1
6.3
3.5
3.2
3.0
2.2
1.4
36.1
Omaha
0.8
1.6
1.4
4.4
3.8
5,2
6,2
5.2
4.S
4,3
3.0
1,4
4L7
Crete
0.7
1.1
1.2
3.5
3.8
4.5
5.6
4.7
3.8
3.6
2.4
l.I
35.5
Valeutine^*,, ,, , .
1.2
1.6
1.8
5.0
3.2
5.3
6.9
6,0
6.2
3.8
3,3
1.5
43.8
Fort KuUy
0.6
0.9
1.3
4,4
4,1
5.2
7.7
4.9
6.7i
3.6
2.8
0.7
41.9
Huron
0.3
0.7
0.8
3.7
3.7
4.1
5.7
4,2
4,1
3.1
2.4
0.7
33.0
Yankton . .^., .. ..
0.4
1,4
1.2
3.3
3.1
4.4
4.6
3.7
2.9
3.0
2.2
0,8
31,0
Northern Slope:
Fort Afisiniboine,.
0.8
1.2
1,2
3.8
4.1
4.2
6.8
5.5
4.8
3.5
2.6
1.1
39.6
Fort Cusier . ,
0.6
1.5
1.3
5.4
6.8
4,9
9.6
8.0
6.1
3.4,
2.9
1.5
ri2.a
Fort Maginnia..,*
1.1
1,4
1,1
3.3
3,2
4.6
0.8
4.6
3.8
2,8
2.0
1.1
35.8
Helena.
la
3.6
2.1
6.1
4.3
5.5
7,2
7-7
6.4
4.3
3.0
2.1
53,4
Poplar River. ....
0.4
0.8
0.8
2.7
4.9
5.7
6.0
4.8
4.4
2,5
1.7
0.7
35.4
Cheyenne .,••..,.
3,3
5.7
4.0
8.2
5.2
10.4
8.0
7.7
8.6
5.8
6.1
3.6
76.5
North Platte
O.S
l.S
1.8
6.4
3.9
6.9
6,0
4.8
3.7
2,8
2.3
1,1
41.3
Middie Slope:
Colorado Springe.
3.0
3.3
4.1
6.7
5.6
4.3
6.7
7.2
6.8
4.6
4.2
2.9
59.4
Denver
2.8
3,7
3.6
7.0
6.8
10,5
8.3
8.5
6,1
4.9
4.2
3.1
69.0
Pike'a Peak
2.1
1.3
1.5
2.1
1.8
1.9
3.0
4.0
3.0
2.3
2.8
1,0
26.8
Concordia. .......
1.3
2.g
1.8
4.8
4,3
6,7
7.3
5.2
4.3
4.5
3.4
1.8
47.2
Dodge City
1.4
2.4
2,8
4.1
4.6
7.4
S.3
6.6
5. .5
5.2
4.2
2.1
54.6
Fort Elliott
1.3
1.9
3.2
5.1
5,4
8,2
7.6
6,2
6,4
4.7
4-^
2,2
55.4
Southern Slope;
Fort Sill
1.6
2.0
2.6
3.8
4.0
4.4
4.8
7.6
6.1
4.2
4.1
2.0
46.1
Abilene
1.8
1.7
3,1
4.2
6.0
6.8
9.5
7.5
6.2
4.6
3.4
1.7
54.4
Fort Davis
5.4
5.7
6.7
8.5
11.0
12.0
11.4
9.0
5.9
6.2
5.7
4,9
96.4
Fort Stnnton , , , - ,
a.&
3.9
6,2
7,-3
9.6
10.9
9.4
11.6
3.9
4,0
3.6
3.8
76.0
■
Evaporation Tables. ^^^^^^^^H
^^^^fe D^pth ef tvaporaihn^ in incheMf at aifffittl service aiathiM — Continued.
^H Btationfi oiid
^H Districti.
11
< '^
If
am
n
li|li
%
9
>
^H SouiherH Plateau:
^M Et ¥mo
4.0
3.9
6.0
a. 4
10.7
13.6
9.4
7.7
6.0
5.2
4.fl
2.1
?10
^H BsntA Fo
3.0
3.4
4.2
6.8
».8
12.9
9.2
9.8
6,0
6.7
5.7
2.7
:^,s
^H Fort Apache
2.6
3.0
3.6
6.S
9.4
9.1
7.1
«.7
6.3
5.2
4.1
2.6
t5.5
^H Fort G mn t • « « . . .
6.2
4.8
0.4
9.2
10.2
13.8
12,4
10*5
9.0
7.9
7.S
4.Q
101.2
^H Prei^cotl > ^ > . . . . .
1.4
2,8
3.6
bA
6.2
8.1
6.0
6.5
4.7
4.9
3.6
2,2
■rfiO
^H Yuma •«.»** .^^ .
4.4
5.2
0.6
9.6
9.0
12.6
11.0
10.2
8.2
8.2
6.5
4.«
y^.T
^H Keeler . ,..,.•••'
3.0
4.0
6.3
8,7
9.3
11.9
12.8
13.9
10.0
8.8
5.S
4.g
lOOti
^H Mtdfik Plattau:
"
^H Furt Bidw«)l ... ,
0.8
t.S
1.8
4.0
5.2
4.0
8.8
8,1
5.0
4,6
2.4
l.S
4g.»
^H \V i n n e niucca . - - ^
0.9
2.8
fi,2
d.l
9.3
lO.l
11.5
12.0
9.9
6.6
3,7
l.g
^J
^B Ball Lake City. . .
1.8
2.7
3.6
7.2
6.9
8.9
9.2
10.7
9.6
6.5
5.0
2,3
7i4
^1 Montro^.
1.8
2.7
3.7
6.2
7.0
11.1
10.2
S.3
6.9
6.2
3.4
2.C
68.3
^H Foit Bridger....
1.0
2.5
2.7
4. a
4.3
6.5
7,7
6.8
5.6
4-2
6.2
4.7
mA
^^^H I^orthem Plea teau:
^^^V Boise City
1.6
2.5
3.3
aa
0.5
6.6
10.0
9.2
7.4
6,2
3.2
1.8
63.9
^ Spokane FalJe...
0.7
1.7
2.7
4.4
5,4
4.4
7,7
0.4
3.8
2.5
1.7
1.4
42.1
H AValla Walla...,
1.1
2.9
3.6
0,2
7.7
5.7
9.9
7.9
5.1
3,4
l.S
2.4
57.7
^H N<K Paeific Coaist:*
^H Kort Can by. ....
1.2
1.1
1.8
2.1
2.8
2.3
1.8
2.9
1.8
l.S
1.5
0.9|
21.1
^H Olyitipiatt*
1.3
1.2
1.8
2.5
4.1
3.3
3,2
3,1
2.4
1,5
1.3
1.1
M.$
^H Fort Angeles —
1.0
0.9
1.8
1.8
2.5;
2.1
2.1
1.8
1.5
1.2
1.3
1,1
lU
^H Tatooflh JslaDtl..
1.2
1.1
l.S
1.4
1.8
1.8
1,4
1.4,
1.4
1.0
1.8
14
Wd
^V Astoria
1.1
1.0
1.6
2.1
3.0
2,7
3.0
2.9
2.6
2.3
l.S
1,2
2&.3
f Portlana
0,9
la
2.4
3.4
5.0
3.2
5.4
4.2
3 4
2.7,
1.8
1.2
S4.7
\ Rogeburg
1.2
1.0
2.7
3.9
4.7
3.5
5.4
4.7
5.0
3.2
1.7
1,0
S9.2
Middle Paciflo ;
1
Coast.-
™
R^d Bluff
3.0
4.6
5.4
6.1
7.0
6.9
11.0
10.7
10.1
10.5
6.9
8-6
H4J
Sacramento
1.8
3.1
3.7
4.3
4.2
5.6
5.9
5-0
6.5
7.3
3.9
2.4
M,3
San Franeieoo.t.
2.7
2.7
3.3
3.1
2.B
3.1
2.4
2,5
3.3
5.0
2.8
3.0
m.:
^0, Pacific CoaH:
Frefiuo
1.8
2.8
3.0
5.0
6.0
7.0
9.1
10.2
7,6
6.7
3.8
2.1
65,S
Los Angeles
2.3
2.0
2.8
3.4
3.0
3.8
8.2
3.5
3.1
4.1
3.0i
3.0
^7::
S4n Di^o,,,,, , .
2.9
2.7
2.5
2.7
3.3
2.8
3.2
3.3
2.9
4.3
3,2
3.7 37 5 1
. J
i
APPENDIX.— a
TWO NEW WATER WHEEL GOVERNORS
The Glocker-White Turbine Governon— The L P. Morris Com-
pany has built a governor for the Electrical Development Company
of Ontario, Canada, which has one novel feature * A cross section
of its distinctive feature is shown in Fig. 41 r.
The governor ball is hollow and contains two chambers, a and b,
communicating with each other through a small opening*, c*
The balls are partially filled with mercury which, when running
at normal speed, the axis of the ball being vertical, is divided be-
tween the two chambers. When an increase of speed throws the
balls outward, centrifugal force causes a flow of mercury from
chamber, a, to chamber, b* This raises the center of gravity of the
ball and increases its lever-arm about the knife edge, j, thus increas-
ing its effectiveness by making its movement increase in a greater
ratio than the speed increases, Similarty a reduction in speed causes
the balls to incline inward and the mercury therefore to flo^v from
chamber, b» to chamber, a, which tends to cause a still greater in-
ward inclination.
The charge of mercury hence increases the sensitiveness of th^
governor balls to small changes in speed.
The centrifugal force of the balls is resisted through knife edges*
K, K, by a spiral spring. Tliis movement is transmitted by levers
to a small pilot valve which controls a larger relay valve admitting
oil under 250 pounds pressure to the cylinder. The gale to be moved
is a cylinder gate opening upward, a force of 15,000 pounds being
required for the purpose. The weight of the gate fs sufficient to
close it and the power- cylinder of the governor is therefore made
single acting. The entire governor is not shown as there are no
other unusual features.
The Allis-Chalmers Governon— This Company has recently de-
veloped a water wheel governor, the following description of which
is taken from their bulletin No, 1612:
•See "The Qlocker-Whlte Turbine Governor'* by W. M. Whtt^ and L. F,
IAiii;dr !n **Power/' Aug. 4. 1908
The Allis-Chalmers Guvernors.
»37
"The Allis-Oialmers Governor is of the oil pressure type and con-
"^ststs of three distinct elements:
rFirst — Governor Stand (see Fig". 4i2) containing the apparatus
Ftg. 4l2.^Vlew or the Governor Stand of the AlllsChalmer Governor*
For controlling the time of application of energy for actiifiting the
ates-
**Second~Regulattng Cylinder for applying energy.
"Third — Pressure System for supplying energy-
738 Two New Water Whetfl Governor. ^^B
**The Governor Head (i), designed to be a highly sensitive yrt
stable apparatus and driven from the Turbine Shaft by Pulley (2),
forms the basic governing element. Any change in its position
mo^^es the Governor Collar (18), thereby shifting the Floatinf
Lever (3), and through it and its connection with the Relay (4)
(which momentarily acts as a stationary fulcrnni) actuates the Reg-
ulating Valve (9), Any movement of this Regulating Valve admits
oil from the Pressure System to either tlie opening or closing side
of the Regulating Cylinder and thereby actuates the Turbine gates.
The Relay (4) forms a mechanical connection between the Regu-
lating Cylinder Ptston and the Floating Lever {3), constituting what
may be termed a moving fulcrum, so that every movement of the
Regulating Piston shifts the fulcrum point and brings the Regu-
lating Valve {9) back to mid position, thereby making the mechan-
ism ''dead beat/* If this movement is adjusted so that the position
of these parts have the proper relation, the Governor Collar will
practically retain a fixed position.
"The Regulating Cylinder cannot however, fully open or close
the turbine gates instantaneously and the above result can only be
obtained within certain liinits, a difference of speed occurring be*
tween no load and full load that requires a certain movement cc
travel of the Governor Collar f 18). Consequently, the speed of the
Turbine at different gate openings will vary slightly and depend
upon the speed of the Governor at corresponding positions oi the
Regulating Piston Stroke.
"Under favorable conditions (open fliime and short penstocks)
the opening and closing time of the gates depends soJely upon the
inertia of the moving masses and **a period! .:al regulation^' can be
obtained ; i, e., the stroke of the Regulating Piston and tlie travel
of the Governor Collar correspond tn time. Under favorable con-
ditions (long penstocks) the closing time is often so influenced by
the "critical time," already mentioned, and by other considcratbna
that *'aperiodicaI regulation" is no longer practicable since a tovD
of Governor Collar would be required that would cause a greater
difference in speed between no load and full load than is commefj
cially allowable. To meet such cobiditions, the **Compeiisatii
Dash Pot'' (7) is utilized.
"In the diagram. Fig. 413, the full travel of the Go%*ernor Collai
is shown as corresponding to a speed change "x*'- The Relay
Stroke, however^ is designed so that only a portion of this travel
cDrresponding to a speed change "y*' is utiUzed j i* e., within this
1.
i
The AUis-Chalmers Governor.
739
limit the Governor, without other mechanism than the Relay, is
"dead beat" and the Regulating Valve by relay action is returned
to mid-position after each movement. The Compensating Dash
Pot, (7), consists of a cylinder having an adjustable bypass and
containing a compound pistoa with auxiliary spring device, the rod
of which IS connected through a suitable lever to the Governor Col-
lar. Arranged sa that its piston takes motion from the Relay actu-
ating shaft, is a positive displacement pump connected by a pipe to
the "Compensating Dash Pot" cylinder. For slight changes of
Fig. 413. — Diagram of AUis-Chalmers Governor.
load, a negligible displacement of oil takes place and the Dash Pot
has a slight damping action only on the governor head, but when
any load change occurs of sufficient magnitude to produce a speed
variation greater than "y" as shown on the diagram, enough oil dis-
placement takes place to bring the auxiliary spring effect of the
Dash Pot piston strongly into action until the fluctuation is con-
trolled and the Goverribf Collar is ag^in brought within the limits
corresponding to "y" speed variatio.n when action ceases. By this
means, a governing clement of maximum sensitiveness can be used
and the regulation of ordinary slight fluctuations made "aperiodical",
'^'cn under the most unfavorable conditions. These elements in
design, therefore, result in the Allis-Chalmers Governor operating
with great quickness and holding the speed variation, due to ordi-
nary fluctuations, within the narrowest limits, yet being absolutely
safe from hunting or overtravel after heavy load fluctuation, even
Under the most difficult operating conditions."
APPENDIX— H.
MISCELLANEOUS TABLES.
TABLE LXXVIII.
EQUIVALENT MEASURES AND WEIGHTS OF WATtR
AT 4^ CENTIORADE-392'* FAHRENHEIT.
U.S.
ImpGrUl
O&llona
Lttera
Cubic
Pounds
Cubic
Feet
Cubic
Iiielies
Clrimlir
Inch
1 Fool
1
,*032l
3.78Sa
.OOSTSS:!
fl.S41l3
.istaa
£3t
£4.5JH«
1.3B0017
1
4.54303
.W4&i3
10.010^
.lOCM^
£77,274
f».41]ft
.264170
.2L'(lia
1
.Wl
330355
.03:^1 «
fll.ft^
i.<:^
204 179
220.11"
ICHK!
1
2203. 5&
^31^03
610^,4
0475 U
.iiyeHs
.OfHiei^J
A'^imz
.0004538
1
.0l6^lrJaa
^.mi
i.«4tr
7Aim^
fl,^32g7
28.5161
. 0^831 K]
m.^mi
1
17S8
aS3.Si»
.0043^
.W9307
.0103^66
.0000104
.rmiom
.Oa057^i7
1
,TWri
^mm
.034
.1&44306
.0001544
,immii
.005454
P.4±:4
]
TABLE LXXrX.
EQUIVALENT UNITS OF ENERGY
WORK
P&AT
rRia
aT0EAiii.toa
Si
a
h
Oi4
^1
P.3
£5
1
.0(KM4«
;3^^
oomaa
.001285
.onniei
.fl003r7
.12
.difl
.OSlfl
.(uti
2240.
1
3t>ti,0M«
.30fi7
s.sres
.TaiB
.8439
268. R17 1
35 Wd
iia.414
154^
7.233
AKK^I
1
,001
.€oes
.00235
,00672
.Pfl73
.U5a
.37%
.0119
723^.18
a ^i^'in
JOOO
1
t.30a
2.3453
2.T241
ja«7.303
115. Kit*
375.51*
4».9»
77a.
.3474
107.51^
.107rt
1
.2530
.ssss
»a.2S
12,4i«
40.3M
5.3it
3085 34
1.377*
4£a.3lH
.4:.**J4
3.Wra
1
1.1023
^o.n
49. 3116
lOft.^
31^21
£«55.4
t ]j<54
371,123
.3671
3 414
.kl03
1
31H,39
4^ Am
1X7 117
183 3
@.MI
.(HJ372
i.u>,t:
.00115
.1073
.Oft,7
.00314
1
ASM
.433
.t&7^4
62 3^
.027H5
e.S257
.ooioa
.0*§03
.00i!i>i
.0S353
7.4Ji
1
X2^
.«If
le.:^
.(KIM51)
n.mm
.00289
.ft!4«
.WWIJ4
.0072*
2 300
.30*e
1
.laei
144.8^
.0S47
L'O.UJO
.02004
.1863
,0471:;
.05457
it. 37
2.318
7 53*4
1
4
1
r
Theoretical Jet
Ve loci lie 3,
74^
H
w
1
TABLE LXXJC
1
V
P VeioetiieM,
in feet per second, due io He^fU—from QfoSO fed.
1
.0
4
,£
.a
.4
*6
.8
.7
.8
.9
.. o.ooo
s.fise
s.^sr
i.fm
5.o?a
6.wn
3.313
6.710
7. ITS
T.OOO
,, 6.030
B.41^
fi.7>f6
9.144
9.4gu
9.H^
10.145
10.437
10. 7W)
11.095
^^^^1
• U.Mi
11 .6J8
11.896
12.1flS
18,425
1S.5**1
13.1^5:2
13.1.9
13.4;*0
18.838
^^^H
,. 1SS«1
14.1SI
14.347
34.seo
14.789
1&.0(M
115.317
15.4^7
15 034
15.830
^M
■ ^ lO.Ottl
tfl.'^40
1«43r
]0.<B1
ii,a^
iT,oia
17.201
I7.3S7
I7.i57l
1 7.76a
■
,, 17.t>34
IS.U'J
la.eaa
IS.444
10. AST
m.^m
13.979
19.148
10.315
19.481
^^fl
1. lfi.«45
n.«OH
l9.gfTo
20.13!
£0.290
ao.448
90.604
£0.760
20.014
31.007
^^M
r. I'l.Sl*
K1.3T0
3l.5Si>
Sl.ft6fl
fl.Rl7
31. OM
£3.110
33. £W
33.899
32. 54 J
^^^^M
, :s.«8&
&f.ft3a
ee.oM
'MAin
^.24-5
23.683
£3.520
38.565
2^.793
£3.937
^^^^M
- 34.061
34.104
s^.ai'ft
24J58
2\Jim
M.Tm
34.850
£4.979
25.107
35.186
^^^^M
.; 25.aod
iafi.4da
35.014
^.740
2:>,mi
85.068
£6.Ut
aa.235
26.857
35.479
^^H
., ai.wo
m.72l
aaj^i
S^.OQO
87.070
37.104
ST. 313
17.438
37.&50
37.687
^^1
. 13^.7f&
Jff.BvS
2«,on
28. 1%^
iaB.242
ia.S56
83.469
36.1^
33.691
38.803
^^^^1
. 3«,»n
29.02)4
29.139
29.249
«S,359
29.4a?1
20.577
30.636
39.704
39.901
^^^^1
, sn coa
80.3 Itt
JW.lta
90. 3i^
30.485
89.E40
A9.645
80.750
3D.B54
80.968
^^^^1
.. ai.Olia
ai.lS5
si.^ietj
81.871
81.474
81.576
81.677
31.770
81.880
31.000
^^1
. ;« n*ii
33.1SI
83, SRI
as.sso
3«.430
83,670
82 m
^.775
82.873
^.mi
^^1
.* *t oca
S3. 165
83,ei\^}
^i.S,^9
83.4^
ffL&51
83.(47
8^.74iS
83.337
88.gffl
^^^^1
./ 34.037
Sl.l-H
84.215
34.300
a4.40;i
84.4^
64. rj"^
34.682
64.77S
^.SfiT
^^^^1
,. a4.0»f
35. net
^15.148
]|5.sa4
85. ail
85.416
;L'i.:>i>T
3-1.597
35.a«8
85.778
^^^^1
,, ss.tiiar
S5.B37
BQ.04fi
86.13S
30.^4
3d.ai3
34U401
sa.4uo
36.57B
36.650
^^H
* 90,7^
80. HI
S0,«28
87.015
37.10S
m,im
37.375
87.88!
87.44?
87.533
^^1
.> 37.e]8
37.703
S7Jt^
87.874
3T,9fiO
3fl.043
8^.]?a
S^.21J
38.296
88.880
^^^^1
. IW.4tt4
»<.5tT
88.tsao
SB.7I4
3H.TO7
8.«.NT11
as.' 63
S9.0i4
39.127
39,209
^^^^1
., iW,2»l
30.373
ao.+»4
Sd.5Ha
3».6l7
39.098
^JW.77S*
3!^.8»JO
39.940
40.031
^^^^1
.. 40.10]
-lO.J^l
40.^L
40,31L
40.4^1
m.^OQ
40.570
40.660
m.rM
40.tJi6
^^H
. 40. «B
40,974
4I.O&S3
41.130
4LC00
41.387
41.864
4L.44S
41.530
41.507
^^1
, 4l.flT4
41.751
'ii.Haa
41.905
41,l)m2
42.0.1S
42.135
42.211
4^.3817
42.368
^^^^1
, 4^,4ao
42.^:^
42.500
43^.6tjfl
42.711
42.810
4^.8m1
40.955
48.01 E
48.118
^^^^1
, 43.1M0
4.1. ^f^
48.380
43.413
4^.4*17
43.5«11
4:Lf£^
48.7<»
4S.783
48.«56
^^^^1
, 43.^
44.00^
44.076
44.]4;H
44.2S9
44.:«0a
U^Wi
44.498
44.510
44.583
^^1
. 44.655
44.737
44.708
44.£t70
4L94;£
46.018
45.0B5
45.156
4.-J.ft27
45.398
^^1
. 4a. 300
45.440
45. an
4V.5SI
l-i-ftSir
4a.7'i!j
45.793
45.808
45,933
46.008
^^^H
, 4e.ora
4A.14S
4rt.*r3
4a.:^i 1
4, ill
46. 4.^0
4«.4rt9
46.559
40.&£8
40.007
^^^^1
. *«.7»
40.»94
46.90Q
4tI.S?7l
47jm
47.KJP
47l7tf
47.344
47.813
47.180
^^^^1
. 4T.44d
47 .5 JO
47.5»4
■*7.fliil
47.719
47.7aa
47.853
47.030
47 .OW
48.054
^^H
. 4d.i^
48.188
46.£»
4^.821
4^.883
48.454
4S.521
48.4S7
48.es8
4«.719
^^1
, 4-(.7B5
46.Bai
4fl.9l7
"JS.9*t!
da.OJi^
49.118
49.179
49.344
40.8^0
49.675
^^^^1
. 49 440
40.005
49.570
i^.mh
40.aO9
49.764
49.^39
40,«»^
49.950
50.038
^^^^1
« AO.oefi
0Q.I5O
50.aj4
6tL2Tfi
.^.843
511,4' 4
50.470
50.d34
5o.5er
5O.0I1
^^^^1
. S0,7^
00.788
&U.851
W.ttl4
60.977
51.040
5K1QB
51.166
51.380
UJi«
^^1
. 5J.SM
51.417
61.479
51.542
51.604
51. M7
51.729
51.791
6% MB
61 .915
^^1
* 51 -ATT
f&Am
K»aoo
5a.l6-J
m.-^H
5a.a*t&
50.847
53.408
53.470
5ir.5^1l
^^^^1
. ».A«»9
ss.a-ja
5^.714
53.775
52.?-3a
f.2.807
53.958
53.018
53.070
53.189
^^^^1
« tS.dOO
B3.iMlk
w.a^i
R^iMi
:>3.44l
sa.&oi
f^.i>ei
fi8.fi21
68.681
63.741
^^^^1
^ A3 .801
5a.^i
53.021
^Mm
54.010
&4.0d9
54.LJ0
frt.ais
54.377
54.835
^^H
. 54.:we
64.455
M.6I4
ai.iSTa
54.03^
&i.fm
54.740
54.308
64.887
54.0ft
^^1
> :w.9M
S'i.04»
tj.lLH
5^}. 159
65.217
56.ir75
55.334
55.393
55.450
55.608
^^^^1
* &5.SM
f^.a23
[o.tiAl
55.r^
5^.7^VT
66.H54
55.0LV
56.9A9
50.0^7
58.064
^^^H
. AQ.Ul
66.199
56.^56
.W.314
w.azo
56.4^
56.4$4
&6.541
BA.C«fl
85.06tt
J
^
J
m
743
1
Miscf^licineous Tables. "
TABLE LXXXr.
Table of three-haliMis ( | ) pormr of numJbm',*
^
H«ibd
'
In
.0.
J
.2
.3
.4
.5
.6
,7
.8
.»
fe««.
0<...
o.onno
o.miA
o.osw
0.1043
0.^530
0.3530
0,4048
osBsr
o.Tisa
6.?ras
1....
i.uouo
1J5H7
] .3145
i.4)m
1,0505
1.8371
3.03^
3.8105
SAim
t.«m
A..„
S,8^H4
ZOi^
B.»:^l
JJ48S1
3.7181
S 9528
4,lfi»4
4.4096
4.9Wi
4»C
a....
cases
^Mm
6.7.4.^
5.W4r
e.se$oa
0.547V
0.8%I5
TJITI
T.-KKl
7.^)W
4...*
a. 0000
a.iioift
S.00T4
8.9167
9.3396
9.0459
9.B«Bfl
I0.l8g4
10.5163
m.««i4
&*...
11.IS09
1K5174
11 »57S
1;^.S015
12.M85
12.8980
13. 3&^
It.OGHO
16.0661
U.laiJ
e..-
14.«iM0
10 0069
lB.4T7fl
1S.S120
10 J BOO
16.8T19
16 9557
iT.aia
17.79»
|8J!i^
*!..»,
18.5S03
ia.»iH5
la.SJliO
19723.^
aOJ.'ftJ*
20 5:^
30. £1518
tI.J600
91 .7841
nm-
8....
fiSrt'n4
S3,Or:aO
;£a48l:<!
S3.9l£rt
»4S405
a4,TSt5
35.^0;!
95,6a]a
30.1060
«,533
ft....
^.(KJOi)
«7,45l£
a7.9CKK»
^.3012
2d.819i
29.asio
29.7445
80,2105
m.mm
tlJ«6
10....
91.t^«!^
aa.oeoa
afl.&7&2
38. (M4
385S90
81,6839
34.5111
25.0000
86.4aM
mm
11...,
36.4$»
aaiKtiEt
37.48114
37.9«ii'i
38,4908
88 ,0984
39 50)9
4D.09(K*
10.6341
41007
!'J.*..
4KQ002
4M.O»]0
4il.6iafl
43. 138^
48fiftJ3
44.l95i
4t.735fl
46.11600
45.79U
mwi
la....
46. mo
47.414N
47,9570
48,5048
49.(iS^I
4t>.(10:i^
50.1544
50.71166,
51,2646
SI .91^
t4*,..
69.3882
5a.1M04
54.6096
54.070^
54 6M0
: 5 2153
55.7^4
6e.3«16
06.9in
sf.s;m
15....
6B.0»14
68 J7^
6{».;i606
59. 847 J
60.43-30
0i,O:U4
01,0153
09.3006
e»,804O
«.«»>
Ifi.,..
64.0000
64, 60130
os.smo
fls.aoso
0fl4l5i
07.0344
07.6036
6S.3M4
08,S99i
19.4.^
n....i
710.OB38
70,7132
71 ,Si3*)
ll.'^Ti
75.580e
7a, am
^,!^90
74.407S
75 0984
mn»
1ft.*..
7S.3rt7S
TT.OtlflO
njW4J>
78.2H55
78.927S
79.5724
NO, 3176
80 8664
St.5t5£
Bi,!^
10....
82.mee
^A74ii
84.1301
H4 78wa
85.4 kiO
BO.IKM
80.77^
S7.43^
ftf.UMO
88-iT»
3U...P
mAiU
WAim
^imo
»1.46»G
OiJ.iair-^
S*J,S1'W
93,4970
M.iaoo
tilOM
fi&.5»4
,»!..,.
n^mu
^imi
97.6130
mMit
98.990'*
@0.O(HH
10O,3!^8O
101,0968
tOLTSM
ioi.#:i
^24.*..
liMAim
im^m^y
104 OOOh
lii&.3il70
106.0160
100.7270
107.438^
103.1510
168 ane
UiJSH
^....
110.S040
lll.OStri
iU.745ti
lia.4700
USJ9i|
113 9JiO
114.6188
115,37HS
iia.uMs
ui.l^
34...,
117.6753
118.81^8
119 0486
lit* 7870
li!0.5«7S
m HHIO
lif^.Ol^O,
133 7576
l«S,50tl
mM*
«a,,..
tsa.oooo
l«J.76]0
1:^0 6033
1^7.^1570
128 0130
U^.TTIKJ
1:20 53»2
lao.iftfTO
1310480
131811:
«!....
192.5744
ias.34o&
m.iora
184.S764
K^.0|56
1S6.41NJ
l37.1fMH
137.96.'5e
138.7400
139, M^
«7..,-
I40.1imw
141.07H8
I4l.«57tl
lid.flHfJ
l^iAS^
VU2im
144.9981
145.7880
1W.577W
H717W1
3iB..K.
140.16^
148.0&72
149.75^]
l.W.&SC^^
15L:J*>iO
15^.1488
152.9490
154.75S2
154, &5«^
m.ws
»+..**
iM.iaftb
166.V78S
157.7880
lagflOOQ
159 41^
mi^sm
161.0410
161.8568
16^.0760
i6»im
^....
104,8166
IflS.iaSQ
166. M^
109,7884
107. 01 U
1S8.44±4
169.2712
170.1030
170. «£»
m.Tift
3L..,
172.0008
1711.4^2
174 2730
175.1128
l75aiiJ>
t7B.7M0
177.0390
m.4804
179,^18
to.i.-^
a:!..*.
Iftl.OtO^
IBl.SKfri
l8bf.Tiyj
l>m.67l6
184.4240
i»&.?r»
180. 1M4
I86.9ft20
187,8403
198.71*
aa....
im.RlQi
i90,4a3a
191. 129(58
Itn-Mdil
19;1.UC2W
193 8060
191.7640
1^.6948
I96.50a«
mr*
34..,,
I96.aiai
190.146U
200. wm
iS>0.9008
201.7016
802.0404
atW.SafS-i
;.^H,4068
ac^jeffM
m.t:u
S3*...
mr,(mi
-JOT.teU^
;50d.ti4Dl}
XWJ.7312
SIO.Q^
^ll.OL'OI
3l;e.41^
213.310*
21i.S^
£it.lUl2
an....
aia.ooOT
^10.SJD]2
^I7.aflril
218.7060
219.0090
280.5700
3»i .4234
223 3812
m.}s&
a?....
5fi».od;£4
223,t!7ftii
S;ia.88aft
2^.3066
nea.Tsm
al«.640t
tM0.5'«*3
!K] 4i»00
wmlmm
ai.sii
38..,,
S;I4.24H0
iss.ir^
3aU.099tJ
837.0^0
837.9560
2H8,8608
'J39.8170
240.7508
241.^40
ns.am
3d....
943. 5&^
^4 4lKi^
:»5.4aL£
iUa.STlB'
!?4?.aiU
348.0540
349. IWS
3=iO.l4S0
m.6i3i
«.ow
40..,.
£5^.eti^
s&a.iisuc^
354.8816
£55.8340
&50.78ai
£57,7413
250.0960
SSH.^Stt
m,m
41..,.
SflsjH'iSW
36a.4d9ij
'2M.4.Mit
265.4152
26B37flg
067.3450
2m.%m
W.SSM
mjv
4.2....
gr*2.)9u
^TB.lOH
iJ74.137tt
S7-.ll«l
S76.0888
2n.Q672
«78.(H50
m^nmt
43....
18^LM«>«J
■41^ A544
-m.mx^
384.MI54
Q&^.ii\m
060,9028
mi.msi
m$m»
tmj&m
WiMtfi
44....
291 §118£
sos.gda:
2a&.mK
204.8530
2Si>.85gO
fflO,85S@
mmm
fle«.ses4
mm
A5....
aoi.btiSH
303,8764
303.8&M1
a>4.8y36
305.9(M2
306.9148
307.9904
^.9101
609 9644
310 r«
46....
i51l.Se72
ais.ixiM
314 0040
815.0448
316.00VJ
317 0-^77
M8.1112
3I9,0S»
330.0000
«i.i»*
47,...
^^Mm
9^f4J^
a^.!lf7U
lai.aoou
Sa6.3»70
327.8710
398.4fI5n
ajs.44ie
330.477^
mill*
4S....
^&fi.'iiil&
33a. Dte?
im.0333
335.4758
8ia,7lB8
$|17,75S»
338.8051
S49KS31I
Mtl »j(n
»iT.ii>
4S....
S4a.iJooi]
»44J)4«6
34ri.0W96
340.1500
347.2079
348. »m
3«9.ai7i
360 3750
avi.4i«
JBllrti
J_
fiO....
sail. 5500
ifM 6L28
355.0790
350.7370
357.7^00
&58a68l
awja90
a«0.99a"i
dTti 0739
m.m
•Fw
)m Water
-Supply Atid iJTfittttloii Paper Ka iWk
J
Three- Halves Powers.
743
TABLE LXXXI^Cantimied,
Table of three'halms (j) power of number.
:iT4.9n3l
441.TtCM
m^ a 1 141
al2 n ^
£^4.CM3i}
&4S.4ISI
57B.lVi4
010.6844
Oafl.5702
M9.&L5U
742.5a4€
7«l.ft>T5
797.S39fi
gTD.iiii
S7e.O&7H
386 934^
409.0017
4-30 183rf
iAl A7<H
+5.i.ai*7i
405.SJLU.!
4r7;Mi2
5J3.1974
&£».£'«^
5IS.<l4fly
MUV74H
574.400S
Oia,fiOH3
tm.ttfioa
ail ft>*»3
«7U,9?*l-'
flUO.^lOO
7aJ.4^Jt;
748. HtW
771.247*
7Ha.03dy
»i7.40M
vit.osds
971.6314
afls.ssa4
877J3fi7
8KB. 0801
399. (BH
410.1130
4J1 30^<>
4,'»S.4tn>7
4tiT.an»7
lT».7fl7fi
4W.b4d3
5i4,(Piehf
i^d,4tf3@
5,19 0990
5^.2100
57,^ 8473
6ea.l7OT
000.7856
0l3.4ftl0
ea9.i6ts
an iBiO
1177. :A)m
mil ,r>'>»
r0l.N324
7itJ.:£&3u
:uL7«ia
7*5.2Ml.l
r^H.so 4
soo.aoen
Bl4/J78a
Mas .a. '14
B42.44>4
ao«,«so4
*<70.W17
ei4,lW73
fti8.e664
fiC8.*4l»4H
QTB-liai
oe8,os^
307 4.111
a7§.2^ii
a>^«jai9
40J.t2&J
41U«;TJ
4a3.TLJ8»
44'i. UiS
4'ta,»4JVi
4^.:»47a
4TU.M22
49i.7>iett
51^.6USt
6f7.C7tK
A3f).gU]
is-i. lOii!
564.4ftl6
6JiS,4S«
OOSfKiOO
eU.7a(H
6^fi&79
64^1,440:
65S.4L57
da«.47aS
67».e3.Mrt
70^,100.1
74S.'^i73
774.t«Ol
7«7.SLl5a
8ni> 70] \
Ki9,7374
S5H.Qt^7
B}^.74+'>
UJKllUQ
WIS. 7^41
91^^.0111
9B».7«73
074.OCK7il
089.5145
aoo.s^Qs
401 ^mi
412. S4n
460.41Q5
4«1 11BI
492.0163
rni4J16l
.^i4i.oaio
5.j3.:J!£;7
5tt^.«£13
578.148H
500 0841
603.SLS7
dn7.7^4
<U0.fi4l9
fi04J77t
707.fiOlfl
TSSO.tLiS
747.ffr7«
7»11.03;*H
775.3749
7S».iU84
803.0C)M
ttiT.oTaa
84-t,3iSitf
Hj9.5031
t<73.fllt4
888. 1857
917.1'«>9
94e.4M1
flat .^nai
976. o§i^
991 .UCX^
9^5704
K» 8^(40
eDI .^Jl^J
408. SIW
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447.4372
470.5750
491 hKX>
&l8.0(ky>
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&4a.£375
MS. Km
flTfl.lfflT
5i9l.»46S
604.5^5
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fua.osLfl
660.0196
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6«5.5Ll.n
70!t,a^79
7*5.7Sr5
740. amj
7da. 111)63
77e.74S»^
7W.5tH3
0rH.4{K$£
318.4K37
«33j.rMO
M6.705ti
1175. sia2
S!W,i^80
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00^ 7845
»n.683»
093.51 es
^0 6582
3HI.4«15
;^92 4l*tl
40.i.444'^
414.r^U
4eiS.Bl31
437. UiW
448.5^*30
400.1179
471,7467
483.407fl
405 2012
f»o;.3£tw
5^0.^11^1
6-^1 3120
55Q.fIl70
568,1705
5IU,IH40i
AQ5.S505
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681 .4144;
6U.8;*7W
6»7S^£68
rt70.410j*
68.1.57114
006.^861
7L0.17BS
728.6096
TBI. 1091
TD0.7«J18
764.S79H
TTS.l^aB
701.9711!
8ttl.80<i&
Bl9.tiM34
W33,06>X'
Bi8.1^Q7
863,3670
87fl.e:oi
flftl,07l5J
00S.5:H9
031.09^
040.4331
WM.SOOQ
U79.061M
Om.OfKH)
371. 7JJ:^
404.. 5557
413.70Ct;
4;!6.»45S
440.*3fHJ
4^1 .27iO
4T2.9I3I
4J^4 6*7n
4VWJ.47T4
60H 4(y:4
644.73fiO
657.na-i**
500.411H*
m\.m74
^04.466^
fWr.ll97
619.80112
68S 6997
645. 6:^46
6&I.6J7-^
671.7131
084.BO31
e«8,8d81
711. 51?*?
724.95^3
7^.4509
753.0il'i5
765.741'- 1
770.5110
799.3601
8f>7.2810
821 .^"9129
835. 87641
849.54H7
863.7^105
87S.nflC?
S9S.5156
008,91172
0J1 .5.VII
U86.IM8
oao.oooi
ftijri 6961
080.554^
995.4945
373 B! Ill
3H3.{t(V^f
894.ti1Sii
405.6<I79
416.tiSD4
438.0782
439.4308
450.S34S
443. 43»
474.0819
485. 822^
407,e04H
509,5901
5:iI.6J70
538 74Ud
54>,9630
570.64116
5^^t5H>
506.7^53
008.aiOL
<!33.veie
646.015£
659,9375
GTJ.OdSS
80Q.2271
«0ej7l8
713.85^4
739.82^
74Vi,4.'Jte
7tf7.1219
780.889^
794.7482
808,6808
8^.6947
836.7890
865. S^l
87V.&G11
898.9609
908,4580
923.0iQ3
987.6616
05S.8784
967.1715
9rt*J,0!WS
US6.09eo
37&.8»E7
4(Hj.7759
417.9119
4Sft.i080
440.67:96
4AIS.0359
476.8514
487. 0W4
408, K5»
510 7074
625.8344
584 OCdJO
fi47.18^
5.70,5iOS7
671.003
£184,4000
50tt.Qe31
609.6818
829.4174
836. Mia
648 8145
601 .3408
674.3514
687.5464
714.1941
7^,6490
741.18f76
7.4.7968
T04.49O4
Thfi.STTO
706.i:i83
810.0888
Ba4>l064
«88.fi0^
mi3.3^«68
8«lfl.M06
BBOJHKIl
895.4073
fl09.t*>97
934.4778
m)9Jmr5
9G8,e6«5
968.6617
968.64i)7
744
Miscellaneous Tables,
TABLB LXXXn.
Table of Jlva- halves (J) powBn of nnnthersi,'
feet.
1.,
».,
«.,
7..
S..
11.,
14.,
15.,
1«.,
17,.
IB.,
I« ,
22. r
St..
Si..
IS*.
m.,
83.,
34.,
as.
ST.
3>t.
O.OOfl
isg.iN2
1RL0I9
BTl,4ld
1191 .5T8
1374. em
1573,061
1788. «40
81^.000
8iKt.034
4i48,5aa
4538,9(Vi
4jh9.«l0
67^0. M^
7347. ITO
ff1S7,809
m I nmeiTii
40 ioiid.2ue
41 'l07fl3.§4K
4J» „„ 11433.030
la }2m.(m
U 1S841.T»1
45 |]8&»4 "
47.,
4S..
eo.
,4tl
H4!!9.
.'mM —
. 15i*a
. urn
, 17677
.^73
.lOi
.01%
I.SflO
lfi.B30
01. no?]
184.3^)
iafl,73^^
349.801
354.190
410. WO
609.801
ftStJST
BBe.os
1209.193
]8na.R0ft
^&ixi.87H
1811. 3li*
BW5. (TTn
2M4.HTH
1851.343
81M.8Tfi
34R0.200
ilSTi.fitU
4970.714
7]L>s6.a$g
7^30.1.13
N;j*^3.709
tOfi?0.433
llKrj,22l
l«flt%.113
7aa
0fiei3S50
.018
l,fl7B
7.1711
1S.S17
S8J4»
ei.oas
&5.71fl
13OJ04
19-3.544
3W,7*«
3iK.Sr7B
410, 7t«
BIB.87B
7:'.fl «4^
000.7117
10i5«.»f^
l-<£ia.045
1418.121 ,
2:W2.142
2Ste.,Vl7
sa»i.oio
8187.876
aaia.flTtjr
4007,410
6012.05:.'
fmi .nno
7251. isa
78ft4.«'
iie-uj.aio
tOHft-LJiSg
ll.'i<W.t«r
13795.567
14507 .9nR
iflors.ssi
10,7S4
64. (m
1^.4T0
310.477
4^,34!
Mr> flia
MS. 1713
778.801
0ia,e&b
10TO.7OS
iQii.saA
i4aivSS4
i«!».4Jia
ie»).7it
SM8,8>ig
3020.551
2010. H4^
3£1B.6;;^
3^7,23^1
3«©4JW*T
4300 .A$5
4e46.WI0
50B8.S76
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.'j^,'9.S7rt
(jgS^t^eOi
&107.H0
0078. I«7
loaio.
109(11.846
lin;J7.2Bj?
I4^8a.7>74
I53«a,tf7i
lH:,'0cii57
17065, lee
.101
£.819
8.938
e 1,31 A
40.613
07.765
1Ei«.6:^
}4a.m2
L'Oi.smi
2J0.91W
34^.806
48S.ni7
541.440
&ir errr
TJ<6.B73
lORfl. 305
J989.9i>n
l>IRa,S5T
IWIFT.flOL
1879.630
2n8..136
^374 .758
£048.740
2d40.ar)9
32&1.505
3.5S1.054
|3»8.£83
46^.7111
&5!H.893
fW7B.3^
P44r.|3a
«IM0.61S
745^.019
7003. ran
&J54.1B8
flI37.510
f744.0ni
.171
110 I0d7i
no^.omi
n7nn.ia->
138^. €05
f4665.444
Ki4iJ8 4CI2
tOSST.lftJ
ATT
S,755
4^.l«7
70. 945
in7.7IH
iM.ono
^10.617
^79.170
3«^7.2-df
446.477
6.S^.439
tm.641
£00.613
945.87^
im>.i
1S«1.140
U73 O^J
16711.141
IBOS.Ttffl
S14?i.a7R
2401 .880
IM77.167
2971.11.5
8^88.661
§615.077
30(15.830
463«.S47
4736. 6«7
5137 51^
5ne9.o]i
eO^K56S
6195.5111
7506.990
@O5L0!S4
«tin.iV]5
IH97J12
1943^.410
lOftt.84?
1776.056
13904.623
14-44.&7g
m5-TO.l5l
16S81 30S
J7U
.27«
10 .901
£4.fi«8
4'i.884
74.211
111.910
159,
£m.89-^
S^.45^
365.617
458.1^
553.5^
nmjm
614.476
961, L1H
im.7»4
1-209.514
l49«.0Si
1700.751
1996.060
elflS.^1
urn. I£l
3705.716
3001.495
3313. ftl2
S64ft 12M
HilOl 01^
4374.370
47*i«.&*l
5179.693
3fl1B.2ftH
tW67.ffH«
^544.070
71^1 ,8»e
756i.081
8104.080
Haao.oae
925«S.959
»^>)*.i9a
i030;i.o5i
1161 .77ft
US44.743
13^84.27]
14'^.0H2
15632 \m
164'^.Wfei
ITa:?6,lG6
.4ta
I.Tflft
tl,B^
77.371
116.198
164.^8
iSt.SSl
ff6.047
374.511
468. S84
574. i^
6M.7W
RW.3S1
Vre.3^
1189. 7ne
1318.066
ir^2 I94
1722.539
IMI».5^
219^. 5H«
£465.096
£134 .412
3082.1-8
^43.402
40SB.338
4412 711
4*ni7.sri
522:^.131
5a>7.ei«
61H.61K
6.702. 89^
7615. ir
«1S9.5.'.5
8T5«.T96
1X^07
ifim^im
na28.9i»
ti@9.9(ifl
i3fj.^4 aia
r3J5ti.^l
14118.676
zfsag.i07
i37l4.a64
16552.096
17413.647
.67*
4.347
13.118
60.4
m.oi4
laO.STf
300.054
3&).8H
47S^iCr|
5H0.1lia
7ir7.457
84S.
Ilfi3.833
1336.744
15«,
1978.130
S£t8.9i'S
21B2.2)3
}t7€9.394
S381 OSR
afris.2K
4074. ^-^
445 1. ?«
4*47.71
&e!M.T36
57?^, -VIS
013I,4SO
6641.
7144. 0U2
7066 .ti»
H2n,2?e
87S4*7^
9m.
1S.IS4
iaB,fl
71%.^
77**, iH
3^71.171
SNA.VIA
l«i«.ir«
144
1 ism. UK
i^iH.asi
l?7i« \^
nSS6,3401
11Dft4.2ilal
120ii6.«^ J
134,111. «JE.' 1
mte.vit iii:^M
i467s.otn iioeija
isTao.awLgo.avf
Relation of Rainfall to Stream Flow. 745
TABLEI LXXXIIL
STiowing relation of mean rainfall to the maximum and minimum diicharge
of varioui riven,
DRAINAGE AREA. 500 TO 1.000 SQUARE MILES
STREAM AND LOCALITY. Are^ lUinWU ^^SSlt
Sq-Milet Inches perSq.Mll«
I. Amsucan Streams. Max. Mm.
Broad river at Carlton. Ga 762 47.73 22.21 .394
Cootawattee river at Carters. Ga 532 52.73 15.17 .588
JDes Plainea river at Riverside. Ill 630 20.75 14.23 .000
Etowah river at Canton. Ga 604 52.73 81.50 .405
Flint river at Molina, Ga ^.. 802 52.73 7.37 .062
French Broad river at AsheviUe.N.C 987 7.S8 .660
Greenbriatriver. month Howard's cr.W.Va. 810 40.70 .120
Honsatonic river. Massachusetu 790 .165
Little Tennessee river at Jndson. N. C 675 66.40 .408
Mahoning river at Warren, 0 590 .017
Mahoningriver 967 .026
Monocacy river at Frederick. .Md 665 38.77 16.98 ,116
Korth river at Port Republic, Va 804 38.77 29.78 .220
NorOi river at Glasgow, Va... 831 38.77 44.80 .180
Olenungy river at Columbus, O. 523 .014
Passaic river at Paterson. N. J 791 45.00 .190
Potomac river, no. branch at Cumberland, Md. 891 38.77 22.82 .045
Potomac river at Cumberland. Md 920 38.77 19.46 .022
Raritan river at Bound Brook. N. J 879 45.94 59.30 .140
Schoharie creek at Fort Hunter. N. Y 948 39.25 44.00
Shenandoah river at Fort Republic, Va . . . . . 770 38.77 .167
Tockasagee river at Bryson. N. C 662 45.30 .003
II. Frbnch Streams.
Armancon river at Aisy r ... 575 49.20 .011
Armancon river at Tonnerre 853 .034
Mame river at St. Pizier 915 80.70 7.73 .101
Mease river at Pagny-la-Blanchecote 573 .039
Meuse river at Chalaines 607 81.51 .041
Mense river at Pagny-sur-Meuse. ... . .^ . . . . 734 . 056
Meuse river at Vignot 817 .085
Mense rivsr at Mt. Mihiel ^ 914 .078
III. German Streams.
Ihna river at Stargard 672 26.60 15.50 . 137
lagst river at its mouth 708 29.50 .200
tocher river at its mouth 768 29.50 .221
Lippe river at Hamm. 965 9.75 .235
Malapane river at Czarnowanz 773 25.04 14 35 .274
Oppa river at Strebowitz 805 24.40 21.95 .256
Stober river at its mouth 620 22.70 3.65
£
♦From paper on Water Supply for New York State Canals, Report of State
Engineer on Barge Canal, 1901.
74^
Miscellaneous Tables*
TABLE LXXXIlL-ConLinoed.
DRAINAGE AREA, 1.000 TO 2.500 SQUARE MILES,
STRIAM AND LOCALITY, Arta,
L AUfiMtCAN SxitKAIiS.
Aod roscoggtn ri ve r a t R u m ford Fmlls, Me. . * 1, 230
Broad Hver at Gaff n^y, S. C .-•**. 1,4H.>
Catawba river at Catawba, N. C**m^*,*** 1,535
Cbaitahoocbee dver at Oakdale, Ga , ,.*»•, 1 ,560
GiBDcse* liver at Mt. Morris, N*Y*, -.,*.*, 1,070
Greenbrlar river at Aedtr^on, W, Va. , * * # ■ • 1.344
iames river at BuciianaD, Va. ,..>..>...,,, 2,05S
feuse river at Haleigb. N. C LOGO
Neuse river at Seltaa. N. C. ,. , 1.115
Ocmulgee river at Macon, Ga. •-,*•■ ^.^..^ 2,425
Oconee river at Carey. Ga . ,.,,,,*,.,,,_♦ 1 ,346
Oostaonala river at Kesaca. Ga ........ i . • 1 . 537
Poton^ac river at Cuuibertand, Md I,3&4
Saluda river at Waterloo, S. C , , 1,056
Schuylkill river at Pbiladelpbia, Pa 1,S00
Schuylkill river at Fairmotint, Pa * » - , • J. 015
Scidto river at Co]umbu$. O. , *-.«,*«. 1,070
Scioto river at Shade vilk. O 1.670
Tar river at Tarboro, N. C ,, 2.290
Yougbiogbeny river at Ohio Pyle* Pa . ,,,, 1,775
II. FltEKCH StI^eams.
AisBe river at Biermes. ..... ,,, ,**** 1,B4]
AiiiDe river at Berry^au*Bac« ..,..,,*,.,..« 2,120
A isne river at Berry^aa-Bac ,.........««»»■ 2, 1 20
Loing river at its junction with the Settle, mt 1,7B5
L ya river. .........*.,......*.... r - . * - - - 1 . 420
Marne river at La Chaussee. ..... i^. .i,,. . 2. 2!>7
Marae river at Chalons. ........... t. .... ^ 2,497
MeU5e river at Verdun .......««....> 1,219
Oise river at Chauny. .....,, ,.^4..*« 1,57/^
Seiae river at Troyea ............... ^^ «.. * . 1 ,314
III. GEaMA^t Strvaws.
Bober river at Sagan ,»..*.,,#,.. 1 ,6.^
Drage river at its mouth. , , ........... 1 .234
111 rivcr-ftt Strasburg • . 1.294
Ka l^ow river at Ufich, ,. ....^ 1,830
Labn river at Diei , 2.008
Lippe ri^ef at Wesel . * . . , . , . . ♦ 1 ^i90
Main river ab^ve mouth of the Regnitf river 1 ,725
Netie river at AntoDsdorf .,,,... 1,036
Netze river above Eicbhorst.... ,. ........ 1,130
Oder river at Hoschialkowit?. ........ . 1,440
Oder river at Annaberg . ,..*..... -,*. l.SOO
Oder river at Olsaa , 2, 250
Obra nver at Moschin ...*...,,...,. 1 ,335
Ruhu river at Mulheitn .......*,♦ 1 .728
Saale river at its junction with the Main.. , . 1.070
Welna river at Kowanowko, near mouth. .« 1,013
Itf HA Annual
DitcbmCi»rv
iDchei.
p«rS4 Uilc
Mat.
Mw,
40.39
25 09
.4:&
47,7S
A^
lai
.!£&
48JI
21.75
.431
38.0&
39.20
.Oftf
44.80
41.55
.041
40. »3
15 56
.14tJ
0.70
,m
49.23
14.92
-157
49.31
7.44
.28a
52,47
14.50
.389
35.28
.011
12.06
,275
.170
12.17
.013
.094
.015
9M
.074
.000
♦.0IS5
7.5S
2SJ0
,016
1 74
.010
,910
2S.33
.110
.104
.051
39.29
17,40
.399
2.11
.W$
9.15
,»27
18.90
19.30
.405
25.60
12 m
J33
11 62
,m
27,44
.K4
.063
*046
21 60
,156
24.60
27 Of*
.219
24.60
43.tK>
,274
.101
33. M
.ne
27.76
.061
3.14 .mt
Relation of Rainfall to Stream FloWc 747
TABLE LXXXni.— Continued.
DRAINAGE AREA. 2,S00 TO 5.000 SQUARE MILES.
Drainag* Mean Annual Discharfe Cu. Ft.
STREAM AND LOCALITY. Area, Rainfall, perSec
si Milea. Inches. per S« Mtie.
I. Ambricam Strbams. Max. Mim.
Black Warrior river at Tascaloosa. Ala. . . . 4.000 88.80 .018
Broad river at Alston, 8. C 4,609 28.2 .12
Cape Fear river at Fa vetteville, N. a. 4,493 16.3 .09
C^tawa river at Rock Hill, S. a 2,987 48.4 .355
Chatuhoochee river at West Point, Ga.... 8.300 53.03 17.87 .252
Connecticut river at Dartmooth,. N. H 8. 287 .306
Coosa river at Rome. Ga '. 4.001 52.78 11 .42 .225
Crow Wing river. Minnesota 8.570 30.84 8.84 .250
Dan river at Clarksville. Va 3.749 38.28 8.80 . 107
Hudson river at Mechanicsville. N. Y 4.500 41 .01 15.50 . 189
Kennebec river at Waterville. Me 4,410 25.20 .006
Merrimac river at Lowell. Mass 4. 085 19 . 83 .310
*Merrimac river at Lawrence. Mass 4.551 20.00 .27
Mohawk river at Rexf ord Flats. N. Y 3.384 23. 10
Mohawk river at Cohoes. N. Y 3.444 33.63 .23*i
Ocanee river at Dublin. Ga 4.182 49.31 0.69 .021
Potomac river at Dam No. 5. Md 4.640 38.77 22. 15 .078
Savannah river at Calhoun Falls, Ga 2,712 47.73 .90 .518
Shenandoah river at MillviUe. W. Va 2.995 89.50 11 .44 .203
Suunton river at Clarksville. Va 3.540 38.28 10.30 . 157
Susquehanna rivei-, w.br..WiUiamsport, Pa. 4.500 11.60 ,178
Tallapoosa river at Milstead. Ala 3.840 9 .50 .091
Yadkin river at Salisbury, N. C 3.399 : 5.0 .225
Yadkin river at Norwood. N. C 4.G14 13.70 .284
II. French Streams.
Aisne river at Soissons 3.040 0.43 .081
Aisne river.above junction with the Oiserivei 3.385 23.50 5.95 .096
Eure river at its mouth 2.980 22.30 2.72 .076
Isere river at its mouth 4.300 21.00 .780
Marne river at Chateau Thierry 3,332 .127
Meuse river at Sedan 2.560 28.33 8.05 ,194
Meuse river at Fumay 3.700 28.33 4.04 .191
Seine river at Bray 3.750 4.05 .003
Seine river at Nogent-sur-Seine 3.594 . 103
Yonne river at Sens 4.270 9,09 ,100
Yonne river at 'Nogent-sur-Seine •. 4,300 30.80 0.37 .140^
III. German Streams.
Main river, below mouth of the Regnitz river 4,650 27.44 . 186
Moselle river at Metz 3.550 29.48 14.92 .199
Mur river at Graz 2.959 12.98 .243
Neckar river at Heilbronn 3. 155 .140
Neckar river at Offenau 4,770 33.35 .107
Oder river at Ratibor 2.580 24.60 21.20 .306
Oder river at Kosel 3.520 24.(50 14.10 .128
Oder river at Krappitz 4.150 24.60 3.80 .187
Regnitz river at its juhc. with the Main river 2.920 25.00 .164
^Figurrs supplied by Mr. Rich. A. Hale. Lawrence. Mass.
y^ Miscellaneous Tables,
TABLE LXXiXnL-ConUDiiad.
DKAINAGE AREA, 5.000 AND OVER 5QUARB MILES.
Dminiet Mean AMBUftt Dwtamizt Cu. Tl
STREAM A^D LOCALITY. Ar», Rdalftll pw Sc«.
S^. Milfeit iDChet. per Sq. Mile.
I, American Stueams. Ma** Wi«-
CoQD«Cticut river at Holyoke* Mass S,0GO 13.20 *03d
ConDecticut river at Hartford, Codd^«,.,.* 10,234
CoQuecticut river at Hartfard, Conii. ..••i. 10.234
Coosa river at Riversj<le, Ala, ,«.,•,..,..•«. 0,850
DcUwar« river. New Jersey ....*...,«••«,« 6,750
Delaware fiver at Stocktoo, N. J * ...^ G,790
Delaware river at Lambert^ville, N. J. • « • • • 6,8^5
i antes river at Ricbmond^ Va, * < ^ ...**.., • 6,S0O
Lftiiawiia river a I CliaT)a»toa, W. Va* . . » . • . 8. 000
Mississippi river ..,,.....,.«,«,...«.,•••* 7^283
Mississippi river above St. Paul 36.065
Mississippi river. . .^,..« ^,, 1CS4,534
Mississippi river «.. 526,500
Mississippi river ..,«.,...,,«, J, 214, 000
Missouri river 17,615
New river at Fayette. W. Va O.2O0
Ohio river at Pittsburg, Fa ., * 19,900
Ohio river 200,000
Ds,wego jiver at Oswego, N, Y« ^ ,.,,>..., > 5,013
Potomac river at Poinl of Hocks, Md ,»,,,, 9. 054
Potomac river. #,,... -,., .«,.,». 11,043
Potomac river at Georgetowo, D. C. *..,,. „ 1 1 , 1 24
Potomac river at Great Falls. Md, , , 11 ,427
Potomac fiver at Great Falls, Md 1 1,476
Potomac river at Chain Bridge, D. C, . * .*. 11.545
Red river, Arkansas. , , , ,..*,*.,..,,,, 07.000
Roanoke river at Neal, N. C .-...„,., 8,717
St. Croi?c river, MiuDesota, ..««..**. ^ . * « . , 5,050
Savanoah river at Augusta, Ga « . . . . 7,294
Susquehaaua, w. branch, at Northutuberland 6,800
Susquebauua river at Harrisburg. Pa. «..,«< .24*030
Tennessee river at Chattanooga, Tenn. .,«, . 21,418
II. French Streams.
Loire river at Nevers .,«*.■«*»•■ 6, 500
Loire river, between Ma toe and Vieuoe rivers 0,&50
Mame river at Cliarentoa. , , , ^ 5.057
Marne river at its junction with the Seine. ,« 5,295
Meuse river at Maestricht, ,..*,,.. , 8,240
Meuse river at Maeseyck . *,**-.,.,..,.•*» ,^ 8, 480
Meuse river above Ruremood ...,,«.,«..... 8, 750
Oise river at CreiL <*,..*«...<•.,....,..... 5, 022
Hti one river at Lyons ♦ ,.****.. 18,000
Seine river at Port a TAoglais ***** 1X624
Seine river at Paris 20,000
Seine river at Mantes.. ..... . ..*..,.,*,,* 25.135
Seine river at mouth of the Eure river,. *,,. 28,593
11!. German Streams.
Elbe river at Torgau 22,000
Main river above moutb of Saale river, , , . , * 5,620
Main river tjelow mouth of Saate river . . . . , 6,900
Main river above mouth of Tauter river. , , . 7*290
Main river below mouth of Tauber river. , , , 8.000
Main river at Frankfort ,...,,.,..,, ***,,. 9,01 0
Meisel river ai Tilsit , * , , 38.000
Moselle river at Kochem. . , , , , 10, 253
Moselle river at Cobleni , ■ 10.340
44.53
,310
44.53
20. 2t
,510
48.08
10.53
,1»7
50.00
.300
45 M
a7.50
/170
45*29
&,7l
,3m
40.83
J91
40.70
13,40
.123
32,34
1,40
.261
25*75
10 73
,01^
.100
.050
,210
15.70
.100
40.70
13.40
.1S»
.114
41*50
*270
37,60
•230
35,35
19,40
.0©
38.77
42.00
*170
38,77
15.70
45,36
41,15
,215
45,36
15.25
.003
^,77
17 J0
.165
30.00
2.32
3821
7.38
,229
33 53
0 00
,4M
47.73
42.50
*272
1753
,074
18.83
*O02
20,78
.199
23,10
.070
.355
.OIU
30.70
467
\08O
42 50
5.ftl
Am
42.50
7,3C
.244
3.01
*317
3.14
AU
30,32
11.83
.333
.046
21,27
5.80
*085
3.09
.001
3.09
2M}0
2 89
*144
.182
.166
.107
.107
T2.50
.121
4.09
.813
8,53
.174
24.7fi
13.01
.160
I
I
I
Relation of Rainfall to Stream Flow. 749
TABLE LXXXIIL -Continued.
DRAINAGE AREA. 5.000 AND OVER SQUARE MILES.
Drminage Mean Annual Ditcbarge Cu. Ft
TREAM AND LOCALrnr Area RainfaU Per Sec
Sq. Miles. Inches. Per Shi. Mile.
m. GSKMAN StRSAVS. Max. Min.
Neckar river At Heidelberg 5^21 32.17 .215
Neckar river at Mannheim ' 5.905 81.02
Oder river at Ohlau...., ' 7.750 24.60 4.17 .215
Oder river at Breslau. below the Ohle river. ^830 24 . 00 10 . 40 .209
Oder river at Steinao. 11.412 24.02 .95 .229
Oder river below mouth of the Warthe-river 28.319 23.62 .61 .212
Saale river at Rothenbnrg 7.282 27.76 5.41 J'K>
Warthe river at Pogorzelice 7.900 ,lxA
Warthe river at Poseo.., 9.620 6.37 .100
Warthe river at Landsberg 4 20.020 21.65 2.56 .19»
H ^jo Miscellaneous Tables^ ^^^^^^^^|
H TABLE LXXXTV. ^^M
^M Mean uvw&ge rainfall, run-off^ and evaporation for 9torage, groftHnff and f«fl
H pjenith^ng periodM for I£ Mtr earns a/ tfm United States,* H
^^^H Feilod^
Muiikltigiam Blvpr^
rrom 18^8 to lBef»^
«iKht yean. Catch-
mant Area, 6>Bl2S
Qeu^mee River, from
law to im nine
y«af«, Catcam«iit
ar«a, ],07Q ttqnare
taili»4.
Crotoo BiTer, from H
1S77 to ll««. tvwCT- ■
three ycttrs. C^lefr ^
ment area, WBS
•qoare mjlei.
Bam
off.
Evap*
ora*
tlon.
RalD.
Run-
off.
Eirap-
ora-
tion.
R«l£U
off.
tiCKt.
H Stor»c**- ..^.,.-
^B^_ Bfflffnldrinf
1B8
II. a
t.3
i.8
1.7
9 J
?:1
19.4
U.A
ft.4
las
1.7
£.0
9.S
7.4
it.i
&4
'lil
^^H
8fli7
ia.i
s«.e
4a3
14.2
S&l
49ii
SL6
»4
^^^H Tertod*,
t^lm QocliUiiat^,
from 1868 to IvOUi
CiitqbiD«iit. aren«
18J nqOAm mllM,
8lldbnry RLror^ from
1M5 to iOftJ. tweDtT-
eix. yeare. Ofttch'^
ment areat 7H,£
square miles.
Ml"* tic Lake, fron
fB78toI«i&.^bt«en
area, 8ll.fi nqaare
mil«L
«•<"•! ^oF
ora-
tJon.
Haln.
Biiii^
off.
Etbp^
tioa.
Rain.
Rtln-
1^,
E«p-
Ota-
^^B etof»g«.... p»
83 1
lie
U.4
I4.fi
£.1
8.»
1£
9,1
£8.K
10.7
ll.fi
1.7
5.i
9.0
R9
mo
4t]
SO. 8
£6.8
M.l
£!^e
£8.ft
44.1
10.0
1.
1 Period
Heshaminy Creek,
fromlF^tolHIW,«!x'
been yean. Catch»
ment area^ I3&.3
Aquare milea.
Perltlomen Cr«ek,
rroEDlS&iColSBO.iix-
leen yeani. Ckt<(^h-
ment area, 1&£
■quare miles.
Tot)tc1coDOae1i.ftr«e>
1864 to irn^ flftefto
yean. Catchmeni
are*, 10£.t mmn
mU«L
Bain.
off.
Erap-
ora*
tioo.
Rain.
■ss-
Erap-
orft<
tlon.
Rain,
Riln-
Off.
tka.
Growing ....... ^. .^ •*..*.
V«r ^....
ia4
ln£ 5 0
«,T 10,7
£9 J
18.7
U.l
]*.T
ft A
a. a
0.0
10 Jl
7.8
E4B
ii.«
4,i
■ jil
4t6
£1.1 £4H
40.0
£».«
».4
fiflll
£14 i a-T
PeHod,
Hudvon RlT«r, ftvfli
laae to ibdi, four-
t«eD yeari. Catib.
mflnt area, 4,fiQD
aqnare milea.
P^q^taQQoek River,
h^m llt«l to isae,
nlae yeaw. Ckteh'
uient area, O.T
■qnare mllea
QntehnMnt «r*i^
IQJSiaqnamiiDaL
Rain,
Ran
off.
Erap'
' ora*
tLuti.
off.
ora^
tltm.
BaliL
Bnn^
Off.
or*-
f|t01'«^ «..««•• •**•.• .«»«•«..
80.6
III
10. t
4.0
7.£
mo
1£l7
11. 1
IP.T
3.1
40
3.8
7.1
1«.«
laa
mi
Ill
8.9
t.«
mi
Heplentiliiiiff....
Yomr ,
44. t
CftS
tnft
40.B
trs
».o
48.0
££.0
fio
•ftom W, a» and l^ Pap«i- JTo TO, H4fter. j
Rainfall, Run-ofiE and Evaporation.
751
TABLB LXXXV— CTroton River, 1868-1899, inclusive,
[C>tehm«tt area«>88M4qv»rB mOes.]
1868.
1809.
187a
Period.
^
""^
Rain-
ftOL
Bun-
off.
BTapo-
ration.
Bids,
tell
Bon-
off.
BVMK>>
nttlon.
swwnty
mtlon.
Stone*... . —
<hvwing
18. •«
14.86
17.85
5.75
U.08
5.99
7.89
8.79
81.88
7.n
15.09
15.75
2.01
4.39
6.14
5.76
10.70
28.42
10.50
10.09
19.01
1.68
.96
9.41
9.08
9.18
Ymr
SLT8
84.08
17.87
44J75
22.15
22.60
49.10
21.58
87.57
1871.
1878.
187a
atoittM
18.88
l&Ol
U.85
9.78
8.81
8.85
lOlll
1&48
8.80
14.67
14.88
10.76
10.81
aoi
4.88
4.96
u.a8
6.37
22.19
8.65
12.58
18.52
1.54
8.20
&8r
BrngHu^Odng
7.U
9.88
ZMtf >•>••«•••••••••>.
«7.88
17.98
89.84
89.85
17.70
21.95
43.42
«.«
20.18
1874^
187S.
1878.
Omwhic-..***!
88.74
11.80
8.88
88.88
8.77
1.80
0.88
9.58
7.08
17.10
18.45
10.38
14.81
5.86
8.41
8.88
10.69
6.92
28.64
7.14
10. U
19.89
1.07
1.85
2.75
6.07
8.78
T«ar .......«»• ^....
44.78
87.88
17.49
48.88
84.08
19.80
89.88
28.81
17.58
18n,
1878..
1879.
wVOWlBflf* ••••••••••••••••>•
17.48
18.17
18.48
11.88
.98
5.48
6.18
18.A
;i8.w
80.99
1L89
1&78
14.19
8.57
5.01
6.80
8.72
11.71
26.17
18.08
6.96
20.81
2.63
1.88
4.88
15.48
5.08
T«ar ..^
48llS
18.81
80l81
49.00
21, n
27.28
50.22
25.88
81.00
1880.
1861.
1882.
18.78
1L48
7.81
18.18
.88
.84
7.69
10.74
878
24:63
9.81
8.96
14.79
1.95
.97
9.74
7.60
7.99
27.91
9. US
19.10
16.85
6.21
11.06
6.87
Biltlnnliririnflr .
12.89
XVSF ••••«•>••■•••••••
W.77
ia7i
85.08
48.10
17.71
25.39
56.04
25.12
30.98
1888.
1884.
1865.
^lomge
19.06
18.10
10.41
11.87
1.09
1.88
7.80
11.01
9.13
21.81
15.72
8.01
16.85
2.34
1.87
7.96
13.38
6.14
2L86
12.80
12.23
15.36
.66
2.98
6l50
Growing ....... ...... ~....
12.01
9.31
Teu>..^.
41.54
18.74
27.80
48.54
21.06
27.46
46.96
19.16
27.82
1888.
1887.
1888.
••«•.
85.45
11.88
8.88
18.18
1.53
1.23
7.-89
10.15
a59
28.05
24.75
7.78
16.44
6.71
2.60
6.61
18.04
5.18
30 33
11.25
18.76
21.74
2.68
8.28
8.68
8.88
BtsliniMilnr
10.58
-
Tmt
46.85
80.98
88.06
55.56
25.75
29.83
60.34
88
752
"Miscellaneous Tables.
TABLE LXXXV— Continued. — Croton River, 1863-1899, iudtutive.
m».
UOOl
IML
Period.
Rain-
faU.
Ron-
tiff.
Brave-
zmtton.
^
^-
KrspO"
ratioiL
«r
%-
Vvapo-
StoTftge
22.40
17.97
16.83
16.86
6.40
8.70
5.H
10.88
10.18
».81
18.81
14.60
19.10
2.61
7.02
6.21
10.80
7.68
».6B
1L26
7.78
.21.22
1.14
&44
Qrowinjf
HLB
R6Pl€*ii»*Kihlnff
<L67
Year
58.00
82.06
S6.56
4».8C
28.68
84.80
46.70
28L47
219
1802.
1808.
1804.
Btorage
22.98
15.37
10. ao
12.87
2.60
2.81
10.06
18.77
7.90
27.84
12.88
11.08
S1.41
1.84
&61
6.98
10.66
7.67
88L24
T.96
17.06
16.66
L8i
4.41
T.A
Growing
lit
Beplenishing
tt.61
Year
48.00
17.78
80.82
60.81
26.76
84.06
48.M
n.86
MlB
1886.
18U6.
1887.
Storage
19.55
11.19
9.54
14.78
1.06
1.27
4.77
10.14
8.27
24.84
12.26
11.27
18.01
2.06
8.18
6.88
10.22
8.14
JO. 66
20.79
8.76
14.64
«.98
8.7B
6ifl
Growing
1181
Replenishing
Id
Year
40.28
17.10
28.18
48.86
28.17
26.19
60.10
21.80
».»
1896.
1809.
Storage
28.81
17.17
13.86
20.08
4.88
8.99
8.78
12.84
9.87
22.66
12.19
10.37
21.88
1.67
1.96
i.a
Growing -- --
latt
Replenishing
8.41
Year
50 34
28.90
80.44
45.22
24.91
20.9
Mean 1868-1876, in-
closiTe.
Meanl8n-1809,ls.
clnaire.
Stor&ge
21.51
11.88
11.61
16.46
2.91
4.00
6.06
8.97
7.61
23.68
13.68
12.06
16.88
2.67
8.42
18^
Growing
Renlenishinf?
u.oi
188
Year
45.00
23.87
21.63
49.88
22.81
M.U
^^^F Rainfall^ Run-ofi and Evaporation.
H TABLE LXXXVI— Late! Cochiimate, I86S-1B00, imluMue,
^P |Oftiaimi0&VAre« - IAJ» iqtittro miles, not loci adinff cwtcbTaent of Dudle y pon^ .J
■
^ - 1
1B64.
1M&. ^1
i Barlod.
£alK
Rtin
oft. ;
TTfttioU.
Eain-
fAlL
Run-
off.
Evapo-
ration.
Bain-
falU
Run-
off.
Erapo- ^H
S9.*9
21. n
16.49
ltt.31
fi.l5
13.18
16.56
11. S4
24.70
6.20
13.47
H.44
1.58
3, IT
30.26
a«2
10.30
29.63
19.43
17.28
1,17
i.ia
11.28 ^1
t™-.-. ,
ff?.€0
m.ri
40.08
43L37
19 19
24.18
Ga43
33.70
^M
law.
18«T.
Idas. ^M
8toTm^.<
OroTln^ , >,„.. »,««
Tcar„„*, „4
n.$7 ».38
S2.13 £.t4
13.40
19.19
18. OS
«o.e7
10.98
18.47
a84
2.43
-10.56
17.83
8.55
29.01
11.49
U.fi5
18.95
4.71
■
m89 H
■
Cl-Bl 1S.W
45.73
Be.«T
2144
86.43
A1.M
14.00
1809.
!87a
^M
28, m
8.6S
Sl.SS
It 83
4.77
16.08
8.S6
18:48
88.60
9.18
13.00
23.72
L91
11, 7»
7. £7
10.15
19.77
11.71
mas
to. 19
2.15
138
- 1
OfDWluiF ^^,...1, ^ ...
Tear, „,
£&BI
19.09
38.32
88.88
S&IS
30.90
45,34
14. IB
»•- 1
ISTI.
1879.
ufiL ^M
0ffHfTlpg .....*. ..*«******<i
14.M
19.68
ILSD
£.gfi
4.89
G.S3
16.83
90.00
11.63
IB.2T
18.51
2.47
1.49
9.ti
t.«9
20 76
12.78
iU
1113
8.68
1.8»
8.01 ^
B^^nWhinr-- -
Te*r„ ,..,...
48. »
U.SB
Ki.m
44.90
26. «e
19.£4
38.18
11.09
MM H
lam
m^
1877.
^
gbevAge - *
iT.eo
15.34
laii
10, W
£.35
a.7&
104
12.99
9.80
20.15
13.28
12.57
1491
1.64
6.54
11,84
9.35
2i.r.
8.76
15. H
15,85
aa4
4-81
0.98
aat
ii.m
in«mrin^ ^^.^. .„
Bmal^iiliihiDijr ..»
Y«Ar ^«.. ...*
4fl,E&
16.86
£9.39
4S.B0
19 77
16.63
45,01
far. 20
ffl.71
1S7B.
1279.
1880.
6(orft|7» , -
Growinf „
Y«r „..
21.38
ISLT*
121 98
19.08
SOT
S.O0
4.80
n 67
19.98
13.fiS
16.83
2.05
1.93
a 13
11 so
3,99
1147
11.06
e&4
.62
J.B6
9.0t
Iff
49.46
£4 £4
BS.84
39,53
20.81
18.71
38.87
10.73
»14
1681.
laei
im
mvtt
£123
a.K
1174
in
9 49
7.18
7.89
29.10
e.50
1S.B8
1199 10.71
.75 6.75
1.89 9. 98
16.82
iwce
6.118
8.31
.18
1.81
8.« ,
Qt^wiufi^ .»........»«.
Qft.ft2
IS. 55
14. £7
4L96
19. IW' sfl.a
80.98
10.09
.. ^
^^H
'^^^^H
^L 754
^^V TABLE LXXXVI
MiscelJaneous Tables.
1
^^^ Period.
im.
Igtt.
"- 1
rail
Razir
oir.
BTapo-
ntlon.
Bun*
fWU.
off.
^H Biori«e.*.
94. T9
. 18.71
6.m
lfi.70
l.M
0.00
IKES
4.73
1».M
11. TO
miA
n.oo
aoB
10.00
10 i4
9.08
04.14
8.06
ILIO
19.97
.57
L9t
LB
o.fl
^H
am
16. SB
as. 07
40. fid
IS 75
ao.90
43.52
£1 46
Itii
I
ieB7.
issa.
18S0.
10. c&
10.91
IBS
7.18
4.70
10.flO
0tJ.T9
15.14
1.04
0.00
8.76
a 12
ILID
fl.79
10.64
14.36
1T96
8.94
0 05
^1
40,55
SIhOI
18. M
55.07
.M,4T
98,00
!>aio
3ai5
n,%
B
leea
1!»1.
.». J
^H Qrowiitc
^H Bopteotahlnt ■-■■■ ■'.
18. la
IT.BS
IT. 17
A. £3
ST. 73
ll.fifi
0.10
£8. SI
a. 88
-0.48
9.69
8. 79
91.11
10.40
0.48
19.47
1.96
£.96
in
III
^H v«.
48. «7
2&.aa
iaoi
«S.fil
a£.G6
15. SB
11. oe
10.11
nn
1
]«e&
im.
- 1
^^1 Rt<^»*gB,___
11.01
7.00
U.IO
1.00
f.Sl
10144
an
5. or
«i.no
7.79
10.04 '
10,^
2M
m7B
8.90
90.18
11.79
18.40
11.9
1.45
0.17
mat
lilt
^^1 Qroirtii^ ,,,,
^^M B^pleni^lng ^
^H Tear ...
11.48
16.81
t4.ffi
39. 7S
13.fiS
06.30
50.68
18.01
3in
I
tm.
IBOT,
■*- 1
^H Ot^wtsff. >.....
SOifll
14.74
8.70
4.0&
0.14
11. M
10. ST
e.oe
11. m
£.58
0.81
0.7T
7»i
86,61
IS. 71
1176
16.15
£45
mm
^S4
n,n
tt.18
42.13
te.so
^90
50.08
06.06
Sl.fi
^v
[
laooL
lOOQ. 1
^^1 StOTS^. L....<. ...*. *.r..v^ » ---» --»--- »
££.ai
a.ia
10.01
IS. 38
1.03
3.00
0.38
^.80
0£5
mm
14.0B
1.49
BLTt
14.S
1%
ID.B
^H r^^orfng- _ _ ^ ,
^^H pjip|]nn lulling , mr
H Year... -„
10.48
S0.S4
m,u
CO. 04
10.80
oe.s
1
Me&n for 0
laOA-lOOO. Inct
years*
oai?e,'
Mmo for 81
186^1900, Inc
moa
l^dO
15 13
I «6
£.99
8.47
0 91
B.J5
11 SO
19,98
14. Ot
8v3t
sa
«.fi
1 RoBleiolsbli)ff.-..i...-......i — - -
^H Tmt ,,
'
40.9S
10.7T
Sl^S
47.18
St 39
iioi
^^P RainfalJ, Run-off and Evaporation.
^M TABLE I^^ULSLVll^Ne^kaminy Creek, 1884-1399, indudvB.
755~^B
Period.
im
ifidS.
laaa. ^1
Bain-
Evipo-
Rain-
faU.
Buav
off.
Erapo-
ratloti.
BaiD-
CalL
Bim-
off.
Erapd- ^H
ratltm. ^|
I ph^
13. Tl
LMfi
.46
iai3
10.fS
11. «8
'l78
a IT
a49
l*.tf7
f.flO
£1.4fi
1.87
.03
... ■
10.80 ^H
^1
r ai^wlag „, ,.
4«.5a
tr.91
11. di
a«j
eo.ae
mM
48. 8»
2xm
^1
1^,
1888.
1880.
1
Orowing,
flftpli^nf^Tiliitf
T.fift
15. «i
1.08
MI8
H.8U
li.lfl
n.i7
1.01
0.02
10,88
2£42
2a.IA
13.44
moo
ii.it
».ii
Y«r...,. .,-
48lT8
n.m
fi7.a4
i^Llfi
m.m
£4.28
W.M
ai.«L
ALU
]i«Q.
im.
11^
^StorajTS ^-...>..«^^ .««..^«.
££:0«
2.1fi
&33
£3.40
15.90
n,74
S.SU
fi,7#
13.37
22fi5
ILW
10.13
18.01
i.m
T54
mi?
aii
Yotr.. -_,„„„......
4e.67
mas
».£!
47. «
22.86
eisi
I4.S8
ia»
»L00
189a
ISM.
laes.
^t/vrmvA
mil
ILOT
ia.ai
a6*
10.*1
1,83
W.46
11. w
ais
T.18
10.3a
ea97
U4I
aa
]&84
Cia
mat
ft.87
GrOTlug •.»••♦*.-.-,■»—«.
BepleiikMny,,.,.,, „^„
Y«v. ,,.,-, —
49^41
m.^
a,*a
eaos
3ft. 10
£Sl«
38. *»
i8.m
fQ.U
liM.
ISOT.
OrowtBff „ -i._ .
Beplenlnhluf „, «_. „.
Year ,„„,.,„„
:::»::
■**•"*'"*
-—
la'W
1LS4
141
aS6
fi.lfl
ii£4
10.»
IT.TO
8.08
10. «»
i^io
aoi
tLSI
ai»
4a 97
l&OO
srr.ar
40.0*
it.xi
tL«
-•""-" - ™
un. 1
W».
StOFftgf^^. .'..x.»...- .. ...^ ...
12.80
1«.S7
ass
aei
10.ffi
1*.47
10.01
L78
L0e
180
7,86
3J8
Growllif „►_„ ..._-
Y««fS.
*<<*«^>
t ••«•«•>
50.83
2L89
»L»
iB.41
u.m
19.lt
■
ft^^H
1
^H 75^ Miscellaneous Tables. ^^^^^^^^H
^^^^^^ TABLE LXXXVTTT-B?rfrfomert Cr^ek, JSS4-IS99, inch(siv«i H
^^^K Period.
IBM.
18S&.
1880
fall.
Ron*
off.
nttlon
Balu-
fall.
fiiU.
Bxsn-
olf.
^^H Stonm* *..«..«*■..'*'.- i>>--
ffi.19
a 06
ll.lfi
90.47
8.Bi
e.40
IS. Si
i,ee
£38
5, IS
8.U
7.11
SG.OS
n.7o
».oo
1A.74
1.01
1
^^B Qnwing
^H Ye«r
4BM
saas
17. 4T
m.n
tBM
».44
4G,7V
B&ll
a.«
mr.
lasa
law.
4
^^H W^e^ikg^ 1.
14 60
1.16
e.9r
laoa
11, 4A
14. IB
l».67
7.40
7.61
10. SG
«.7B
».4A
mm
1
171
lifl
8.N
^H Orovtsg......
i5.afi
m.m
».»
14.01
mM
ii84
a9r^
mu
_«,n 1
IMQl
mi.
- 1
^^H fttni^ljfA
B4.08
10.81
la.is
8.11
1L£4
fi.TU
n.m
18.81
8.16
17.»
km
G.M
&.4e
11.00
9.38
ISM
KOI
^^H &QplnnijiblQf ..,,
^H ir^*
mu
a&.7B
ea.ae
<».u
mm
aiOT
«4.0B
S0.98
mu)
^^H
^H
IBBS.
liW.
IfiGG.
^^H fi4^A14g4
n.ie
is.io
10 18
IT. 11
4.05
10.88
8.n
15.77
«.05
6 IB
8.«0
V.7^
mtt
10.88
6.S5
1*U
.ra'
in
km '
^^H Rop Ipniili tug' -.Aia. ....■«..
^^^^
i4M
m,^
n.u
4B.M
moo
tt.M
4a dG
IT.W
flL;7
IMG,
- 1
^H fh^^ff*
1&.0&
4.1fr
9.TS
12 fi
10.43
SD.OO
ia89
10, or
mar
ion
T.n
^H W"^"'"ff
^^ BiDlvHiYifiiff
^K v»*
4a. 60
17.28
^M
43L70
17.71
mm
1808.
- 1
VlQllKS'0* ■■*.*•■•<..... d .*.'. -
— *—
llfifi
Uk74
1,98
8.1»
8.60
9.BG
8,79
14.12
11. »
i.40
4.01
•■
flpOTrtng ■■■■■■■■■■■p^^, , ^
SiVlMUiTnf
Y«kr... ,
48.0(7
-flOS
«7.04
4S.r
RV
"1
.™.-.......j
Rainfall^ Run-o£E and Evaporation.
757
TABLE LXXXIX— TbfcicAron Creeh 1S8A-1898. inclutdve.
I
1884.
1886.
1886.
Period.
%{!!-
^csr
S3S2:
^^
^r
Bvapo-
nttion
Rain-
f»lL-
Bvn-
off.
Ssss:
Stormse
28.08
17. 5£
7.fiT
8.68
1.86
-1.21
laoo
8.08
21.88
U.81
10
10.46
1.64
2.04
2.41
0.77'.
7.08
28.64
11.10
0.06
27.70
127
104
176
Orowinff
188
'Rm^lffliiiihiTiff .... .
7.01
* — •
Tear
61.68
86.16
18.40
48.17
28.98
19.84
48.80
88.10
16.60
^1 — . _ .
1887.
1888.
1880.
Stonce
Ofuftiiig. ..•••...
21.80
10.10
8.71
18.44
4.80
.01
&18
14.80
6.80
28.68
12.98
18.04
27.r
1.90
iai4
1.16
10.07
6.00
86.18
28.00
21.84
17.82
1146
18.70
.7.81
11.46
Rirplimitlilliff ,
7.84
Yeer
47»60
M.16
28.86
67.69
80.60
18.08
7187
4107
2140
1800.
1801.
1802.
fitonce
26.00
16.48
ia20
10.01
2.64
6.46
108
11.06
4.76
28.07
10.77
7.18
20.28
4.90
2.08
184
14.78
6.18
28.48
U.22
KL86
10.78
1.62
147
187
OrowlDir ^
170
7.18
Teer
60.78
27
28.78
60
27.26
22.76
46.80
24.76
2106
1806.
1804.
1801
fiffmir^
22. 8B
14.82
U.81
22.06
&10
4.08
an
12.72
7.26
27.04
8.96
17.88
21.86
.84
8.11
6.80
8.11
0.68
fi.86
12.46
188
10.01
L48
.28
1.44
Orawlng.
1190
A 86
Yemr
48.96
28.21
20.74
61.88.
80.80
21.08
40.48
21.86
18.78
1808.
1807.
1888.
0tofmg«
21.80
18.78
U.68
12.80
1.01
4.tt
0.80
10.86
8.06
2a 82
17.82
8.78
18.98
6.12
1.08
8.80
12.20
8.80
26.40
ia87
1180
21.90
1
119
120
Onnrteir ........... T .... ,.-
0.87
8.81
Yeu* .^-....
48.to
.10.78
28.80
46.02
21.08
26.80
61.07
27.80
2188
INDEX
A.
Abbe, evaporation relations...., 141
icceleration,
and retardation of water Im
penstock .., eyo
curve of .*. 6S^
elTect of, on water supplied
to wheel - . - , 455
of gravit7 .«...,»•, jfS
Action tuTbines (see Impulse
Turbines) 244
Adam's, A, L., Values of ooefa-
cienta for wcxod stave pipe 60
Air chamber .«.«.., • 461
Alr^ energ7 in* .,,.*,,..,...,,, . 22
AJllS Ch aim erf Co^
Sewalls Falls turbines...... 612
turbine governor T3o
Turaer^fl Falls power plant.. 514
Altitude, effect of on rainfall... 124
American turbines. 11, la, 249. 256, 268
buclcetB of t7S
Foumeyroa 250
Fr&neis ...,.*. 24S
Impulse p . . . ^ . ^ 275
Jonval 252
practice of v&rfous manufao-
turers in measuring the di-
ameter of , . 28G
reaction, type. efSciency of. . 247
catalogue relations of diam-
eter and speed of 326
relations of diameter ai>d
discharge of 339
relation of power and diam-
eter of. 342
relation of speed and ^It-
charge in .,,»...», 346
American Turbl nee—Con. taqe
relation of speed and power
in ..• 350
speoiHc speed of S50
Ampere * • • 33
Aprons for dams, preliminary
study of, for dam at Kll bourn. . 585
Archibald, E. M., discussion of
efEect of load factor on coat of
power 623
Atkins* wheel and case 273
Atlantic drainage, hydrographs. . 100
Auxiliary power,
cost of 658
effectB of.. 631
hydrograph «howing amount
of, necessary to maintain
power at Sterling, DL.,.. 635
necessary to maintain ftxed
power on a southern river 631
itudy of, for report on water
power 6S0
Back water curve* , J>8
literature on 78
study of, for report on water
power 678
Ba rker's mlH $,239
Basin's formula. 10, 68
diagram for solution of*... 61
Bearings.
Oeylin glass suspensioii . . . . 39<1
horizontal lignum vttae 2fl3
hydraulic balancing piston of
Niagara Falls Power Co.
£93, 294
of borlsontal turbtnee
I
760
Index.
Bearlngs^-OoiL face
vertical cross or hanging
bearlosB of Niagara Falls
Power Co..,» 293
Tertical turbine. » 2R0
Bolt losses .«*,.,« 30
Bends In a stream, effect of on
distribution of Telocity** .*.<* 212
BetlTa Dam, India, automatic
drop shutter for...«»» 610
Blnni^e, ^eixander A,«., «.«••.,« 123
Borda turbine . . , , « . 241
Boyden, Uriah A..*,,,,,,, %
dittuser • . * 305, 307
Fourneyron turbine of,, 249,251
turbine of . , -....-_ 250
turbine tests of , 360
Brake wheel. W, 0, Weber.*,,.. 376
Breait water wheels ,•..,,, 3
British thermal unit 32
equivalents of 34
per minute, eQuIralents of. . 35
BrowUr Ralph T.,. .,,.,,, 275
Buckets,
American 276
ttodds *,.,... 274
Ellipsoidal ,.. 274
Hug'B 274
Kaights 274
Moore's 274
Felton ,.,* 274
modem chaDges In 13
of tangential or Impulse
water wheels 274
CadiaVs turbine, 239
Canals,
determination of economic
cross section G4
of Holyok© Water Power
CJompany ._ , 56S
for Peshtigo River develop-
ment « 573
Capacity,
Influence of cbolce of machin-
ery on 525
Of each part of a system , . . 2B
of prime movers,... *..,.,,, 528
Capacity — Con. w
Case Turbine Manufkcturlsf
Com pan jr^
tests of a 30'' re^la? torf^I^
tests of a 30' special....,.-.
Channel condition, ^Ted of on
gradient .•...«...•... 2173
Ohanuel grade, effects of on tha
hydraulic gradient of a stream 2^)^
Characteristic curro^
consideration of m turbine
from p #1
of Tremont-F ourno7ron
wheel .....,..«.»•....... #3
of a 45'' Samson wh€«l.. 41fMll
of a turbine, constrnctlon of m
of a Victor turbine 403-40^
of Improved New American
turbine ..,..,, 405
of Wellman-Seaver-Morgan
61* turbine ,,**,... 403
Chase. Mr, Stewart, agent of
Holyoko Water Power Co.,..- Ul
Chestnut Hill reservoir, evapom*
tlon from water surface of... 143
Chesuncock log way * S2^
Chezy'a formula., - 45
applied to pipes ,,.*
diagram for the solution of ES-^
Chinese Nora. * . , i!
Chippewa River. .,..., , , , lH
Christiana Power Station. Nor-
way, typical electrical lighting
load curve 434
Chute case, the....* .*•#,. 2!
Closed penstock, predetermina-
tion of apeed regulation with
U2. m
Oochltuate basin, relations be^
tween precipitation. evaporft>
tlon, runoff and temperatare
on ,, *. 14&-liiO
Coeffltlents,
of discharge for weirs.,.. 6S,7I
of dlacharg« through sub-
merged orlQces and tubei 45
of entrance losses 42
relation of to hydraulic ra-
dius on Wisconatn River.*
Index.
761
PAGE
Columbus Power Company, plant 546
Combes, tests of reaction wheels 859
ComiK>nnd motion 37
Conant, R. W., estimate of operat-
ing expenses of yarions rail-
way power stations 650
Concord Electric Company, plant
of 553
Connecticut Rirer, table showing
relation of rainfall to run-ofT
on the storage, growing and re-
plenishing period 159
Connections of,
governor to gates 493
by cable 477,495
by draw rods 492
by shafts and sectors... 494
turbines to machinery, vari-
ious methods 531
vertical wheels to generator 507
ConnorsYille, Indiana, regulation
of pumping plant 441
Conservation, laws of energy. ... 21
Constantine, Michigan,
details of head gates at 613
elevation of head gates at.. 613
rear view of head gates at. . 613
Contractions 42
Control of governor from switch-
board 492
Conversion of,
energy units 33
power 26
Cornell Hydraulic Laboratory,
experiments on float measure-
ments tfy Kuichling, Williams,
Murphy and Boright 229
Cost,
effect of size of units on. . . . 526
of auxiliary power 65S
of coal, effect of on the cost
of power 665
of developed water power . . . 652
of development of various
American water power
plants 650
of development of various
foreign water power plants 651
Cost — Con. PAOK
of development of water
power ^ 647
of distribution of power 653
of gas power, estimate of... 665
of motor installation 657
of operation, estimate of for
various proposed Canadian
plants 654
of operation of various street
railway power stations..-. 661
of water power development,
relation of capacity to.... 648
relation of head to 649
of water power plant, esti-
mate of Canadian 649
Cost of power,
effect of cost of coal on.... 665
effect of partial load on.... 654
from sub-station 656
literature on 672-673
per H. P. per annum in vari-
ous plants 659
transmission 656
steam at 22 power plants. ... 660
steam, estimate of 664
steam generated electric
power to the consumer... 669
water power 647
Cost, value and sale of power... 646
Coulomb 33
Crest, effect of changes in lengths ' '"t.
on head 100
Crops, dally consumption of water
by 135
Cross section, and slope, estima-
tion of flow from 219
Croton River, rainfall, run-off and
evaporation 751
Cubic foot, equivalents of 34
Current meter,
methods of computation for 227
observations and computation 223
Price's electric 222
rating curve 221
rating station at Denver, Col-
orado 223
readings, method of making 225
the use of 221
H 762 Im
^M CDTT«nt wheels *,,...„, 1,^41
rm
Danville, nilnols, concrete tnd
timber flshway at * • . . tl*
^1 Crlt&der ratei......p fS^aOO
^H diagram Bbowlng eddlei
^M c&UMd b7 302
H
^1 Bam and power plant, relations
Danville, Illinois, section of om-
crete dam at,,.*..--*,**,.* $W
Dayton Globe Iroa Works Gom^
pany ..♦-,,.**,..*......-, IS*
American turbine, devilop-
menl of.. .** SU
Increase In speed of..., 2SI
mnner of,..-.. £C|
<aiaracterl«tle cnrve of an
Improved New America
turbine , M
^m Dam at,
^M Holyoke during Hood....... &91
■ DanylUt. ruinafs. section of Sn
H Kilbonm. WlHcongla, with
^M movable creat............ 60^1
^B MeCaira Ferry, eectlon of.. B92
■ 8eweira Falls, timber i94
^H of Holy ok e Water Fower
^M Company *.......... &90
^m of The Montana Power Com-
^H pany. near Butte.... &3S
^B Dama,
^B appeTKlagee to. .««.«.. 80S
^H upr^nB frtf i ....... . F??'^
double horizontal wheel SIS
double hort^onlal wheel m
closed penstock 5U
test of a 44* turbine 711
two pairs of turbine units la
tandem , . ^ Sit
Deflecting mozz]e, governing Im-
pulse wheel with. .,*,..- 4B
Denver. Colorado, current meter
rating station,. ,„ M
■ calculations for atahllity of 587
mm consideration of various fao-
~ tors In ,. „ 589
effect of design of, on head IOC
flood flows over**--*,..**,, 533
Depreciation #, ^53
literature on ..,,,,,* 6TI
Developed power, annual ooit of U2
Development of,
American turbine..,.,,,.,,, I5i
capacity, speed and power of
a 48* turbine.... , 257
Leffel's wheel. .,, m
» for water power purpoiefl. .. &79
foundations ot...*..***m*... 5S]
heights of 5S0
Ij Impervloufl construction of* » 586
1 literature on 59S
movable 100, 60^
obje<;t of confitruction of 579 1
' overturning of 586,
plants located in , 574
potential energy,,, _.,».... IS
the turbine...^ 4
water power In the U. S.... H
Diameter,
graphical relations ot dto-
cbarge to. -.,,,,.,,,.,.,. , 33*
preliminary study of dam
for Southern Wisconsin
Power Co * . . &85
of runner.* *,, iS5
of a turbine, expression for
relations of power to 338
of a turbine, relation of dls*
charee to » . . S17
prlnciplea jf 4. on struct! on of
579-581
eliding on tmse 689
etabUItr of masonrr B8G
timbor crib at Janeavllle,
Wis. , ,,._ 583
1 types and detaila. _ 5tJ4
Datialde turbine ^24I|
of tnrblne wmter wheals, prao- fl
tlce of varloua manufac- ^
turers In measurmg 2g^J
Diameter and dlscUaTie of vari<
oui American tor buna,.. ^«., 311
Index.
76J
PAOB
Diameter and power*
graphical relation of In tur*
bines of homogeneous de-
sign 841
of yarionB American tnr^
bines 842
Dlftoser, Boyden 805-307
Discharge and speed of yarious
American turbines 846
Discharge curre 95
of Potomac River 282
Discharge, curves of at various
gate openings under given
speed, calculated from
actual tests 398
graphical relations of dia-
meter to 333
measurement of 372
of a turbine at a fixed gate
opening 832
of certain American and
European rivers, rates of
maximum flood 168
of rivers, relation to rainfall 745
of thirteen water wheels of
homogeneous design and
difTerent diameters 337
of turbine proportional to
square root of head 332
of turbines, relation of speed
to 345
of yarious Michigan rivers.. 188
of various turbines at full
gate, graphically ex-
pressed 333
of wheel un4er flxed gate con-
ditions, equation for 332
over weirs, comparative 68-69
relation of diameter to, in
American turbines 339
relation of power to diameter
of a turbine 337
relations of speed to for a
12 inch Smith-McCormick
turbine 335
Distribution of,
IK>wer, cost of 653
rainfall Ill
Distribution of— CJon. page
total annual rainfall in Wis-
consin 114-lir»
velocity, eftects of ice cover-
ing 215-
water at various plants, ex-
amples of 567
weekly rainfall in Wisconsin 117
Dix, J, L. ft S. B., Jonval turbine 255
Doble, ellipsoidal bucket 274
needle nozzle 302-306
nozzle, stream from 307
runner 277
tangential wheel 24S
Dodd bucket 274
Dodge Manufacturing Co., Instal-
laUon by 533-534
Dolgeville Electric Light and
Power Co.. plant of 548
Draft Tube, the 302-304
Drainage area, relations to flood
discharge 168
Drop-shutter, automatic for
dam 610
Duration curves of:
Ausable River 187
Grand River at Grand Rap-
Ids 187
Grand River at North Lans-
ing 187
Kalamazoo River 187
St. Joseph River 187
Thunder Bay River 187
various Michigan rivers for
1904 187
Dynamo, efficiency of 24
B.
Earthen dams, literature on 596
Eastern Gulf drainage, hydro-
graphs of 190
Eau Claire, adjustable flash-
boards at 611
Economy,
principles of. 82
value of improvements in*
tended to effect 670
Economy in operation of power
plant 627
t
■
1
Economy Light and Power Co,,
K JoUet plant of ....««..
H MorrU plaat of *....
H ta inter gates for MorriB plant
" wheels of * . . 410
Inc
B71
672
605
-411
302
305
304
,375
21
U
21
246
2il
12
247
24
. 24
24
54
247
23
247
23
23
329
424
23
32
3&1
ZU
23
21
W
20
740
41
41
41
22
Energy— Con. ^i^tm
literature of. ^..•«*«««,^,,. 11
losses In an hydraulic plant 21 fl
Losies In a pumping plant.. II V
losses In steam power plant. Si
mathematical expression of i^
no waste of in nature. ,.*,., 2^
•f fuel *.» 11
Eddies,
m as caused bj cylinder gatf « *
H as caused hy partial closure
^K of reeister G^^tea.^ ....«• i • *
potential and kLntttc IT
potential .*«*.*«#.«« 20
y through opening and pai^
tlally cloaed wicket gate. .
Etlctenrcy ^ .•*,,..,.,,,.,. t > 31
deflnitloQ of* ,t,..««t^p
thermal ,,-.-* 10
required to change penstock
velocity _..., 44«,I5«
transmtasioa and transforma-
tlon of *♦,* U
natural limit to. ..,,,«.**••
of a combined plant. *.....•
frf a dy^am<*, .«....«..■.•....
units, conversion of U
units of.* *•«..•....•, It
of turMnee, relative
of a Fourneyron tarbin©..,^
of a furnace * . . »
of American type of reaction
turbine .. ...... ..>....i.
Enlargements, midden ......•♦., H
Entrance head * , ^ , * * 43
Equivalent measures and weight!
of water W
Equivalents of energy T4I*
Escber. Wyss and Company:..,, ISO
double turbines at Chivres
near Geneva 2S2
Jonval turbine at Geneva
Water Works ,,,.... 211
of an hydro-electric plants,
of a abaft. ...i«<» «••«■■,»•■
of a steam engine. ,p,.,4»<<
of rftna.1 s#*f*tim^, iii»*tt>T-
of Jonval turbins* . a ■>•••■» *
of pumping engine ..•■.««•*«
Estimate of cost, for report on
water power ,*»** tS3
European practice in,
turbine coaa tru c Uon .....,,* 210
water wheel design ..,,.,,, 77$
Uuropean type of turbine,*,. ,,, H3
European vertical turbine, atept
nf md
of tangential turbtnee,,..«.
of the machine* * 1, ■ H •*•■«•< •
n rapt' trail limlfR tli^ ...__---
t^latifinft of fD and. . . ......
Electric lighting load curve. ^i,.^
BTJectrlc lighting, losses in hy-
draulic plant for ..«««.**»*«•••
Electric units. ..*«.•*»<<••««•*•
Evaporation , , - ,. * W ^
and temperature on Lake
Cochltuate, relations of.. 150
annual in the United Statn
nt-m
Chestnut Hill reaervolr, , • H3
literature on ,...,,4«. ,«,,«, Hi
Emerson, James,
testing of turbinet by
tests by *«^4«*(i*. *•>••■•■•
Energy *,-», p..^*
conservation, laws of «
definition of
differentiation of. ..,«,...«•
equivalent units of i ■«•■•««««
monthly from free water sup-
faces,
Augusta, Ga., ClnrinnatL,
Ohio. Des MofneSp Iowa,
Detroit, Mich., Helena,
Mont, Uttle Rock, ArlL.
exertion of hy.
momentum «•**«
weight
preasu re ,,..,,.*,..,...
In the alr^ .................
k
Index.
765
Eraporation — Coil page
monthly from free water Bur^
faces— Con.
Montgomery, Ala., New
Haven, Conn., Olympia,
Wash., Palestine, Texas,
Sacramento, Cal., Spo-
kane, Wash., Topeka,
Kans., Winnemucca, Nev.,
Yuma, Ariz., and at varl-
ious points in the U. S.. . 140
of water 20
precipitation, mn-ofC and
temperature, relations of
on upper Hudson River... 154
rainfall and run-ofC for vari-
ous periods 750
relation to precipitation, run-
off and temperature on
Lake Cochituate 149
tables 732
F.
Factory friction tests, data anid
results of 655
Factory load curves 424, 42S
Faeoch and Picard 252
Failiires of Dams, literature on. . 601
F^rbalm 3
Fairmont pumping station 252
Falling stream, effects of on grar
dlent 201
Fanning, J. T 15
Financial considerations of water
power development 640
Fishways: 614
In dam at Danville, Illinois,.. 618
in timber dam at Sterling,
ni 619
of Fish Commission State of
Wisconsin 619
literature on 632
Fitzgerald, Desmond. On evap-
oration 137
Fits Water Wheel Company.
OTordiot wat^r wheels of 243
Flvo-halves powers of numbers. . 744
Flash boards, 100, 609
Flash Boards — Con. page
adjustable at Ean Claire,
Wis 611
and supports, Rockford Wa-
ter Power Company 609
literature on 622
Float Measurements 226
at Lowell by Francis 229
Float Wheels 1-3
London water works 1
Flood discharge, American and
European rivers 168
of rivers, relation to rainfall 745
Flood Flow, study of for report
on water power 678
Flood flows, data on 583
Floodgates 606
Flood over Holyoke dam 592
Flow,
comparative mean monthly
of Wisconsin and Rock
Rivers 178
distribution of velocity dur-
ing various conditions of. . 212
effects of low water 107
estimates of,
from cross sections and
slope 219
by weirs 219
in open channels, methods
for the estimate of 219
in open channels, literature
of 198
in reaction wheels 317-320
in tangential wheels 316
measurements of by the de-
termination of velocity... 221
mean monthly of various
Eastern streams, in chron-
ological order 173
mean monthly of various
streams, arranged in order
of magnitude 173
of water in pipes 59
of water through orifices. ... 64
•Ter weirs 64
power of a stream as affected
by 79
relations of guage height to 208
7&5
Ind
ex*
PACE
Flow and liead, relations of . . . * ♦ , tZ
Fly-ball governor, — first used** 3
My wheel-*** *57
Foot pound. ....,^. * Z2
Foot, cubic foot per mlnutep
equivalents of t*- 36
Foott cubic foot per stcondi
eaulvaJenta of.* .* 35
Foot gaJloa, equivalents of...*.* 34
Foot pound, equivalents of,,.* 84
Foot pounds per minute^ equivar
lenta of * 35
Forests, effect on evaporation. , , , 1I3§
Foster, H. A., tests of steam
power plant.., * 6G0
FouDdatlona of dams «,.*«^.5S1
Fourneyron turbine, 11, 239, 250. ZO^
character ifltlc curve of 401*
data of .*-. 70a
diagram of double turbine
of tlie Niagara Falls Water
Power Company*.. , 253
efficiency of........... 247
Fox Hiver, hydrograph at Rapid
Croche *,**,.* ,...628
Francis, J, B 11.378
float meaBurements at Low-
ell . 220
formula for dam on the Mer-
rimac River **..** 69
Inward flow wheel..,. 259
teats by , 353
turbine at Boott Mills, teet
data of* * 703
turbine, original.... 12
Fraser River, high water dis-
charge at Mission Bridge 170
Frtctlon lost • 44
in asphalt coated pipe 03
In lap-riveted pipe , . , . 01
In wood stave pipe. , 63
Friction in pipes, condufta and
channels, first principles .,.*.. 44
Friction loads In factorl^ S55
Friction of reaction wlisels,
losses by. , , « « 31S
Fri^ell's formula for sharp cres-
ted weirs. tJ9
Fuel, energy of ..,.••.••..•*... U
Furnace eC&cIeney^ ..*..,,, Si a
I
Gangulllet and Katter*a formula 17 ^
Garratt, A, C, discussion of coaneo
tion of governors to gates 493
Gas plant, estimate of capital
cost and annual cost €65
Gate hoists and head gates. . Gil, 517
Gate movement, permissible rate
of . . *.., 451
Gate openiug, discharge of a tar*
bine lit various* **„*.*..*. t%t _
Gates and guides of Girard Im* H
pulse turbine. , * ••*•••..* S04 H
Gates, f
cylinder ,,,, 300
details and operating devices
of Snoqualmie FoJls tur^
bine - ., 303
flood **.**.,, ^ *..*»* S06
for overshot and breaet ^
wheels • S H
register SOI H
wicket ** •.*-..*., 30O-SfitM
Guage heights,
and heads available at Kil*
bourn. Wis ..,,- ^9
fluctuation^ In .,*,.,.. SOO ^
relations at various statieca H
on the Wisconsin river*,*. 20S
rslatton of to flow. ..,,.,.., WS
Gears and shafting, losses fn.... ^
Generators and motors^ ordlnarr
efflclency of *,,,*.^... 11
Generation and transmission ot
energy, power losses in. , .... . ft
Generation of power from poten-
tial source , SS
Genesee River, run-ofT diagram.. \^
Geneva, Switzerland 210
water works, Jonval tQrbfn«
at m
Geological conditions,
oifects on run-off .,,** ITf d
study of for report on watsr B
power -.-.-** C+i ~
Index.
767
Gcjlln Glaflfl aaspeniton bearing 290
Qcjlin-JoDTiJ turbia^* «....«..,.
...., 249, 25i. 290, Zm
of Niagara Falls Paper Mill
Company 25@
Olrard turbines.
K curreDt .,.. ,.... 239
^r Gatae and ^Idea of 306
general vlow af 2S0
impulse 278
longitudinal section of . . 279
runnere of , 2S4
' with draft tube 278
rnnner of 280
Glrard type for partial tur-
bine ..,,., 273
type of water wheels .*
., .269, 276, 307
Clock er White turbine governor 735
Governing,
Impulse wheels with defleet-
Ing nozzles.. 470
regulation with variable
speed and realatance 441
water wheels, present statiis
of ,..-..,• 443
govern or, *
Allia Chalmers hydraulic.*^. 735
ant i- racing mechanical 473
calculations, nomenclature
for .-.*.-„ . 447
connections,
by cable ,,,,..477, 495
hy draw roda 492
by abaft and sectors.... 494
control from swUchboard 492
details and appllcatloo, of
Woodward ....,,,,,, 477
diagram of Lorn bard Repl ogle
mechanical 479
effect of sensltlrenea^ and
rapidity of 457
essential features of an hy-
draulic * 481
for watei* wheels flrst used 3
general consideration of..., 491
Glocker-Whtte . , 735
Governor — Con. paub
Lombard-Replogle mechan-
ical *,.,..,, 47^
Lombard type "N" hydraulic 410
operating results with Lom-
bard - 485
problem of water wheei 44S
section and plans of Wood-
ward 476
aection of Woodward vertical
compensating mechanical 475
simple mechanical , . , 472
Sturgaaa hydraulic... 486
the Ideal 443
Woodward compeneating. » , . 474
Woodward standard. 471
speciflcatlonB ,*..,. 467
Grade, effect of change In., 205
Gradient, effect of channel con-
ditions on 203
efTects of rising or falling
stream on , 201
Graqd River, at Lansing Mich-
igan , , . , - 1S5
Graphical, ^
analysts of relation of power,
head and flow at Kllhourn,
Wisconsin , . . , . ^ . . . , 105
determination of stream flow
from m^surementa 230
Investigation of the rela-
tions of power to head and
and flow 103
relation of energy and veloc-
ity in reaction turbines. . . 321
representation of head 97
representation of the laws of
motion , , 38
study of head 104
study of power at Kllbourn 104
Gravity wheels 237, 23S
Great Lakes, hydrograph of dis-
charge of the. . . , , , . 180
Growing period.,.,,,,-*, 157
Guides and bucketa of Tremont
turbine ... ., 251
Gulf drainage, hydrographs of.,
--.p-»**, 190, 192
7<58
1
■
Inc
289
533
3S0
133
423
422
531
99
97
100
42
4i
97
104
373
S24
673
93
41
741
79
83
lOS
3S7
613
613
1«.
Head Gates— Con, Faw
rear view of, at Constat! tine,
Michigan 4..,, €11
Haaglag bearing^ Uie Nlagwa
Falls Power Company
H&rQ63S and drtviog sbeayes,
Sou tbwes tern MiEBourt Light
Co. ,.,.
Harper, Joba h., teatfl of Laflel
turbines at Niagara . . , «
Harrington, N. W.. effect of for-
ests on rainfall and BYspora-
tlon -.-**-
Head race, plants wltli.,*.^.^,, 67ft
Head water crurve....... H
Heat,
solar, »«**•#•..** *««^*.*«** 10
units of, . ^ ...••.•• • • . • 32
Heights of dams, limit of ....,.< , m
Henry, Professor, conclusions on
the rellabOtty of rainfall rec-
ords ..t<^.» *.... 12S
Henschel turbine. ..••■.•**•..•. 235
Hercules turbine, test of a 54 Inch 710
High head developments * &7S
High head or type "B" runner., 2SS
High water. Ftaser River at Mis^
slon Bridge, B. C , * . , . 170
History of water power develop-
ment ,. ,, .1,14,U
Hoist for tainter gates. ......... m
Holyoke Machlue Company, test
of a 54 Inch turbine., ««,.,«.. 710
Holyoke testing flume , , .SS4, 37&
arranged for horlsontaJ tur-
bines .-* 317
Hartford Electric Light Co.,
increase in sale of energy
of ,
load curve of. ,«*•.,.•>•<••*
Headt at KUbourn dam. ........
showing ebanges In , . . ^
under various conditions
effect of design of dam on
available •**.«*..,,». i * . ,
entrance ..,,..,..»f««-#«>«
friction **t«*t««.*««*w*» *
graphical representation of, .
H graphlraJi study of...,,.,.**
1 measurements of. ,*.,,, •,...
I on turbines, relation to speed
P and diameter
study of for report on water
power , ,
Tartatlons In ,,
velocity
velocity In feet per second
due to - , * * . i ..,,.,.
plan of. ...ii4>*....pp, •«•••, 3f ^
Holyoke Water ^Power Company,
canals of .,..•....*.. * S58
view of dam during flood. » . . 531
view of masonry dam of,.*.. SSO
Horse power, ,...-... ••»•«..»*«. 32
and efRclency of proposed tnr*
blues for McCall Ferry
Power Company *•... 41S
equivalents of., «••«• ti^
Head aod flow,
huportaflce of for power pur-
poses ^
relations of, ,**...«. ^ .«,,, *
speed relation of from tests 41S
Horse power hour. .,,.,. * SS
Houck Falls power station, tett
of Victor high pressure ttirhloe
at - 353
variations of* ...,,,,.,
H^i4 and power.
effect of number of wheels
on ..,,,♦ 1. .. * , ^ ^ ,
Howd-Francls turbine. . • • . . ^*b* 24^ ■
Howd Sammel B,*. . U^|
selection of turbine for uni-
form *....«,«••,......•««
^ll««^l ^f ,,,!,,, , 55*^B
Hudson River ^|
Head gates,
at Cons tan tine. Michigan 612
details of for Mr. Walt Tal-
cott. Rockford, Tlllnols....
dlscbargo arranged in chroiKK H
ical order ♦, *** 173^^1
arranged in order of ^M
magultude , ^**** 174 ^H
^^^^^^^^^^^^w ^^^p 769 ^M
Hudson Rlrei^-Coii- WAm
Hydrographs— Con, faqe ^|
runoff diagram of -**.. 1&5
MVTnparftfivP frntfi iHfTPfPTit ^H
table showing relation of
hydrologlcal divisions of ^M
rainfall to run oft for the
storage, growing aud re-
th^ TT P IF4 t*^^ ^1
continuous 24 hour theoreti* ^|
pleniahing period. ....... 15S
cal power at Kilbourn S8 ^M
Hudson RiTer Power Transmti-
for full range of condiUoiit ^M
afon Company.
of rainfall and temperature 82 ^H
speed records from plant of 486
when none are available 83 ^H
Spier's Falls plant o( 64S
■
Hug bucket...... 274
Alcovy River..... 191 H
Hnnking, A. W,. notei on water
Atlantic and Eastern ^H
power equipment. . . * 338
Gulf Drainage........ 190 ■
Hnnting or racing of water
Ausable River lU ■
whepls ..*.. ., 447
Bear Btver, Utab in ■
CMttenango River...... 191 H
Hunt-McCormlck runner.. 267
Hunt runner of The Rodney Hunt
Clear Creek.,.* 192 ™
Machine Company............ 2S9
Coosa River IW
Hurdy-Gurdy wheel . . , 241
Discharge of Great I^kes ISO
Hydraulics, general literature on 75
Fox River.-*,...,* €2S i
Hydraulic governor,
Grand River ^H
AlltB Chalmers..,,,,-....-. 73 j
at Grand Rapids. . . ^M
details of Lombard.,, 4S1
186,191 ■
essential features of. 481
nt Mnrth T.aT,«lflir %m M
Glocker- White - , , 735
Hood River m ■
Sturgefis type "N" 4S8
Iron River. Mlchlgmn... Ill ■
Sturgeas, the .....,,, 486
Kalamazoo River 186 ^M
Hydraulic gradient.
Kalawa River 19$ ■
1 effects of channel grade and
Kenneb€C RiTer. Iff ■
obstructions on 204
Kern River 193 ^H
' effects of variable flow on... 200
of a stream.
Licking River IM ^^
Meramec River. lit
i after constrnctlouof dam 94
Mississippi Valley and
1 effects of variable flow on 202
Gulf Drainage.. 191
1 under various eondltlona
Niobrara River,. 19S
r of f!ow 93
Ohio Valley and St. Law-
rence Drainage ....... Ill
Hydraulic plant, energy losses
In . , 25
Otter Creek ,. 192
Passaic River...... 1^2-^183
Perklomen Creek 190
HTdranlics. ................... 40
of the turbine.... 309
Hydraulf c type of relay, , . 471
Rio Grandu Rlvar 192
Salt River 19i
Hydro-electric plant.
efflelency of ,,»,,.,,,. 24
San Gabriel River l%%
loss^ In •.,,... 26
Seneca River *.« Wl
Hydrographs , ,,, SO
Spokane River lit
as power curves , . 89
St, Joseph Rlvn* ^ lit
available at some other point
Tennessee RlTer. *,,*,, Itl
on the river- . ... 82
Tbunder Bay RItot.,,.* 18t
available on otber rivers S3
Walker River, California J9S
47
4
H Tio Index. ^^|
^^^^ HTdrographs — Con. fage
ti^
^^^B We^ern drainage. **.... 193
Impulse turbfDeB (see alno Tan- H
^^^^^^. Wisconsin River,
gentlal Wbeels) ^
^^^^^^^H at KUbourn, baaed
..„. 237,241,244,246,301,111
^^^^^^^K meaaurementfl
^^^^^^P at Necedab S6
angle of discharge* «..•.,,«, JU
early development of ,., 2S}
^^^^^ at Necedab, WIl 81,192
^^^1 Yadkin River 190
^^^^1 YellovL stone River • • • « 192
ffflciency of.,» •■•«••.. 24r
governing of. »,.,,,.•*...... 47fl
regulation of^.^.-.^..-^^...^.. ISS
^^^^H power hydrographs at.
' ^'O t« A ■h*ii*«'^r*A %r *■ * m w A «•■««■■■ •■I'nnBai B4f*
^^H KUboum 90-91
J-
^^^B Sterling. minolB 625
James Leffel and Company ».... 26$
^^^^1 reliability of comparative... S7
characterlBtic curve of a 45
^^^^1 showing continuouB pow^
Inch Samson wheel . . , 41M11
^^^^1 at Kilbonrn, with actual
curve showing efficienoy, .
^^^1 head . ,..,101:
power and discharge, UB^ ^
^^^H fibowing power of plant aa
der various h^uis, calca- ^^
^^^^M Influenced by variable head 110
lated from character Istld
^^^H study of a stream from*.. ... 131
^^^^H use of comparative 83
curves ....,,»,•«....••»« 412
double horizontal tnrMns.... 517
^^^^H use of local ........>.<«,.*. S3
double horizontal turbine
manufactured hf 2IS
^^^^P when none are avallablet **, S7
^ when available 82
double runner of l%%
^^^^ Hydro logical dlvlstonB of the U.
four pairs of 45 Inch Samson
^^^H 8,, com para tlTe hydro-
horizoutal turbines..., .. StI
^^^^L graphs from 1S9
tests of wheel at Niagara. . > . SSO
Janesvllle, Wiaconain:
^^^
dam during high water. fiSt
^H Ice condttloBS*
dam showing low water.,,., 5s:
^f maximum velocities In a ver-
Joltet plant of 'Bmnomj Li^ht
■ ileal plane ,*>.,,.. 517
and Power Company.-*... BTl i
rating curve for. ..,..,,,,. 217
witb overshot and breast
tloliet, water power at* ....... .« It
Jolly, J. ^ W., Holyolce, Maaa,.. m
wheels *,*.-,*.*....,_.,. 3
test of a 57 inch turbine...* 1^
test of a 51 Inch turbine*.,. 713
lee covering, effects of, on dlstrl'
butlon of velocity. *.,..... 215
Jonva], t
liUnois River basin, comparison
of mean monthly rainfall
turbine, *.,-«...«p.,,., 2S9-tSf i
efflc-iency of * . liT
and run-off... .,,. 147
at the Oeneva Watar Works Jll
Improved New American tur-
bine .._...,.... 257, 259, 300
tests of a 30 Inch.. ...«**,, T5S
tests of a 30 Inch BpeclAl....7tl
calculations from character*
the American... ., «« SI
istlc curves of* .....,.»,. 407
K.
characteristic curve of * » * . . . 406
sectional plan of 262
Kennebec Rtrer discharge.
impnlBe and reaction turbines. . 311
arranged in order of ma^nJ*
relative advantage of . , * 24r>
conditions of operations ot. * 245
tnde .,*.,. ITI
ehronologlcaJly arranged... Itt
^
lodejc*
771
Kilbanm dam,
dlagrram showtXLg dianges In
head at.«,. ....,<-, 99
bead uiuler varlotia coadl-
ttQDS of flow ,.,.... 97
Kii ! JO u rn, Wlacons in ;
guag« heights and head
avallahle at......,., 99
fraphlcal study of power at 104
b€ad gate hoists at , $17
hydro^aph showing contlDU-
oufl power with actual head 101
hydro graph showing 24 hour
horse power, 88
hydrograpli of Wisconsin
River baied on flow at Ne-
cedah. Wis. . . 86
plant of Southern WlBconaln
Power Company.,., §21, 563
power hydrograph 90
power hydrograph, H. P.
hours with pondage , 10, 19
power of the wheels under
variations in flow. »...,., 106
rainfall above..,,..,,, 129
Kilowatt hour 33
Kinetic energy 33, 34, 36
Knight bucket.. , 274
Koechlin ^ , . . . . 8
Kulchling. Emll:
dlacuasion of rainfall and
run-off - 162
graphical relations of die
charge area for maximum
flood, American and EJuro-
pean rivers. , . 168
Kutter'a coefficient "n**, ,,..»,., 47
Kulter's formula. 47
diagrams for the solution of 48-49
L.
Lake Oochltuate, rainfall, run-off
and evaporation.... 763
l«alE€ Superior Power Company,
plant of 570
Lap-riveted pipe, friction loBsea t»3
Laws: of energy conservation... Zl
of motion, graphical repra-
sentation of. 38
Laws — Con. PAeE
of motion, Newton*i .... 3S
l^axy overshot water wheels (see
frontispiece) ..*.,... 14
Leffel and Company, the Jamea
(See also Jamea Leffel &
Go) 13
tests of a &6 inch turbine... 709
teat of a 45 Inch Samson tur-
bine .....,,.. 713
Leffel turbine,.... 243
diagram of efficiency, dis-
charge and power at Niagara 380
tests of, at Logan. Utah zn
Lighting, losses In generation and
transmission of power tor.... no
Limit turbines... .....-*., 244
Llppiacott, J. B. and S. G. Ben-
nett, relations of rainfall to
run*off In California...... p.. . 177
Literature:
back water ami interference 78
cauaes of rainfall 131
concerning dams 595
deacrlptlTe of hydraulic and
hydro-electric plants..... 556
disposal of rainfall 144
effect of altitude on rainfall 132
evaporation 144
floods *. 196
flow of water over weirs.... 77
flow of water through pi pea 76
general hydraulic , » 75
measurement of rainfall , . . . 132
power and energy..^. S9
percolation . . . . ..... 144-
relations of rainfall and
stream flow 195
resulta of stream flow meas-
urements 194
stream gauging . 233
turbines 353
turbine testing. 383
water power development. , 16
Lloyd, E. W., data concerning the
power load on various central
stations, due to various classes
of coasuraera. ... 667
^
■ ' ^^^^
^^^^^^^^^^^^B
PAQB
PACT
^H Load oond Ideas for m&itlnium re-
Lombard -Repl Ogle meebanlcal
^^M tiirr° 1 ■ II 1 1 ■ ■ 1 ■ ■
431
420
governor ... ^ ,•,..,.,«». » 478, 47S
^H Load eurre. ...«...*»<..*...,«**.,
London Hydraulic Supply Gom-
^H tactorr ^ * -
424
pany, maximum days of pump^
^^^^1 for aharp thunder Btorm peak
426
ing , i'3
^^^^1 In relation to machine selec*
London water wheels, float
^^H
433
wheels ....,.<.... 1
^^^H New York Ed 1 bo it Company,
tiOndon Water Works, undershot
^^^^B for day of maxlinum load . .
^^^B of Hartford Electric Light
42i)
whchc] iiiT^ fn 1 1 ■ ,1 I 1 1^1
Losses. ^B
^^^^H Company .,...,,..«,.,,..
422
In an hydro-electric plant.. .« U
^^^H df li^ht &nd oow^r olant
421
in belts U
^^^^1 literature on ,
439
in machinery,, St
^^^^B maximum days of ptimpliag,
in turbines ..,, 27,371
^^^^1 London Hydraulic Co
429
1^0 w heads, vertical shaft tur-
^^^^1 Pennsylvania railroad shops 42?
bine for m
^^^^H relation of power, mJpply and
Low water flow, effects of lOT
^^^^1 demand, diagrams of ,
435
Machine factor, definition of.,,. 0$
^^^^1 relation of, to stream flow
Macbine, ideally perfect , , 1^
^^^^H and auxiliary power. .....
431
Alacbtne selection, load curfe la ^M
^^^^H atudv of for renort on water
relation, to * . . . 4JS^
^^^^1 power .......
679
Machinery, losses In S3
^^^^1 typical factory
42S
Madison, Wisconsin, diagram of
^^^V typical railway,
430
fluctuations of monthly rain-
^V Load factor.
fall at,. iz:
^1 definition of .
433
Manchester^ England, sharp thun-
^H effect of on co^t of power, Ar-
der storm peak. ,,,•*,. i2i |
^ clitbald ...<..
€62
Maps of.
L effect of on cost of steam-
average annual rainfall In
^K generated electric power to
the United States, .... 112-11?
^H the consumer. ... .....
eei)
average aunual rainfall to
^H Infiuence of on operating ex-
Wisconsin . . , • ,•.*.. 115
^V penses ,
€62
rainfall conditions in tM .
literature on ..,,..,,,,,..,. .
43d
United States, July 16-17 111
Logan, tJtah, tests of Leffel tur-
wp*ikly ilisft-lhTitfrtn nf f^lnt ^fl
bines at
370
fail Jn Wisconsin-.. IItS
1 Log way ..* .....♦,„
€21
Manufacturlni? purposes, losses la ^M
utilization of energy for tw^M
at Lower Dam, Minneapolis^
Minn
621
Market price of water powef,,.f SCI^^|
in the Chesuncook timher
Masnnrv rtnrnQ ^H
' dam . . . , . . ,
Lombard governor.
620
nt'*rn 1 11 re nn ■■■■■■ , > ^^^|
stability of ,....,... §V^|
operating results with
4gn
\f flfta Sl^l
deftails ol
481
Mass diagram showing rnn-«»S ^M
type "R^^
484
from Tochickon Creak . .^ CSl^B
type '^N" 4S0
Lombard hydraulic relief TElves 49fi
Mathon DeCour...... **,»*' ^ V
McCall'a Ferry dam, section of... ^t^t
Lombard relay valve.
483 I
McCormlck, John B 13, SC^'^H
Index.
773
PAGE
McCormick turbine 267, 269
test of a 57 inch 708
test of a 51 inch 711
test of a 39 inch 717
Mechanical governor,
anti-racing, Woodward 473
Lombard-Replogle 478
simple, Woodward 472
Mechanical type of relay 471
Merrill, Wisconsin, rainfall above 129
Merrimac River discharge,
arranged in chronological
order 172
arranged in order of magni-
tude 174
Meter, the wheel as a 365
Michigan drainage area 185
Michigan rivers,
comparative hydrographs of
various 186
discharge in cubic feet per
second per square mile of
drainage area 188
Mississippi Valley Drainage, hy-
drographs of 192
Missouri River, variations in the
cross-section of, near Omaha,
Neb 210
\fomentum, exertion of, energy
by 41
Moore bucket 274
Morin, tests in 1838 359
Morris Company, I. P 252, 268
diagram of double Fourney-
ron turbine 253
estimate for turbine for Mc-
Call-Ferry Power Co 412
graphical diagram of rela-
tions of power and head . . . 413
graphical diagram of test of
wheel of The Shawinigan
Power Company 382
Shawinigan Falls turbine... 270
Trenton Falls plant of The
Utica Gas and Electric Co. 511
Morris, Elwood, 9
first systematic tests of tur-
bines in U. S 359
PAOX
Morris plant of Economy Light
and Power Co 672
Motion,
compound 37
laws of 36
uniform 37
uniformly varied 37
Motor installation, capital cost
and annual charge on 657
ordinary efficiency of 31
Movable crest for dam at KUr
bourn, Wisconsin 608
Movable dams 100, 603
at McMechan, W. Va 603
literature on 622
Mullin's formula (used by East
India engineers) 69
Murphy, E. C, methods of corrent
meter computation 227
Muskingum River, run-ofF diar
gram of 156
table showing relations of
rainfall to run-off for vari-
lous periods 156
N.
Necedah, Wisconsin,
hydrograph of the Wiscon-
sin River at 96
rainfall above 129
rating curve of Wisconsin
River at 96
Needle nozzle, Doble, cross section
of 306
Neshaminy Creek, 167
rainfall, run-off and evaporsr
tion 754
Nevada Mining and Milling Com-
pany, plant of 555
New American turbine 257
test of a 44 inch 714
runner of 260
Newell, F. H., estimates of rela-
tion of rainfall to runj-off 174
Newton's laws of motion 86, 38
Niagara Falls,
estimate of the cost of hydro-
electric plant at 648
774
Index.
Klagarm Fialli — Con, paoe
first power at * * 15
power development E7d
water power at ^«..«4.. 22
Niagara Fallfl Hydraulic Power
and Manufacturing Company
255, 26G
Niagara Falls Paper Company, ♦, 254
Niagara FallB Power Company,
the vertical bearing used by 291
double horizontal LeITel tur-
bine of the 265
testi of wlieelB of , . < 3S0
Niagara River, hydrograph of dis-
charge of * . * .... 179
Niagara Falls Water Power Com-
pany , * 2G2
Niagara Foumeyron turbine. . • . 250
Nomenclature for^
governor calculations. . 447
turbine discussion 310
Nora. Chtneee ,•..••*.•*•** 1
Northern Hydro-EIectrlc Power
Company, hoists for taluter
gates for 606
Northern rivers, monthly rainfall
and run-off. , * 165
Nunn, P. N„ turbine testa at Lo-
gan, Utah.,. - 379
O.
Oberchaln. Matthew and John. , 267
Obstructions,
effect of change In 205
effects on channel grade, and
on the hydraulic gradient 204
Ogden pipe Hue, experiments on 6i)
Ohio Valley drainage, hydro-
graphs of 191
Oliver Power Plant, wheel har-
ness of , . 530
Outario Hydro-Electric Power
Commission, estimates by. ... .
64g, UB, 654, 656, 657, 664
Upon etinnnela, flow in, Uteratura
o« ^ 198
Open penstocks,
application of method to. . . . 465
p red etermi nation of speed
Open PenstocKs — Coiu FAflf
regulation for wheels set
In .,«• ^ ,,.«..,. . 4C1
OperattoD, economy ln,...« ^2!l^
Operating expenses, ^M
effect of load factor on 6f^|
estimate of for various pro- ^|
posed CaDadian plants.,,, 6S4
ratio of individual items to
total ,. en
OrlQces, ^^
flow of water through , . fi^|
submerged l!^^
Oscillatory waves In long pen-
stock , , . , 451
Outward radial fiow turblDes.,, 2H
Overload ..,, G£iH
Overshot water wheels 8, 24^H
Laxy ...,,.. 14
I
Pacific Coast, development of ^
wheels on. . ^ 2TS
Paddle wheels , 241 _
Paris water works, undershot
wheel used in IIJ
Partial load, eifect of on cost of
power 634'
Partial turbine. ....,,*., 244 '
Passaic River,
hydro graphs of » . . * 1IM8I
rainfall on drainage area of
m-ii!
relations of rainfall to ruit-
off , . _ . ...... 18i-l£lj
run-off diagrams of 15
Pel ton,
bucket . . . . , 2W
tangential water wheel ran-
ner ..,♦.. I
Water Wheel Company 275*5711
wheel 27$, SOT *
Penstock velocity,
change of ...,..,„._ 4$3
energy reiiuired to ch&nge
- • * 446-45G
Percolation, literature on...^,., 144.
Periods, growing » , , isfl
Ind
ex.
775
Perloda— Oon. ^ace
replenishing , ^ . ^ ..... , 167
storage .....,,..* 157
Perklomen Creeks HT
rain tall, ruQ-oS and evapora-
tion 756
Pe&bt!go River development, pro-
file of... 574
Philadelphia, water wheel teats
in 1S60 at > 3G0
Pile fouudations for damB. . 603, 603
plobert and Tardy S
Pipe,
Cii€zy*s formula 60
Darcy's formula 60
flow of water In ,..•,* &§
literature on flow of water In 76
looses in asphalt coated. ... 62
Plant capacity 525
Plant design, study of for report
on water power 6S1
Plant of.
Columbus Power Company,, 546
Hudson River Traasmlsslon
Company at Spier's Falls 546
Nevada Mining and Milling
Company ....,.»., 55S
South Bend Electric Company 54d
Sterling Gas and Electric
Compatiy . . 537
The Concord Electric Com-
pany ,....,,. Sg3
The Dolgeville Electric Light
and Power Company 643
The Lake Superior Power
Company , , 570
The Niagara Falls Paper
Company 257
The Shawinlgan Water and
Power Company, , , 550
Winnipeg Electric Railway
Company 553
York Haven Water Power
Company *. 537
Plants,
Located In dams 574
with concentrated fall...... 564
with divided fall 564
with head race only 670
PAOR
Piatt Iron Works Company
. . .267, 268, 2T6, 295, 300, 301, 30S
characteristic curves of a Vic-
tor turbine , 402-405
graphical diagram of test of
25 inch Victor high pres-
sure turbine. ,->... 3S2
relations of efficiency to dis-
charge at various revolu-
tions ^ . > , 405
the Snociualmle Falls ruc-
tion turbljie... 272-27S
test data of 48 inch turbine 704
test of a 42 inch turbine 715
test of a 45 inch turbine.,,, 712
tests of a 36 Inch turbine 720
testa of a 33 inch turbine 723
Poncelet'a wheel . * . . 4, 241
Pondage,
effect of limited, on the powder
curve 624
effect of on power. . , , , 624
hydrograph on Fox River
showing effect of Sunday
shutdown of hydraulic
plants . . , 628
hydrograph showing effect of
, • e2f
Sftudy of for report on water
power , * , „ , 679
Pondage and storage,
analytical method for calcu-
lating ,,,, 644
Pctential energy , ,., 20, 3i
development of 19
generation of power from* ... 26
Potomac River.
discharge arranged io chron^
ological order 172
discharge arranged in order
magnitude , 174
discharge, velocity and area
curve of ,*.*..*, 233
Power,
actual conditions under
which same Is furnished
to consumers from central
stations 668
U
776
IndeXi
at Kll bourn, fraphlcal study
of , ...-„,,-... 104
Gbarges for hj Cataract
Power and C!o adult Co. of
Buffalo *....... e70
conversion of..*... •«• 26
development of
at Niagara Falls,,* 576
study of for report on
water power , 680
effect of on pondage , * fi24
from municipal sub-station,
estimated cost of 65S
literature on 672
measurment of . . . . ^ • ^ 375
of the Ki I bourn wheels un-
der yarlatloDs in dow 106
of plant as influenced by var*
iable bead, hydrograph
etiowing 110
of plant, efTect of bead on.. 100
of steam.. * .*. 33
of stream as affected by flow 79
of turbine,... - ^25
expreesioa for, . . , 336
of homogeneous design.. 34 L
proportional to hi . . * . 33b
of water. . . 33
relation of to head in a 12
inch Smitb-McCormick tur-
bine 336
sale of..... 666
tran,smiBBioa of. ............ 26
ntilization of,. 26
Power and diameter,
graphical relations of in tur^
bines of homogeneous de-
sign 341
of irarious American turbines 342
Power and energy, literature on.. 3fl
Power aad speed of turbines,
relations of 347
various American 350
Power curve,
effects of limited pondage 624
hydrograph as a. . S9
Power, head, and flow, relation
of at Three Rivers, Michigan 103
PAGE
Power hydrograph at Kllbonm 31
Power hydrograph at Sterling,
Illitjots ..,.-...*•.. C2S
Power losses in generation and
transmiaalon of energy 27
Power plant at Turner's Falls. ... Ui
Power station,
and dam, relation of, ....... Ul
study of site of for report on
water power «« Ulm
Power transmission^ I
estimate of investment, an-
nual charges and costs, . . « €5€
literature on ,....,.. 673
Precipilaiioii,
in United States, types ef
monthly distribution,...,. lU
relation of evaporation, run-
oK aud temperature to, oa
Lake Cochituate. .,,*,*.,, W
runoff, evaporation and tem-
perature, relations on Sud-
bury River basin.. 151
run-off. evaporaUon and tem-
perature, relations of on
Upper Hudson River. . 15*
variations at stations closely
adjoining ....... Hi
Pressure, exertion of energy by. . *1
Pressure or reaction tuj bines..,. 214
Price's electric current mt-ter..,. 232
Prime movers. possibiUties of . , . . hZi
Prony brake. W. O. Weber , 377
Pumping engine, efficiency of,,.. 3(3
Pumping plant,
at Goanorsville, Indiaaa. reg-
ulation of ,,..,... 441
energy losses in steam and
electric * , . . . 25
R.
Raceways,
of Hoi yoke Water Power
Company MS
of Sterling Hydraulic Com-
pany .-..,.,, W*
Racing or hunting of water
wheels ...,.**,,.,. ,,,,,,. H*
^
Index.
777
PAGE
Harln%, r&lue of 456
Racks, trash 536
Iaif^.er and Williams, expert-
pients of 65
'Ufter. George W.,
discussion of rain fall 125
discussion of Vermuele's for-
mula 148
graphical comparison of dis-
charge over weirs 68, 69
graphical diagram showing
discharge over weirs with
irregular crest 72-78
report to the Board of Engi-
neers on Deep Waterways 65
Railway load curve, typical 430
Rainfall,
accuracy of records of 122
at Merrill, Wis 129
annual at,
Augusta, Ga 120
Cincinnati, 0 120
Des Moines, Iowa, 120
Detroit, Mich, 120
Helena, Mont 120
Little Rock, Ark 120
Madison, Wis 120
Montgomery, Ala 120
Moorhead, Minn 120
New Haven, Conn 120
Phoenix, Ariz 120
Sacremento, Cal 120
San Antonio, Texas 120
Spokane, Wash 120
Tacoma, Wash 120
Topeka, Kans 120
Winnemucca, Nev 120
annual, local variations and
periodic distribution of 121
conditions in the United
States 118
data, availability of 87
disposal of 133
distribution of Ill
in United States, types of
monthly distribution of... 123
literature on ISO
literature on disposal of 144
Rainfall — Con. pagx
maps and records, accuracy
of 122
monthly mean at,
Augusta, Ga 127
Cincinnati, 0 127
Des Moints, Iowa 127
Detroit, Mich 127
Helena, Mont 127
Littie Rock, Ark 127
Montgomery, Ala 127
Moorhead, Minn 127
New Haven, Conn 127
Sacramento, Cal 127
San Antonio, Tex 127
Spokane, Wash 127
Tacoma, Wash 127
Topeka, Kans 127
Tucson, Arts 127
various points in United
States 127
Winnemucca, Nev 127
observations, accuracy in. . . . 126
on the drainage area of the
Wisconsin river 129
records, value of extended.. 124
relations of annual to run ofF 177
study of, Ill
as affecting run-off 126
for report on water
power 677
rate or intensity of 133
relation to river discharge.. 745
run-off and evaporation, for
various periods 750
variations of at stations
closely adjoining 125
Rainfall and Altitude 124
Rainfall to run-off
monthly relation of 162
on southern rivers 166
on Northern rivers 166
on Sudbury River for each
period of the water year. . 161
ou upper Hudson River for
each period of the water
year 160
relations between monthly
depth of 164
7n
Index.
E&lnf&ll to ruD-ofl — Coil pack
rcQatloEs between, on the
Pasaaic river 1%2-lBZ
relation of, for various per*
lods on tlie Connecticut
River - ..*,* 169
relations of, for various per*
lods on the Hudson River 15S
relations of, ou the Hudson
and Genesee River, dlar
gram of.... *.,**** 1S5
relation of periodic «... 159
Rating curve,
changes In head due to
changes in cross section , . 96
current meter .«. S2i
for WaliklH Elver, Ice and
open conditions. 217
for WiscoEiin River at Kll-
bourn, Wisconsin 209
Inf nence of stream eroea sec-
tton on 95
Rating or discharge curve * h 95
Rating station for current meters,
Denver, Colorado. ............ 223
Heftctlon and Impulse turbines.. 211
relative advantages of 245
Reaction turbine 237, 239, 316
American type. .>>«.. 256
arrangement of.. 500
condition of operation of , . * , 245
diagrams of , 240
economical operation of 313
friction of 318
general conditions of opera-
tion 500
graphical relation of energy
and velo<*lty In.... 321
graphical relation of velocity
and energy ia flow through 320
minimum residual velocity
of water In leaving buckets 31^
necessary submergence of . . . 501
path of jet 317
r el at 1 ve ve I oc i ty of the bucket 318
residual velocity of water
from * - - , 318
Snoqualmle Falls.. 272,273
WAm
Register gatet ....... ^...,.. SOI, S04
diagram showing eddjlng
caused by , * w SOS
Hegulatlon of Impulse wheels... iaZ
Eegulatiou of turblneSp com para- ^
tive ...,. IStB
Reinforced concrete dams, litera-
ture on . »•.••.,.*.,,• 601 ^
Eelayi ■
hydraulic type ot^,^^m**^*~. 471
mechanical type of , * * , 4T1
Relay Valve, Lombard 4%%
Relief valves,..*... ...495-49S
Lombard hydraulic 4&R ^
on end of penstock* . . p . , , , , . 4£^l V
Sturgees .p.. ,**......« 19^
Rennie . 3
Replenishing period - . . . Ill
Report of water power, genera]
outiiue of. ..... .... Ut
Resistance and speed, relation of 440
Retardation of water in penstock IM
of on gradient , 201
Rising or falling stream, effects ^
Rlsler^ M. B.^ eatlmate of daOy I
conaumption of waier by differ-
erent kinds of crops 185
Rivers* M
comparative hydro grt^^h of H
various In Michigan. .*..* ItS ^^|
hydrographs of, ™
Alcovy River.. < p., 190
Bear River, Utali- *,.... IW h
Clear Creek , > -- 192 ^
Chlttenango Creek,.,,*. IM
Coosa River IT
Grand River at Grand fl
Rapids 151 ■
Hood River ..,.>., 1&3 fl
Iron River*,,,.*. IM ^
Kalawa River 1*3
Kennebec River * IW
Kern River lU
Licking River .*... W
Meramee River.,,,,.,.. I9i
Niobrara River 1S3
Rivers, hrarographB of— Con, TAtm
Perkloisen Creek m
Rfo Grande River 192
Salt River... 192
lex. 779 H
Runner — Con, face ^H
of Glrard turbine. ....•....« 280 ^^1
Run-off (see also Stream Flow). ^|
relatioaa between monthly ^H
San Gabriel River 193
Seneca River,.,,.. 191
SDokano River ^...... 19JI
study of for report on water ^|
power >.,.... 676 ^^
and rainfall, monthly rela- ^H
tion of,, ,, 163 ^1
and rainfall, monthly rela^ ^H
tions on Southern Rivers. . 16S ^U
and rainfall, monthly rela- ^M
tions of on Northern Rivers ICb ^M
diagrams ^H
of Hudson and Genesee ^|
River 155 ■
of the Muskingum River 1S(^ ^H
of the Passaic River 155 ^M
effects of area on. ..... . 179 ^H
ejects of geological condU ^M
tions on,, 177 ^M
effects of rainfall on 1S6 ^H
Influence of storage on the ^H
distribution of. IT^ ^M
influence of various factors ^M
lie ^M
Tennessee River ..-.*♦,, 191
Walker River lai!
WlBconsin River at Ne-
cedah, Wis,, ... .-,<., 192
Yadkin River 190
Yellowstone River 193
monthly discharges m cub.
ft per sec- per square mlje,
Ausable River 188
Grand River at Grand
Rapids 18S
Grand River at Lansing,
Mich , 1§3
Kalamazoo River. ,,,.,. 1S3
Manistee River, 1S3
Muskegon River. ,, 188
St. Joseph River 18S
Thunder Bay River 118
White River 188
relation ot rainfall and vnu-
1 ofr on ,,.,,*..*ii.,t 165
mean annual of the rivers of ^M
Rcck-flll dLius. literature on..,.. 597
Rockford. ininols.
details of head gates for Mr.
Wait Talcott ,. 616
Hash boards and supports at. . 609
Rock River,
at Rockton, niinois 165
1 cotnparison of mean monthly
flow with Wisconsin River 178
Rodney Hunt Machine Company
,*.,,.*, 267-268
precipitation, evaporation and
temperature, relations of ^^
on Upper Hudson River.. 154 ^M
precipitation, run-off and tem- ^M
perature. on Sudbury River ^H
basin, relatione of 151 ^H
rainfall, and evaporation, ^M
for various periods.**.... 750
relation of periodic rainfall
to .,,.. 15^
relation of annual rainfall to
175-177 1
relation to precipitation* eva- 1
poration and temperature 1
on Lake Cochimate 140
1
Sale of power, , . . . €46-666
Rome, water wheels In 14
Rotary converters, losses in. 29
Rotation of water wheels, direc-
tion of.... 2S3
Rou^ 4 Ciives * &
Rou^ Volant, , . 8
Runner,
details of > ,.. 285 i
Its material and manufacture 284 :
Improved New Amerleao.... 261
an equitable basis for.. 663
literature on , , 671 ^^^d
7^o
Index.
PAGE
Valine Hl?er, croea section at
paging atat[on 2ZB
Samson turbine,... ,«...«« 265
section and plan of. 263
teat of a BS Inch 703
teat of a 45 Incli 713
top and outside riew of run*
ner of , » 261
character I ^Ic curve of a 45
Incli 410-411
Schlele turbine 239
Science of hydraul Ice 40
Scotcli turbine ..♦ .7, 239
SeatOe and Tacoma Power Com-
pany, The 26S
Sew all's Falls, vertical turbines
for .,., .,.,... 512
Shaftiafj. efficiency of , * . * 24
use oI«...«,* ^^^
Sbawlnlgan Falls turbiae,.. 268. 270
runner of. - . 271
efficiency and discharge dta^
gram of ,*,.., 381
Sbawinigan Water and Power
Company, plant of . . . , 550
Shock, due to sudden changes in
velocity . . 4 19
Shutter, automatic drop at Ba-
tavla* India 610
Site of dam for power station,
stud? of for report on
water power » CSl
Slope, estimates ot flow from. ♦ . , 210
Smeaton's experiments on water
wheels ,.,.......,..,.... 357
Smith, Mamitton, Jr's., coefficients
of discharge for weirs 74
Smilli-McCormick turbine,
relations of head to discharge
of 334
relations of power to head ia
a 12 inch , S36
runner of ,.*..*., 067
Smith turbine.. £67
S. Morgan Smith Company...... 267
curve of relatione of dis-
charge and speed from ac-
tual testa 30S
S. Morgan Smith Co. — Con. wkm
curve of turbine from actual
testa ..,. *..,. 31)9
relation of efficiency to speed
in a 33 Inch wheel , %%
relation of power and speed
from actual turbine tests,, ZH
test of a 33 inch turbine 717
tests of a 33 inch special tur-
bine .,. ,..., 721
turbine, relations of speed
and efficiency ia.<,*,^««.,, SSIjfl
turbines for Ccnicord Electric ™
Co. .,.*.,.. 513
two pairs of turbine units ta
tandem ......*........... Sli
SnoQuatmle Falls reaction tur^
bine , 27:!, 211
diagram showing relation of
gate guides and buckets.. 301
diagram showing rigging for
opening and operating
gates . . , - ^ . . * , , , , , . aO'
thrust bearing of,, 3^1
Solar energy, .,.,,.,.-.,. ^ • * . 15. 21
South Bend Electric Company's
plant . . , , , ^ ♦ Hf
Southern Wisconsin Power Com-
pany,
dam witll movable crest ut
Kilbourn, Wis.... 6fll
head gate hoists for, *#*.».« SI?
Kilbourn plant of 521-50
preliminary study of dam for 5SJ
Southwestern Missouri Light Co,,
harness and sheaves of . . . , •t^^
Special New American runuefv- 5^i
Spectfications for governor.. — -i^"^
Specific speed or system curve tt
turbines .. ^ ,.«..«.,,«...«,,* . ^^^
Speed,
economical speed of any
wheel ,....,.,.....,. — 3-^
relatlonj necessary for con-
stant *- ^^3
relation of turbine speed to
diameter and head.. ^ 321
Speed and discharge of varioui
American turbines .*
^
Indea
781
PAGE
Speed and power of turbines.
relation of 347
Speed and power, selection of a
turbine for, under fixed heads. . 387
Speed and power of various Am-
erican turbines 350
Speed and resistance, relation of 440
Speed, <f> and horse power, ex-
perimental curve showing rela-
tion of 415
Speed of rotation, measurements
of 373
Speed of turbines, relation of
discharge to 345
Speed records from Hudson River
Power Transmission Co 486
Speed regulation,
detailed analyEis of 688
for plant with open penstock,
predetermination of 461
plant with closed penstock. . 462
plant with stand pipe 463
graphical analysis of 693
influences opposing 4.^3
Speed relations, graphical expres-
sion of 329, 331
Special New American turbine. . . 257
Spier's Falls plant of Hudson
River Power Transmission Co. 546
Spouting velocities of water.... 741
Stability of masonry dams, litera-
ture on 595
Stand pipe, 458
dlBCUBsion of relative speed
regulation 696
fluctuation of head in b99
numerical problem 466
predetermination of speed
regulation with 463
8t Clair River,
drainage and guage heights
on 200
liydrograph of discharge of
the 180
variations in velocity in the
cross section of 211
Steam and electric pumping
plant, energy losses in 25
PAGE
Steam engine, efficiency of 24
Steam plant, capital cost and an-
nual cost of per brake H. P. . . 664
Steam power 8S
Steam power plant, energy losses
in 24
Steel dams, literature on 601
Sterling Gas and Electric Com-
pany plant 537
Hydraulic Company, race-
ways of 567
power hydrograph 62.^
tainter gates in U. S. dam at 604
timber flshway in dam at... 619
St. Lawrence drainage, hydro-
graphs of 179. 191
St. Mary's River, hydrographs of
discharge of the 180
Storage, 624
calculations for 635, 636
diagram showing effect of
large storage capacity.... 633
effects of limited 629
effect of maximum 635^
influence of on distribution
of run-off 17&
limited, effect on low water
flow at Kilbourn 62^
literature on 64&
study of for report on water
power 67S
period of 157
Stout, Mills and Temple 13, 25G
Strabo, reference on water wheels 14
Stream flow,
broad knowledge of neces-
sary for water power pur-
poses 80
estimates of 169
factors of 79
graphical determination of,
from measurements 230
literature on 19S
maximum 16:(
measurements, necessity of. . 213
relation of load curve to 434
value of single observations 80
782
Index.
Stream flow — Con. page
variation of from year to
year 82
Stream guaging,
application of 231
cable station for 228
Stream, stady of from its hydro-
graphs 181
Stnrgess governor, test results
with 491
hydraulic governor 486
Type N, section of 489
relief valves 498
Submerged orifices 43
Submergence of reaction wheel.. 501
Sub-stations, estimated cost of
power from 65G
Sudbury River, rainfall and run-
off of for each period of the
water year 161
Sudden enlargemenf g 42
Swain turbine 13, 249
test of a 36 inch 718
Switchboard, control of governors
from 492
T
Tailwater curve 96
Talnter Gates,
for Morris Plant of Economy
Light and Power Co 605
in U. S. dams at Appleton,
Wis 607
in U. S. dam at Sterling, Il-
linois 604
Talladega Creek 166
Tangential wheels (see also Im-
pulse Wheels) 241
angle of discharge from buck-
ets of 311
Atkin's wheel and case 273
early forms of 8
effect of angle of discharge
on eflaciency 315
efficiency of 247
maximum work 314
path of Jet 316
runners of 284
Tangential wheels — Con. page
Telluride double. 2,000 H. P. 275
Tate, Professor Thomas, on evap-
oration , 141
Taylor, J. W., turbine 300
Telluride double tangential wheel 275
Telluride transmission plant, the 276
Temperature an4 evaporation, re-
lations of on Lake Cochituate
basin 150
Temperature, precipitation, run-
off and evaporation, rela-
tions of,
on Sudbury River basin — 151
on the Upper Hudson River 154
on Lake Cochituate 149
Test data of turbine water wheels 703
Testing turbines 355
purpose of 370
flumes for at Holyoke 364
machinery for, importance of 355
by James Emerson 361
early methods 359
literature on '. 383
plan of apparatus for by
James B. Francis 374
illustration of methods and
apparatus 378
Test results with Sturgess gov-
ernor 491
Tests,
curve showing discharge and
speed of wheel from actual 398
factors that Influence the re-
sults of 371
of water wheels,
at Philadelphia in I860.. 360
by Messrs. Samuel Weber
and T. G. Ellis 862
in place 373
the value of 3C9
Thermal energy 2i>
Thermal units, British V.
Thompson's turbine 239
7*hree-halves powers of numbers. 74 J
Three Rivers, Michigan, variation
in power at 103
Thrust bearing at Snoqualmie
Falls 295
Index.
7S3
PAOK
Thunder Bay River 165
Thurso. J. W.. 279
Tidal mill 14
Timber dam,
at JanesvUle 582
at Seweivs Fails 594
of the Mbntana Power Ck)m-
pany, near Butte 693
Timber flshway,
of Fl3h CammlBsion State of
WlEH^onsln 619
tn dam at Sterling, Illinois.. 619
Tohirl.-oTi Creek 167
diagram sbQwing annual run-
off from 638
mass curve of run-off of 630
monthly discharge from
drainage area of 643
monthly rainfall in Inches on
drainage area of 643
rainfall, run-off and evapora-
tion 757
Topographical condition,
relation of run-off to 175
study of for report on water
power 677
Traetton purposes, transmission
of power for 26
Trade Dollar Mining Company,
power plant of 532
Transfo relation of energy 23-33
Transformers, losses in 29
Transmisstaa of energy 23
losses in 27
for traction purposes 26
literature on 673
Transverse curves of mean veloc-
ity in stream cross sections... 211
Tiash racks 530
Tremont-Fourneyron wheel,
characteristic curve of *409
diagram of 21
efficiency of 247
guides and buckets of 251
Trenton Falls, N. Y., plan of
power development at 575
Tub wheel 8
PAGS
Turbines,
American, Francis U
Cadiats, Fourneyron, Fran-
cis, Girard Current, Hen-
schel, Jonval, Schiele,
Scotch, Thompson's 289
advantages of 9
arrangement of«
horizontal 604
reaction 500
vertical shaft 501
axial flow 244
bearings of,
horizontal 292
vertical 239
calculation of,
a more exact graphical
method for 896
graphical method, effi-
ciency and speed at
various heads and gates 395
diagram of estimated
power at various heads 897
to estimate operating re-
sults under onie head
from test results at
another head 889
to estimate results of one
diameter from tests of
another 391
capacity of,
power and speed of a 40^^
wheel under 16' head 260
characteristic curve of 400
classification of 243, 506
complete 244
connection of, to load .'. 531
conditions of operation of
245, 384
constants of 310,351
design of, first principles 311
details and appurtenances.. 284
development of 4
in Europe 277
in United States 248
discharge,
measurement of 872
784
Index.
I
Turbines — Con. page
at fixed gate opening 333
Cundamental ideas of ^
gates of 290
htBtory of , S, 9
borissontal 244
horlzontaJ, multiple tandem. GIT
hydraulics oft practical 303
Impulse or acUon^.... ..... 244
Inatallalions of,
horizontal ,,,, S13
tandem ,,••*,*.,«,..,., 529
vertical , 507, 510
Inward radial flow.,.., 244
limit 244
literature on , 353
mbted flow 244
number of, effect on head and
power lOS
partial . . , 241
©ntward radial flow.,,. 244
power of mod era, Increase In 13
power of 333
practice, modern changes In 13
radial flow.... 244
reacttoa or pressure 244
re^la t i o n , com pa rati ve . , , . . 487
relations , 321
of discharge to diameter
In various wheels 333
of diameter and speed. . 320
of discharge to diameter 337
of efficiency and speed of
3S'' turbine, graphical. 395
of efficiency and speed of
a 4^"" Victor, curve of 322
of cp and di.'*rh!iri;e
(graphical) at full gate
for various wheels*.., 333
of head to discbarge of a
12" Smith -McCormick. 331
homogeneous series, di^
ameter and speed 326
homogeneous series, pow-
er and diameter.. 340,341
to estimate results for
variable head from
tests under fired head 393
of power to diameter ua-
Turbines — Con, Fi
der unit head (graphl*
cal) ,. ,,.344
of power and speed of
a 33^ wheel 391
of power and speed, 4S*
Victor ( graphical r, , . 31S
of power and head, I, P.
Morris Co 41t
of speed to diameter and
head ,,., 321
of speed to discharge.-. Zih
of speed to discharge for
a 12^ Smitb'McCormlck 3.V>
of speed and power.,.,, 347
runners of,
built up t . . . 294
cost ....*.... 214
details of.. .^,.... 2IS
how made. . . . , 2S4
Shawinlgan Falls....... 271
Scotch
selection of %$i
basie for..... Z$l
for speed and power to
work under a fl:ced
head 387
uniform head and power 2S7
Shawinigan Falls., 27(3*
Bp€ed, increase of. .......... 359
speed relations of ......... . 330
support of.. ..«*,.*...,.,»•• S3^
Swain .,.,,- ,, It
testing of., ,. 35&
tests,
by James Emerson...... 3^1
literature on , . 3S3
methods and apparatus
for , , . , 3 i J-i
plan of apparatus for, by
Francis 37*
value of..... 270,1^9
vertical ,,,,,,•,••,*.♦ t\
vertical and hoHzonta!,*. .,, 544
vertical shaft for low heads** aDI
Un win's estimate of losses In -&
units, two pairs In tandeiD
&ll,S31
Turner's Falls power plant *. ^V
M
I
I
I
i
Index,
78S
PAGE
' Tultoa'a fdrmula. , < * * * . G2
Tweeddale*s report to tbe Kansas
State Board of Agriculture... 136
Tyler. Benjamin . . * 6
T^ mpaoum, Egy pttaa 14
Umbrella covering,
testa of ...,,,,.. 729
to prevent vortices. ,»,.«^p . 72S
Unbalanced wheels 524
Dnderahot wheels. , 2
early application to mine
drainage i 1^
Ualform motion*...^...,^.*.... ST
Uniform speed, value of,., 444
Uniform varied motion 'dl
United States.
annual evaporation in the 138-130
average rainfall of, map 112-113
comparative bydrographs
from different bydrologlcal
divisions 183
development of water power
in , 14
flrit wheel in. ,,. 0
mean annual run-off of the
rivers of , \ 152-163
rainfall conditions in, July
leth and 17th 118
Units of, energy ,,.. 32
beat ,.,., , 32
potential energy. 34
University of Wisconsin,
experiments on 12"" S. Mor-
gan-Smith wbeeK ... . . 32a
enperiments on submerged
oriflees at ,,......*,.* 43
Unwln, Professor* . , 26
Upadachee River..,.. 166
Utlca Gas and Electric Co., Tren-
ton Falls plant of. ........... Sll
V.
Valves, relief.. 493
Velocities, position of mean and
maximum In a vertical plane
under ice,. ..., 217
4i
Velocity, PACK
changes of penstoclc. 4SS
effects of ice covering on dis-
tribution of.,,.. 21&
energy required to change
penstock 446, 456
measurements of flow by the
determination of 521
relative, of tbe bucket In re-
action wheels............. Zl%
residual, in reaction wheels 313
shock due to sudden changes
In , 443
variations In the crosfl aeo
tlon of a stream 210
Velocity curves,
for open and Ice covered
streams, comparative mean
vertical 2ie
ideal vertical 213
of Potomac River £3S
Velocity head..... .• 41
Vermnele, C. C 148
formula !or the relation be*
tween annual evai>oration,
precipitation and run*off . . 148
Vertical Geylin-JonvaJ turbine,
diagram of.,...*. .. 2S4
Vertical turbine,
arrangement of ............. 501
for low heads 500
for Sewairs Falls ,..,. 512
bearings of 289
Vertical thrust or hanging bear-
ing of Tbe Niagara Falls Power
Co. .*..,. 29a
Vertical tmrbtnes^ some Installa-
tions of. 507
Vertical turbines and their con-
nectlon , , * 507
Vertical turbtnea In series, some
installations of 5ia
Vertical Suspension ball hearing 291
Vertical suspension oil pressure
be&rlng . , , 292
Vertical velocity curves. in
streams . 211,213,214,213
Victor turbine.
character Istln curfeB of^ .402-4QS
786
Index,
I
Victor turbine — Con. page
efflcleDcy-speed cunre of a. 48'' 322
relation of efflctency to the
number of revolutiona, . ♦ , 405
runner of ..2fi7, 2GS
teats of,
data of a 48''...,,* 704
teit Of a 45^w.,.. . 712
of a 43" ,,.- 713
of a 36" ,•.,,. 72a
of a 33* 723
MtruvluB* descrtptlon of wator
wheels . . . » p ..«.>... ^ 14
Volt ,-.<,..<♦ 33
VoIt» coulomb, eQutvalente of. . . M
Vortioea, effect of an umbrella up-
on the formation of . ....... i.. 720
Wallklll River, rating cur?e for 217
Warren, H. E., on predetermina-
tion of speed regulation.. 462
WaaC€ of energy, none In nature 20
Water,
clrculatfoQ of , * « ^0
evaporatioii of.......... 20
Water hammer.. 635
due to Budden changes In ve-
locity 449
Water power , , , 33-70
chronological development of 15
cost of development. ..,,*.. 617
development In the U, 8 H
market prife of , . . . 663
sources of 79
Water power development,
examples of ,*.., 537
financial consideration of . . . 64ft
history of 1-14-16
inveBtlgatlon of . < 675
purposes of 646
relation of capacity to ooit. . 64S
claeaificatton of types. «....* 662
costs of various,
American 6S0
Canadian G40
Foreign 651
Water power property value of. 671
Water power purposes, dams for S^fl
Water supplied to whe^l. effect of
slow^ acceleration on ,-.*,,,.* . 4SS
Water wheels {see also Turbines) HI
Barker's Mill. ...... ........ 5
breaat ..,,*.....,...,•,.,.. t
Chinese Nora ^ 1
classification of ,... til
current * 1
early types of...... 1
float 1-a
borlssontal, some liistallatfoaB
of ,, ,., 511
installation of tandem a!9
Laxy overshot on Isle of Man H
overshot ..-.-,... 3. 213
Poncelet 4
Rou^ a Cu vee S
Rou6 Volant. , ,....«.» I
SmeatoQ's experiments on.,. 331
testing of ,,..,_,. 3S6
tests at Philadelphia In 1160 Z^
tub t
undershot ...<...^ t
use of,,. ....•«. 241
wry fly ---- -. •
Water wheel governors («««
Governors) .,* 4ii)-735
problem of ,......., *. 445
types of i .« . 470
Water year, the , , . ^ . . . 1S7
rainfall and run'off of the
Hudson River for each
period of. ... . 150
rainfall and run^olf of the
Sudbury River for each
period of* ....,.,,,. p Ul
raiufall and runoff of var!^
ous rivers.. 750-71
Waters, W. A., graphical anal)-aSi
as proposed by **,..,....,,.. . 115
Wntt, the equivalents of ,.,,,..« . ^
Weber, Samuel . . .,....».,«. II
and T* G. Ellis, turt>ine teati
by ,...*•.. 38-
Weher, W, 0.,
plan of brake wheel *. 311
plan of prony brake. . . » ». SI
Index.
787
PAGE
Teeklf rainfall In Wisconsin,
distrfbution of 117
height, exertion of energy by.. 41
heights of water, equivalent
measures and 740
^eirs,
coefficients 65 et seq.
formulas for 64
measurements of flow by.... 219
comparative discharge over 68-69
comparative discharge with
irregular crest 72-73
flow over 64
literature on flow of water
over 77
(Tellman-Seaver-Morgan C 0 m-
pany 299-300
characteristic curve of 51"
wheel 408
Western drainage, hydrograph of 193
Vheeler, L. L.,
design of flshway by 614
tainter gates designed by... 606
Hieel harness of Oliver power
plant 530
iTheel pit 535
Wheels (see Turbines),
Atkins' wheel and case 273
effects of number on head and
power 108
gravity 237
impulse 237-301-3^3
other American 266
reaction , 237
/liitlaw, James 6
^cket gate 300-301
diagram showing condition of
flow through open and par-
tially closed 301
Winnipeg Electric Railway Com-
pany, plant of 553
iTisconsin,
diagram of fluctuations of
monthly rainfall at Madi-
Wisconsin — CJon. page
son 122
distribution of average an-
nual rainfall in 116
distribution of total annual
rainfall in 116
distribution of weekly rain-
fall in 117
maps of annual rainfall in
114-115
rainfall on drainage area of
Wisconsin River 121>
Wisconsin River,
comparative flow of 8&
comparison of mean monthly
flow with Rock River.... 17*
drainage area of 84
hydrograph at Kilbourn,
based on observations at
Necedah 86
hydrograph in 1904 81
monthly rainfall and run-oft 165
rainfall on the drainage area
of 129
rating curve at Kilbourn... 20I>
rating curve at Necedah. ... 96
relations of coefficient to hy-
draulic radius 199
relations of gauge heights at
various stations on 206
Wood, R. D., and Company 254
Geylin-Jonval turbine 256
Wood stave pipe friction losses. . 63
Woodward governors,
compensating 474
details and applications of.. 477
standard 471
Work Z2
Wry fly wheel t
York Haven Water Power Com-
pany, plant of 537
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