I
LIBRARY
UNIVERSITY OF CALIFORNIA.
*
Class
I m
THE STEAMENGINE
AND
OTHER HEATMOTORS
BY
W. H. P. QREIGHTON, U. S. N. (RETIRED)
Professor of Mechanical Engineering, Tulane University of Louisiana
SECOND EDITION, REVISED AND ENLARGED.
FIRST THOUSAND
NEW YORK
JOHN WILEY & SONS
LONDON : CHAPMAN & HALL, LIMITED
1909
Copyr'ght 1907. 1909,
BY
W. H. P. CREIGHTON
Rnbrrl Brutnmonb an2> (Company
Nrjo fork
PREFACE TO THE SECOND EDITION.
IN the second edition I have endeavored to utilize such
constructive criticisms of the first edition as came to my atten
tion. Five plates are used to illustrate engine details and each
part is named on the plate itself. The first chapter now includes
a number of calculations of a general character which were intro
duced to give the student a better view of the entire subject.
The boiler, the engine, and the condenser are brought together
so that the functions of each form parts of one picture in the
student's mind. The inertia of the indicator piston and two
of the difficult cases in the Zeuner valve diagram construction
are discussed. The addition of tables and diagrams facilitates
finding loss of head in steam or air pipes. As the use of logarith
mic crosssection paper has not yet become common, a descrip
tion of its use in connection with PV n curves is given. The dis
cussion on Hirn's analysis is now followed by very complete
tables giving the mean effective pressure and the steam per horse
powerhour for condensing and for noncondensing engines of the
fourvalve type. Tables of corrections for initial condensation
under various pressures are also given. A comparison of the
ideal and practical consumption of steam under a variety of
circumstances may thus be made quite easily.
The engineer has to deal with the transfer of heat through
metal surfaces. Prof. Perry's theory of heat transfer and formulas
for finding the mean temperature of the heating and cooling fluids,
as well as for finding the rate of heat transfer per square foot
per minute per degree difference in temperature, as given by
Hausbrand, have been added. A much more complete discussion
of the design of feedwater heaters and airpumps both wet and
dry for surface, jet or barometric condensers is presented. The
iii
iv PREFACE TO THE SECOND EDITION.
theoretical discussion of flywheels is followed by a discussion
of belt and balance wheels for A.C. and B.C. generators with
tables and empirical formulas, so that practical sizes for ordinary
cases may be easily found.
A final chapter has been added on steamengine details. The
student is supposed to have had " Strength of Materials," From
the empiricalrational formulas in this chapter, he may obtain
practical answers which he can profitably compare with those
derived from theory. The forms of the various details may be
obtained from catalogues. This last chapter is due to the labor
of students in Cornell and in the University of Wisconsin, super
vised by Professors Barr and Gould.
While some students cannot afford the time to take up treatises
on the gasengine and on refrigeration in college, every student
can afford to spend a week on those subjects. Two short chap
ters in this book include all the theory on those subjects which
is given in quite large treatises. The student therefore discovers
that books on those subjects should have no difficulties that he
cannot master by himself if the occasion arise. It is, of course,
realized that the short time so given can, in no sense, take the
place of a regular course in these subjects if the student can find
the time.
The thanks of the author are due to those whose matter is
quoted in the text and especially to Professor Peabody for his kind
permission to insert Table IX, which is compiled from his latest
tables.
W. H. P. C.
PREFACE TO THE FIRST EDITION.
THE instructor is seldom compelled to drive students who
comprehend their textbooks. The student's comprehension may
be gauged by his ability to apply principles to the solution of
problems containing legitimate difficulties. He cannot hope to
overcome the difficulties that are inherent in the application of a
number of principles if his knowledge of these principles is foggy
and inaccurate. Therefore it is only fair to the student that
the text should be clear and its style attractive; numerous
illustrations should be given; especial stress should be laid on
fundamentals; the errors that he is liable to make should be
pointed out; prolixity in details and undue terseness should be
avoided, and it is of extreme importance that a proper sequence
of subject development should be maintained not only in the
main subdivisions but also in every paragraph and sentence. All
subjects in a technical course should be valuable not only
for the instruction they give but also for the opportunity they
present to train the student to think. The major value of text
books should be instructional. This value the student develops
in his home study. The instructor brings out the training value
of the subjects by problems of proper complexity.
This book possesses the following characteristics:
The history of the steamengine has been omitted. After a
student has advanced far enough to appreciate its import, the
story of the development of heat motors may be given by the
instructor. The first chapter is devoted to a bird'seye view of
the entire subject with illustrations of the main elements of a
steamengine plant and to the general relations of the different
vi PREFACE.
forms of energy. Similarly, each subsidiary subject is opened
by a general picture of that subject, so that the general relations
of the parts may be seen.
While an earnest effort has been made to make the work
simple, no principles have been omitted that should be contained
in a work intended for undergraduate students of college grade.
The Committee on Standard Rules of the American Society of
Mechanical Engineers have formulated rules that should be studied
by every student. These rules have been incorporated in the
text in positions dependent upon the development of the sub
ject. In this way duplication of the same matter has been
avoided.
In the development of a new subject, students put the great
est stress of their attention upon the phases first presented, and
then lightly assume that they can make the necessary modifi
cations for the more complex cases. On this account, and because
it is easier to pull down than to build up, the author has always
developed the most complex case first and then shown the deriva
tive or more simple forms. This inversion of the usual method
gives a better picture of the subject in its entirety.
In developing a complex subject many formulas are derived.
In no way can these formulas be deemed of equal importance.
In so far as the student is concerned, the formulas that give answers
most directly are usually of the least importance. Memorizing
the derivation of formulas or substituting in them is of little value.
And yet there are about two dozen formulas that should be so
well known that they are, in effect, memorized. These are mother,
backbone, or fundamental formulas. All problems, either literal
or numerical, should start with one or more of these formulas.
Their incessant repetition brings a comprehension that can be
attained in no other way.
The text calls for many complete designs. These, of course,
may be more or less crude, but they are of great value in develop
ing much unexpected ignorance of principles and giving definite
ness to the student's conception of a machine or of its action.
For example, few books complete the design of both ends of a
slidevalve and draw both indicatorcards when a finite connect
ingrod is used. If the instructor insists on the student making
PREFACE. yij
a complete design, a number of mistakes will be made almost
inevitably.
Attention is called to the method of drawing indicatorcards
for compound engines directly from round numbers. The ease
with which the different points on the diagram are found enables
the effect of changes (as, for instance, in the L.P. cutoff or in the
receiver volume) to be seen at once in the varying areas of the
cards. Of course the object aimed at is the comprehension of
principles.
The fundamental principles of thermodynamics are applied
not only to the steamengine but also to gasengines and gas
producers, refrigerating machines, steam turbines, and boiling
in a vacuum. In the discussion of these machines vague gen
eralities have been avoided, even if the discussion is limited to
the application of general laws. The endeavor has been to make
the foundation broad and strong enough to carry any super
structure that the instructor wishes to erect on it. The discus
sion on steam turbines starts with elementary mechanical prin
ciples of jet action, and by a stepbystep advance (omitting no
proof, giving no outside references, and using diagrammatic
sketches freely) a definite picture of the machine is built up.
The author appreciates the courtesy of Professors Carpenter,
Peabody, Reeve, Stodola, Thomas, and Thurston's heirs and
that of the American Society of Mechanical Engineers and the
American Society of Naval Engineers in giving free permission
to use either text or plates of their publications. The author
also thanks those manufacturers who loaned cuts of their pro
ductions.
Letters containing honest criticism, suggestions, problems, or
encouragement will be appreciated by the author and publishers.
W. H, P. C.
CONTENTS.
CHAPTER I.
PAGE
REVIEW OF ELEMENTARY PRINCIPLES AND GENERAL VIEW OF STEAM
ENGINE PLANT 1
Elementary Principles, 1. Work and Torque, 2. Energy, 2.
Various Forms of Energy, 3, 4. Temperature, 5. Thermal Unit,
Mean and Standard, 5. Thermometers, 6. Absolute Temperature,
7. First Law of Thermodynamics, 8. Mechanical Equivalent of Heat,
9. Second Law of Thermodynamics, 9. Apparatus in a Steam
engine Plant, 10. Steamboiler, 10. Draft, 13. Separator, 13.
Origin of all Power, 15. Action of Steam in a Steamengine, 15.
Bearing Details, 17. Corliss Cylinder Details, 16. Governor Details,
19. Crosssection of Cylinder, 20. Plan and Side Elevation of Cylinder,
21, 22. Surface Condensers, 23. Air Pump, 23. Circulating Pump,
25. Jet Condenser, 26. Bourdon Gage, 27. Mercury Column, ?8.
Rates versus Quantities, 30. Horsepower Definitions, 31. Rates
Equivalent to a Horsepower, 32. Brakes, 35. Efficiencies, 35. Heat
Value of One Pound of Coal from Chemical Analysis, 36. Boiler Horse
power, 36. Usual Rates of Evaporation in Boilers, 36. Calculation of
Grate Areas, 37. Usual Steam Consumption of Engines and Pumps,
37. Power for Electric Lighting, 39. Boiler Horsepower and Pump
Displacement for Electric Plants, 39. Combining Efficiencies, 40.
Heat Consumption of a Steamengine Plant, 41. What becomes of
Heatunits, 44. Names of Engines, 44.
CHAPTER II.
STEAMENGINE INDICATOR AND ITS CALIBRATION 46
Steamengine Indicators, 46. Reducinglevers, 58. Reducing
wheels, 59. Method of Taking Indicatordiagrams, 61. Care of Indi
cator, 63. Actual Point of Cutoff, 65. Inertia of Indicator Piston, 65.
CHAPTER III.
CURVES AND THE WORK OF EXPANSION 68
Method of Drawing Hyperbolas, 68. Commercial Cutoff, 70.
Clearance, 72. Ratio of Expansion, 72. Finding the Indicated Horse
power, 73. Testing Indicatorsprings, 74. Isothermal Expansion
Curve, 77. Diagram Factor, 81. Elimination of Clearance Steam, 84.
ix
X CONTENTS.
CHAPTER IV.
PAGE
2EUNER AND BlLGRAM VALVEDIAGRAMS AND DESIGN OF PLAIN SLIDE
VALVES 85
Throw of Cranks and Eccentrics, 85. Piston Travel with a Finite and
an Infinite Connectingrod, 86. Slidevalve Definitions, 88. Width of
Port and Port Opening, 90. Angle of Advance, 92. Valvediagram,
93. Geometrical Relations of Elements of the Zeuner Diagram, 97.
Valvediagram Problems, 99. Bilgram Diagram, 103. Dimensions of
Steam Ports and Pipes, 110. Practical Considerations in Design, 111.
Formulas, Tables, Diagrams for Loss of Head in Steam and Air Pipes,
115. Pipes of Equivalent Carrying Capacity, 119. Defective Indi
cator Diagrams, 122125.
CHAPTER V.
MEASURING THE EFFECTS OF HEAT 126
Effects of Heat, 126. Molecular Motion, 127. Evaporation, 127.
Elemental Effects of Heat, 130. Specific Heat, 131. Specific Heat of
Solids and Liquids, 132. Specific Heat of Gases, 132. Specific Heat of
Gases at Constant Volume, 134. Specific Heat of Gases at Constant
Pressure, 134. Fundamental Equation of Perfect Gases, 135. Boyle's
Law, 137. Charles' Law, 137. General Expansion Curve, 139. Adia
batic Curve, 141. To Draw the Curve PV n = C, 143. Logarithmic
Crosssection Paper and Method of Layingoff PV n Curves, 144. Rela
tion between T, V, and P in Adiabatic Expansion, 148. Heat Energy
Represented by Areas, 148. Area Equal to Heat in a Perfect Gas, 149.
Area Equal to Heat Added when the Gas is Heated at Constant
Volume, 149. Area Equal to Heat Added when the Gas is Heated in
any Manner, 150. Area Equal to Heat Added when the Gas is Heated
Isothermally, 124. General Fundamental Equations of Heat Added
152. Carnot Cycle, 154.
CHAPTER VI.
MEASURING THE EFFECTS OF HEAT ON WATER AND STEAM 160
Melting Solids, 160. Boilingpoint of Water, 160. Heat of the
Liquid, 162. Expansion of Water when Heated, 163. Vaporizing
Water, 163. Heat in and Heat Required to Produce Steam, 165.
Changes in Regnault's Tables, 167. Quality of Steam, 169. Super
heated Steam, 170. Equivalent Evaporation, 170. Calorimeters, 172.
Determination of Water Equivalent, 176. Normal Reading, 178.
CONTENTS. XI
CHAPTER VII.
PAGE
MEASUREMENT OF HEAT LOSSES 180
Causes of Wetness of Steam, 180. Foaming, 181. Nonconducting
Coverings, 181. Initial Condensation, 186. Laws of Compression of
Steam, 188. Weight of Steam Accounted for by the Indicator, 191.
Drysteam Fraction, 193. Hirn's Analysis, 194. Heat Interchanges,
198. Example of Hirn's Analysis, 198. Tables to Find Actual Steam
Consumption of Fourvalve and Corliss Engines both Condensing and
Noncondensing, 201. Actual Results in Practice, with Leaky Valves,
204.
CHAPTER VIII.
ENTROPY 207
Entropy, 207. Construction of Waterline, 210. Construction of
Steamline at Constant Pressure, 212. Construction of Saturation
Curve, 213. Construction of Adiabatic Expansion Line, 214. Work
done during Adiabatic Expansion, 215. Velocity of Steam passing
through a Nozzle, 216. Construction of Constant Volume Line, 219.
Work done when the Curve of Expansion is the Curve of Constant
Steam Weight, 222. Construction of Constant Heat Curve, 224.
Deriving a Temperatureentropy Diagram from an Indicatordiagram,
225. Carnot Cycle, 228. Rankine Cycle, 228. Ratio of Economy of
an Engine to an Ideal Engine, 229. Temperatureentropy Diagram
of a Real Engine, 230.
CHAPTER IX.
CONDENSERS AND AIRPUMPS 232
Jet Condensation, 232. Jet Condensers, 233. Air Leaks, 234.
Design of Jet Condensers, 234. Barometric Condensers, 236. Syphon
or Ejector Condensers, 238. Surface Condensers, 239. Amount of
Cooling Water, 241. Heat Transfer through Metals, 242. Professor
Perry'o Theory of Transfer of Heat, 243. Finding the Mean Difference
of Temperature between Heating and Cooling Fluids, 245. Principles
of Open and Closed Feed Heaters, 248. Relative Value of Heaters and
Purifiers, 254. Heating Surface in Feed Heaters, 255. Discussion of
the Rate of Heat Transmission in Condensers, 257. Contraflo Con
densers, 260. Thermal Efficiency, 263. Economy in Vacuum Pro
duction, 264. Surface Section Ratio, 265. Coolingtowers, 265. Cor
rect Absolute Condenser Pressure, 267. Wet Vacuumpump Design,
268. Efficiency of Airpumps under Variable Loads, 269. Edwards'
Airpump, 2 2. Dryair Pump, Design 273. Practical Airpump
Airpump Ratios, 274. Airpump Cards, 275. Definitions of Air
pumps, 273. Design of Airpump for Surface Condenser, 278. Wet
Vacuumpump for Jet Condenser, 281. Dry Airpumps for Counter
current Barometric Condenser, 282. Cooling Air in Condensers, 282.
xii CONTENTS.
CHAPTER X.
PAGE
SMALL AUXILIARIES ..... ........ ................................... 285
Feedpump Cards, 286. Feedpump Design, 287. Reciprocating
Circulatingpump Design, 288. Airchambers on Circulating Pumps,
289. Centrifugal Circulatingpump Design, 290. Injectors, 292.
Weight of Feedwater per Pound of Steam, 293. Efficiency of Injectors,
294. Operating Injectors, 294. Reheaters, 297. Oil and Water
Separators, 298.
CHAPTER XI.
MULTIPLEEXPANSION ENGINES ....................................... 300
History of Multipleexpansion Engines, 300. Record Tests made in
the Last Five Years, 303. Laying Out Theoretical Cards of Compound
Engines, 304. Tandem Compound without a Receiver, 306. Tandem
Compound with a Receiver, 308. Cross Compound, L.P. Cutoff
before Halfstroke, 310. Cross Compound, L.P. Cutoff after Half
stroke, 313. To Find the Size of the Cylinders of a Compound Engine,
315. To Combine the Indicatorcards from a Compound Engine, 317.
True Ratio of Expansion in Compound Engines, 320. Diagram Factor
in Compound Engines, 322.
CHAPTER XII.
REVOLUTION CONTROL ....................... ....................... 326
Fundamental Equations, 328. Centrifugal Force, 329. Kinetic
Energy, 330. Flyball Governor, 327. Sensitiveness, 333. Practical
Forms of Flyball Governors, 334. Power of a Governor, 338. Fric
tion of a Governor, 338. Adjustable Eccentrics, 339. Valvediagrams,
Swinging Eccentrics, 341. Shaftgovernors, 343. Angular Accelera
tion, 347. Springs, 347. Inertia Governors, 348. Linkmotion, 352.
Open and Crossed Rods, 356. Position of the Saddlepin, 358. Link
arc, 359. Equivalent Eccentric, 359. Buckeyeengine Valve, 360.
Meyer Valve, 365. Corlissengine Valves, 366. Setting Corlissengine
Valves, 366. Poppetvalves, 370.
CHAPTER XIII.
SPEED VARIATION CONTROL 373
Turning Effort in the Crankshaft, 373. Net Steampressure, 37^.
Variable Velocity of the Piston, 375. Pressure Required to Accelerate
the Reciprocating Parts, 376. Reciprocating Parts Considered as
Concentrated at the Center of the Crankpin, 377. Accelerations,
Finite Connectingrod, 379. Pounding of the Engine, 380. Tangential
Pressure Curves, 382. Approximate Formula for a Flywheel, 384.
CONTENTS. xiii
PAGE
Design of Belt Wheels, 386. Empirical Formulas for Weight of
Balance Wheels for Engines Directconnected to A.C. or D.C. Genera
tors, 387. Analysis of Rites Inertia Governor Stresses, 390. Counter
balancing, 400. Shaking Forces, 403. Calculation of Phase Departure
of Directlyconnected Engines, 405.
CHAPTER XIV.
STEAMENGINE TESTS 411
Rules for Conducting Steamengine Tests, Standard Rules, A.S.M.E.
Object of the Test, 411. General Condition of the Plant, 412. Dimen
sions, 414. Coal, 415. Calibration of Instruments, 415. Leakage of
Steam, Water, etc., 419. Duration of Test, 421. Starting and Stop
ping a Test: (a) Standard Heat Test and Feedwater Test of Engine;
(b) Complete Boiler and Engine Test, 422. Measurement of Heatunits
Consumed by the Engine, 424. Measurement of Feedwater or Steam
Consumption of an Engine, 425. Measurement of Steam used by
Auxiliaries, 427. Coal Measurement, 428. Speed, 429.
CHAPTER XV.
SUPERHEATED STEAM AND STEAMTURBINES 431
Superheated Steam, 431. Foster Superheater, 432. Purpose of
Superheating Steam, 434. Thermal Laws, 435. Heat Required to
Produce Superheated Steam, 435. Intensity of Superheating Required
to Prevent Initial Condensation, 435. Data of a Test of an Engine
using Superheated Steam, 438. Entropy Diagram of Superheated
Steam, 441. Superheated Steam in Compound Engines, 442. Dura
bility of Superheaters, 443. Steamnozzles, 443. Zeuner's Formula,
445. Velocity and Weight of Steam Discharged from a Nozzle, 446.
Elementary Mechanical Principles Applicable to Jets, 447. Impulse
Due to a Jet Moving on a Curved Blade, 449. Maximum Efficiency
Under Various Conditions, 456. De Laval Steamturbine, 456.
Theoretical Design of De Laval Turbine, 458. Curtis Turbine, 459.
Theoretical Design of Curtis Turbine, 460. Friction Losses in the
Curtis Type, 461. Parsons' Steamturbine, 465. Analysis of Parsons'
Steamturbine, 473. HamiltonHolzwarth Steamturbine, 477. Com
bination of Engines and Turbines, 478. Turbine Auxiliaries, 478.
CHAPTER XVI.
GASENGINES AND GASPRODUCERS 480
Lenoir Cycle, 480. Beau de Rochas Cycle, 480. Practical Details
and Data, 482. Calorific Power of Compound Gases, 484. Rise in
Temperature in Gas Combustion, 485. Producergas, 486. Gas from
Soft Coal, 489. Calculation of Theoretical Pressure in Gasengines, 490
Indicator and Entropycards of Gasengines, 490. Diesel Cycle, 496
xiv CONTENTS.
PAGE
Data from a Diesel Engine Test, 499. Rules for Conducting Gas and
Oilengine Tests, Code of 1901, 501: Objects of Tests, 501; General
Condition of the Engine, 501; Dimensions, 501; Fuel, 502; Calibration
of Instruments used in the Tests, 502; Duration of the Test, 504;
Starting and Stopping a Test, 504; Measurement of the Fuel, 504;
Measurement of the Heatunits Consumed by the Engine, 505 ; Measure
ment of Jacketwater to Cylinder or Cylinders, 506; Indicated Horse
power, 506; Brake Horsepower, 506; Speed, 506; Recording the
Data, 507 ; Uniformity of Conditions, 507 ; Indicatordiagrams and
their Analysis, 507 ; Standards of Economy and Efficiency, 507 ; Heat
Balance, 508; Report of Tests, 509; Temperatures Computed at
Various Points of the Indicatordiagram, 509. Complete Form for
Gas and Oilengine Tests, 512515.
CHAPTER XVII.
BOILING IN A VACUUM 516
General Description of Evaporation in Vacuo in Mulitple and Single
Effects, 516. Theory of the Multiple Effect, 519. Theory of Single
Effect or Vacuumpan, 520. Double Effect, 521. Triple Effect, 522
Measurement of Density of Liquids, 524. Description of a Vacuum
pan, 527.
CHAPTER XVIII.
REFRIGERATION 530
Theory of Refrigerating by Dense Air, 530. Ammoniacompression
System, 532. Entropydiagram of a Compression System, 534. Re
fiigeration Units, 536. Complete Form for a Steamengine Test, 537
543.
CHAPTER XIX.
CONSTANTS FOR LOWSPEED STEAMENGINE DESIGN 544
Pistonrod, 544. Connectingrod, 544. Main Journal, 545. Crank
pin, 546. Crosshead Pin, 548. Crosshead Shoes, 549. Steam Ports
and Pipes, 549. Exhaust Ports and Pipes, 550. Belting, 550. Weight
of Engine, 551. Steam Cylinder Details, 551. Flywheels, 553.
CONSTANTS FOR HIGHSPEED STEAMENGINE DESIGN 556
Pistonrod, 556. Connectingrod, 556. Main Journal, 557. Crank
pin, 558. Crosshead Pin, 560. Crosshead Shoes, 561. Cylinder
Details, 561. Steam Ports and Pipes, 563. Exhaust Ports and Pipes,
563. Belting, 563. Flywheels, 564. Reciprocating Parts, 564.
Weight of Engine, 565.
CONTENTS. XV
APPENDIX.
PAGR
Table I. Properties of Familiar Substances 571
' ' II. Hyperbolic or Naperian Logarithms 572
" III. Heating Values of Various Substances 572
" IV. Oxygen and Air Required Theoretically for the Com
bustion of Various Substances 573
' ' V. Relative Humidity, Per Cent 573
" VI. Weights of Air, Vapor of Water, and Saturated Mixtures
of Air and Vapor at Various Temperatures and Con
stant Pressure 574
" VII. Entropy of Water and Steam 575
" VIII. Saturated Steam 576581
' ' IX. Saturated Steam Entropy (for Condenser Pressures) 582
X. Mean Pressures for Various Methods of Expansion 584
" XI. Mean Pressures for Various Methods of Expansion 585
' ' XII. Mean Pressure Ratios 586
" XIII. Terminal Pressure Ratios 587
" XIV. Flow of Steam through Pipes 588
" XV. Specific Heat (C p ) of Superheated Steam at Constant
Pressure 58$
ENTROPY DIAGRAM 590
INDEX . , .591
OF THE
UNIVERSITY
OF
MLIFOR*^
THE STEAMENGINE AND OTHER
HEATMOTORS.
CHAPTER I.
REVIEW OF ELEMENTARY PRINCIPLES AND GENERAL
VIEW OF STEAMENGINE PLANT.
THE student will avoid much unnecessary confusion by keeping
always clearly in mind :
1. The difference between an essentially elementary and a com
pound quantity.
2. Elementary quantities can only equal elementary quantities.
Twisting moments can only equal twisting moments.
Compound quantities, derived from work or changeable into
work, can only equal compound quantities that can be de
rived from work or can be converted into work.
3. The two sides of an equation must be similar in kind homo
geneous.
4. A pull, push, torque, or work cannot exist unless there is at
the same time an opposing pull, push, torque, or work of
exactly equal magnitude.
5. While in nature neither matter nor energy is ever created or
destroyed, there is an unceasing tendency to perfect change.
6^ He should know the fundamental formulas of a subject as he
knows the multiplicationtable, and he should formulize his
work as much as possible and substitute in formulas as little
as possible.
7. Clearness is often obscured in the terseness of a derived formula.
2 THE STEAMENGINE AND OTHER HEATMOTORS.
Force, whether it be a push, pull, or an attraction such as
gravitation, is an elementary quantity. Linear distance is also
elementary. Unlike force it may be compounded with itself, as
in areas and volumes.
Force and distance may be combined to form two distinct
compounds which should never be confounded with nor equated
to one another. Force overcoming an equal resistance through a
distance does work. The force is exerted THROUGH a distance.
One pound lifted a foot is a footpound, because there is a resist
ance of one pound through a foot. One pound dragged a foot hori
zontally on a rough surface does not require a footpound of energy,
because the resistance ordinarily is not one pound. If the coeffi
cient of friction is 4%, then the work would be .04 foot
pound.
Force acting AT a distance produces a turning moment, twist,
or torque. Here there is no motion. If motion is impending, it
is not in the direction of the distance factor of the twisting mo
ment. A twisting moment and work may exist at the same time,
as in a moving crank. Imagine all the forces acting on a crank
pin reduced to a single force (that may vary in amount), always
perpendicular to the crankarm. The torque at any instant is the
force, at that instant, multiplied by the length of the crankarm
=the distance from the center of the crankpin to the center of
the shaft. The work per revolution would be the mean force mul
tiplied by the distance that the center of the crankpin moves in a
revolution.
PL = work or twisting moment (according to the conditions)
in footpounds, foottons, or inchpounds, according as
P= pounds or tons;
f length of arm in twisting moments;
L=feet or inches! ,. : ,,  ,, , . ,
[ distance the force moves through in work.
EXAMPLE 1. A winch 8 inches in diameter has two crankhandles,
18 inches radius, 180 apart. Two men use it to raise buckets of
stone, whose total weight is 200 pounds, from a hole 40 feet deep.
Neglect friction. What torque does each exert? What work does
each man do per revolution? What is the best direction for each
man to exert his strength?
ELEMENTARY PRINCIPLES. 3
Work may be stored up; it is then called energy. Energy
occurs in many forms that may be grouped into the three divi
sions potential, kinetic, and vibratory.
Students are liable to confuse potential energy and torque.
When work is stored up in the form of potential energy, all motion
has disappeared; for example, the tightened spring in a watch or
the water in an elevated tank. In these cases there is no motion,
but we notice that it takes force acting through a distance to wind
the spring or raise the water. Under theoretical conditions the
spring in unwinding and the water in descending from the ele
vated tank have the power to perform as much work as was
expended originally in tightening the spring or raising the water.
It is its potency or power to do work, if required, that gives the
name potential to this form of energy.
Kinetic energy is energy of motion. As the number of revolu
tions of the flywheel increases above the normal it is absorbing
footpounds of work that it will give out later in slowing down.
The riflebullet with small mass must have high velocity to do
the work of penetration. Any mass moving in any direction at
any velocity possesses kinetic energy.
Energy of vibration seems to be made up of kinetic and po
tential energy, and yet it is quite different from either. The most
obvious example, of course, is the pendulum. At the bottom of
its swing all its energy is kinetic, at the top it is all potential.
Between the top and the bottom there is a continual interchange:
descending the pendulum is converting potential into kinetic
energy, and ascending this process is reversed.
The main characteristics of this form of energy are the small
amount of energy involved and the length of time that it
persists.
Waves are vertical vibrations of the surfacewater; sound is a
vibration of the air, and light is a vibration of the luminiferous
ether. Great distances are traversed by waves and sound, but
they are insignificant when compared to the millions of millions
of miles travelled by the feeble vibration called light. As the
amount of energy is so insignificant the ether that transmits the
vibrations must be wonderfully adapted for the purpose.
Below is given a classification of different forms of en
THE STEAMENGINE AND OTHER HEATMOTORS.
ergy in which the forms already given appear as subdi
visions.
JForm of Energy.
Factor of Intensity.
Factor of Extent!
Name.
Unit of Measure
ment.
Name.
Unit.
Mechanical, pot.
Mechanical, kin.
Electrical, pot. . .
Electrical, kin. . .
Chemical, pot. . .
Chemical, kin. . .
Thermal, kin. . . .
Thermal, pot. . . .
Distance
Velocity
Potential
Potential
Affinity
Temperature
Temperature
Feet
Feetpersec.
Volts
Volts
Force
Mass
Charge
Current
Mass
Pounds
Pounds T G
Coulombs
Amperes
Molecular weight
Degrees (Fahr.)
absolute
Degrees (Fahr.)
absolute
Entropy
Entropy
From Reeve, Thermodynamics of Heatengines.
Most of the forms of energy tabulated are seen to be made up
of two elemental factors and hence must be compound and of
the second degree.
It may be assumed that there is evidence in plenty that each
of the above forms of energy can be transformed into one or more
of the other forms above given. They must all be compound,
since a number of them are evidently so. The student is probably
more or less familiar with all the forms save the last one. We
shall assume that we have shown that thermal energy or heat is
compound and is made up of two factors.
If these forms of energy can be converted into one another
they must all be either simple or compound. If compound, they
must be compound in the same degree (just as an area cannot
equal a cube), and ultimately it would seem that they ought to
be reducible to the product of the same factors. Further, it is
not necessary, in any conversion of one form into another, that
one of the above forms of energy should be transformed into one
other form alone. Indeed this rarely takes place. But if any
quantity in an equation of conversion is of the second degree,
every quantity connected to the others by the + or sign must
also be of the second degree.
The following table gives tersely examples of the change of
each form of energy into each of the others :
ELEMENTARY PRINCIPLES.
f Electrical
Mechanical into j Chemical.
I Thermal.
f Mechanical
Electrical into \ Chemical.
I Thermal.
Chemical into
f Mechanical
I Electrical.
I Thermal.
Dynamo.
Cartridges (Trigger striking)
Friction.
Electric motor.
Electrolysis.
Electric lights.
Work done in collecting a gas arising
from dissolving a solid in acid.
Wet batteiy.
Combustion.
Expansion of furnace walls.
Electropile.
Growth of vegetation.
f Mechanical.
Thermal into j Electrical.
[ Chemical.
Ex. 2. Give other examples of all the different forms of energy
and of the change from one form into one or more other forms.
Ex. 3. Give all the different forms of energy that appear when a
heavy gun is fired at night.
Temperature. Temperature is a quality of heat and may be
said to measure its INTENSITY. It is obviously one of the factors
of heat, for by doubling the intensity of heat, as measured from a.
true zero, we double the heat in a body. It is one of the factors
of heat, as a foot is a factor of a footpound. It is not heat any
more than a foot can in any way be a footpound. Temperature
is elemental in character. Its unit of measurement is called a
degree. Each degree on any assumed scale, such as the Fahren
heit, Centigrade, or Reaumur, is supposed to measure equal vari
ations of intensity of heat. But the variation measured by the
Fahrenheit degree is only 5/9 of that measured by the Centigrade
degree and 4/9 of that of the Reaumur. This arises from the
fact that the same variation of intensity of heat the variation
that exists between the temperature of freezing and boiling water
at atmospheric pressure is divided into 180 parts on the Fahren
heit scale, into 100 parts on the Centigrade scale, and into only
80 parts on the Reaumur scale.
Thermal Unit. Two such units are available, the standard
British thermal unit, B.T.U., which is the quantity of heat required
to raise one pound of water from 60 F. to 61 F., and the mean
B.T.U., which is the 180th part of the heat required to raise water
from the freezing to the boiling point. The latter is the more
easily and certainly determined and corresponds to the mean
calorie now becoming standard abroad.
6 THE STEAMENGINE AND OTHER HEATMOTORS.
Calorie. The French unit of heat is a calorie. It is the meas
ure of the quantity of heat that is required to raise one kilogram
(2.2 pounds) of water from 4 to 5 Centigrade or yfo of that
required to raise one kilo of water from to 100 C.
As heat is a compound quantity, its units of measure, a B.T.U.
and a cal. are compound. One calorie =3.968 B.T.U.
Cold. Since heat is a form of energy it has a positive exist
ence. This cannot be said of cold. There is no such thing as a
quantity of cold. All bodies, then, are hot, i.e., possess heat.
Some are hotter than others. When the latter are said to be
colder than the former, the term colder is to be interpreted as less
hot.
Minus Temperature and Minus Pressure. Similarly we shall
find that there are no such quantities as minus degrees of tem
perature or minus pounds pressure. In fact we must take par
ticular pains to have all measurements in absolute units, viz.,
measured from a real zero.
The Fahrenheit and Centigrade zeros are purely arbitrary.
At a true zero of temperature a body will possess no heat, or, in
other words, the molecules of the body will be at rest, all vibra
tion having ceased. Now the boilingpoints of solid hydrogen,
nitrogen, and oxygen are far below either of the abovementioned
arbitrary zeros, and hence the true zero must be still lower.
While air is not a perfect gas, yet welldried air will serve to make
a good thermometer for the investigation of low temperatures.
Airthermometer. The principle of an airthermometer is
shown in Fig. 1. The bore is supposed to be absolutely uniform
and the drop of mercury is supposed to be a frictionless, weight
less piston, perfectly airtight. Let the piston be any convenient
distance from the bottom when the whole tube is immersed in a
tub of water and melting ice, the temperature of the mixture being
constant at 32 F. The air below the mercury must be entirely
free of moisture. Measure accurately the distance the piston is
from the bottom of the tube. The atmospheric pressure (sup
posed to be 14.7 pounds per square inch) is constant and is the
sole pressure on the drop of mercury. The tube is now trans
ferred to a vessel of clean distilled water boiling freely in the
open air. The height to which our frictionless piston now rises
ELEMENTARY PRINCIPLES
is now marked. The increase in volume when the work is properly
done is 0.3654 times the original volume. This corresponds on the
Fahrenheit scale to a rise of 180, so that the rise per degree is
3654 1
"~"JOQ~ =0.00203 =A7yTa of the original volume.
1.3G45"V
GT3 C
212
0'
FIG. 1. FIG. 2.
Airthermometer.
Absolute Temperature. It is now evident that if we had cooled
the air below the freezingpoint, for each (Fahrenheit) degree of
cooling the (original) volume, 7, would have decreased 1/492.6F,
and, on the supposition that there would be no change of charac
teristics, the zero of volume, the zero of temperature, and the
zero of heat possession would be 492. 6 below the Fahrenheit
freezingpoint or 460.6 below the Fahrenheit zero.
In Fig. 2 the above calculation is shown graphically.
Let ab = initial volume;
ce= final volume;
oa= initial temperature absolute = TI ;
oc= final temperature absolute = T 2 .
8 THE STEAMENGINE AND OTHER HEATMOTORS.
Then
ceab:ab::T 2 T 1 :T 1 , or 0.3654:1 : :180:7V /. T l =492.6 F.A.
Hence the ordinary Fahrenheit temperature is converted into
Fahrenheit absolute degrees by the addition of 460.6 degrees. In
a similar way, the ordinary Centigrade degrees are converted into
Centigrade absolute degrees by the addition of 273 degrees.
As all known gases have been liquefied, it is evident that none
of them can be reduced to zero volume, as the law ceases to hold
with a change of state! In the case of the socalled permanent
gases the law has been shown to be true far below any tempera
ture required for engineering purposes.*
The measurement of temperatures by thermometers seems a
very elementary process. The difficulties are only appreciated
when great accuracy is required. In theory, the mercury of the
ordinary glass thermometer is supposed to expand equal amounts
for equal increments of heat, the bore of the capillary tube is
supposed uniform and to vary uniformly or not at all with the
addition of heat, and the glass is supposed to be in such a molec
ular condition that the bore will not change with age. In accurate
work, these quantities vary and accurate calibration is requisite
before use. Some forms of pyrometers for the measurement of
high temperatures depend upon the difference in expansion of
copper and steel rods. In practice they do not work well. For
very high temperatures the increase in electrical resistance of
platinumrhodium wires with increase of temperature is meas
ured and the temperature is then calculated.
Ex. 4. Convert 77 F., 17 F., 13 F. to Centigrade degrees.
Ex. 5. Convert 25 C., 5 C., 15 C. to Fahrenheit degrees.
Ex. 6. Convert 79.36 B.T.U. to calories; 45 calories to B.T.U.
Ex. 7. Convert 350 F. to Fahrenheit absolute temperature; to
Centigrade absolute temperature.
First Law of Thermodynamics. Heat can neither be created
nor destroyed. Heat and mechanical work are mutually con
vertible, and a definite ratio exists between the thermal units
that disappear (or appear) and the foot pounds of mechanical
work that appear (or disappear).
* See Journal Franklin Inst., Nov. 1906, page 375.
ELEMENTARY PRINCIPLES. 9
Joule determined this ratio as 772 footpounds to 1 B.T.U.
More recently Rowland fixed the ratio as 778 footpouncls to 1
B.T.U. The latter value will be used.
Joule allowed a known weight to descend a known distance,
doing mechanical work by revolving a paddle in a vessel filled
with water. Due precautions were taken to prevent heat radia
tion as far as possible. The heat that did radiate was calculated.
The tendency of the water to circulate with the paddles was de
stroyed by properly placed baffleplates. The known weight
descending slowly a known distance gave the footpounds of
work, and a known weight of water heated a measured number
of degrees of temperature gave the equivalent number of thermal
units. Of course this experiment was performed many, many
times with proper precautions. For instance, the containing
vessel and the apparatus in the water became heated and this
amount of heat had to be considered. One way to do this was
to heat the apparatus to the maximum temperature before
putting in the water at the original temperature. The apparatus
would thus lose to the water as much heat as it would afterwards
absorb.
Second Law of Thermodynamics. Heat cannot pass from a
cold body to a hot one by a purely selfacting process. Heat in
many ways is compared to water. We say that water will not
run uphill. And yet, nothing is more common than water going
uphill. It is witnessed in the rising sap in the tree, in the evap
oration of water, in all forms of waterworking machinery. It is
evident that the expression should be " water will not run uphill
unaided by some exterior agency." Similarly, heat flows unaided
from a hot to a less hot body, but will not flow in the reverse
sense, viz., from a cold to a hot body unless aid is received from
some exterior source. In refrigeration, heat is made to flow from
water into ammoniagas at the same or a higher temperature by
the following artifice. The ammoniagas is compressed and
cooled at the same time. Suppose that the heat abstracted is
just equal to the heat that is added by compression. The result
is liquid ammonia at the same temperature as the original gas.
If the liquid ammonia is allowed to expand in pipes surrounded
by water, the ammonia will abstract the heat that is required for
10 THE STEAMENGINE AND OTHER HEATMOTORS.
its gasification from the pipes and water. The actual flow of heat
is from 'the water to the colder ammoniagas. The final result
of the whole process is that heat is, by the aid of mechanical
work, taken from one body (the water) and put into another (the
ammonia) that was originally warmer.
Steamplant. The most elementary form of steamplant con
sists in:
A steamboiler and chimney.
An injector or steampump to supply the boiler with water.
A steamengine with the necessary piping.
In a complex system we may have :
Steamboiler with mechanical grates.
Induced or forced draft.
Economizers.
Separators in the pipeline.
Multiplecylinder engines or steamturbines.
Steamjackets around the cylinders or in the cylinder
heads.
Some form of exhaustreheaters.
Some form of steamcondenser.
Airpump.
Circulating pump.
Feed water pump.
In noncondensing engines the exhauststeam may pass
through a feedwater heater.
Steamboiler (Fig. 3). The furnace, the heattransmitting sur
face and the chimney must be designed so that a certain amount
of coal can be regularly burned and the resulting heat utilized in
the formation of steam with the greatest practical economy. The
furnacegrate must be placed in such position that the fireman is
able not only to distribute the coal properly but also can keep
the incandescent fuel properly levelled, free from holes and clear
of clinkers Great economy of combustion is only secured by the
admission of the proper amount of air at the right time. When
bituminous coal is thrown on the front of the grate it needs very
little air as long as it is only drying out and heating up. When
ELEMENTARY PRINCIPLES.
11
the coal commences to give off combustible gases the airsupply
should be proportionally increased.
The heatingsurface of the boiler is that surface (above the
center of gravity of the fire) which has water on one side and hot
o
CC
?
1
g;
f
P
a
gases on the other. It should be so arranged that repairs may
be easily made, the cleaning of either the inside or outside of the
heatingsurface should not be difficult, and its position should be
such that the steambubbles forming on it should free themselves
and rise easily.
12 THE STEAMENGINE AND OTHER HEATMOTORS
The draft, whether produced by a chimney or by means of
fans, should be ample at all times. Chimneydraft is called nat
ural draft, while all forms of mechanically produced draft are
termed artificial draft.
ELEMENTARY PRINCIPLES. 13
DESCRIPTION OF THE PARTS ILLUSTRATED IN FIGURES 4 AND 8.
Part
No.
*2
*3
*4
5
6
7
8
9
9
10
10*
11
12
12*
14
14*
15
15*
16
Name of Part.
Steamcylinder (1 and 2) (pump
body in small duplex pumps).
Cushionvalve.
Cushionvalve stuffingbox.
Cushionvalve stuffingbox fol
lower.
Handwheel.
Steamcylinder head.
Steamcylinder foot.
Draincock.
Steampiston.
Pistonvalve.
Steampiston ring.
Pistonvalve ring.
Steampiston nut.
Exhaustflange.
Exhaustpipe.
Steamchest.
Pistonvalve chest.
Steamchest cover.
Pistonvalvechest heads.
Steampipe.
Part
No.
17
17*
18
18*
19
19*
20
201
20 J
21
22
23
23*
24
25
26
27
28
*29
Name of Part.
Steampipe screwflange.
Slidevalve.
Auxiliary valve.
Valverod.
Pistonvalve rod.
Valverod nut.
Tappetnut.
Valverod gland.
Pistonvalverod gland.
Valverod stuffingbox nut.
Pistonvalve rod stuffingbox
nut.
Valverod head.
Valverodhead pin.
Long valverod link.
Short valverod link.
Cradle.
Crossstand.
Upper rockshaft.
Lower rockshaft.
Long crank.
Short crank.
* Not shown on cuts or sectional drawings.
Artificial draft is easily regulated to effect the combustion of
various kinds of fuel at different rates of combustion. Under
proper management it makes more economic combustion possible
by providing a more accurate regulation of the airsupply, poorer
coal may be burnt, and a steadier supply of steam may be fur
nished independent of weather conditions.
Where the draft is produced by a chimney the temperature of
the gases leaving the chimney is generally between 500 F. and
600 F. In Europe it is quite usual to put less heatingsurface
in the boiler than is usual in this country and then force the feed
water through the tubes of an economizer placed in the path of
the gases to the chimney. With artificial draft it is possible to
have the final temperature of the gases less than the temperature
of the water in the boiler. This is done by having the coldest
feed water heated by the coldest gases (just entering the chimney)
and the hottest feed (just entering the boiler) heated by the hot
gases just entering the economizer (Fig. 3). If the boiler absorbs
70% of the heat of the fuel, a boiler and economizer together may
absorb 82%. Against this saving must be charged the interest
on the cost of the economizer and fan and on the value of the
14 THE STEAMENGINE AND OTHER HEATMOTORS.
space occupied, as well as the cost of running the fans and an
allowance for depreciation and repairs.
Fig. 4 illustrates a section of a small pistonpacked pump that
may be used for feeding the boiler. On page 13 are given the names
of all its parts, as well as those of the airpump and jet condenser
shown in Fig. 8. The student should familiarize himself not only
with the names but also with the use of all the different parts.
There are numerous methods of actuating the steamvalve of feed
pumps, and the best way to comprehend the mechanism is to take
the pumps apart and put them together again and operate the
pump. The work must be done over again if the pump does not
work properly. For engine details, see pages 1722.
Steamseparator. Later it will be shown that it is extremely
desirable that the steam entering any steamcylinder should be
as free from water as possible. Advantage is taken of the fact
that water is much heavier than steam and, by causing the steam
to whirl, centrifugal force carries the water to the circumference
of the containing vessel. When this is accomplished great care
must be taken to keep the water out of the line of action of the
steamcurrent or it will be picked up again. An efficient sepa
rator should furnish dry steam to the engine. Fig. 5.
The Steamengine. It is usual to speak of the work done by
the steam in a steamengine. Strictly speaking this is incorrect*
We shall find that the steam is an agent, just as the connecting
rod is, receiving a certain amount of energy in the boiler and very
inefficiently delivering a very small part of it in the engine. We
shall learn that the difference in temperature of the steam as it
enters and as it leaves a steamcylinder is greater than the differ
ence in temperature of the hottest day in summer and the coldest
day in winter. As the weight of steam entering and leaving a
cylinder is the same, it is evident that a large amount of heat has
disappeared. The engine has done work, however, and there must
be some relation between the heat that has disappeared and the
work that has appeared. At the very outset we see not only that
the steamengine is a heatengine, but also the necessity of under
standing the laws of heat and the laws governing the interchange
of heat and mechanical energy. Thermodynamics is the science
that treats of the relations of heat and mechanical work.
ELEMENTARY PRINCIPLES.
15
The origin of all the power of any steamengine lies in the
coal that is burnt on the boilergrate. When we assume that a
certain engine will make a certain number of revolutions, we
either assume or we must provide sufficient boilerpower to de
liver such a quantity of energy to
the engine that the latter, with an
efficiency of 3 to 15 per cent, will
develop the required power. The
boilerpower is determined by the
amount of coal burnt and the
efficiency of the boiler.
If steam is admitted alternately
to each side of a steampiston, for
evident mechanical reasons the
motion of the latter is given to a
pistonrod that moves backward
and forward in the same straight
line. Usually this motion is com
municated to a crosshead, and the
reciprocating motion of the latter is
converted into a rotary motion by
means of a connectingrod and
crank. Such an engine is called a
doubleacting engine. Where steam
is admitted to only one side, the FIG. 5.
connectingrod may be directly Station Separator,
connected to a pivotpin in the piston. When a plane can be
passed through the connectingrod and the crankarm, the crank
is said to be on a center. When the piston is nearest the crank
it is on the crank center, when it is farthest away it is on the head
center.
The action of steam in a steamengine is as follows : The pres
sure of the steam from the boiler causes the piston to move through
a part of its stroke to a point at which, by some kind of automatic
mechanism to be described later, the steamsupply from the boiler
is cut off. The piston must complete the stroke having only the
diminishing steampressure and the energy stored up in the mov
ing parts to supply the pressure necessary to overcome resistance.
16 THE STEAMENGIXE AND OTHER HEATMOTORS.
If the crankpin has a uniform motion, by Newton's First Law
the resultant of all the pressures exerted on the crankpin must ex
actly equal the resultant of all its resistances just as if the crank
pin were at rest. If at any time there is a difference, acceleration
(change of velocity or variable speed) positive or negative im
mediately follows. It is evident, then, that variation in rapidity
of motion causes the equality that must exist between the driv
ing and resisting forces.
When the piston has reached the end of its stroke all the steam
that produced its motion must be allowed to escape to some place
of lower pressure, otherwise the piston on the returnstroke would
compress the steam. Compression in excess lessens the amount
of external work done, and is neither desirable nor economical,
as the object of an engine is the production of external work.
The steam may be exhausted into :
(a) A receiver or vessel that will serve as a reservoir to
hold the steam till it is fed into another cylinder
working in a lower cycle of pressures than the pre
ceding one.
(&) The atmosphere.
(c) A condenser.
After an engine has been started and is running regularly, it
is evident that, when exhausting into a receiver, the amount of
steam entering that vessel must exactly equal the amount leav
ing, as otherwise the pressure in that vessel would continuously
increase or decrease, which would prevent the engine from work
ing. The pressure in the receiver will fluctuate with the admis
sion and emission of steam and may be greater or less than the
atmospheric pressure.
When the steam exhausts into the atmosphere, the back pres
sure on the piston will be the barometric or atmospheric pressure
increased by the pressure necessary to overcome the frictional
resistances of the pipe system between the cylinder and the at
mosphere. The usual assumed back pressure then is either 14.7,
or more roughly 15 pounds per square inch where pipe friction
may be neglected.
When the steam is exhausted into a condenser the back pres
ELEMENTARY PRINCIPLES.
17
Lilting Bolt Holes
Side Liners
Oil Grooves
Babbitt ^Xx^ " Bottom SheU
FIG. 6. Lower Brass.
Bottom Wedge
, Collar
Bottom Wedge Adjusting Bolt
Lock Nut
Main Bearing Bottom Wedge and Adjusting Bolt
(Furnished only when specially ordered;
Fro. 7.
Oil Cups
Main Bearing Cap Cover
Hand Hole Cover
Main Bearing Cap
Lock Nut
Side Liner Setscrews
Bottom Wedge
Adjusting Bolt
(Furnished only when
epecially ordered)
FIG. 8. Bearing Details.
18 THE STEAMENGINE AND OTHER HEATMOTORS.
ELEMENTARY PRINCIPLES.
19
20
THE STEAMENGINE AND OTHER HEATMOTORS.
Planished Sheet Steel Laggi
\Heat insulating Filling
Corliss Steam Valve.
Back Cylinder Head
Back Cylinder Head Studs
Baok Cylinder Head Bonne
Exhaust Port
Corliss Exhaust Valve
Throttle Valve
Planished Steel Lagging
Heat insulating Filling
.Corliss Steam Valve Chamber
Front Cylinder Head
Front Cylinder Head Studs
Piston Rod Gland Studs
Piston Rod Gland
\Piston Rod Packing
t
Corliss Exhaust Valve
Planished Sheet Steel Lagging
Heat insulating Filling
Exhaust Chest
Exhaust Flange
Exhaust Opening
Exhaust Pipe'
FIG. 11. Crosssection of Corliss Cylinder.
et Screw
Built up Piston
Piston S E ider
Bull Ring
Piston Nut
FIG. 12. Pistcn Details.
Babbit and Harris
Brass Keeper Packing Rings
(Coiled Spring \
Solid Piston with Babbit
and Harris Packing
FlG. 13.
ELEMENTARY PRINCIPLES.
21
22
THE STEAMENGINE AND OTHER HEATMOTORS.
ELEMENTARY PRINCIPLES. 23
sure against the piston may be reduced to 1/2 pound per square
inch above absolute zero of pressure with the very best condenser
equipment, or to 3 pounds per square inch with an ordinary equip
ment. Keeping in mind that the temperature of steam depends
in some way on the rate of vibration of the molecules of the
steam, and its pressure depends on the rate or number of molec
ular impacts on the containing vessel, we readily see, when steam
is deprived of 90% of its heat, and its volume reduced to 1/1500
of the volume it possessed when entering the condenser, that
there must necessarily be a great reduction of pressure. The
unavoidable pressure in the condenser would be that due to
the vapor of the feedwater if there were no leakage of air
through the stuffingboxes and the joints of the condenser
and exhaustpiping, and no air and other noncondensible gases
in the feedwater. If these gases accumulated, it is evident
that the back pressure might finally be greater than that of the
atmosphere. Hence an airpump properly designed and placed
must be used to remove all the condensed steam, vapor, and air.
This pump discharges its contents into a tank called a hotwell.
The vapor and air escape into the atmosphere, and the solid water
can then drain downwards into the suctionchamber of a feed
pump which forces it through the feedpipe into the boiler. There
are two principal methods of condensation :
(a) By means of a surface condenser.
(b) By means of a jet condenser.
Surface Condenser and Airpump. One form of a surface con
denser with its necessary pumps is shown in Fig. 16. The exhaust
steam from the enginecylinder enters the condenser at A and is
divided into many streams by the scatteringplate 0. The steam
is condensed into water by coming into contact with the cool
tubes and then flows down pipe B (closed to spaces V and S) into
space below valves S. The suction valves, S, open upward.
It is well to keep in mind that there is no motion in steam,
water, or air unless there is a difference of pressure. The ex
hauststeam flows into the condenser only so long as the pressure
there is less than the pressure in the cylinder. There is no such
thing as the vacuum drawing or sucking in the steam. Hence we
24 THE STEAMENGINE AXD OTHER HEATMOTORS.
ELEMENTARY PRINCIPLES. 25
see that the valve S will remain open only so long as the pressure
in the pump is less than the pressure in the condenser decreased
by the pressure necessary to overcome the compression of the
spring that tends to seat S. If there is not enough water to fill
the pump, air and steamvapor will fill the remaining volume
above the water. On the return stroke, S will close and valve V
will open. The air will be forced past the open valve V and will
be followed by such part of the water as is not required to fill
the clearancespace that exists in the cylinder and passageway
between the valve V and the piston when on the dead center.
From the chamber above V the air escapes into the atmosphere,
and the water runs through a pipe (shown as a dotted circle) to
the hotwell. The vertical pipe at B connects B and space S, but
is closed to space V.
Circulating Pump. On the right of the same figure is a
crosssection of a circulating pump. It is evident that the cool
ingtubes mentioned above would soon acquire the temperature
of the entering steam if the heat is not absorbed by some other
medium. The object of the circulating pump is to take water at
some low temperature, as 60 to 90 F., and circulate it through
the tubes in such manner that it will absorb the greatest amount
of heat possible. It will be found that this can best be done by
bringing the coolest water in contact with the coolest steam and
the hottest water in contact with the hottest steam. In this case
the circulating water passes through the pump in the direction of
the arrows. It then passes through the lower nest of tubes in the
direction of the arrows, the watert'ght diaphragms determining
the direction of flow. It circulates through the upper nest of
tubes in a similar manner, and when it leaves the condenser
it has a temperature of 110 to 130 F., each pound of water
having absorbed some 50 or 40 B.T.U. (11060 to 13090), more
or less. This circulating water is often called injoctionwater as
it enters the condenser, and is called dischargewater as it leaves.
The condensed steam is called feedwater, and tho feedpump is
the one that is used to force it into the boiler. Hot feed water
must never be LIFTED by the pump, as the pumpchamber will fill
with vapor on the suctionstroke, and the requisite pressure will
not be obtained on the deliverystroke to force the water into the
boiler.
26
THE STEAMENGINE AND OTHER HEATMOTORS.
Jet Condenser. Fig. 17 represents a jet condenser and its air
pump. This is an old form that is rather uneconomical of space,
but it illustrates the principles clearly, which is important. The
exhauststeam enters the condenser by the pipe just above the
waterjet. The injection water and steam come into actual con
tact and assume a common temperature. The airpump in this
case is vertical (which is desirable) and contains three large cir
cular valves. These are made of hard rubber, are held fast in the
FIG. 17.
center, and are bent up in a saucer shape with an excess of pres
sure on the bottom side. The duty thrown on one valve should
be distributed among several valves. The lowest is the foot
valve, the one in the piston is a bucketvalve, and the top one is
the deli very valve. Raising the piston reduces the pressure in the
space between it and the footvalve. If the condenser pressure
is greater than this, the footvalve rises and water and more or
less air or vapor enters the airpump. The air passes through the
water so that when the piston descends the former passes first
through the bucketvalves of the piston. The water passing
through last serves to seal the valves and fill the clearance volume.
A small modern jet condenser is shown in Fig. 18.
ELEMENTARY PRINCIPLES.
27
The Bourdon Gage (Fig. 19). This gage is used to indicate
pressures. These are indicated on a marked dial by the move
ment of a hand. The latter receives its motion through a
mechanism which multiplies the motion of the free end of a
curved elastic metal tube of flattened or elliptical crosssection.
The long axis of this section is perpendicular to the plane of the
tube. The steam or gas is admitted at the fixed end into the
interior of the elastic tube. As the pressure increases, the
FIG. 19. Double Spring Bourdon Gage.
elliptical section becomes more round. This tends to increase
the inside arcs at right angles to the section, and as a conse
quence, the free end tends to move away from the fixed end.
To measure very heavy pressure in hydraulic work, the long
axis is placed parallel to the plane of the tube or dial. The
effect of increase of pressure is now to shorten the inner arcs
and increase of pressure is followed by the movement of the
free end toward the fixed end.
This gage may also be used to measure vacuum or the differ
ence between the absolute pressure in some vessel and the
28
THE STEAMENGINE AND OTHER HEATMOTORS.
absolute pressure of the atmosphere. When so used it is usual
to mark it in inches of mercury rather than in pounds.
Mercury Column. Let Fig. 20 represent a Utube, about
40 inches long, open at one end, C, to the atmosphere and
connected to the condenser or other source of vacuum at
D. Let it be filled with perfectly
pure mercury free from tin or other
adulterations to some level, AB, if
the pressure at D and C are equal.
If now the pressure is reduced in D,
the mercury in the left leg will rise
and it will fall in the right leg. At
any instant, let the distance EF mark
the difference of level.
As the mercury is in equilibrium,
the sum of the vertical forces must
be zero, we have : The pressure in the
condenser in pounds per square inch +
the weight of the column of mercury,
EF, must equal the pressure of the
atmosphere in pounds per square
inch.
Suppose the pressure in the con
denser is reduced to absolute zero and
1 the mercury rises to some point G
then HG represents the weight of the
atmosphere. Evidently then GE +
FH, or twice GE, represents the ab
solute pressure in the condenser when
the vacuum therein is not perfect. Now the height HG, at the
sealevel, is ordinarily 30 inches of mercury, and the height EF
is the quantity marked on all forms of vacuum gages. Hence,
ordinarily 30 inches minus EF in inches is the absolute pres
sure in the condenser. To be exact, instead of 30 inches
the height of the barometer in inches should be used. If,
for instance, the barometer reading is 29.83 inches and the
vacuum is 26.7 inches the absolute pressure in the condenser
is 29.8326.7=3.13 inches.
FIG. 20.
ELEMENTARY PRINCIPLES.
29
If we call the atmospheric pressure 15 pounds per square
inch and the barometer 30 inches, it is evident that 1 inch is
equivalent to  pound pressure, but more accurately, 1 inch
equals 0.491 pound.
Names of Parts. It is desirable that the student learn, as soon
as possible, the technical names of the different parts of the steam
engine, the steamboiler, and the various auxiliaries and appliances
of a steamplant. He should recognize, know the use of, and make
30 THE STEAMENGINE AND OTHER HEATMOTORS
fair sketches from memory of pistons, pistonrods, crossheads,
crosshead pins, crosshead slipper, crosshead guides, connecting
rods (both strap and club end), gib and key, crankpin, crankarm,
crank, crankpin brass, crankpin journal, bearing, liner, capnuts,
frame backbone, holdingdown bolts, cylinderbonnets or covers,
cylinderheads, junkring, follower, springs, rings, boss of a wheel,
eccentrics, eccentricsheaves, eccentricrods, stuffingboxes, pack
ingglands, Stephenson link, dashpot, reachrod, parallel rod,
saddleplate, rocker, separator, steamloop, steamtraps, sight
feed lubricator, indicatorcocks, reducing motion, steamgage,
vacuumgage, receivergage, jackshaft. He should trace the
course of the steam from the boiler through the steampipes, the
engine, the condenser, and the pumps back to the boiler. Engines
and pumps must be taken apart that this may be done.
Rates versus Quantities. It is important to distinguish between
pressure and pressure per square inch. Pressure per square inch
is a rate or an intensity. Pressure per square inch can never be
pressure any more than velocity can be distance. Pressure per
square inch multiplied by square inches gives pressure, just as
velocity must be multiplied by time to give distance.
An expression for work is used which is so terse that much con
fusion results unless its factors are kept clearly in mind :
Work=PF,
where P= pressure per SQUARE FOOT;
V = volume, in CUBIC FEET, SWEPT THROUGH BY P.
Keep clearly in mind that V =AL, where A =area in square feet
and L is distance in feet. Therefore PA = pounds and L=feet,
so that
PAL =PV = footpounds.
Evidently the same result will be obtained if P is taken in
pounds per square inch, if we take care to use A in square inches.
In other words, P is now only 1 /144th of its former value, but A
is 144 times as large.
In steamengine problems it is frequently convenient to use
P in pounds per square inch. Evidently then, to obtain foot
pounds when P is in pounds per SQUARE INCH, we must take the
area of the piston in SQUARE INCHES and the stroke in FEET.
ELEMENTARY PRINCIPLES. 31
Graphical Representation of Work. As external work is the
product of two factors, it may be represented by a closed area, as
in Fig. 37. The ordinates represent pounds and the abscissas
represent distance in feet. If the ordinates represent a rate or
pressure in pounds per square inch, then the area of the piston in
square inches is assumed as a constant multiplier. If the ordi
nates are laid off as pounds per square foot, the area of the piston
in square feet is assumed.
Horsepower. When work is done at the rate of 33,000 foot
pounds per minute, then that RATE is tersely, but arbitrarily,
termed a horsepower. Hence if the total number of footpounds
of work done by a machine per minute be divided by 33,000 the
quotient is the rate of the machine in horsepower.
Indicated Horsepower. The mean effective pressure that is
exerted by the steam on the piston of a steamengine may be
found practically by means of an instrument called the steam
engine indicator, or it may be calculated from theory. For the
present, we shall assume that we have the mean effective pressure
per square inch. This multiplied by the area of the piston in
square inches gives the total pressure. Multiplying the stroke in
feet by the number of strokes per minute gives the distance
through which, or over which, this pressure is exerted in a minute.
The product of the total pressure and the total distance passed
over per minute gives the footpounds per minute.
footpounds of work per minute PLAN
33,000 = 33,000'
where P =mean effective pressure per square inch;
L= length of stroke in feet;
A =area of piston in square inches; T
A' =2 X revolutions per minute (strokes) for doubleacting
engines;
= 1 X revolutions per minute for singleacting engines ;
= the number of impulses for gasengines.
Ex. 8. Find the indicated horsepower of an engine having a cyl
inder 20 inches in diameter and a stroke of 48 inches; the mean effec
tive pressure per square inch of piston area is 33 pounds; the number
32 THE STEAMENGINE AND OTHER HEATMOTORS.
of revolutions per minute is 50. The engine is doubleacting. In
practice this is expressed more tersely. The diameter of the cylinder
is always the first dimension and the stroke is the second one. Thus
the above may be written: Find the I.H.P. of a 20"X48" engine;
revs. 50; M.E.P. = 33.
Ex. 9. Required the M.E.P. of a 12"X20" engine of 50 I.H P.;
revs. 100.
Ex. 10. Find the diameter and stroke of an engine to give 100
I.H.P. with a M.E.P. of 44 pounds, assuming the stroke to be 3/2 the
diameter of the cylinder, the number of revolutions being 50 per
minute.
The ordinary rating of a machine in horsepower should be
the rate at which it is safe or economical to run it. Temporarily,
engines may be made to develop power at greater rates than
their normal ones, but in the end hot bearings, lack of economy,
breakage, or other evil will probably arise. In some cases, how
ever, it is economical to drive an engine to the limit of breakdown
and buy a new one when necessary. In design, due regard must
be paid to demands for power for shorttime intervals. This is
illustrated in the powerful motors required in streetcar work.
Rates Equivalent to a Horsepower :
33,000 footpounds per minute.
550 footpounds per second.
1,980,000 footpounds per hour.
42.42 B.T.U. per minute.
2545 B.T.LI, per hour.
746 watts or 746 voltamperes.
1 kilowatt = 1000 watts =1.3405 horsepower.
Brake Horsepower. This term applies to the power delivered
from the flywheel shaft of the engine. It is the power absorbed
by a frictionbrake applied to the rim of the wheel or to the
shaft. A form of brake is preferred that is selfadjusting to a
certain extent, so that it will of itself tend to maintain a con
stant resistance at the rim of the wheel.
"One of the simplest brakes for comparatively small engines
which may be made to embody this principle consists of a cotton
or hemp rope, or a number of ropes, encircling the wheel, ar
ranged with weighingscales or other means for showing the strain.
ELEMENTARY PRINCIPLES.
33
An ordinary bandbrake may also be constructed so as to embody
the principle. The wheels should be provided with interior flanges
for holding water used for keeping the rim cool.
"A selfadjusting ropebrake is illustrated in Fig. 21, where it
will be seen that, if the friction at the rim of the wheel increases,
it will lift the weight, A, which action will diminish the tension
at the end, B, of the rope, and thus prevent a further increase in
the friction. The same device can be used for a bandbrake of
the ordinary construction. Where space below the wheel is lim
FIG. 21. Hopsbrake.
Standard Engine Tests,
FIG. 22. Ropebrake.
ited, a crossbar, (7, supported .by a chaintackle exactly at its
centerpoint may be used as shown in Fig. 10, thereby causing
the action of the weight on the brake to be upward. A safety
stop should be used with either form to prevent the weights
being accidentally raised more than a certain amount.
"The waterfriction brake is specially adapted for high speeds
and has the advantage of being selfcooling. The Alden brake is
also selfcooling.
"A waterfriction brake is shown in Fig. 23. It consists of
two circular discs, A and B, attached to the shaft, C, and revolv
34
THE STEAMENGINE AND OTHER HEATMOTORS.
ing in a case, E, between fixed planes. The space between the
discs and planes is suppliei with running water, which enters at
D and escapes at the cocks, F, G, H. The friction of the water
against the surfaces constitutes a resistance which absorbs the
desired power, and the heat generated within is carried away by
the water itself. The water is thrown outward by centrifugal
action and fills the outer portion of the case. The greater the
depth of the ring of water, the greater the amount of power ab
sorbed. By suitably adjusting the amount of water entering and
leaving, any desired power can be obtained. Waterfriction
FIG. 23. Alden Brake.
brakes have been used successfully at speeds of over 20,000 revo
lutions per minute."
Brake Horsepower. The power that an engine can deliver is
termed its brake horsepower, since it may be measured, when
small in amount, by some form of brakedynamometer (Fig. 21).
The difference between the indicated and the brake horsepower
is the friction horsepower. After an engine test, the load is
thrown off the engine when possible and cards are taken. From
these the power to run the engine with no load is determined.
This power is evidently the friction horsepower, and by subtract
ELEMENTARY PRINCIPLES. 35
ing it from the indicated horsepower the brake horsepower is
determined.
The mechanical efficiency of the engine is =j ^r p
As seen above, the minute is used as the unit of time in meas
uring the rating of an engine in horsepower. For some other
purposes a minute is too small a unit for convenience. The con
sumption of water and coal per minute would be small decimals
that would be awkward to use and difficult to remember. Hence
the consumption per hour of those articles for each horsepower
indicated by the engine is the unit adopted. Hence such an
expression as "Consumption of coal per H.P.hour =2.1 pounds "
is to be interpreted " There were burnt on the grate of the furnace
2.1 pounds of coal per hour for each I.H.P." In other words, for
N horsepower the total consumption of coal per hour would be
2.1 A 7 pounds.
Efficiency. A crude definition of efficiency is
What you get
What you paid for it*
While it is not difficult to express the actual efficiency of a mech
anism under certain circumstances, the theoretical efficiency can
only be expressed under ideal conditions. For instance, the
efficiency of a woodturning machine might be very low at low
speeds and very high at high speeds; its efficiency might be low
when operated by an inexpert workman and high when operated
for a short time by an expert.
Boiler Efficiency. The efficiency may refer to the grate and
boiler, or the grate, boiler, and economizer (if there is one). The
efficiency is
B.T.U. delivered by the boiler per hour
Heat in the coal burnt per hour
The heat delivered is measured from the temperature of the feed
water taken by a thermometer placed in the feedpipe close to
the boiler.
The heat in the coal may be found by calculation from a
36 THE STEAMENGINE AND OTHER HEATMOTORS
chemical analysis of a sample of the coal, or a sample may be
burnt in a coal calorimeter and its heat equivalent found.
If the percentage of carbon present in one pound of a sample = C
"hydrogen " " " " " =H
" li " " oxygen " " " " " " =
the total B.T.U. in one pound of coal = 14,5000 + 62,000(HA
The maximum efficiency of a given boiler would only be secured
when the coal in quality, fineness, thickness of bed, rate of burn
ing was best suited to the kind of grate, furnace, and intensity of
draft. The method of firing, the amount of air admitted, and
other variables dependent on the skill of the fireman enter into
the result.
To avoid these ambiguities the A. S. M. E. has adopted a
standard boiler and a standard coal. The standard coal when
burnt in a standard boiler is to give 12,500 B.T.U. , of which the
boiler is to deliver 10,000 B.T.U., having consequently an assumed
efficiency of 80%.
Boiler Horsepower. The capacity of a boiler to form steam
is expressed in the following terms : Suppose water, at 212 F.,
is fed to a boiler and converted into steam at that same tem
perature, 212 F. A boiler horsepower is the capacity to evapo
rate 34J pounds of water per hour from water at 212 F. into
steam at 212 F. We shall find that it takes 966 thermal units
per pound of water, so that to evaporate 34J pounds of water re
quires 966 X34J = 33,305 B.T.U., or approximately 33,000 B.T.U.
This rate must not be confused with an engine horsepower.
The latter is a rate in footpounds per minute but the former is
a rate in thermal units per hour. They are not directly related.
A 500horsepower engine might require boilers of any power
varying from 150 to 1000 boiler horsepower, depending on the
thermal efficiency of the engine.
Rate of Evaporation. Good water tubular boilers evapo
rate 810 pounds of water per pound of coal. Heating boilers
below 20 horsepower evaporate 46 pounds of water per pound
of coal. With the usual poor firing found in practice these
results are frequently too high by one or two pounds of water.
ELEMENTARY PRINCIPLES.
37
Grate Area. The grate area required may easily be found
from the formula,
34.5XH.P.
G
ExC
G= grate area in square feet;
E = pounds of water evaporated at 212 F. per pound of coal;
C = pounds of coal burned per square foot of grate area per hour.
It is usual to assume a combustion of 15 pounds of coal per
square foot of grate with natural draft. It ranges from 10 or
12 for anthracite to 25 for gaseous bituminous coal.
AVERAGE STEAM CONSUMPTION OF ENGINES.
Pounds of Steam per I.H.P. per
Hour.
Noncondensing.
Condensing.
Simple high speed
3632
2823
Simple medium speed
3430
2622
Simple Corliss
3026
2420
Compound high speed. . .
2624
221 &
Compound medium speed
2823
2217
Compound Corliss. . .
2622
2016
Compound Corliss, over 500 I.H.P
2420
1814
AVERAGE STEAM CONSUMPTION OF DUPLEX PUMPS.
Type of Pump.
Pounds of Steam per
Hour per Delivered
Horse power.
Simple noncondensing
80240
Compound noncondensing
6575
Triple noncondensing
3550
High duty noncondensing
2834
The tables are arranged in the order of steam consumption,
but the amounts given are for engines in good condition. If
the valves or pistons leak the amounts given above may be
exceeded by thirty to forty per cent. While the boiler supplies
the above weights of steam per I.H.P. of the engine, each pound
(weight} of the steam indicated above needs more heat than
that required to convert one pound of water at 212 F. into steam
at 212 F. This variable factor called the " Factor of Evapora
tion" depends upon the feedwater temperature and the boiler
pressure. For the present, this factor may be assumed to be
38 THE STEAMENGINE AND OTHER HEATMOTORS.
1.2. To obtain the corresponding boiler power then it will be
necessary to multiply the total steam consumption of the engine
by 1.2 and the quantity so found should ordinarily be increased
by 10 to 20% to allow for auxiliaries, future expansion and over
loading the engine.
For example, what boiler horsepower would be required
for an electric light plant containing 300 I.H.P. of highspeed
compound engines?
If run noncondensing the engines would require
300X28=8400 pounds of water per hour.
The heat required to evaporate this water would be equal to
that required to evaporate 8400X1.2 = 10,080 pounds of water
from and at 212 F. Allow 15% of the last amount for auxil
iaries and unforeseen emergencies and we have 10,080X1.15=
11,592 pounds of water to be evaporated from and at 212 F., or
as the necessary boiler horsepower.
The factor of evaporation may be obtained more accurately by
substitution in the following equations.
Let F e = factor of evaporation;
T\ = temperature of the steam ;
1= temperature of the feedwater;
TH = total heat in thermal units to produce one pound
weight of steam at temperature Ti from feed
water at t\.
TH = 1091.7+ . 305(^32)  (t 32)
966*
Steam Consumption of Pumps. The steam consumption
of pumps is very great, and, in the case of pumps which are started
and stopped at intervals, it is excessive through the condensa
tion that occurs (during the quiescent intervals) in the steam
pipe leading to the pump. Allow 120 pounds per horsepower
hour for boiler feedpumps running at a practical constant rate;
allow 200300, for power actually used, if they are started and
stopped frequently.
ELEMENTARY PRINCIPLES.
39
To obtain the work of the pump multiply the weight of
water lifted by the vertical height in feet through which the
water is lifted. This estimate must be increased by a percent
age based on pump slippage, friction, and other losses. An
ordinary allowance is 50%. In case the resistance is given in
pounds pressure per square inch, as occurs when water is pumped
into a boiler, divide the pressure in pounds per square inch by
0.4 and thus obtain the " head in feet."
Electric Lighting. Directcurrent arcs usually use 10 am
peres at 42 to 52 volts, the most satisfactory light being at 46
to 47 volts.
Enclosed Arcs. Directcurrent enclosed arcs consume about
5 amperes at 80 volts or 400 watts. Alternating enclosed arcs
usually take a current of 6 amperes at 70 or 75 volts.
The power required for electric lighting may be determined
by assuming that one horsepower, at the lamps, is consumed
by the number of lamps given below.
NUMBER OF TYPE OF LAMPS SUPPLIED BY ONE HORSEPOWER.
Number of Lamps.
Type and Power of the Lamp.
12
6
2.2
1.5
1 to 1.5
16 candlepower incandescent
32 candlepower incandescent
Halfarc open
Full arc open
Closed arc
Assume the mechanical efficiency of the engine as 90%, the
efficiency of the generator as 90%, and the line efficiency when
the lamps are in or near the building as 90%; we have a total
efficiency of 73% between the engine and the lamps. From
these data the boiler horsepower may be determined.
Example. What boiler horsepower will be required to
furnish steam to highspeed compound noncondensing engines,
using 28 pounds of water per I.H.P., which drive generators
for the following lights: 2000 16 c.p. incandescents, 1000 32 c.p.
incandescents, and 50 A.C. closed arcs.
2000^12 = 167
1000 j 6 = 167
50^ 1= 50
40 THE STEAMENGINE AND OTHER HEATMOTORS.
Dividing 384 electrical horsepower at the lamps by 0.73 we
obtain 525 I.H.P. for the engines.
Required the pump displacement per minute and the boiler
horsepower to operate the feedpumps for 300 I.H.P. of high
speed compound engines. Water lifted 5 feet, boiler pressure,
160 pounds.
If run noncondensing, the actual requirements are 300X28
= 8400 pounds of water per hour. The theoretical displace
ment should be twice this amount to allow for slippage, ineffi
ciency of pump and emergencies. Pump displacement per
minute should be
8400X2
60X6^5 = 4 ' 5cU ' ft 
/160 _\8400
\~4~ /~60~
The delivered horsepower will be 33 QQQ = 1.7.
The actual horsepower may be 1.7x1.5=2.5.
Assume a water consumption of 100 pounds per horsepower
and it is evident that the boiler must evaporate 250 pounds of
water per hour for the pump. Assume a factor of evaporation
of 1.2 and the boiler horsepower required will be
250X1.2
The steam needed by the engines is 525X28=14,700 pounds.
With a factor of evaporation of 1.2 we have
14,700X1.2
34.5
as the boiler horsepower required.
Combining Efficiencies. If one pound of coal contains 14,000
B.T.TJ. and the efficiency of the boiler is 75%, what percentage
of the heat liberated in the furnace of the boiler appears as
energy at the lights? Assume 28 pounds as the water rate of
the engine.
ELEMENTARY PRINCIPLES. 4 1
The engine receives 28x966x1.2=32,457 B.T.U. from the
^^ ooo v fio < (
boiler per hour and utilizes ' "" = 2545 B.T.U. ' 7
I I O
2545
Thermal efficiency of the engine is 7T A ^ = 7.8%. The com
bined efficiency is then .75 X. 078 X. 90 X. 90 X. 90 = .04. Hence
14,000 X. 04 = 560 B.T.U. is consumed at the light.
Heat Consumption of a Steamengine Plant.* "The heat con
sumption of a steamengine plant is ascertained by measuring the
quantity of steam consumed by the plant, calculating the total
heat of the entire quantity and crediting this total with that por
tion of the heat rejected by the plant which is utilized and re
turned to the boiler. The term engineplant as here used should
include the entire equipment of the steamplant which is con
cerned in the production of the power, embracing the main cyl
inder or cylinders, the jackets and reheaters, the air, circulating
and boilerfeed pumps if steamdriven, and any other steam
driven mechanism or auxiliaries necessary to the working of the
engine. It is obligatory to thus charge the engine with the steam
used by necessary auxiliaries in determining the plant economy,
for the reason that it is itself finally benefited, or should be so
benefited, by the heat which they return, it being generally
agreed that exhaust steam from such auxiliaries should be passed
through a feedwater heater and the heat thereby carried back
to the boiler and saved. The indicated horsepower is that de
termined by steamengine indicators. It should be confined to
the power developed in the main cylinder or cylinders.
"The temperature of the feed water is the actual temperature
under working conditions and should be taken near the boiler.
"The heat consumption of gas and oilengines of the internal
combustion class is found by ascertaining the total heat of com
bustion of the particular fuel used, which should be determined
by a calorimeter test, and multiplying the result by the quantity
of fuel consumed. In determining the total heat of combustion,
no deduction is made for the latent heat of the watervapor in the
products of combustion.
* See Trans. A. S. M. E., Vol. XXIV. Standard Rules.
42 THE STEAMENGINE AND OTHER HEATMOTORS.
"The indicated horsepower should be confined to the power
developed in the main cylinder or cylinders, and should not in
clude that developed in the cylinders of auxiliaries.
" The thermal efficiency is expressed by the fraction
2545
B.T.U. per H.P. per hour"
The heatunit expression of economy does not in itself show
whether the engine is working to its best advantage any more
than the expression of the steam consumption, since the tempera
ture at which the heat is supplied is a very important factor in
determining the efficiency of engines, as there is only a limited
choice in the temperature at which the heat is rejected. The
m rji
highest possible efficiency being measured by ^ b , where T a
1 a
is the absolute temperature of the steam entering the engine and.
Tb is the absolute temperature of the condenser.
Ex. 11. If the net or brake horsepower of an engine is 92% of
the I.H.P. and the electrical horsepower is 94% of the brake horse
power, find the I.H.P. of an engine to give 750 kilowatts.
Ex. 12. If the above efficiencies are assumed, find the coal re
quired per kilowatthour if 2 pounds are required per hour per I.H.P.
Ex. 13. If the heat received by each pound of steam from the
boiler is 1100 B.T.U. , and the engine utilizes only 10% of this in
work as shown by the indicatorcard, how many pounds of water per
hour must be pumped into the boiler per I.H.P.?
A graphical illustration of the answer to the question "What
becomes of the heatunits ? " is given in Fig. 24 for an excep
tionally economical engine.
Of the 186,600 B.T.U. generated by burning coal on the grate
there is a loss of 10,000 units by radiation from the boiler; the
remainder divides into two streams. About 70% is absorbed by
the boiler and the rest passes through an economizer on its way
to the chimney. The feedwater contains 5450 units when it
reaches the economizer, and there it absorbs 15,750 more units
that otherwise would have been wasted. The heated feed water
receives the hot water from the jackets and delivers (after losing
some heat by radiation) some 27,650 units to the boiler. A total
then of 159,250 units have been saved, and with small loss are
ELEMENTARY PRINCIPLES.
43
delivered to the engine. Here the losses are very great, only
25,390 units being delivered by the engine. As this result is
obtained in a recordbreaking engine, the amount delivered in an
ordinary engine or in an uneconomical one is left to the reader.
It is the province of this book to discuss the laws that govern the
saving and the wasting of heat in the steamengine and other
heatengines.
44
THE STEAMENGINE AXD OTHER HEATMOTORS.
In Fig. 25 we have a similar diagram for an ideal plant, show
ing that 104,200 B.T.U. only are necessary to do the same work
in a purely theoretical engine working between the same tempera
ture limits. The ideal efficiency may be approached but never
will be reached by any practical engine.
The names of engines indicate:
Their use: Marine, rollingmill, agricultural, electriclight,
sawmill, donkey, switch.
ELEMENTARY PRINCIPLES. 45
The number of revolutions : High, medium, slowspeed.
Character of steam expansion: Simple, compound, triple
expansion.
Treatment of the exhaust: Condensing or noncondensing.
Position of the cylinders: Horizontal, vertical, inclined,
directacting, inverted.
Number of sides of piston acted upon by the steam : Single,
doubleacting.
Character of the valvegear: Corliss, gridiron, plainslide,
doublepoppet, Marshall, pistonvalve.
Character of the cutoff gear : Meyer, Buckeye, Corliss, au
tomatic, adjustable, variable.
Kind of governor: Throttle, flyball, flywheel, or shaft
inertia.
Position of valvegear with reference to the cylinder and
shaft: Righthand, lefthand engine.
Direction of rotation : Running over, running under.
Movability: Stationary, portable, marine, steamboat, dredge.
Connection to the crankpin: Overhung, tandem, cross
compound.
Reversibility: Link, shifting eccentric.
Enclosing of the moving parts : Enclosed engines.
Concentration on one baseplate : Selfcontained engines.
Ex. 14. What I.H.P. will be required to raise 100,000,000 gallons
of water per day through a height of 40' if the combined efficiency of
engine and pump is 50%?
Ex. 15. If the total B.T.U. in one pound of coal is 14,500, what
is the combined efficiency of an engine and boiler if 200 pounds of
coal are burnt per hour in the furnace of the boiler to run a 100I.H.P.
engine. .
Ex. 16. One pound of coal contains .88 pound of carbon, .03
pound of hydrogen, .04 pound of oxygen; the remainder is ash.
33% of the heat generated is lost in the chimney gases. How many
B.T.U. are absorbed per hour if 200 pounds of coal are burnt per hour?
Ex. 17. If the work (expressed in B.T.U.) done by an engine, as
shown by the indicatorcard, is 8% of the heat that was given to the
steam in the boiler and it is known that the boiler only absorbs 70%
of the heat that is in the coal, find the number of pounds of coal that
are required per hour per I.H.P.
CHAPTER II.
STEAMENGINE INDICATOR AND ITS CALIBRATION.
Steamengine Indicator. The steamengine indicator has but
one fundamental requirement, namely, to give a graphical record
of the steam or other gaseous pressure that existed on either side
of a piston of an engine for any or all positions of that piston.
Two quantities must be absolutely exact the measure of the
steam pressure and the measure of the contemporaneous position
of the piston. Some of the numerous sources of error will be
pointed out later. Fig. 26 illustrates a crosssection of the Crosby
indicator. Steam from one side of the enginepiston is admitted
through 6 to the piston, 8, whose movement, resisted by the pressure
of the atmosphere and the compression of the spring surrounding 10,
is communicated to a parallel motion which causes a pencil, secured
at 23 in the pencilbar, 16, to move in a straight line parallel to
one of the elements of the paperdrum, 24. If a paper is fastened
to the drum by the two clips, shown broken above 25, and the
pencil at 23 is pressed against the paper, then by rotating the
drum, when piston 8 is exposed on both sides to the atmosphere,
a referenceline, called the atmospheric line, will be drawn. Sup
pose steam, whose pressure is 40 pounds above the atmosphere,
is admitted below piston 8. If the stiffness of the spring is
such that it compresses 1/5" and this movement is multiplied
five times by the lever, 16, then 23 would rise 1 inch above the
atmospheric line, hence for measurements on the diagram on the
drum the scale of the spring would be 40 pounds =1". If now
the drum be rotated, a line parallel to the atmospheric line pre
viously drawn will be made if the pressure on piston, 8, remains
constant. If the pressure varies, then the pencilpoint will either
rise or fall and a curved line will be made on the paper. If,
46
STEAMENGINE INDICATOR AND ITS CALIBRATION. 47
however, any point on this curve be taken, its height above the
atmospheric line represents the gage pressure of the steam on
piston 8, and its abscissa represents the amount that the drum
was rotated from its initial position.
The record made by an indicator takes the form of a closed
figure called a card or diagram. The length of a card does not
exceed 3" or 4", and, in highspeed engines, it is better not to
exceed 1" or 3". The height of the card should not exceed 2",
and in highspeed work a height of 1J" is plenty. We have seen
the significance of the vertical movement of the pencil, and there
remains only the horizontal movement of the paper caused by
the rotation of the drum. Suppose the stroke of an engine is 12"
and we want a card 3" long, the reduction of the motion of the
enginepiston is then 1/4. If the ends of the atmospheric line
correspond to the deadcenter positions of the enginepiston, then,
for each 1/4" that the drum moves from its initial position when the
pencil is at the end of the atmospheric line, the piston of the engine
should move I" exactly from the corresponding deadcenter.
* "Part 4 is the cylinder proper, in which the movement of
the piston takes place. It is made of a special alloy, exactly
suited to the varying temperatures to which it is subjected, and
secures to the piston the same freedom of movement with high
pressure steam as with low; and, as its bottom end is free and
out of contact with all other parts, its longitudinal expansion or
contraction is unimpeded and no distortion can possibly take
place. Between the parts 4 and 5 is an annular chamber, which
serves as a steamjacket, and being open at the bottom can hold
no water, but will always be filled with steam of nearly the same
temperature as that in the cylinder."
In the above paragraph many desiderata are pointed out, but
no real evidence or data are given to prove the assertions beyond
the evidence of the cut. Catalogues give much valuable informa
tion, but students should be trained to give only the proper value
to the statements they contain for obvious reasons.
"The piston, 8, is formed from a solid piece of the finest tool
* Quoted from Practical Instruction for Using the Steamengine Indicator,
Crosby Steamgage and Valve Co.
48
THE STEAMENGINE AND OTHER HEATMOTORS.
steel. Its shell is made as thin as possible consistent with proper
strength. It is hardened to prevent any reduction of its area by
wearing, then ground and lapped to fit (to the tenthousandth
part of an inch) a cylindrical gage of standard size. Shallow
channels in its outer surface provide a steampacking, and the
moisture and oil which they retain act as lubricants and prevent
FIG 26. Crosby Indicator Cresssection.
undue leakage by the piston. The transverse web near its center
supports a central socket, which projects both upward and down
ward; the upper part is threaded inside to receive the lower end
of the pistonrod; the upper edge of this socket is formed to fit
nicely into a circular channel in the under side of the shoulder of the
pistonrod when they are properly connected. It has a longitudinal
slot which permits the straight portion of the wire at the bottom of
the spring, with its bead, to drop to a concave bearing in the upper
end of the pistonscrew, 9, which is closely threaded into the lower
STEAMENGINE INDICATOR AND ITS CALIBRATION.
49
part of the socket; the head of this screw is hexagonal and may be
turned with the hollow wrench which accompanies the indicator."
The above paragraph gives some idea of the care used in the
design of the piston. The moving parts of an indicator should.
FIG. 27. Crosby Indicator Outside Spring.
be theoretically without weight (on account of inertia stresses) r
and should be frictionless. With the advent of superheated steam
and the use of outside springs, this firm changed the shape and
size of the indicatorpiston. For, they say (Fig. 27), "the other
and more important difference lies in the shape and size of the
piston. This piston is 1 square inch in area and is in form
the central zone of a sphere, thus affording great active force with
a very light pencil mechanism. In other words, this piston serves
as a universal joint to take care of the torsional strains of the
spring when it operates the pencil mechanism of the indicator.
50 THE STEAMENGIXE AXD OTHER HEATMOTORS.
"The Pistonrod, 10, is of steel and is made hollow for lightness.
Its lower end is threaded to screw into the upper socket of the
piston. Above the threaded portion is a shoulder having in its
under side a circular channel formed to receive the upper edge of
the socket when these parts are connected together. When mak
ing this connection BE SURE that the pistonrod is screwed
into the socket as far as it will go, that is; until the upper edge of
the socket is brought firmly against the bottom of the channel in the
pistonrod. This is very important, as it insures a correct alignment
of the parts and a free movement of the piston within the cylinder.
"The Swivelhead, 11, is threaded on its lower half to screw
into the pistonrod more or less, according to the required height
of the atmospheric line on the diagram. Its head is pivoted to
the pistonrod link of the pencil mechanism.
"The Cap, 2, rests on top of the cylinder and holds the sleeve
and all connected parts in place. It has a central depression in
its upper surface, also a central hole, furnished with a hardened
steel bushing, which serves as a very durable and sure guide to the
pistonrod. It projects downward into the cylinder in two steps
having different lengths and diameters; both these and the hole
have a common center. The lower and smaller projection is screw
threaded outside to engage with the like threads in the head of
the spring and hold it firmly in place. The upper and larger pro
jection is screwthreaded on its lower half to engage with the light
threads inside the cylinder; the upper half of this larger projec
tion, being smooth vertical portion, is accurately fitted into a
corresponding recess in the top of the cylinder, and forms thereby
a guide by which all the moving parts are adjusted and kept in
correct alignment, which is very important, but which is impossi
ble to secure by the use of screwthreads alone.
"The Sleeve, 3, surrounds the upper part of the cylinder in a
recess formed for that purpose and supports the pencil mechan
ism; the arm, X, is an integral part of it. It turns around freely
and is held in place by the cap.
"The Pencil Mechanism is designed to afford sufficient strength
and steadiness of movement with the utmost lightness, thereby
eliminating as far as possible the effect of momentum, which is
especially troublesome in highspeed work. Its fundamental kine
STEAMENGINE INDICATOR AND ITS CALIBRATION. 51
ma tic principle is that of the pantograph. The fulcrum of the
mechanism as a whole, the point attached to the pistonrod, and
the pencilpoint are always in a straight line. This gives to the
pencilpoint a movement exactly parallel with that of the piston.
The movement of the spring throughout its range bears a con
stant ratio to the force applied and the amount of this movement
is multiplied six times at the pencilpoint. The pencillever, links,,
and pins are all made of a hardened steel; the latter, slightly taper
ing, are ground and lapped to fit accurately, without perceptible
friction or lost motion.
"The Pistonspring is of unique and ingenious design, being
made of a single piece of the finest steel wire, wound from the
middle into a double coil, the spiral ends of which are screwed
into a brass head having four radial wings with spirally drilled'
holes to receive and hold them securely in place. Adjustment is
made by screwing them into the head more or less until exactly
the right strength of spring is obtained, when they are there
firmly fixed. This method of fastening and adjusting removes all
danger of loosening coils, and obviates all necessity for grinding
the wire, a practice fatal to accuracy in indicatorsprings.
"The Foot of the Spring, in which lightness is of great impor
tance, it being the part subject to the greatest movement, is a
small steel bead firmly ' staked' on to the wire. This takes the
place of the heavy brass foot used in other indicators, and reduces
the inertia and momentum at this point to a minimum, whereby a
great improvement is effected. This bead has its bearing in the
center of the piston, and in connection with the lower end of the
pistonrod and the upper end of the pistonscrew, 9 (both of which
are concaved to fit it), forms a ballandsocket joint which allows
the spring to yield to pressure from any direction without causing
the piston to bind in the cylinder, which is sure to occur when .the
spring and piston are rigidly united, as is the case in other indi
cators. Designing the spring so that any lateral movement that
it may receive when compressed shall not be communicated to the
piston and cause errors in the diagram is of extreme importance.
"The Drumspring, 31, in the Crosby indicator (Fig. 27) is a
short spiral, while in every other make a long volutespring is used*
"It is obvious from the large contact surfaces of a long volute
52
THE STEAMENGINE AND OTHER HEATMOTORS.
spring that its friction would be greater than that of a short open
spiral form; also, that in a spring of each kind, for a given amount
of compression, as in the movement of an indicatordrum, the
recoil would be greater and expended more quickly in the spiral
than in the volute form.
"If the conditions under which the drumspring operates be
considered, it will readily be seen that at the beginning of the
stroke, when the cord has all the resistance of the drum and
spring to overcome, the spring should offer less resistance than at
any other time; in the beginning of the stroke in the opposite
direction, however, when the spring has to overcome the inertia and
friction of the drum, its energy of recoil should be the greatest."
Indicatorsprings. Springs are made to the following scales:
4, 8, 12, 16, 20, 30, 40, 50, 60, 80, 100, 120, 150, 180. The spring
to be used is determined by the fact that the height of the dia
gram should not exceed If".
* Tabor Indicator. Fig. 28 illustrates the method of making a
pencilpoint describe a straight line w r hen the pencil is attached
FIG. 28. FIG. 29.
to a lever that tends to describe a circular arc. "A stationary
plate in which is a curved slot is firmly secured in an upright posi
tion to the cover of the steamcylinder (or on the outside spring
indicator to a bracket on the steamcylinder). On the pencilbar
* Quotations from " The Tabor Indicator."
STEAMENGINE INDICATOR AND ITS CALIBRATION
53
is a rollerbearing which is secured to the bar by a pin. This
roller moves freely in the curved slot in the guide upright and
controls the motion of the pencilbar. The position of the slot
and guide upright is so adjusted and the guideroller is so placed
on the pencilbar that the curve of the guide slot controls the
pencil motion and absolutely compensates the tendency of the
pencil to move in a curve."
"The springs used on the Tabor indicators are of the duplex
type, made of two coils of wire fastened exactly opposite to each
other on the bases. This arrangement equalizes the side strain
on the spring and keeps the piston central in the cylinder, avoid
ing the excessive friction caused with a single coil spring forcing
the piston unequally against the side of the cylinder." The
springs for inside and outside use necessarily differ, due to the
differences of temperature to which they are exposed. Those
intended for outside springs are marked D, as in Fig. 29 ; the inside
springs are unlettered. The table gives the safe pressures for
springs of different strength.
Maximum Safe Pressures to which

springs can be subjected.
Scale of Springs.
Pounds Pressure per Square Inch
with Square Inch Area Piston.
To 200
To 300
Revolutions.
Revolutions.
8
10
10
15
10
12
20
15
16
28
22
20
40
32
24
48
40
30
70
58
32
75
62
40
95
80
48
112
95
50
120
100
60
140
115
64
152
125
80
180
145
100
200
160
120
240
195
150
290
250
200
375
330
Fig. 30 represents a Tabor indicator with outside spring.
The motion of the indicatorpiston, which is in the steamcylinder
54 THE STEAMENGINE AND OTHER HEATMOTORS.
below the spring, is given to the parallel motion shown in front
of the spring. The indicatorcard paper is held on the paper
cylinder by the two clips shown at the end of the pencilbar.
Motion is given to the drum by a Houghtaling reducing motion.
It is well known that a worm and wormwheel afford a simple
means of securing a large reduction in the velocity ratio between
two shafts at right angles to one another, since one complete
revolution of the worm causes the wormwheel to rotate through
an angle measured by the pitch of one tooth. It is also well
known that it is desirable to stop the motion of the paperdrum
to change indicatorcard papers without disconnecting the cord
that gives motion to the paperdrum.
In the Houghtaling reducing motion, the forward motion of
the crosshead of the engine is conveyed through a cord to a
detachable pulley whose diameter is about 1/12 the stroke of
the engine. The motion of this pulley is given to its shaft only
on closing the clutch shown to the left of the pulley. A worm
turned on the shaft gears with a wormwheel attached to the
paperdrum. The rotation of this drum during the forward
enginestroke winds a volutespring. The unwinding of this spring
on the returnstroke furnishes the power to rotate the drum.
In setting the valves of an engine it is very desirable to take
cards from each end of each cylinder during the same revolu
tion of the engine. This may be done by the use of an electrical
attachment to the indicator. Essentially it consists of an electro
magnet that draws the pencil to the paper during the passage
of an electric current through the magnet and withdraws the
pencil when the current is broken.
"In cases where diagrams are to be taken simultaneously,
the best plan is to have an operator stationed at each indicator.
This is desirable, even where an electric or other device is employed
to operate all the instruments at once; for unless there are enough
operators, it is necessary to open the indicatorcocks some time
before taking the diagrams and run the risk of clogging the pistons
and heating the highpressure springs above the ordinary work
ing temperature."' f
t See Trans. A. S. M. E. Standard Rules.
FIG. 16.
55
STEAMENGINE INDICATOR AND ITS CALIBRATION. 57
Dimensions of Standard Tabor Indicator. Diameter of pis
ton, 0.7978 inch; stroke of drum, 5.5 inches; range of pencil
motion, 3.25 inches; diameter of drum, 2.063 inches; height of
drum, 4 inches; ratio of multiplication of piston motion, 5 for 1.
Dimensions of Small Drumindicator. Diameter of piston,
0.7978 inch; stroke of drum, 4 inches; range of pencil motion,
2.35 inches; diameter of drum, 1.5 inches; height of drum,
2.875 inches; ratio of multiplication of piston motion, 5 for 1.
Attachment of the Indicator. For accurate work the indi
cator connections should be short and direct, especially in high
speed engines. The indicator may be used at any angle, but
the vertical position is generally preferable. The usual plan is
to bore a hole in the side of the cylinder so as to pierce the bore
in the clearance space out of the currents of steam and beyond
the piston when on the deadcenter. After tapping these holes
for 1/2" pipe, a short quarterbend of that size, threaded at
each end, is screwed into these holes. A bushing and a straight
way cock which generally only fits one style of indicator com
plete the connection.
When drilling holes, it is necessary either to take off the cylin
derheads to remove the metal chips or to carry a low steam
pressure that will blow the chips towards the driller. No red
or white lead should be used, as particles of it may get into the
indicator and injure it.
Before drilling the holes the following should be considered:
1. The relation of the holes to the piston and ports.
2. The position, method of fastening, and accessibility of the
reducing motion.
3. The convenience of the operator in taking cards.
"The use of a threeway cock and a single indicator con
nected to the two ends of the cylinder is not advised, except
in cases where it is impracticable to use an indicator close to
each end. If a threeway cock is used the error produced should
be determined and allowed for. The effect of the error pro
duced by a threeway cock is usually to increase the area of the
diagram. This is due to the tardiness of the indicator in respond
ing to the changes of pressure. In an investigation made by
one of the committee, which was carried out both on short
58 THE STEAMENGINE AND OTHER HEATMOTORS
stroke engines running at high speed and longstroke engines
running at comparative slow speed, it was found that the in
creased area of the diagram, due to the sluggish action produced
by the threeway cock, ranged from 3 to 7 per cent as compared
with an indicator with a short and direct pipe." f
Drum Motion. The motion of the paperdrum may be derived
from the crosshead or any other part of the engine whose motion
coincides with that of the piston. Various devices have been
invented to reduce the crosshead motion to that required by
the drum. In most of them a cord is used. This cord should
not stretch appreciably under the stress to which it is subjected
and it should always maintain the same path. It should not,
for instance, radiate in different lines from a point at different
positions of the crosshead.
Reducinglever. Before the introduction of the portable
forms of reducing motions, consulting engineers had frequently to
devise a reducing motion on the premises visited. . A common
form of the reducinglever is shown in Fig. 31. The support
for the pivot on the top has been omitted. In some cases the
ceiling over the engine afforded the necessary base; in other
cases a substantial frame had to be erected. As rigidity is more
important than strength alone it is well to take a straightgrained
piece of wood, planed on both sides, V thick, some 3" wide at
the top and 2" wide at the bottom. It should swing without
vibration in a vertical plane parallel to the guides of the engine.
The top pivot should be vertically over the middle of the bot
tom stud when the latter is in its midposition. To maintain a
constant length of leverarm, the lever must carry a fixed stud
(Fig. 31a) at the bottom and the necessary lost motion vertically
will take place in a slotted plate carried by the crosshead. This
stud should be at the top of the slot on both ends of the stroke.
The length of the lever is the distance between the centers of the
pivot and stud and this should be at least 1.5 times the stroke.
It is evident that if the crosshead carried a stud and drove
the lever, the connection therein being slotted, the radius of the
lever would be variable. The cord connection shown is inaccu
t See Trans. A. S. M. E. Standard Rules.
STEAMENGINE INDICATOR AND ITS CALIBRATION. 59
rate and a better one is shown in Fig. 32. The sector compels
the cord to keep always in the same path.
The Brumbo pulley (Fig. 32) is another form of the reducing
lever that is frequently used in locomotive tests. The rim of the
FIG. 31.
FIG. 32.
sector is grooved to receive the cord that connects with the
indicatordrum. The lever and sector have a common pivot.
The drivinglink is from onequarter to onehalf of the length
of the leverarm. The latter should be vertical in midposition
and the drivingpin in this position should be below the line
of motion of the crosshead onehalf the versine of onehalf the
arc of oscillation of the lever. In other words, the drivingstud
in midposition is as much below the line of motion of the cross
head in midposition as it is above it on the two ends of the stroke.
Reducing wheels. Figs. 30 and 33 show different designs
of reducing wheels. When properly made and handled they
give accurate results. They can be tested by moving the pis
ton inch by inch, being careful to take up all lost motion and
measuring the corresponding rotation of the drum. In making
calibrations of this or any other sort the student should be care
ful to see that the practical conditions are identical with the
test conditions. An indicator reducing motion was calibrated in
60
THE STEAMEXGINE AND OTHER HEATMOTORS.
the above manner and gave perfect reduction when the engine
was jacked over, but gave imperfect results when the engine
was working. This resulted from attaching the reducing motion
FIG. 33.
to the lower guide, which, when the engine was under full load,
was found to vibrate enough to distort the card.
Pantographs theoretically give a perfect reduction. Numer
ous joints must be avoided, as each must be free from lost motion.
"Fig. 34 shows a pantograph device at midstroke. This is
made of bar iron nicely riveted together. The indicatorcord
may be attached at 6. The end a is attached to a pin on the
crosshead. The fixed fulcrum is at c. a, b, and c must always
lie in the same straight line, and ed and bn must be parallel
and equal to fg. Also af + nf= stroke of piston f by the length
of the indicator diagram." *
* Quoted from Practical Instruction for Using Steamengine Indicator^
Crosby, page 32.
STEAMENGINE INDICATOR AND ITS CALIBRATION. 61
"In Fig. 35, / is a rod moving in a slide parallel to the pis
tonrod. Link bd is attached to /, and link ae to the crosshead,
a, 6, and c must always lie in the same straight line, ae + bd
and ec4cd= stroke of pistonslength of indicator diagram."
In Fig. 36, a and b are fixed ends of cord wrapped around
FIG. 35.
FIG. 34.
FIG. 36.
pulley D. Indicatorcord is attached to small pulley d and
passes around guidepulley e. D and d are attached to the cross
head. Diam. D^diam. d=strokeof pistons by the difference
between stroke of piston and length of card." *
"The most satisfactory drivingrig for indicating seems to
be some form of wellmade pantograph, with drivingcord of
fine annealed wire leading to the indicator. The reducing motion,
whatever it may be, and the connections to the indicator, should
be so perfect as to produce diagrams of equal lengths when the
same indicator is attached to either end of the cylinder, and pro
duce proportionate reduction of the motion of the piston at
every point of the stroke, as proved by test." f
Method of Taking Indicatordiagrams. 1. Before attaching an
indicator to an engine be sure to blow steam freely through the
pipes and cock to remove any grit that may have lodged there.
* Practical Instruction for Using Steamengine Indicator, Crosby, page 32.
t See Trans. A. S. M. E. Standard Rules.
62 THE STEAMENGINE AND OTHER HEATMOTORS.
2. If the indicator has been unused for some time, or if it
has been handled by others so that its condition is unknown,
it should be taken apart and cleaned with gascline. " An occa
sional naphtha bath is good for an indicator, as it thoroughly
cleanses every part." If any grit or other obstruction gets into
the cylinder it will seriously affect the diagram and lead to bad
results. It is not difficult to detect such trouble, and it should
be remedied at once by taking out the piston, detaching the
parts, and cleaning them as above described.
f "It is essential to know whether the indicator is in good con
dition for use, especially to know that the piston has perfect
freedom of motion and is unobstructed by undue friction. To
test this successfully detach the spring and afterwards replace
the piston and pistonrod in their usual position, then holding
the indicator in an upright position by the cylinder in the left
hand, raise the pencil arm to its highest point with the right
hand and let it drop; it should freely descend to its lowest point."
The piston may be dented or burred from a fall or the upper
part of the cylinderbore may be dirty. It is better to have
the piston fit rather loosely than \he reverse, f "No diagrams
should be accepted in which there is any appearance of w r ant
of freedom in the movement of the mechanism. A ragged or
serrated line in the region of the expansion or compression line
is a sure indication that the piston or some part of the mechanism
sticks; and when this state of things is revealed, the indicator
should not be trusted, but the cause should be ascertained and
a suitable remedy applied. Entire absence of wiredrawing of
the steam line, and especially a sharp, square corner at the begin
ning of the steam line, should be looked upon with suspicion,
however desirable and satisfactory these features might other
wise be. These are frequently produced by an indicator which is
defective owing to want of freedom in the mechanism. An
indicator which is free when subjected to a steady steam pressure,
as it is under a test of the springs under calibration, should be
able to produce the same horizontal line, or substantially the
same, after pushing the pencil down with the finger, as that
traced after pushing the pencil up and subsequently tapping
f See Trans. A. S. M. E. Standard Rules.
STEAMENGINE INDICATOR AND ITS CALIBRATION. 63
it lightly. When the pencil is moved by the finger, first up
and then down, the piston being subjected to pressure, the move
ments should appear smooth to the sense of feeling.
f " The point selected for attaching the indicator to the cylinder
should never be the drippipe or any point where the water of
condensation will run into the instrument if this can possibly
be avoided. The admission of water with the steam may greatly
distort the diagram. If it becomes necessary to place the indi
cator in such a position, as may happen when it is attached to
the lower end of a vertical cylinder, the connection to the indi
cator must be short and direct, and in some cases it should be
provided with a dripchamber arranged so as to collect the water
or deflect it from entering the instrument."
3. Adjust the drumcord so that the drum rotates freely with
out knocking at either end of its stroke. If the cord is too short
it will break or turn the indicator in its coupling if the latter
is set up too tight. Beginners therefore should not set this
coupling up taut before attaching the cord.
4. Lubricate the indicatorpiston with ordinary cylinder oil
for pressures above the atmosphere.
5. Warm up the indicator by admitting steam for a few
seconds.
6. Shut off the steam by means of the cock in the in
dicatorplug. This admits air to the bottom of the indicator
piston.
Bring the pencil in contact with the paper and rotate the
cylinder. This gives a reference line for pressures called the
atmospheric line. Many prefer to draw this line after taking
the card.
7. Turn the steam on the indicator, press the pencil, and
take one or more cards.
8. RECORD ALL THE DATA.
The commercial indicatorcards have forms printed on one
side of the cards. This form should be filled out and in addi
tion any information that has any probability of being of future
value. One should remember that questions may arise other
t See Trans. A. S. M. E. Standard Rules.
64
THE STEAMENGINE AND OTHER HEATMOTORS.
than those of present interest. It is much better to have too
many than too few data after the test is over.
It is advisable to make notes of special circumstances such as
the end of the cylinder which is represented by the card, the
size of pipes and ports, pressures at the boiler and at the throttle,
description of the boiler and special incidents and accidents.
On a locomotive diagram note the speed from the time elapdng
in passing mileposts, the position of the link and throttle, the
character and number and weight of cars drawn, the grade, the
size and position of the blast orifice, character of the coal and
quantity burned, amount of water taken on.
In marine work take data that may be of value from the
ship's log.
Fig. 37 is an indicatordiagram from a noncondensing engine
in good condition. In most steamengines it is desirable that
Release
FIG. 37.
the crankpin revolve at uniform speed. We shall find that
this necessitates a very irregular motion of the piston. As the
latter approaches the end of the stroke it slows down, coming
to absolute rest at the end of its stroke, since it must reverse
STEAMENGINE INDICATOR AND ITS CALIBRATION. 65
its motion. On the return stroke the speed increases to a point
near midstroke and then decreases as before. The card shows
that the valve commences to open for steam just before the
piston finishes the preceding stroke, at A, so that when the pis
ton is actually on the deadcenter and instantaneously at
rest the valve is open the amount is called lead and admit
ting steam. The pressure against the piston rises rapidly and
remains constant as long as the opening of the port is sufficient.
When the piston is halfway between B and C the port has its
maximum opening and the valve starts on its return to close
the port. With a diminishing port opening for steamsupply
the piston is now moving faster than it did in the earlier part
of the stroke. This combination results in a diminution of pres
sure in the cylinder, since an increasing difference of pressure
is necessary to give an increasing velocity to the steam that is
required to supply an increasing volume. It is evident that
BCD changes curvature at C, the center for BC being below
and that for CD being above those curves. The actual point
of cutoff, C, or piston position at the instant of port closing, is
at the point of tangency of these two curves. "f "This cutoff
may be located by finding the point where the curve is tan
gent to a hyperbolic curve."
Inertia of Indicator Pistons. Put a card on the drum of an
indicator and rotate the drum uniformly. There being no steam
on the indicator, pull the piston up by hand and let it drop during
the uniform rotation of the drum. A figure, similar to Fig. 38,
will be made, the spring causing the piston to vrorate above
and below its proper position harmonically, i.e., in uniform periods
of time. The amount of vibration is gradually lessened by the
internal molecular friction in the spring as well as the various
external resistances.
The movement of the piston of an engine is very irregular,
but the movement of the crank is generally uniform. Equal
distances along the circle of the crankpin then measure equal
periods of time. If the crests and hollows in a highspeed engine
card be projected on the crankcircle it will be found that
t See Trans. A. S. M. E. Standard Rules.
66 THE STEAMENGINE AND OTHER HEATMOTORS.
FIG. 38.
150 
Steam Pressure 105 Pounds
Revolutions 250
Spring 60
FIGS. 39 AND 40.
STEAMENGINE INDICATOR AND ITS CALIBRATION. 67
they occur at uniform arc distance apart. This shows that the
sudden impingement of the steam on the indicator piston pro
duces an harmonic vibration similar to that just described.
(Figs. 39 and 40.)
All cards from highspeed engines should show some ten
dency to wave as it is a natural effect. If it is taken out by
friction, the cards are surely in error. At the same time a large
wave motion should be avoided by using heavier springs. Fig.
42 was taken from the engine giving card, Fig. 39, at the same
FIG. 41. FIG. 42. FIG. 43.
speed, tne omy difference being the use of a heavier spring.
In slowspeed engines, the vibration spends itself in the admis
sion line due to the lessened amount of the blow and the length
of time required to make the admission line. Similarly, there
will be less vibration if the compression is heavy, as the blow
at admission is lessened. Figs. 41 and 43.
EXERCISES. Take an indicator apart and examine its construction
carefully. Give a technical description of the indicator. Describe
gage testers, reducing motions, or other apparatus in your laboratory,
taking particular pains to express yourself clearly, to arrange your
ideas sequentially, and to use technical words correctly.
CHAPTER III.
CURVES AND THE WORK OF EXPANSION.
Methods of Drawing the Hyperbola PV =C (Fig. 44). The
isothermal curve of expansion of perfect gases and the curve
of expansion of steam in a cylinder is assumed to follow the law
D
FIG. 44. Method of Drawing an Hyperbola.
"The product of the absolute volume and the absolute pressure
is constant for any stage of the expansion." To draw the curve,
the absolute pressure, and absolute volume at one stage of the
expansion (or the compression) is sufficient.
First Method. From any point C draw the line of zero volume
CB and the line of zero pressure CD. Being given the absolute
pressure CB and the absolute volume Be of some point c of the
curve lay them off and determine the position of c. Through c
draw a horizontal line BA and a vertical line cb of indefinite
68
CURVES AND THE WORK OF EXPANSION.
69
length. From C draw radiating lines at random, cutting the
vertical line cb and the horizontal line BA. Through the points
of intersection draw lines parallel to CD and CB to intersect in
points e, f, g, h, and a. A smooth curve drawn through these
points will be the curve required. If the abscissa and ordinate
for any one of these points are known, by similar triangles it is
easy to show that their product is equal to the product of the
same quantities for the original point c. If it is desired to pro
duce the hyberbola from a upward the same method may be
employed, but the line BA is now ba and the line cb is replaced
by a A.
The line CB is called the clearance line. A line parallel to CB
and tangent to the indicatorcard at the extreme left will cut
off the clearance on CD. CD is also called the perfect vacuum
line.
C V 4 &' d'
FIG. 45. Method of Drawing an Hyperbola.
Second Method (see Fig. 45). It is well known if a rectan
gular hyperbola and its asymptotes are given that if a straight
line is drawn cutting the curve in two places and both asymp
totes the distance of one of the points on the curve from one
asymptote is equal to the distance of the other point on the
curve from the other asymptote. Suppose that we have the
asymptotes CB and CD and any point a of the curve. Through
a draw several radiating lines similar to a'aW. Only one is drawn
to avoid confusion. Lay off W equal to aa' ' b in each will
70
THE STEAMENGINE AND OTHER HEATMOTORS.
be a point of the curve. Any of the points b will serve as a
did for finding other points. The same method of construction
will serve on the compression curve FE.
fThe Point of Cutoff ." The term 'cutoff' as applied to
steamengines, although somewhat indefinite, is usually con
sidered to be at an earlier point in the stroke than the beginning
of the real expansion line. That the cutoff may be defined in
exact terms for commercial purposes, as used in steamengine
specifications and contracts, the Committee recommends that,
unless otherwise specified, the commercial cutoff, which seems
to be an appropriate expression for this term, be ascertained
as follows: Through a point showing the maximum pressure
E C
H G
FIG. 46. Fourvalve Engine.
Slowspeed Commercial Cutcf^ ~
during admission draw a line parallel to the atmospheric line.
Through the point on the expansion line near the actual cutoff
draw a hyperbolic curve. The point wheie these two lines inter
sect is to be considered the commercial cutoff point. The per
centage is then found by dividing the length of the diagram
measured to this point by the total length of the diagram and
multiplying the result by 100."
"The principle involved in locating the commercial cutoff
is shown in Figs. 46 and 47, the first of which represents a dia
gram from a slowspeed Corliss engine, and the second a dia
gram from a singlevalve highspeed engine. In the latter case
where, owing to the fling of the pencil, the steam line vibrates,
t See Trans. A. S. M. E. Standard Rules.
CURVES AND THE WORK OF EXPANSION.
71
the maximum pressure is found by taking a mean of the vibra
tions of the highest point."
The commercial cutoff, B, as thus determined is situated at an
earlier point of the stroke than the actual cutoff, D, referred to.
Fig. 37. Steam being elastic entirely fills an increasing volume,
but its pressure diminishes, as is seen by the decreasing ordinates
of the expansion curve CD. We have already seen that it is
necessary to reject the steam during the returnstroke. At the
point D, where there is another change in the curvature, the
exhaustvalve opens and the pressure rapidly falls as the pis
ton moves to the end of the stroke at E. The piston now returns
and the steam is forced out by the piston sweeping it out. As the
resistance is constant the backpressure line is parallel to the at
H
FIG. 47. Single valve Engine. Highspeed Commercial Cutoff
BC
mospheric line XY. If the exhaustpassages had been short and
ample the line EF would have practically coincided with XY.
We have seen how the atmospheric line was drawn. But
pressures measured from it are not absolute pressures, as we
well know that the atmospheric pressure is some 14.7 pounds
per square inch above zero pressure. The steamgages used on
boilers indicate not the steampressure in the boiler but the burst
ing pressure, which is the difference between the steampressure
inside and the atmospheric pressure outside. Hence, to obtain
the absolute or true pressure above zero we must add the atmos
pheric pressure to all pressures that are measured above the
atmosphere. The barometer gives this pressure in inches of
mercury that can be converted into pounds per square inch by
72 THE STEAMENGINE AND OTHER HEATMOTORS.
14.7
multiplying by =0.491. In all localities near the sealevel
sufficient accuracy is attained by using 14.7 pounds per square
inch as the atmospheric pressure.
Parallel to XY (Fig. 37) and at a distance below it equal to
14.7 pounds to the scale of pressures of the indicatorcard, draw
a line HK. The ordinates of any point of the card measured
to this line give the absolute pressure in the cylinder. At C
then the pressure in the cylinder is CL.
Clearance. Place the piston at the end of its stroke, then
the space between the adjoining faces of the cylinderhead and
the piston, including the volumes that lead into this space (such
as ports up to the valveface, drippipes, indicatorpipes, water
relief pipes), is called clearance. In welldesigned engines of
large size it is from 3 to 5 per cent of the volume swept
through by the piston, in plain slidevalve engines the percentage
varies from 7 to 15 per cent, in pis ton valve engines it varies
from 12 to 25 per cent.
Method of Drawing Clearanceline. One writer has pro
posed the name cylindrus for the volume swept through by the
piston. This is the volume shown by the indicatorcard, since
any part of the stroke passed over by the piston becomes volume
when multiplied by the area of the piston. If the clearance
volume at each end is 5% of the cylindrus we obtain, on dividing
the clearance by the area of the piston, a linear distance that
is 5% of the stroke. This distance may be added to the proper
end of the atmospheric line when the length of that line orig
inally represented the length of the stroke. In Fig. 37 lay
off XM =5% of XY. Then the absolute volume of the steam
at any point L is NL and its absolute pressure is CL.
t Ratio of Expansion. The ratio of expansion for a simple
engine is determined by dividing the volume corresponding to
the piston displacement, including clearance, by the volume
of the steam at the commercial cutoff, including clearance.
f For example, in a simple engine, referring to Figs. 46 and 47,
the ratio of expansion is the entire distance HF, including clear
t See Trans. A. S M. E. Standard Rules.
CURVES AND THE WORK OF EXPANSION. 73
ance, divided by the distance EB, including clearance; that is,
HF
EB'
Indicated Horsepower. In finding the indicated horsepower
(see page 31), we assumed the mean effective pressure. This
quantity may be found if we have a correct average card or
from the average of a number of cards. Suppose Fig. 37 is such
a card. With a triangle erect perpendiculars HE and KB tan
gent to the extremities of the card. At H lay off HJ, making
any angle with HK. Assume any distance HI and lay it off
ten times to some point /. Join / and K. Draw IP parallel to
JK. Bisect HP at a. Lay off HP ten times from a and through
the points so found draw the dotted ordinates as shown. These
ordinates are the mean ordinates of a series of consecutive trape
zoids. On a long slip of paper lay off these ordinates consecu
tively. Measure the total length and divide by the number of
ordinates and thus obtain the length of the mean ordinate. This
mean length multiplied by the scale of the spring used in the
indicator when the card was taken gives the mean pressure.
The mean gross forward pressure is the mean ordinate of
HEDCBK. The. mean back pressure is the mean ordinate of
HEABK. The mean effective pressure is the difference of the
two preceding pressures.
t"The indicated horsepower should be determined from the
average mean effective pressure of the diagrams taken at intervals
of twenty minutes, and at more frequent intervals if the nature
of the test makes this necessary, for each end of each cylinder.
With variable loads, such as those of engines driving generators
for electric railroad work, and of rubber grinding and rolling
mill engines, the diagrams cannot be taken too often. In cases
like the latter, one method of obtaining suitable averages is to
take a series of diagrams on the same blank card without unhook
ing the drivingcord, and apply the pencil at successive intervals
of ten seconds until two minutes' time or more has elapsed, thereby
obtaining a dozen or more indications in the time covered. This
tends to insure the determination of a fair average for that period.
In taking diagrams for variable loads, as indeed for any load,
t See Trans. A. S. M. E. Standard Rules.
74
THE STEAMENGINE AND OTHER HEATMOTORS.
the pencil should be applied long enough to cover several suc
cessive revolutions, so that the variations produced by the action
of the governor may be properly recorded. To determine whether
the governor is subject to what is called 'racing' or 'hunting'
a 'variation diagram ' should be obtained; that is, one in which
the pencil is applied a sufficient time to cover a complete cycle
of variations. When the governor is found to be working in
this manner, the defect should be remedied before proceeding
with the test."
Testing Indicatorsprings. " To make a perfectly satisfac
tory comparison of indicatorsprings with standards, the calibra
tion should be made, if this were practical, under the same
FIG. 48. Indicator spring Testing Apparatus.
conditions as those pertaining to their ordinary use. Owing to
the fact that the pressure cf the steam in the indicatorcylinder
and the corresponding temperature are undergoing continual
changes, it becomes almost impossible to compare the springs
with any standard under such conditions. There must be a con
stant pressure during the time that the comparison is being
made.
CURVES AND THE WORK OF EXPANSION. 75
" The apparatus used for testing indicators at ordinary
pressures above the atmosphere is shown in Fig. 48. The indi
cator is placed at A on top of the cylinder B. The cylinder B
is made of a piece of 6inch standard pipe about 2 feet long.
The pressure is measured by means of a plugandweight device, C,
which is spun around so as to eliminate the effect of friction.
The bottom of the plug is at the same level as the pipe D. The
Ushaped pipe E is filled with oil. Before starting to calibrate
the indicator, the petcock F is opened slightly in order to allow
any air in the pipe G and the siphon H to escape. The siphon H
is surrounded by water contained in the vessel /, which condenses
the steam which enters it through the pipe D, so that when all
the air present is allowed to escape through the petcock F, the
pipe G and the siphon H will be filled with water. / is a petcock
for removing any water that may collect at the bottom of the
siphon E after the apparatus has been in use for a long time.
The pressure is adjusted by regulating the amount of opening
of the valve K in the supplypipe L, which furnishes steam, water,
or compressed air to the apparatus, and also by adjusting the
valve M in the escapepipe N. is a valve for removing any
water which may collect in the bottom of the cylinder B when
steam is used, and for draining out the water after calibrating
under hydrostatic pressure. The pan of the plugandweight
device C is limited in its movement by means of a fork which
comes in contact with it only when the pan is in the extreme
positions. The two prongs of this fork are shown in section at
P and Q. R is a gage for showing the approximate pressure.
The readings of the gage R are not used in testing the indicator,
but as a general guide in the use of the apparatus. The diam
eter of the plug in the plugandweight device is 0.5" and the
hole in the bushing is 0.505". Both the plug and bushing are
ground true. The average area of the plug and of the hole in
the bushing is used in calculating the weight required for a given
pressure.
"In testing indicators with steampressure, the steam is
brought to the maximum pressure to which the indicator is to
be subjected; the indicatorcock is then opened and closed
quickly a number of times to heat the indicator. The steam
76 THE STEAMENGINE AND OTHER HEATMOTORS.
is then released from the cylinder B, and the atmospheric line
is taken after turning the indicatorcock to the proper position.
In taking the atmospheric line, as well as the lines for any other
pressure, the pointer of the indicator is first pressed upward,
and then released and a line taken, then pressed downward and
released and a line taken, the indicator being rapped sharply
with a small wooden stick before taking each line, as has already
been explained. After taking the atmospheric line, steam is
admitted through the valve K, until the panandweight device
is balanced while being rotated. This requires a very fine adjust
ment, and the line is not taken until there is no tendency for
the plugand weight device either to rise or fall." *
t "We recommend, therefore, that for each required pressure
the first step be to open and close the indicatorcock a number
of times in quick succession, then to quickly draw the line on
the paper for the desired record, observing the gage or other
standard at the instant when the line is drawn. A corresponding
atmospheric line is taken immediately after obtaining the line
at the given pressure, so as to eliminate any difference in the
temperature of the parts of the indicator. This appears to be
a better method (although less readily carried on and requiring
more care) than the one heretofore more commonly used, where
the indicatorcock is kept continually open, and the pressure is
gradually rising or falling through the range of comparison.
"The calibration should be made for at least five points,
two of these being for the pressures corresponding as near as
may be to the initial and back pressures, and three for inter
mediate points equally distant.
" For pressures above the atmosphere, the proper standard
recommended is the deadweight testing apparatus, or a relia
ble mercury column, or an accurate steamgage proved correct,
or of known error, by either of these standards. For pressures
below the atmosphere the best standard to use is a mercury
column.
"The correct scale of spring to be used for working out the
mean effective pressure of the diagrams should be the average
* Jacobus, " Testing Indicators," Trans. A. S. M. E., Vol XX.
f See Trans. A. S. M. E. Standard Rules.
CURVES AND THE WORK OF EXPANSION. 77
based on the calibration, and this may be ascertained in the
manner pointed out below.
" When the scale of the spring determined by calibration is
found to vary from the nominal scale with substantial uni
formity, it is usually sufficiently accurate to take the arithmetical
mean of the scales found at the different pressures tried. When,
however, the scale varies considerably at the different points,
and absolute accuracy is desired, the method to be pursued is
as follows: Select a sample diagram and divide it into a num
ber of parts by means of lines parallel to the atmospheric line,
the number of these lines being equal to and corresponding with
the number of points at which the calibration of the spring is
made. Take the mean scale of the spring for each division and
multiply it by the area of the diagram enclosed between two
contiguous lines. Add all the products together and divide by
the area of the whole diagram; the result will be the average
scale of the spring to be used. If the sample diagram selected
is a fair representative of the entire set of diagrams taken during
the test, this average scale can be applied to the whole. If not,
a sufficient number of sample diagrams representing the various
conditions can be selected, and the average scale determined
by a similar method for each, and thereby the average for the
whole run."
Isothermal Expansion (Fig. 49). We may suppose that
the walls allow heat to pass through them and that we have a
source of heat so arranged that the temperature of the gas is
not allowed to fall but is kept constant during the expansion.
The law of isothermal expansion is PiVi=P 2 V 2 =P s V 3 =PV
or PV=C. Note carefully that when a subscript is used the
quantity to which it is added is no longer variable, for it denotes
a fixed value for that problem. PI is the admission pressure
in this discussion and could not be used for any value of the
pressure during the expansion. On the contrary, take any point
on the expansion curve, the ordinate at that point measures P
and the abscissa measures its volume, V. Hence P\V\ and P 2 V 2
are specific values of the general formula PV. As the area of.
the piston is a common multiplier to all parts of the stroke, it
is evident that if we take an infinitesimal part of the stroke it
78
THE STEAMENGINE AND OTHER HEATMOTORS.
becomes an infinitesimal part of the volume when multiplied
by the area of the piston. It may be called dV and when mul
tiplied by P it becomes work. It could be written (PA)dL,
where PA is equal to the total pressure and dL is in feet.
The work done during admission is PiFi. The work done
rv*
during expansion is / PdV.
J YI
But P varies with V, and to integrate we must have but one
FIG. 49.
variable and that must be V. The variable P must therefore
be expressed in terms of the variable V.
But PiV 1 =PV, therefore P= pA
Substitute this value of P and we obtain for the area BCDE
under the expansion curve
Pi 7i (log, F 2 log. Fi) =P 1 V 1 log, ? =P 1 V 1 log, r.
CURVES AND THE WORK OF EXPANSION. 79
As r is the ratio of the final absolute volume to the initial ab
solute volume of the gas it is called the ratio of expansion.
Log s r is an abstract quantity and the expression P\V\ log s r
shows that the work done during expansion is (log e r) times the
work of admission. The subscript e denotes that a table of
Naperian or hyperbolic logarithms must be used (Table II).
The total gross forward work, HABCDG, is then
The mean gross forward pressure would be found by dividing
by 7 2 ,
Pi 7^1+ Ing, r) _P T (l+log e r)
V* r
The quantity that is actually desired is the mean pressure
of the diagram ABCRLMA, which would be the mean pressure
of the theoretical indicatorcard.
Let V c =GF, the volume of the clearance (when multiplied by
A, the area of the piston);
7 3 =GK, the volume of steam enclosed in the cylinder
when the exhaust valve closed;
7 3 .. ,
y=r c = ratio of compression;
' C
P C =MF, the pressure that the compression steam would
have if compressed into the clearance volume ;
ML be an isothermal curve or follow the law P7=C.
Therefore P 3 7 3 =P C 7 C
and
area MLKF =P 3 F 3 log, ^P.V e log, ? P C V C log..
' c V c V 3
Evidently
HAFG=P 1 V C ,
FMLK =P 3 7 3 log, ^ =P 3 7 3 log e r ff ,
LRDK=P 3 (V 2 V 3 ) }
80 THE STEAMENGINE AND OTHER HEATMOTORS.
ABCRLMA
The mean effective forward pressure = y _y = Pm e '
Theoretically, these formulas apply only to the isothermal
expansion of perfect gases. Practically, they are used for the
expansion of steam in the steamengine. The temperature of
the steam falls during expansion, but, owing to the reevapora
tion of condensed steam, the actual expansion curve as shown
by the indicator follows the law PV=C.
The area of a piston is 1000 square inches; the stroke is
38 inches; clearance 2 inches; cutoff is 6 inches from the begin
ning of the stroke; initial pressure is 75 pounds gage; the back
pressure is 16 pounds absolute; the exhaust closes 4 inches from
the end of the stroke; the engine is doubleacting, making 100
revolutions per minute. Draw the card, find the P me and the
theoretical I.H.P., taking clearance into consideration.
Initial pressure absolute, 75 + 15=90.
=48.
Total area HBCDG =Pi7i(l +log< r).
90 X 1000 X 1(1+1.6) =156,000.
HAFG =90 X 1000 x & = 15,000
LRDK = 16 xlOOOX ft =45,333
4 + 2
r loge  = 8,800
69,133
69,133
86,867 ft.lbs.
At 100 revolutions per minute the wo.k would be
86,867 X 200 =v!7,373,400 or ; = 526 I.H.P.
86,867
= loOOxTi ' Pounds per square inch.
CURVES AND THE WORK OF EXPANSION. 81
Ex. 19. Air at a constant pressure of 60 pounds per square inch
absolute is admitted into a cylinder, without clearance, till the piston
sweeps through 3 cubic feet. The air is then cut off and the piston
sweeps through 9 more cubic feet, the temperature remaining con
stantly at 100 F. On the return stroke, the air is exhausted at 15
pounds per square inch absolute. Find the gross and net work per
stroke, P m and P m , and the pounds of air required per stroke. Draw
the card. How many B.T.U. were added during expansion?
Ex. 20. Air is drawn into an aircompressor at 14 pounds per
square inch absolute and 70 F. It is compressed till the pressure
is 42 pounds absolute and the volume is 60 cubic feet; valves then
open and the air is forced out at that constant pressure. If the com
pression were isothermal, find the net work per stroke, P m and P me)
and the weight of dry air compressed. Draw the card.
Ex. 21. The area of a piston is 4 square feet and its stroke is 2
feet. Steam at 60 pounds per square inch absolute is admitted to
the cylinder till the piston moves 8 inches from the beginning of its
stroke when the steam is cut off. If the steam expand in accordance
to the law PV=C, and the back pressure on the return stroke is
15 pounds absolute, find the gross and the net forward work per
stroke, P m and P m e Draw the card. No clearance.
Ex. 22. Steam at 75 pounds gage (90 pounds absolute) is admitted
to a cylinder 20"X24" (20 inches diameter and 24 inches stroke).
Cutoff at 1/4 stroke. Back pressure 15 pounds absolute or gage
pressure. The engine is doubleacting, making 90 revolutions per
minute; no clearance. Draw the card. Find the P m and P me and
the I.H.P.
Ex. 23. In a cylinder with clearance when the piston is on the
return stroke, the back pressure of the steam in the cylinder is 16
pounds absolute when the exhaustvalve closes and the volume is
3 cubic feet. At the end of the stroke the clearance volume is 1
cubic foot. Draw the recompression curve and find the work of
compression in footpounds.
Ex. 24. Take the same data as in Ex. 22, but cutoff at 1/9 stroke,
and find the same quantities.
Diagram Factor. ''The diagram factor is the proportion
borne by the actual mean effective pressure measured from the
indicatordiagram to that of a diagram in which the various
operations of admission, expansion, release, and compression are
carried on under assumed conditions. The factor recommended
82 THE STEAMENGINE AND OTHER HEATMOTORS.
refers to an ideal diagram which represents the maximum power
obtainable from the steam accounted for by the indicatordia
grams at the point of cutoff, assuming first that the engine has
no clearance; second, that there are no losses through wire
drawing the steam either during the admission or the release;
third, that the expansion line is a hyperbolic curve; and fourth,
that the initial pressure is that of the boiler and the back pressure
that of the atmosphere for a noncondensing engine, and of the
condenser for a condensing engine.
"The diagram factor is useful for comparing the steam dis
tribution losses in different engines, and is of special use to the
engine designer, for by multiplying the mean effective pressure
obtained from the assumed theoretical diagrams by it he will
obtain the actual mean effective pressure that should be developed
in an engine of the type considered. The expansion and com
pression curves are taken as hyperbolas, because such curves
are ordinarily used by enginebuilders in their work, and a dia
gram based on such curves will be more useful to them than
one where curves are constructed according to a more exact law.
" In cases where there is a considerable loss of pressure between
the boiler and the engine, as where steam is transmitted from
a central plant to a number of consumers, the pressure of the steam
in the supply main should be used in place of the boiler pressure
in constructing the diagrams.
" The method of determining the diagram factor is best shown
by referring to Figs. 50, 51, 52, which apply to a simple non
condensing engine and a simple condensing engine.
In Fig. 50, RS represents the volume of steam at boiler
pressure admitted to the cylinder, PR and OS being hyperbolic
curves drawn through the compression and cutoff points re
spectively. In Fig. 51, the factor is the proportion borne by
the area of the actual diagram to that of the diagram CNHSK.
In "Fig. 52, the factor is the proportion borne to the area of the
diagram CNHSK. In Fig. 51, where the diagram is the same
as in Fig. 50, the distance CN is laid off equal to RS shown
in Fig. 50, and the curve NH is a hyperbola referred to the
zero lines CM and MJ. In Fig. 52, the distance CN is found
in a similar way.
CURVES AND THE WORK OF EXPANSION.
S N
83
FIG. 50.
^Boiler Pressure
C/ N'
 "v
CNis equal to US in. Fig. 31a.
> Line of Zero Pressure
FIG. 51.
Boiler Pressure
CWis determined in the same way
as ^ST in Fig. 31a,
Line of Condenser Pressure
FIG. 52.
Diagram Factor.
Line of Zero Pressure
84 THE STEAMENGINE AND OTHER HEATMOTORS.
Elimination of Clearance Steam. RS or CN measures the
net steam that passes through the cycle. We shall find that an
entropy diagram measures the heat added; that is, the heat of
formation of the admission steam measured above its proper
feedwater temperature. It is then necessary to eliminate the
clearance steam from the diagram. Figs. 51 and 52 show how
this is done.
It is important to note that the diagram factor is based on an
ideal diagram the backpressure line of which is neither the zero
line nor the expected backpressure line, but an ideal line of back
pressure. The ideal backpressure line for a condensing engine is
the assumed pressure in the condenser and in a noncondensing
engine it is the atmospheric pressure. Compressing the steam to
boiler pressure is in effect avoiding the complication of consider
ing clearance. Note further that the pressure during admission
is the boiler pressure and hence the efficiency of the pipe line is
included n the diagram factor. If the line loss is very great the
steam pressure at the throttle may be used, but that fact should
be specially noted. Hence in choosing a diagram factor or in
finding it practically for a definite case, it is essential that these
elements be properly applied.
CHAPTER IV.
ZEUNER AND BILGRAM VALVEDIAGRAMS AND DESIGN
OF PLAIN SLIDEVALVES.
The Throw of Cranks and Eccentrics (Figs. 53 and 54;.
The throw or radius of a crank is the distance from the center
of the crankpin to the center of its shaft or the distance R in
Fig. 53. As it is evident from the definition that the length
of the crankpin radius does not affect the crank throw, a modi
fied form of the crank may be obtained by increasing the radius
FIG. 54.
of the crankpin till its periphery extends beyond the shaft as
in Fig. 54.
This form of crank is called an eccentric.
Its throw or eccentricity is the distance from the center of
the shaft to the center of the eccentric or the distance SP in
Fig. 54.
The eccentricity or throw of an eccentric is improperly called
the radius of the eccentric. The radius of the eccentric circle as
shown above does not affect the properties of the eccentric as
an eccentric.
The travel of a valve in one direction is twice the throw
of its eccentric (unless modified by leverarms), viz., 2SP=AB.
85
86 THE STEAMENGINE AND OTHER HEATMOTORS.
Piston Travel with a Finite Connectingrod (Fig. 55).
Let R=OD crank throw;
L = Dd = connectingrod length;
ab = travel of crosshead ;
then with centers a and d, draw the arcs CAC' and Dg, using the
length of the connectingrod as a radius to the same scale that
A0= crank throw. It is evident that ad = CD=Ag = the travel
of the crosshead = piston travel for a crank rotation of 6 degrees
from OA.

d
FIG. 55.
Drop the perpenaicular D/; then, from the figure, we see
that the piston travel for a finite connectingrod is equal to
fg + fA = LL cosa + RR cos 6=L(l cos a) +R(1 cos (9).
Piston Travel with an Infinite Connectingrod. As the cen
ter d, Fig. 55, is moved to the left by the use of longer rods, the
curve Dg approaches closer to Df and when d is at an infinite
distance the arc becomes the straight line Df.
With an infinite rod the travel is therefore
fA =RR cos 0.
a
The equation for a finite rod gives the same result when
and L = oo.
Fig. 56 shows a crankpin working in a yoke; the motion
produced is equivalent to that which would be produced by a
theoretical rod of infinite length. It is used in some forms of
VALVEDIAGRAMS AND SLIDEVALVES.
87
steampumps. It is usual to consider the eccentricrod as a rod
of infinite length, as it is often forty times the eccentric throw
in length. The connectingrod is usually only five to seven times
the crank throw in length, and in accurate work the exact posi
tion of the piston for different crank positions must be found.
The graphic methods given above are usually preferred in the
solution of all valvediagram problems.
Position of a Slidevalve. The position of the piston is always
found by measuring the distance it is from the beginning or end
FIG. 56.
FIG. 57.
FIG. 58.
of its stroke, as shown above. It is very convenient in finding
the position of a valve to measure the distance it is from its mid
position. This is never done with pistons, but is always done
with slidevalves. As the eccentricrod is generally assumed as
infinite in length we have, Fig. 57.
if r\ = eccentric throw
and </> =the angle that the eccentric radius is from its midposition,
bd =7*1 sin (f) = distance valve has moved from its midposition.
It is evident that the valve will be in its midposition when
the eccentric is in its midposition, oc, if oa and oe are the posi
tions of the eccentric when the valve is at the ends of its travel.
Effect of Finite Connectingrod. In all steamengines every
effort is made to have the crankpin move with uniform velocity,
viz., pass over equal spaces in equal times. If the crankpin
does this, it will be found that the motion of the piston is quite
irregular and the shorter the connectingrod the greater is this
irregularity. To prove this take any crankcircle, as in Fig. 58,
88
THE STEAMENGINE AND OTHER HEATMOTORS.
and divide it up into equal arcs AD, DB, etc. The student
should compare the amount of motion for equal crankangles:
1. At the ends and middle of a stroke.
2. At the two ends of a stroke.
3. During the forward and return strokes.
4. With connectingrods of different lengths.
The Slidevalve. We have seen that the sum of all the impacts
of the steam molecules on the face of the piston causes it to move
and so converts some of the kinetic energy (or energy of motion)
of those molecules into work. If the supply of steam be cut off
after a certain amount of it has entered the cylinder, more energy
may be extracted from the steam that has entered by allowing
it to expand. It will do this if the resistance be gradually lessened.
There are a number of variables to consider, but we may
assume for the present that variation of velocity will bring about
the necessary equality between the steampressure and the resist
ance, the velocity increasing if the resistance decreases and be
coming less with increased resistance.
FIG. 59.
The slidevalve controls the admission of the steam auto
matically, cutting it off after a certain percentage of the stroke
has been passed by the piston, opening a relief or exhaust
passage at or near the end of the stroke for the escape of the
foteam from the cylinder during the return of the piston. Near
the end of the return stroke, complete escape of steam is pre
vented by closing up the passage used for exhaust. The conse
quent compression of the steam in the cylinder serves as a
cushion and tends to prevent pounding.
VALVEDIAGRAMS AND SLIDEVALVES.
89
Valve Laps. The amount the valve overlaps the outside edge
of the port when the valve is in its midposition is outside lap
(see Fig. 59, o, o'). Similarly the amount the valve overlaps
the inside edge of the port when the valve is in its midposition is
inside lap (see i, i', Fig. 59). In its motion to and fro it is evi
dent that the valve overlaps the ports both inside and out vary
ing amounts. But any valve has but one midposition in each
stroke, hence inside and outside laps are fixed quantities for any
valve and can only be reduced by chipping or planing off the
valve and thus reducing o or i,
It is not practical to draw the whole engine for each illus
tration, hence to the right of each figure are line sketches (not
to scale) showing the relative crank and eccentric positions for
any valve position.
When the entering steam occupies the space S the outside
lap is called steam lap and the inside lap is exhaust lap. These
names are reversed if the entering steam occupies the space E.
It is not necessary for the steam laps to equal one another and
the exhaust laps may be unequal, zero, or negative.
Throw of the Eccentric (Fig. 59). The eccentric Oe being
directly connected to the valve it is evident if the former be
FIG. 60.
FIG. 61.
FIG. 62.
rotated from its present midposition to a horizontal position
that the valve would move a distance Oe to the right or left in
accordance with the direction of rotation. From an inspection
of the figure we see that the valve must move the outside lap, o,
to bring the valve and port edge and edge and any further move
ment will be called portopening. The throw of the eccentric
must equal the lap + the maximum portopening. Highspeed
enginevalves are designed with considerable overtravel, as TO,
Fig. 62, is called.
90 THE STEAMENGINE AND OTHER HEATMOTORS.
Lead is the amount in inches that the port is open when the
piston is at the beginning of its stroke. Examining Fig. 59, we see
that, as the exhaust lap is always less than the steam lap, any
movement of the valve to open one port to steam will open the
port on the other side of the piston a greater amount. Hence
exhaust lead is always greater than steam lead.
We may now follow the crank through one revolution.
Width of Port and Portopening. By the width of the port
is meant the invariable breadth of the port at the valveseat,
or p in Fig. 60. The maximum portopening PO may be less
than, equal to, or greater than the width of the port p, Figs. 60,
01, and 62.
Fig. 63: Crank OC on the deadcenter, head end; piston P
is at the beginning of its stroke; the left port is open the amount
of the steam lead; the right port is open the amount of the exhaust
lead; the eccentric is at some angle, coe (to be determined in
amount later), ahead of the crank, i.e., in the direction of
rotation.
Fig. 64: The eccentric has moved to its extreme righthand
position; the left port has its maximum opening to steam; the
right port has its maximum opening to exhaust; the piston has
moved to the right to its position, P.
Fig. 63 : W3 turn to the first figure and note the dotted posi
tions of crank and piston. The valve is moving to the left and
is about to cut steam off from the left side of piston P f .
Fig. 65: The piston is at the end of its forward stroke to the
right and is at the beginning of its stroke to the left. The right
hand port is now open the steam lead and the left port is open
the exhaust lead.
Fig. 66: The eccentric and valve are in midposition twice in a
revolution. Both ports are closed. The steam is expanding on
one side and is being compressed on the other. The kinetic
energy of the parts keeps up the motion. Note the position of
crank and piston for the midposition of the valve.
Practical Considerations. If the steampressure is the same
at the two ends of a pipe there is no motion of the steam. To
secure velocity, there must be a difference of pressure and to secure
high velocity the difference becomes considerable. If the port
VALVEDIAGRAMS AND SLIDEVALVES.
91
opening is small the steam often has to flow at velocities of 6000
to 20,000 feet per minute to fill the volume behind a rapidly moving
FIG. 63.
FIG. 64.
!
FIG. 65.
FIG. 66.
piston. This necessitates an appreciable difference in pressure
between the steam in the cylinder and that in the steamchest.
92 THE STEAMENGINE AND OTHER HEATMOTORS.
This explains the rapid falling off of steampressure at cutoff in
highspeed engines.
The following values will give approximate idea of the amount
of steam lead given to engines. Experience will show that these
values may be modified to suit other conditions.
Diameter of Cylinder. Steam Lead.
8" to 20" 1/32"
20" " 30" 3/64"
30" " 40" 1/16"
Angular Advance. Fig. 63: If the eccentric were in mid
position, oc' ', Fig. 63, when the piston was at the beginning of its
stroke, steam could not enter the cylinder as the valve would be
in midposition. Keeping the crank and piston stationary we
must move the valve to the right a distance = steam lap + steam
lead. To do this we must rotate the eccentric ahead of the 90
position some angle, a, such that r sin a = steam lap + steam
lead. This angle, a, marked c'oe in Fig. 63 or DOE in Fig. 67 is
called the ANGULAR ADVANCE. Fasten the eccentric to the shaft
(90+ a) ahead of the crank. If the eccentric rod and valvestem
are the correct length the valve will be properly set.
Amount that the Valve has Moved from its Midposition. If
the eccentric was fixed at E, Fig. 67, when the crank is on the
FIG. 67.
deadcenter OC the valve has been moved Ed = r sin a = lap 4 the
steam lead from its midposition. If the crank rotates through
VALVEDIAGRAMS AND SLIDEVALVES. 93
an angle, 6 (carrying the eccentric through the same angle, as the
eccentric is fixed now to the shaft), the eccentric will be found
at E f , the valve having moved r sin (a + 0} from its midposition.
The student should draw the crank and eccentric in various
positions and find the corresponding positions of the piston and
valves as in Figs. 6366.
Valvediagrams. In the discussion on valvediagrams the stu
dent must keep clearly in mind :
1. When the crank is on the deadcenter the piston is at the
beginning of its stroke and the ports are open the amount of the
steam lead on one side of the piston and the amount of the exhaust
lead for the other port on the other side of the piston.
2. The eccentric is ahead of its midposition an angle a of such
magnitude that r sin a = lap + the lead.
3. The angle a is invariable, the eccentric being keyed to the
shaft (90 + a) ahead of the crank; so that if the crank rotates
6 degrees from its deadcenter the eccentric rotates the same
angle. Hence the eccentric is (a +6) from its midposition, thus
placing the valve r sin (a + 6) from its midposition.
4. Referring to Fig. 59 we see .that if we subtract the steam
lap from the amount that the valve has moved from its midposition
we obtain the amount of portopening to steam on one side of the
piston, and if we subtract the exhaust lap on the other side of the
valve we obtain the amount that the other port is open to exhaust
on the other side of the piston.
5. Negative portopening indicates the amount that the valve
must be moved to obtain a position where the port is just about
to open. For instance in Fig. 59 the valve is zero inches from
its midposition; subtracting the lap gives a minus portopening
(numerically = the lap) and shows how far the valve overlaps the
port. If, in that same figure, the valve is moved to the left we
must consider that amount as negative if motion to the right is
considered positive. Subtracting the lap then gives a larger
negative quantity, which we see represents the amount of the
overlap or the amount that the valve would have to be moved
to just open the port.
6. Fig. 59: The opening of the central part E does not enter
into the diagrams. Our only care must be to have it of such
94
THE STEAMENGIXE AND OTHER HEATMOTORS.
magnitude that the valve when moved to its extreme right or left
position will still give plenty of room for the steam that is ex
hausting from either the right or left port.
7. The engine and diagram must not be confused. In the
engine, when the crank moves, the eccentric and valve also move.
Once the diagram is constructed the only movable quantity is a
line representing the crank, the rest of the diagram remaining
stationary. The amount of motion of all the other elements of
the valve is found by proper interpretation of the diagram.
Pig. 68: Assume the crank to revolve clockwise and the con
FIG. 68. Zeuner Diagram.
nectingrod to be to the left. In the diagram lay off the angular
advance, a, negatively. On OE thus obtained lay off OF = the
throw of the eccentric. On OF as a diameter construct a circle.
Let the crank rotate through any angle, 0, from its deadcenter
UNIVERSITY
OF
VALVEDIAGRAMS AND SLIDEVALVES, 95
position, OB. Then the Zeuner diagram construction depends
upon the fact that "any intercept, OG, of the crankline by the
valvecircle represents the amount that the valve has moved from
ITS MIDPOSITION."
Proof. Connect F and G. OGF is a right angle, being in
scribed in a semicircle.
OG = OF cos p = OF cos (90  (a + 6)) = OF sin (a + 6) = r sin (a + 6)
But (Fig. 67) r sin (a + 0) = distance valve has moved from its
midposition.
To the same scale lay off OK = the steam lap and draw the
lap circle IQL. In the diagram many of the crank lines next
mentioned are not drawn, as it would confuse the diagram.
On the deadcenter postion OB the port is open J7 = the
steam lead.
In the crank position OE the port is open the maximum amount
FQ, as the portopening decreases with further rotation of the
crank.
In the position OL, steam has been cut off, as the portopening
has been decreasing and is now zero.
In the position ON the valve overlaps the port MN\
In the tangential position ON' the valve is zero distance from
its midposition or is in its midposition.
In the position OP the valve overlaps the port PR.
In the position OS the valve is at its maximum distance towards
the left and overlaps the port by the lap + the eccentric throw = SF.
The right port is consequently widest open. In each of the
above cases the position of the left edge of the steamvalve is the
one described.
When the throw and angular advance have been determined
for one end of the valve from the data, necessarily, they are de
termined for the other end of the valve, as there is only one
eccentric having a fixed throw and a fixed angular advance.
As the throw and angular advance of the eccentric are fixed
there is. no reason why the lower circle (of the same diameter)
constructed on the prolongation of OF should not serve to indicate
the openings of the other steamport for the other side of the
96
THE STEAMENGINE AND OTHER HEATMOTORS.
piston for the returnstroke. Lay off the proper steam lap and
proceed as before.
Returning to the position OL we see, by referring to Fig. 68,
that the valve is moving to the left (although the piston is moving
to the right, the crank not having reached the right deadcenter
yet). When the crank reaches the tangential position ON' the
valve is in its midposition. The left port, or head end, is now
closed by the amount of the exhaust lap and any further move
ment to the left reduces the overlap. Now movements to the
left of the central position are measured by intercepts on the
lower valvecircle. Therefore describe the arc VW with a radius
OF = the exhaust lap on the left side of the valve. From consid
Steam CufcQff
FlG. 69.
erations similar to those that have preceded we see that when
the crank has rotated from the position OB to:
VALVEDIAGRAMS AND SLIDEVALVES. 97
07, the exhaust port on the left side or head end is just
about to open.
OF, that the port is open the exhaust lead to permit the
returnstroke.
OA, the exhaustport has its maximum opening.
OW, the exhaustport has closed and compression of the
steam that has not escaped commences.
By drawing an arc with a radius equal to the exhaust lap of
the right side of the valve on the upper circle, in a similar manner
the exhaust events for the right side of the piston or crank end of
the cylinder may be indicated.
Geometrical Relations of Elements of the Zeuner Valve Dia
gram. Suppose the diagram drawn (Fig. 69. Draw a crank
circle of any radius OA, it will represent the crankcircle to some
scale. Then
1. OH bisects A' OB and COD.
2. HFO, HEO, and HIO are right angles, being inscribed in a
semicircle, HE and HI are tangents to the lap circle.
3. Draw a circle NHP with OH as a radius; join the intersection
N and P of this circle with the two crank positions, steam admission
and steam cutoff; the line NP so drawn is tangent to the lap circle.
4. Drop the perpendiculars JL and JK, then JK = FG = ihe
steam lead.
In the following problems assume an infinite connectingrod :
Ex.25. Throw of eccentric = li", angle of advance =30, steam
lap = ^", exhaust lap = J". Find the angle at which steam is ad
mitted and cut off, and the exhaust opened and closed; the steam
lead, exhaust lead, and maximum opening of the port to exhaust.
Ex. 26. Stroke is 4', steam is cut off at f stroke, and is admitted
at 1" before the beginning of the stroke, the exhaust is opened at
3" before the end of the stroke, the throw of the eccentric is 2"; find
the proper angle of advance, the steam and exhaust laps, and the
point on the stroke when the exhaust closes.
Ex. 27. Stroke is 3', steam is cut off at 27", steam lead is J" ', the
exhaust closes at 30" from the beginning of the stroke, throw of the
eccentric is 1J"; find the maximum portopening to steam and ex
haust, and position on the stroke when the exhaust opens.
Ex. 28. Given the throw of an eccentric = 2", the external lap =
98 THE STEAMENGINE AXD OTHER HEATMOTORS.
I", steam lead = i", exhaust lap = J" (negative); find where the
steam is cut off and where the exhaustvalve is closed if the stroke
is 2'.
Ex. 29. Stroke is 2', steam is cut off at 20", the lead is ", the
outside or steam lap is f ", no exhaust lap; find the angular advance,
throw of eccentric, and where the exhaust opened and closed.
Problem. The amount that the port is to be open for any
particular position of the crank, the position of the crank itself
when the steam is cut off, and the amount of lead being known.
To find the lap of the valve, throw off the eccentric, and its
position with regard to the center lines of the crank.
The solution of this and the next problem are modifications
of those given in " Designing Valve Gearing," by E. J. Welch.
The solutions are theoretically exact if the angularity of the
eccentricrod is neglected. Practically, however, the solution
depends upon the intersection of lines making a small angle with
each other and it is difficult to determine the exact point of
intersection.
Draw AB (Fig. 70) to represent the amount the port is to
be open at the given position of the crank and lay off AC to rep
resent the required amount of lead. From the point C draw CD
to represent the position of the crank at which the steam is to be
cut off from the cylinder. Draw CE at right angles to CD and
AF at right angles to AB. These lines intersect at G. Bisect
the angle EOF by the line GH. This bisectrix is a locus of the
required center N since EG and FG are tangents to a circle whose
center is N.
From C lay off CI to represent the crank position when the
valve is open the required amount AB. If we draw CPL per
pendicular to CI it will be tangent to an unknown circle, aGP,
at some unknown point, P, where TP is the required opening
at the required angle. Similarly, if we draw BW perpendicular
to AB, it will also be a tangent to the same circle. The bisectrix
of the angle, PLW, so formed, will be LN, which is the locus of
the center of this unknown circle, and it will intersect the other
bisectrix, GH, at N, the required center of the unknown circle.
Draw NC and the diameter of the valve circle will be obtained.
VALVEDIAGRAMS AND SLIDEVALVES.
99
NW are
To check the position of the point N, see that NP and
equal and that N lies in GH.
Problem. The greatest amount that the port is to be opened,
the position of the crank when the steam is to be cut off from
the cylinder, and the amount of lead being given. To find the
lap of the valve, the throw of the eccentric, and its position
relative to the center line of the crank.
Draw AB (Fig. 71) to represent the greatest amount that the
FIG. 7?.
port is to be opened and lay off AC equal to the given lead.
Draw CD to represent the crankangle at cutoff. A perpen
dicular to CD at C and a perpendicular to AB at A will both
be tangent to the unknown lap circle. The bisectrix, GJ, of the
angle EGF so formed is the locus of the point M.
Lay off GU equal to AB and erect the indefinite perpen
dicular HKL Prolong the bisectrix JG till it intersects HI at
some point K. In the completed but unknown figure we see
that the radius PM (equal to the unknown diameter, MC, of the
valve circle) is to GU as MK is to GK. Join C and K. With G
as a center and GU (equal to AB the maximum port opening)
r.s a radius draw the arc UL. Join G and L. Draw CM parallel
100 THE STEAM ENGINE AND OTHER HEATMOTORS.
to GL and intersecting the bisectrix GJ at M. The triangles
LKG and CKM are similar and therefore MK:GK::CM:LG.
It therefore follows, since three terms of this proportion are the
same as three terms of the preceding proportion, that the fourth
terms are equal, viz., that PM = CM.
FIG. 71.
The diameter of the valve circle having been found the re
maining points are easily found.
Problem. Given ratio connectingrod to crank = 5; steam lap
1/2", exhaust lap 1/8", and steam lead 1/16" (all on headend);
width of steamports 1/2", throw of eccentric 1J"; steampressure
40 pounds per gage, back pressure 2 pounds above atmosphere,
VALVEDIAGRAMS AND SLIDEVALVES. 101
clearance 10%. Draw the theoretical indicatorcard for the
head end of the cylinder and sketch the valve when the piston
is at the beginning of its stroke and again when the valve is in
its extreme position to the right.
Solution. Draw the indefinite straight line XOY. From any
point lay off OG = steam lap, and GF = the steam lead on head
<end; erect indefinite perpendicular FH, with as a center and a
radius = the given throw of the eccentric describe an arc cutting
FH at H] draw OH, it will be the diameter of the valvecircle and
HOT will be the angular advance; with a radius OG describe the
lap circle EGI] with a radius = the given exhaust lap describe the
arc RSj with a radius OJ7 = lap + the width of port describe the
arc UWV, then WH will be the overtravel.
With a center at and a radius equal to the crank radius
to some convenient scale, describe the crankcircle XBY; with a
radius five times as great, describe the arc of the connectingrod
CiXC>2. Draw the various crank positions, as OB, and find the
corresponding piston positions such as B f by laying off BCi
from X.
Project XY on any parallel line below the diagram and obtain
X'Y , the length of the card; lay off X'Z to obtain the line of no
volume or clearance line. Lay off the absolute pressures 40 + 15
pounds and 15+2 pounds and obtain the steam admission and
backpressure lines Z'B" and C"S. Project B' Co Z>" and draw the
isothermal expansion curve B"T> n ' project (7, the position of the
piston when the exhaust closes, and obtain 6~' and draw the isother
mal curve of compression C"C m '. Find the points of steam
admission and exhaustopening and sketch in the expected
curves.
On a parallel line lay of 12=.*team lead; 13= width of
port; 26= the width of valve = steam and exhaust lap + width
of port.
To draw the valve in its extreme righthand position lay off
34 = the overtravel and then 47 is the width already found. It is
evident that 79 ought to be at least as wide as the other port which
is exhausting through 79. If the valve is thrown into its extreme
102 THE STEAMENGINE AND OTHER HEATMOTORS.
FIG. 72.
VALVEDIAGRAMS AND SLIDEVALVES. 103
lefthand position it should go about an eighth of an inch beyond
8. This prevents the formation of a ridge at that point.
Ex. 30. If the data given in the above problem had been for the
crank end, draw the indicatorcard.
Ex. 31. Assume the indicatorcard found in Ex. 30 for the head
end and draw the crank end of the valve.
Ex. 32. Suppose that the eccentric in Ex. 30 was insecurely fast
ened and slips backwards (or ahead) some 30, draw the card.
What is the effect on steam admission and cutoff, exhaustopening
and compression?
Ex. 33. Diminish the throw of the eccentric J" in Ex. 30, and
also increase the angular advance 30 5 . Draw the card.
Ex. 34. Draw the indicatorcard for the crank end of Ex. 29 if
the valvestem is made J" too long.
There is another form of the Zeuner diagram that is frequently
seen. In this form, instead of using a negative angular advance,
a negative rotation of the crank is used. To illustrate this, lay
off the diameter of the valvecircle of Fig. 68 to the right of OD
a degrees and construct the diagram. To find how far the valve
has moved from its midposition when the real crank has moved
through an angle 6 clockwise from a deadcenter OB, make use
of an imaginary crank rotating the same angle anticlockwise from
the headcenter position OC. To find the piston positions make
use of an imaginary connectingrod that is swung from the right
if the real one is on the left. Finally, when the indicator card is
found it will apparently be for the right side of the piston, when,
of course, it belongs on the other side. The methods may be
characterized as rights and lefts, and either may be gotten from
the other by looking through the paper at the diagram instead
of directly.
Bilgram Diagram. The Zeuner diagram cannot be accurately
constructed with certain data owing to the necessity of finding the
intersection of lines that meet at a small angle. For instance if
the position of the crank when the steam is cut off, the amount of
lead, and the maximum portopening are the data, the construction
of the Zeuner diagram is complex and accuracy is difficult to
104 THE STEAMENGINE AND OTHER HEATMOTORS
attain. There are several more recently devised methods that
are better than the Zeuner in some respects. We shall prove the
construction of the Bilgram diagram.
FIG. 73.
With any point as a center and a radius equal to the throw of
the eccentric describe the circle BFC. This circle is often used for
the crankcircle since the scale of that circle is arbitrary. If the
real engine is revolving clockwise from a deadcenter position OB,
lay off from the opposite center, 0(7, the angular advance, a, as
shown and thus obtain the fixed point P. As in the Zeuner,
nothing is to move but the crank. Further we must imagine that
the crank has thickness and we must distinguish between the side
marked R and the side marked L.
The Bilgram diagram depends upon the fact that the perpen
dicular let fall from the point P (found as above) on any crank
position, OF (prolonged when necessary), = the distance that the
valve is from its midposition. Call all of one side of FG by the
letter R and the other side by L. If the perpendicular is dropped
on the side marked R, the valve is on the right of its mid
position; if it is dropped on the L side, the valve is on the left
of its midposition.
Let the crank move through any angle, 6, from its deadcenter
position to some position OF. Drop the perpendicular PH on
OF (prolonged if necessary). From the diagram we see that
PH = r sin (a + 6), which we know is the amount that the valve
has moved from its midposition.
VALVEDIAGRAMS AND SLIDEVALVES. 105
As the portopening = the distance that the valve has moved
from its midposition minus the lap, it is evident that, if with P
as a center and radii equal to the steam and exhaust laps we
describe the circles Pe and Pi, we may automatically subtract the
lap and obtain the portopening.
As the crank rotates from the position OF to 01 the distance
PH increases and is a maximum in position 01, which is perpen
dicular to OP.
The portopening decreases to position 02, where cutoff takes
place, as the valve is evidently (in this construction) moving to the
left and is only the amount of the steam lap from midposition.
At OP the length of the perpendicular has reduced to zero and
the valve is no distance from midposition, i.e., is at midposition.
The perpendicular now falls on the L side J)f Ihe crank and
increases in length, showing that the valve is moving to the left
from its midposition. Opposite 01 or at 08 the valve is furthest
to the left and therefore the right or crank end port is widest open.
The perpendicular is now becoming shorter, showing that the
valve is returning to midposition, which it reaches in a crank posi
tion opposite OP or at OQ.
Further rotation causes the perpendicular to fall on the R side
of the crank, showing that the valve is moving to the right from
its midposition, and when it moves the amount of the lap the crank
is in position 04, in the prolongation of the tangent to the lap
circle position 03, and the valve is about to open the port.
Further rotation brings the crank to the deadcenter OB and
the diagram shows the port open the amount of the steam lead mn.
The locus of the point H is a circle drawn on OP as a diameter.
By referring to Fig. 59 it will be seen, if the valve has no exhaust
lap, that exhaustopening takes place for the head end when the
valve attains midposition in its motion towards the left and the
exhaust closes again in the midposition of the valve on its return
to the right. In Fig. 73 when there is no exhaust lap, exhaust
opening takes place for the head end in crank position OP and
exhaustclosure in position OQ.
The effect of giving positive exhaust lap is to delay the opening
and hasten the closure of the port as compared to the effect of
no lap. Hence, if there is positive exhaust lap, Pe, exhaust
106
THE STEAMENGINE AND OTHER HEATMOTORS
opening will take place in crank position 05, whilst exhaustclosure
will take place at 06, which is ahead of OQ, where compression
wo^ld have commenced if there had been no exhaust lap.
These effects must be reversed if the exhaust lap, Pe, is negative
instead of positive. In that case opening would take place at
09 and closure at 07.
Piston positions must be determined as in the Zeuner diagram
by the use of arcs having the length of the connectingrod as a
radius.
To obtain the effects on the crank end, the point Q, opposite
P, must be used as the center of the lap circles since the angular
advance and throw of the eccentric are fixed quantities. The laps
and leads may be the same or different from those on the head
end. The effect of changes can only be determined by finding
first the crank position of important events and then determining
the corresponding piston positions. If the laps are the same on
head and crank ends, the piston positions of steam admission and
FIG. 74.
cutoff, exhaust opening and closing, will be different at the two
ends.
An examination of the fundamental principles of all forms of
slidevalve diagrams will show that they depend on laying off
the angular advance on one side or the other of either a vertical
or a horizontal line and the measurement of a perpendicular.
VALVEDIAGRAMS AND SLIDEVALVES. 107
Geometrical Relations. The construction of the diagram from
data to find other quantities requires a comprehension of the
geometrical relations that exist between principal lines in the
complete figure.
The radius of the circle KPM is always the throw of the eccen
tric, mn is the amount of the steam lead (Fig. 74).
The angle POC is always the angular advance laid off with an
opposite rotation from the deadcenter opposite that of the real
crank.
The lead line KM, steam cutoff line 02, steam admission line
04 prolonged, and a line ad drawn parallel to any crank position
Ob at a required amount of portopening ab for that crank position
are all tangent to the steamlap circle. The locus of the center of
the lap circle must be the bisectrix of the angle between any two
such tangents. The intersection of any two such loci gives the
required center P. A similar series of tangents may be drawn
to the exhaustlap circles.
Ex. 35. Apply the Bilgram diagram to the solution of Exs. 25 to
29.
Ex. 36. Stroke is 2', steam cutoff at 20" from the beginning of the
stroke, steam lead J", valve is to be open f " when crank has made
an angle of 30 from the beginning of its stroke.
Ex. 37. Stroke is 3', steam lead is J" ', steam cutoff at 24", ex
haust opens 15 before the beginning of the returnstroke and closes
30 before the end of the returnstroke; find the angle of advance,
throw of the eccentric, and inside and outside laps.
Ex. 38. Stroke is 2', steam is cut off at f stroke, maximum port
opening is 1"; find the throw of the eccentric, angle of advance, and
the outside lap.
Problem. Draw the crosssection of a plain slidevalve to
comply with the following conditions: Width of ports 1/2";
overtravel on the head end 1/4"; cutoff on both head and crank
ends 3/4 stroke; stroke 18"; steam admission commences on
head end when the piston is 1/4" from the end of its stroke ;
exhaust opens at 9/10 stroke on both ends; ratio of connecting
rod to crank = 5; initial steampressure 60 pounds absolute; back
pressure 15 pounds absolute; clearance on each end 10%. Assume
thickness of cylinder parts as 3/4".
108 THE STEAMENGINE AND OTHER HEATMOTORS
Construction (Figs. 75, 76). Lay off the stroke XY on
a scale 2" = !'; draw crankcircle X2Y', lay off connectingrod arc
FIG. 75.
CiXC2', lay off cutoff points B and E' and find crank positions
02 and 02'; lay off XA = l/4" and obtain 04 crank position at
steam admission and prolong, thus obtain 03, a tangent to the
FIG. 76.
lap circle, head end; the maximum portopening, head end, being
given, layoff arc SS' with a radius = 3/4"= width of port + over
travel. Three conditions for the lap circle being given, ordinarily
VALVEDIAGRAMS AND SLIDEVALVES.
109*
the circle is easily drawn. In this case the locus of the center is
on OP, the bisectrix of the angle 203, and it is not difficult, practi
cally, to obtain the center P so that a circle can be drawn tangent
to 02, 03, and the arc SS'. The exhaustopening at C gives crank
position 09, and as this precedes OP the exhaust lap Pe on the
head .end is negative. For the crank end, the throw of the eccentric
and the angular advance (since there is only one eccentric) are
fixed and, therefore, the position of P' is determined. With a
center at P f draw a circle tangent to 02', this gives the steam
FIG. 77.
lap. Find the crank position corresponding to exhaustopening
at C' and draw the crank position 09' at exhaustopening. As
this position follows position OP' the exhaust lap on crank end is
positive. The leads and portopenings differ considerable from
those on the head end.
Dimensions of Steamports and Pipes. It is easy to determine
the area of a steamport if you have enough experience to determine
what lineal velocity the steam may have in any particular case
without too much loss of pressure. The roughness of castings
does not vary much with their size, but its influence on the veloc
ity of steam in a passageway 1/8" wide is enormous when com
pared to its effects in a passageway 4 7/ wide. "TEe~aIIowaBle"^team
110 THE STEAMENGINE AND OTHER HEATMOTORS.
velocity will vary then with the size of the ports, their roughness,
their length, and their freedom from sharp bends. We must
distinguish between maximum portopening (when it is less
than the width of the port), width of the port in the valveseat, and
the width of the passageway for steam below the valveseat.
* Formerly when engines cut off at 5/8 stroke, a lineal steam
velocity of 100' per second ( = 72,000" per minute) was allowed.
Nowadays 150' to 500' per second is allowed in obtaining the
maximum portopening with ordinary or usual cutoff in highspeed
engines; the width of the port at the valveseat is determined
by allowing 125' to 150' per second, whilst the passageway, if used
by the exhauststeam on its return, is designed on an allowance
of 125' per second.
The effects of size, roughness, cutoff, and variable piston ve
locity are all merged in the choice of the velocity factor. Then
the volume swept through by the piston in cubic inches per
minute divided by the factor expressed in inches per minute =
area of the port in square inches.
Let a = area of steamport, or maximum portopening, or area
of the steampassageway;
A = area of the piston in square inches ;
L = stroke in inches;
N = number of strokes;
F = 72,000", 90,000", 108,000", or 144,000" per minute;
ALN
'1^
In the case of highspeed engines with shaftgovernors the student
will note that shorter cutoff is obtained by automatically diminish
ing the travel of the valve. As a result the maximum port
opening at the economical cutoff (j or ^ stroke) is so small that
the factor F in many cases exceeds 360,003 inches per minute.
This portopening is often only one and a half to twice the
steam lead.
A crosssection at right angles to the one shown in Fig. 59
should demonstrate that the exhauststeam will not be choked in
its exit from the cylinder. Hence the design of a cylinder should
* For a full discussion, see Trans. A. S. Naval Engrs., Vol. XVI, No. 2.
VALVEDIAGRAMS AND SLIDEVALVES. Ill
be examined to see that ample area for the passage of both live
and exhaust steam into and out of the cylinder has been provided.
The height, h, under the valve (Fig. 77) should be at least equal
to the width of the port; a curve should be made as at c to pre
vent the formation of eddycurrents that would be formed with
a rightangled corner. When the piston passes a deadcenter,
the valve will lift if much water gets into the cylinder; hence,
to prevent the bending of the valvestem its connection to
the valve must be a sliding fit to permit the latter to lift off
its seat. The trouble has been merely indicated to allow the stu
dent to provide suitable remedies. Steam and exhaustpipes
should not be screwed into the castings, as the castiron thread
is very weak and the movement of the pipes, generally having
long leverarms, soon causes leaks that cannot be stopped. Pro
vision should be made in the design for flange connections.
PRACTICAL CONSIDERATIONS.
Lead. The thickness of a penknife blade is enough lead for
an engine up to 12 inches diameter of cylinder, 1/16" to 1/8" for
cylinders up to 21 inches in diameter, 1/8" to 1/4" for cylinders up
to 30 inches diameter; in large engines it often amounts to 1/2
inch or more. In some highspeed engines where the compres
sion is very high, the lead is much reduced or made negative.
Width of Port. In the steamengine, heat is transformed into
work at a comparatively low efficiency and, therefore, it does not
pay practically to convert any of that work back into heat. It is
desirable that the steampressure on the piston should be as near
boiler pressure as possible. In very small engines the friction of
the walls is a much more important factor than it is in large
engines. For example, let L be the length of a steamport and B
its width in the case of a small engine and 8L and SB similar
dimensions in a large engine. Then
Perimeter _ 2 (L + B) 16(L + ff)
Area LB 64L
in the two cases, showing that, in so far as friction is influenced
by skinfriction, the small cylinder has eight times the friction
112 THE STEAMENGINE AND OTHER HEATMOTORS.
that the larger one has. The velocity usually allowed is 6000
feet per minute. This is too high for cylinders of 6 or 8 inches
in diameter and is too small for cylinder diameters of 40 inches and
upwards. In highspeed engines, whilst the port may be designed
for 6000 feet velocity, it will be found that, in most cases, the port
is not fully opened by the valve when the engine is at normal
speed. In other words, at less than normal load the port opening
is considerably less than the width of the port. As far as the
valve motion is concerned, it is desirable to have a small port
area, as valve friction and all valve dimensions may be diminished.
In some cases the crosssectional area of the steampassage is
increased just under the valveseat. This increases the clearance
volume and economy requires the clearance to be reduced to
a minimum. As the area of the port is desired in square
inches we may take the linear velocity as 72,000 inches; then
72,000 X area of port in square inches = the volume swept through
by the piston in cubic inches per minute.
It is to be distinctly understood that the assumed velocity is
a rate and that it is not influenced by the cutoff or the unequal
piston velocities at different parts of the stroke. As the velocity
rate is determined empirically, it is better to merge all small
variations in that factor. The area found above is the area of
each port and not the sum of the two ports; the cubic inches
swept through by the piston is
where r = radius of piston in inches;
1 = stroke of piston in inches;
s = number of strokes.
Thickness of Cylinders. The thickness of cylinder walls is
governed by the necessity of providing sufficient passageways for
the metal in casting and of securing sufficient rigidity in the
casting at all times but especially during boring. It is of the utmost
importance on account of internal shrinkage stresses that all
parts of the casting be of uniform thickness whether demanded
by strength or not, and that all parts making angles approximately
at right angles with each other should be well filleted.
VALVEDIAGRAMS AND SLIDEVALVES. 113
The following are given as approximations :
t = Q.QQ3DVj> for small cylinders
= 0.03v / Dp for medium and large cylinders;
D = diameter of bore of cylinder ;
p = maximum pressure in pounds per square inch.
Thickness of the Bridge between the Steam and Exhaustport.
In general the bridge should be the same thickness as the rest of
the cylinder casting, but in every cass it is necessary to put the
valve at the end of its motion in each direction to see that the
outside edge of the valve does not go beyond the bridge and open
a direct communication between the steam and exhaustpassages.
This, of course, can occur only in valves having overtravel. There
should be at least 1/8 to 1/4 inch seal between the steam and
exhaust space under the valve at all times.
Width of the Exhaustport. Put the valve at the end of its
travel, then the inside edge of the exhaust lap for one port should
not contract the passage of the exhaust from the other steam port.
Slidevalve Problems. The following are all the elements that
enter into slidevalve problems.
(1) Angle of advance.
(2) Throw of eccentric.
Length of connectingrod L
Crank radius ~R'
Crank End. Head End.
(4) Inside lap. (4) Inside lap.
(5) Outside lap. (5) Outside lap.
(6) Amount of steam lead. (6) Amount of steam lead.
(7) Amount of exhaust lead. (7) Amount of exhaust lead.
(8) Portopening, or width (8) Port  opening, or width
of port and overtravel of port and overtravel
(+or). (for).
The crankangle or piston The crankangle or piston
position of: position of:
(9) Steam admission. (9) Steam admission.
(10) Steam cutoff. (10) Steam cutoff.
(11) Exhaustopening. (11) Exhaustopening.
(12) Exhaustclosure. (12) Exhaustclosure.
(3) must always be given. (1) and (2) are always the same
for both ends. If four elements of one end and two of the other
114
THE STEAMENGINE AND OTHER HEATMOTORS.
are given a complete solution is generally possible. Care must be
taken that there is no conflict between the four e laments chosen.
Valve Ellipse. Use is sometimes made of diagrams that
represent graphically the relative and actual velocities of travel
of the piston and of the valve. Divide the path of the crankpin
ABC into any number of equal parts and, by the use of the
connectingrod, find the corresponding piston positions. At the
points so found, lay off an ordinate that represents the amount
that the valve is from its midposition at that time. These ordi
nates are readily obtained from the crank positions on the Zeuner
or Bilgram diagrams when there are no intermediate linkages.
FIG. 78.
If any such exist, as in the Corliss engine, the actual position must
be plotted graphically. (Fig. 78.)
Lay off 54 = outside lap;
43 = steam lead;
41 = the maximum port opening;
12 = the overtravel;
24 = exhaustport;
56 = the inside lap;
67 = the exhaustport opening;
78= exhaust overtravel.
VALVEDIAGRAMS AND SLIDEVALVES 115
Then a6 = the period of steam admission;
bd = the period of steam expansion;
cd = the period of prerelease;
ef period of compression.
A rapid variation in the length of successive ordinates indicates
rapid movement of the valve. It is desirable that a valve should
open and close with the maximum possible rapidity and be prac
tically motionless during the time that the valve is either wide
open or closed, especially if there is heavy pressure on the back of
the valve during such periods.
Steampipe.* When steam flows through a pipe we must con
sider not only the properties of the steam but also that of the pipe
and the influence of the surroundings or environment of the pipe.
(1) We must consider the difference of pressure between two
points on the pipe line, the quality of the steam, its volume and
pressure.
(2) The length and diameter of the pipe, the number and
character of elbows and bends, the number and kind of valves,
and the condition of the interior surface of the pipe influence the
loss by friction.
(3) The covering of the pipe, whether it is in the air or under
ground, the character of the ground whether wet or dry, the ex
posure to winds, the position of the pipe and its drainage, influence
condensation losses.
The heat losses, indicated above, manifest themselves in a loss of
pressure and in the formation of water from the condensation of
steam. The heat losses or changes may be divided into four
divisions: (1) those caused by friction, (2) condensation, (3)
expansion, (4) gravity.
Let E a = initial energy at any crosssection of the pipe;
E b = the energy at another section of the pipe;
Ef = loss of energy due to friction;
E c = " " " condensation;
E e = " " " expansion;
E g = " " " gravitation;
* For data on the flow of superheated steam in pipes see Foster in the Trans
actions of A. S. M. E., Vol. 28.
116 THE STEAMENGINE AND OTHER HEATMOTORS.
If W pounds are raised h feet the footpounds of work required
v 2
will be Wh. If h be expressed in terms of velocity we have h = and
therefore Wh = W^. If a cubic foot of water weighs
W pounds and the crosssection of a pipe is one
square foot, then to raise the waterlevel one foot
at h feet high would require approximately a pressure
of Wh pounds exerted through one foot or Wh foot
pounds. If the waterlevel is lowered one foot, the
water at C can exert Wh footpounds due to its energy.
This is true only on the supposition that the tube is
frictionless. Hence, in practice, the issuing velocity is
less than that due to a head hi. This new head hu is
the head that would be required in a frictionless
pipe to produce the actual velocity. The difference
hihii=h f is then a friction head. Another way of FIG. 79.
expressing the same is as follows. The friction is
proportional to v 2 (the velocity squared). By making it a pro
v 2
portional part of ~ we may also express it as a proportional
part of the head that produces the velocity. The friction is
directly proportional to the wetted surface nDL and is inversely
proportional to the crosssectional area or r~, or, combining
/
these two, is proportional to ^^ == ~/v or ^ e * oss ^ head
4
9 A T VAT
friction is/ o~~n" = ^/J hence the work of friction Wh f =Wf^jr.
*/ O
If we consider a welllagged horizontal pipe, E c and E g may
be neglected and E t may be disregarded, as it represents change
of the form of energy rather than its loss. Hence for this case
v 2 L
we have E a E b =E f ^Whf = W'f 2^, where v is velocity in
feet per second, L is the length and D is the diameter of the pipe in
feet. Now, as a rule, we want to find the loss of pressure in pounds
per square inch due to fractional losses. It requires a difference
of pressure to produce a given velocity in a frictionless pipe, and
VALVEDIAGRAMS AND SLIDEVALVES. 117
considering friction, there would have to be a greater difference
to produce the same velocity.
If we took a column of the gas under consideration h f feet high
and one square foot crosssection its volume would be h f cubic
feet, and if it weighed d pounds per cubic foot its total weight
would be hfd and the pressure per square inch would be
f . .
TT =pf pounds per square inch.
144
p,144 f v 2 2_ T . . . . .
~T~ =/ 7 D L * Unwm glves / = ^( X + T )>
where K is a constant and D is the diameter in feet.
We have therefore
3 \v 2 2L
If W = weight of steam delivered per minute and v is its velocity
der second,
_TF1_ 1 W
~ 60 d xD 2
3 \1 W 2 2L
and if D be changed to d inches,
W 2 L
dd 5 20.664'
The following experimental determinations of K have been
made:
K = 0.0027 for steam, Carpenter;
0.0028 for air, St. Gothard Tunnel Experiments;
0.005 for air, Arson;
0.005 for water, Unwin.
Substituting the value, K= 0.0027 for steam the loss of pres
sure is
118 THE STEAMENGINE AND OTHER HEATMOTORS.
Hence
p/= 0.000131
W
3.6\TF 2 L
dd 5 '
The value 0.0027 was determined by Carpenter on pipes 1, 1J,
2, 3, and 5 inches in diameter and of 90 to 230 feet in length.
Table XIV was calculated by E. C. Sickles from the above
formula, using 0.0026 as the constant. To use the table look in
the left half section of the table under the heading " Discharge
in pounds per minute" for the discharge nearest to the given
discharge. Then, on the same horizontal line in the right half
section under the heading " Drop in pressure in pounds, etc.,"
in the column under the given pressure will be found the drop in
a straight pipe 1000 feet long. The heading of the column con
taining the nearest discharge gives the pipe diameter.
For shorter pipes containing elbows and valves, corrections
have to be made. In addition, on account of the eddies formed
at the mouth of a steampipe when it enters squarely into the
steam space, a correction called the " friction of entrance" has
to be made. Complex formulas have been devised for these
corrections, but they are practically useless. It is customary to
add (to the actual length of straight pipe) lengths whose friction
would be equivalent to the friction of the piece in question.
FRICTION OF ELBOWS, VALVES, ETC.
Friction of
Equivalent Straight Pipe.
Entrance
60 diameters
Globe valves
60 diameters
90 elbows
40 diameters
Gate valves
No friction
A compound engine of 300 I.H.P. uses 18 pounds of water
per I.H.P. Initial pressure is 135 pounds gage. The steam
pipe will contain two globe valves and two elbows and 90 feet
of straight pipe. What will be the size of the steampipe and
the probable drop of pressure in a welllagged pipe?
VALVEDIAGRAMS AND SLIDEVALVES.
qrjA y i o
TJQ = 90 pounds of water per minute. From Table XIV
a 4inch pipe will supply 97 pounds of water per minute with a
drop of 6.83 pounds, at 150 pounds absolute pressure, in a 1000
feet of straight pipe. The given pipe is equivalent to
Straight pipe ............................ 90 feet
Entrance = 60X I 4 2 .................... 20 "
Elbows = 2X40X'& ................ 27 "
Globe valves= 2x60Xi 4 2 ................ 40 "
177 "
177
The drop in pressure will therefore be X 6.83 = 1.2 pounds
per square inch.
The curves below are illuminating in that they show at a
glance the rapid drop of pressure when steam travels at high
velocity through small pipes. The curves are practically
derived from the formula given above. They are calculated for
100 pounds absolute and 100 feet of pipe length and may safely
be used up to 12,000 feet velocity and a drop of 10 pounds
pressure. Within the above limits values taken from the figure
may be used for other lengths and densities by multiplying the
result taken from the figure by the given pipe length and given
steam density and dividing the product so obtained by 22.71
which is 100 times the density of steam at 100 pounds
pressure.*
Equation of Pipes of Equivalent Carrying Capacity. While
the crosssectional areas of pipes are proportional to the square
of their diameters, their carrying capacity is not so proportioned
as friction will make a very considerable difference when there
is a large ratio between the diameter of the pipes compared.
Let W\ be the weight of fluid discharged by a pipe whose
diameter is d\ and W 2 be the weight discharged by a pipe of
diameter d 2 . Then if R is the ratio of the weights discharged
* See Gebhardt, Power, 1907.
120 THE STEAMENGINE AND OTHER HEATMOTORS.
by the two pipes of equal lengths and discharging the same
fluid we shall have
10

10"
tt
14*
16"
9000 4000 6000 8000 10000 12000 14000 16000 18000
Mean VelocityEeet per Minute
FIG. 80. Friction Head in Steampipes.
From the formula we see that 43 twoinch pipes are required
to equal the carrying capacity of one eightinch pipe.
VALVEDIAGRAMS AND SLIDEVALVES. 121
Ex. 39. How many pounds of steam initial pressure, 125 pounds
gage, will be delivered per minute from a 6" pipe, 1000' long, with a
pressure drop of 16.4 pounds?
Ex. 396. What will be the loss in pressure of a pipe 6" in diam
eter, 150' long, containing 4 elbows ani 2 globe valves (wide open),
if the steam velocity is 8000' per minute. Initial pressure at the
boiler, 125 pounds gage.
Ex. 40. Find the size of the steampipe and of the steam and ex
haustports of a Corliss engine. Assume length of port = diam. of
cylinder. Stroke = 3 diameters, I.H.P. = 45, initial pressure, 75 Ibs.
gage; noncondensing; cutoff \ stroke; revs. 94.
Ex. 41. Engine 12"X12", 300 revs., I.H.P. = 100 at 100 Ibs. ini
tial pressure, and J cutoff, back pressure 16 pounds absolute. Design
a valve to cut off at f stroke, head end, with an overtravel = J width
of port. Assume exhaust lap = 0. Assume length of port = 0.8 the
diam. of cyl.
Ex. 42. Design the valve for the L.P. cylinder of a tripleexpan
sion engine. Diam. cylinder is 72", stroke 5', revs. 75, cutoff at 0.7
stroke, steamlead angle 15, exhaust opens at 0.9 stroke, length of
connectingrod 15'.
122 THE STEAMENGINE AND OTHER HEATMOTORS.
01 per cent of Ideal.
40.0 Horse Power
WTbs.Boi1er Press.
90 per cent of i'dcal.
C2.4 Horse Power
KlbaBoiler Press.
64 per cent of iden'
15 Horse Power
FIG. 81. Loss by Cylindercondensation.
^ i
FIG. 82. Typical AdmissionLines.
(From Carpenter's " Experimental Engineering.")
VALVEDIAGRAMS AND SLIDEVALVES. 123
Bottom of cyflnder
Steam side.
Vacuum side.
FIG. 83. Unsymmetrical Valvesetting.
FIG. 84. Variation of Load.
(From Carpenter's "Experimental Engineering.")
124
THE STEAMENGINE AND OTHER HEATMOTORS.
FIG. 85.
FIG. 86.
c
Fio. 88.
VALVEDIAGRAMS AND SLIDEVALVES.
High_Pressure Cylinder 12 x 20
175 Rev.per Minute
125
FIG. 89.
Low Pressure Cylinder 14 x 20
FIG. 90.
Before the trouble was located
FIG. 91.
After the trouble was located
FIG. 92.
QUESTION. What caused the defects in indicator diagrams, Figs. 89 and 91?
CHAPTER V.
MEASURING THE EFFECTS OF HEAT.
THE sensations produced by heat and its effects on bodies are
matters of common experience. The hand held near the fire
experiences a sensation that we say is produced by heat. The
best conception of heat, however, is obtained by accurately measur
ing its effects. Under its influen3e solids increase in temperature,
i.e. grow hot, usually increase in volume, diminish in strength and
change many other physical characteristics such as the power of
conducting heat and electricity; liquids rise in temperature, change
many of their physical and chemical properties, and finally evapo
rate.
In heating bodies the rise of temperature does not continue
indefinitely but ceases for solids when they commence melting
and for liquids when they commence boiling. When solids are
heated, the increasing rapidity of vibration of the molecules is
shown by the increasing temperature; the length of the path is
very slightly altered, as is shown by the very slight change in
volume. At the meltingpoint, the rapidity of vibration is so great
that the molecular attraction is at the point of being overcome and
any further addition of heat cannot increase the rate of vibration,
as the molecular attraction cannot oppose the increased stress;
consequently the temperature remains constant and all the heat
is spent in disgregation work. The energy of vibration is kinetic;
the heat producing change of state or disgregation work is then
stored up as potential energy. Similarly when liquids are at the
boilingpoint, all the heat added is spent in overcoming the molecular
attraction, giving increased amplitude to the molecular paths and
performing the external work inseparable with increasing volume.
Hence as in the case of melting solids, this heat is stored up and
126
MEASURING THE EFFECTS OF HEAT. 127
is potential energy. It is called latent heat or concealed heat,
since it is not indicated by a thermometer.
All bodies at any temperature above absolute zero possess heat.
This means, in accordance to the modern theory, that their mole
cules are in a state of vibration more or less rapid, depending
upon the temperature of the body.
In solids the mutual attraction of the molecules generally limits
all movements to fixed paths. Hence, in general, solids retain their
form and mass at ordinary temperatures. An exception must be
made in the case of such solids as musk, camphor, arsenic, and ice,
which may evaporate at ordinary temperatures.
In liquids the motions of the molecules have been compared
to that of dancers in the Virginia reel. Their motion is vibratory,
rotatory, and progressive. The molecules revolve around one
another, pick up a new partner as the old one is released, and
revolve about the new one in turn. This free motion allows the
liquid to assume a plane upper surface and the form of the
vessel.
No gas is absolutely perfect, but dry air, oxygen, nitrogen and
hydrogen, at ordinary atmospheric temperature and pressure, are
so far ABOVE the temperature at which their liquids boil that they
act like perfect gases. Substances that are liquid at ordinary
temperatures are converted by heat into vapors or imperfect
gases. Steam, for instance, is an imperfect gas. By superheat
ing, however, a stage is reached where it practically follows
the law of perfect gases.
Liquids may be converted into the gaseous condition in two
ways that are often confused but which are really very different
from one another. Any liquid if left exposed to the atmosphere
will finally evaporate. Clothes will dry in freezing weather.
This evaporation will occur at any temperature, although usually
there is a lower limit. For mercury, for instance, this is 14 F.
Let us consider the evaporation of the water from a pan in
the open air. Rapidity of evaporation will be secured
1. By increasing the evaporating surface, putting the
water in two pans;
2. Changing the air frequently over the pan, by fanning
the air;
128 THE STEAMENGINE AND OTHER HEATMOTORS.
3. Performing the experiment on a dry day rather than on
a wet one;
4. By heating, but riot necessarily boiling, the water.
The truth of the above may be demonstrated by experiment.
To perceive why they are true we must keep in mind the motion
of the molecules in a liquid as described above. In its vibratory,
rotary, and progressive motion, at intervals, at the surface all
of these movements, at the same instant, may be in one direction
only. If that total motion in one direction takes the molecule
out of the liquid with sufficient energy, it may move out into the
air instead of falling back into the liquid. The gradual loss of
molecules from the surface in this manner is evaporation.
At the same temperature and pressure, dry air is heavier than
moist air (see Table VI), hence the water molecule tends to rise
till the temperature or the pressure or both are lowered, when
equilibrium will be established. The hotter and drier the air
the more rapid the evaporation. Usually this process is very
The usual commercial method of forming steam by boiling is
a very different process, governed by very different laws. Unfor
tunately for clearness, the term evaporation is also generally used
for this process. In this, operation steam is not slowly formed
at the surface of the liquid, but there is a rapid formation of steam
bubbles on the heating surface and therefore in the mass of the
liquid itself.
Consider for a moment the conditions that must exist on the
inside of one of these little bubbles. It is evident that the mole
cules of steam must impinge on the waterenvelope of the bubble
with sufficient energy to form a pressure that will keep the water
back. The intensity of this pressure must be equal to the intensity
of the steampressure on the surface of the water increased by
the weight of the column of water vertically above the bubble.
If the steampressure increases, it is evident that the temperature
of the steam inside the bubble will have to increase, since the
required vibratory energy is proportional to the temperature.
Consequently with each steampressure there is a corresponding
steamtemperature necessary for boiling.
In the power of increasing the length of the path of vibration
MEASURING THE EFFECTS OF HEAT. 129
gases differ essentially from liquids. Hence the volume of a gas
increases to completely fill an enlarging volume, whereas the
volume of a liquid remains practically constant under the same
circumstances.
In the gaseous state, the attraction of the molecules for one
another is extremely slight. The molecules are in incessant
motion in straight lines, striking one another and the containing
envelope, thus producing the pressure that they exert on the
enveloping vessel.
When they strike one another (if they do), they rebound
without loss of energy. We are much interested in what happens
when they strike the envelope.
1. If the latter is at the same temperature as the gas, it is
also in a state of vibration and the molecules will rebound with
out loss of energy.
2. If the envelope is cooler than the gas, some of the energy
of the molecule will be communicated to the envelope, which is,
probably, losing heat by radiation, and the molecule will rebound
with diminished energy.
3. If part of the envelope is movable and (as a result of all the
combined instantaneous impacts) motion ensues, the rebound will
be with diminished energy as part of the energy is consumed in
producing the motion against a resistance. When the molecules
rebound with diminished velocity it indicates a lowering of tem
perature, viz., a loss of heat.
It is of great importance to comprehend fully these effects as
they explain how steam loses heat in doing work against a mov
ing piston in a steamcylinder. Anything that tends to reduce
the sum total of molecular velocities means a loss of heat, viz.,
a lowering of temperature. If the piston moves and the tem
perature of the gas (and therefore the heat in the gas) is kept
constant, heat must be added (equal to the work clone) from some
external source of heat.
Heat cannot be expended without an equal quantity of en
ergy appearing in some other form. If the heat equivalent of
each elementary change is known, then the total heat expended
will be the sum of the heatequivalents. Every heatunit that
disappears as heat must be balanced by the production of some
130 THE STEAMENGINE AND OTHER HEATMOTORS.
change of equal thermal value. In the less complex cases less
Leat is required, the decrease being equal to the heatequivalent
of the changes that did not take place.
We saw above that when the molecules of a gas were allowed
to do work they rebounded from the surface that yielded to
their bombardment with less velocity than from an unyielding
surface whose molecules are vibrating in unison with the gas, i.e.,
possessing the same temperature. If a gas does external work,
it loses heat equivalent to the external work done. If work is
done on the gas ; then the gas gains heat equal to the external
work done on it.
It is important to keep in mind that the difference between
1. The total heat required to heat a substance from one
temperature, ti, to another temperature, t 2 , and
2. The increase cf the amount of heat in a substance
when heated from t\ to 1%
is always the external work.
Let us take the most complex case possible and itemize every
source of heatexpenditure. Heat a solid to the meltingpoint,
melt it, heat the resulting liquid to the boilingpoint, evaporate
it, and heat the vapor under ONE cf several sets of conditions.
The exceptions to the events as stated below are of little impor
tance to the student at present. These events are:
1. Temperature of solid rises.
l a . It expands against external pressure.
2. Temperature remains constant, but melting is taking
place.
2 . Expansion against external resistance.
3. Temperature of liquid rises.
3. Liquid expands against external resistance.
4. Temperature remains constant till all the liquid is evap
orated.
4 a . Change of volume against external resistance.
5. Temperature and pressure increase, the volume remain
ing constant;
or 5'. Temperature increases, pressure remaining constant;
5 </. Volume increases against constant external pressure;
or 5". Temperature increases;
MEASURING THE EFFECTS OF HEAT. 131
5o". Volume increases against varying pressure;
or 5'". Temperature constant, volume and pressure varying.
A careful examination of this apparently complex series of
events will demonstrate that they may all be grouped under
three heads, each of which is absolutely elementary in its nature.
Heat is expended to produce
(a) A rise of temperature: 1, 3, 5, or 5', 5" kinetic energy.
(6) A change of state: 2, 4 potential energy,
(c) External work : l fl , 2 a , 3a, 4 a , or 5a', 5 a ", 5'" mechan
ical energy.
The heat required to produce any one of these events is not
used to do two things. For example, when a substance is heated
a few degrees we see that there is not only a rise in tempera
ture, but also that the substance either expands or contracts.
What is meant by (a) is the heat that, theoretically, is required
to produce the rise of temperature alone.
When solids, liquids, or gases expand the external work is
equal to the product of the increase in volume in cubic feet mul
tiplied by the mean pressure (in pounds per square foot) (page 30)
that resisted the expansion. This product is footpounds of
work, and divided by 778 will give its equivalent in thermal units.
The expansion or contraction of a substance when heated
may always be measured without reference to any other heat
quantity. Hence the (c) events may always be found directly.
Then, when there is a combination of any one (a) or any one
(b) event with its corresponding (c) event, it is evident that, by
measuring the total heat required to produce the two simul
taneous events, the value of the (a) or the (&) event alone may
be found by subtracting the heat equivalent to the external
work or (c) event from the total measured heat.
Physicists, by careful measurements and determinations,
have found the heat necessary for the (a) and (6) events for one
pound (or unit weight) of most substances and tabulated the
results. By proper use of these tables we may calculate the
quantity of heat required in the most complex cases.
Specific Heat. Different amounts of heat are required to
raise equal weights of different substances through one degree
rise of temperature. If a body expands, some external work
132 THE STEAMENGINE AND OTHER HEATMOTORS.
is done equal in amount to the pressure per square foot that was
acting on the body multiplied by the change of volume in cubic
PdV
feet divided by 778, or ==$ . The change of volume of solids and
/ /o
liquids on being heated is so slight and the heat equivalent to
the resultant external work is so minute that it may be neglected.
Let h = total heat to raise 1 pound through 1F.;
s=heat required to raise the temperature alone = change
of intrinsic energy = change of heat as heat in the
body;
i = heat expended in overcoming the molecular attrac
tions = disgregation work = work done incident to
change of state;
e = external work due to change of volume under pressure;
h = s +i+e (B.T.U. per pound).
In the case of solids and liquids not only is e very small, but i
is practically zero except close to the meltingpoint of solids
and the boilingpoint of liquids. Hence, in engineering questions,
the heat required per pound per degree rise in temperature of
solids or liquids is that required to increase their sensible tempera
ture alone.
The amount of heat required to raise one pound of water
one degree Fahrenheit, called a British Thermal Unit, or B.T.U.,
is adopted as the unit, since, from experiment, we know that more
heat is required to increase the temperature of one pound of water
one degree than is required by one pound of any other substance
except hydrogen gas. See page 5.
The Specific Heat of Solids and Liquids (C) is that fraction of
a B.T.U. that is required to raise the temperature of one pound
of a substance in either of those states through one degree Fahren
heit. Hence to raise W pounds from ti to t 2 requires
W'C(t 2 ti) B.T.U.
Specific Heat of Gases. We must distinguish between perfect
and imperfect gases. Vapors are imperfect gases which on the
addition of heat become more perfect and eventually may be
made to act like perfect gases by the addition of sufficient heat.
There is no such thing as absolutely perfect gases, but the socalled
MEASURING THE EFFECTS OF HEAT. 133
permanent gases, dry air, hydrogen, nitrogen, oxygen, which at
ordinary temperatures and pressures are far removed from the
conditions required by their liquids, may be termed perfect
gases. Imperfect gases or vapors are not far removed from the
conditions of their liquid, but may reach that state by the recep
tion of a large quantity of heat.
In the case of perfect gases it is usual and practically correct
to assume that no energy (heat) is required to separate their
molecules. Theoretically the molecules, having mass, must have
the mutal attraction called gravitation. This force of attraction
must exist even if all other forces of mutual attraction are lost.
As a matter of fact, in the condensation of the socalled permanent
gases, use is made of this minute mutual attraction of the mole
cules. In the cases of imperfect gases, some heat is spent in over
coming molecular attraction. In the case of steam, for instance,
it is now recognized that its specific heat is variable, and many
scientists are now at work on the determination of the specific
heat of superheated steam at various temperatures and pressures.
Recent work in gasengines leads to the conclusion that the
specific heats of the gases used in those engines are not the same
at high pressures and temperatures as they are at low ones. As
no final conclusions have been reached, the student, in engineering
problems, may assume i = for all gases perfect and imperfect.
There still remains the other factor e = external work. If
solids and liquids are not allowed to expand when heated, the
pressure that is exerted is equal to that which would be necessary
to compress them back to the original volume had they been
allowed to expand freely. These pressures are enormous. On
the other hand, in the case of gases the increase of volume is
considerable if the gas ic allowed to expand, and it is also feasible
theoretically to prevent all expansion. Practically, of course, the
vessel does change volume with increase of temperature or pressure
or both, but the change is relatively so slight as to be negligible.
Specific Heat of Perfect Gases at Constant Volume. If a gas is not
allowed to expand, no external work is done since work is the
exertion of a pressure (against an equal resistance) through a
distance. If either factor (pressure or distance) is zero, the work
is zero. Mere increase of pressure, then, is not work. Hence if
134 THE STEAMENGINE AND OTHER HEATMQTORS
i and e are both zero, all the heat applied to the gas appears as
heat in the gas, or increase of intrinsic energy. Its sole effect
is to increase the rapidity of vibration of the molecules, and this
results in an increase of pressure on the containing vessel and an
increase of temperature as measured by a thermometer. Hence
The Specific Heat at Constant Volume, C v , of a perfect gas is
the fraction of a B.T.U. that is required to raise one pound of
the gas through one degree Fahrenheit, the volume of the gas
being kept constant.
Therefore, if W pounds of a perfect gas are heated from t]
to to F., the heat required would be
irc^fe ^ ) B.T.U.
Another variation of the general rule occurs when a gas is
heated and the pressure is kept constant. When one pound of
a gas at constant pressure is heated one degree, the heat equivalent
to the external work done is a fraction of a B.T.U. which may be
added to C v , thus obtaining a new coefficient, C p . It is evident
that the external work done by 10 pounds of gas heated 10 de
grees will be 100 times as great as that done by one pound of gas
heated one degree. The expenditure of heat for external work
varies with W(t 2 /i). Hence
The Specific Heat at Constant Pressure is that fraction of a
B.T.U. that is required to heat one pound of a gas one degree
Fahrenheit and do the external work if the gas is allowed to
expand against a constant resistance. To raise W pounds of gas
from ti to t 2 and do the external work that accompanies expansion
under constant pressure requires
W C p (t 2 ti) B.T.U. '
Ex. 43. In a nonconducting, nonheatabsorbing box are 30
pounds of water at 75 F. What will be the final mean temperature
if 5 pounds of lead at 50 C., 3 pounds of copper at 300 F., and 4
pounds of cast iron at 50 C. are thrown into the box? (Table I.)
Ex. 44. If \ pound of hydrogen is heated from 75 F. to 90 F.
under constant pressure, how many B.T.U. are required? If the
volume had been kept constant, how many B.T.U. would have been
required? How many footpounds of external work were done in
the first case?
MEASURING THE EFFECTS OF HEAT. 135
Ex. 45. It requires 73.2 B.T.U. to heat 3 pounds of a certain gas
from 60 F. to 160 F. under constant pressure, and 16571.4 foot
pounds of external work are done. What gas is it? What is the
increase of heat in the gas?
Ex. 46. Two pounds of dry air at 75 F. and 20 pounds per square
inch pressure are heated and cooled several times. At the end of the
operations, by plotting a curve of the variations of pressure, and vol
ume it is found that 77,800 footpounds of external work have been
done, and that the volume of the gas has been doubled and its tem
perature is 475 F. How many B.T.U. were expended, and what is
the increase of heat in the air?
Ex. 47. Two pounds of air under 20 pounds per square inch pres
sure and at a temperature of 200 F. are allowed to expand; heat is
added so that, notwithstanding the fact that the gas is expanding
and doing work, its temperature remains the same. If 100 B.T.U.
were added to the gas, find the number of footpounds of external
work that were done.
Heretofore we obtained our answers in thermal units by using
C p and C v . To obtain an answer in footpounds it was necessary
to multiply by 778. The answer may be obtained directly in foot
pounds by multiplying by the corresponding constants K p and K v
= 778C P and 778C V from Table I. The difference of these con
stants (KpKv) is a constant which will be called R.
Derivation of the Fundamental Formula, PV = WRT.
The truth of this formula is demonstrated by the correct results
obtained by its use.
Imagine a piston of any constant weight P resting on a perfect
gas weighing W pounds. Cool the gas till its temperature is
reduced to absolute zero and its volume is also reduced to an inap
preciable quantity. If the gas is now heated under constant
pressure, it will take W(C P C v ) thermal units to do the external
work per degree rise of temperature in accordance with our defini
tions. If the gas is heated T degrees absolute, the heat required for
the external work is W(C P  C v ) T. Expressing this in footpounds,
W(K P K V )T, it may then be equated to the external work done
under a constant pressure P through a volume V, or
py = W(K P  K V )T = WRT.
In the derivation of this formula we eliminated all internal
heat. It cannot be used, therefore, in the determination of quan
136 THE STEAMENGINE AND OTHER HEATMOTORS.
titles of heat. It shows a relation that exists between physical
conditions alone.
In its use only one quantity must be kept constant, and that
is the mass of the gas. Hence for any gas if
PI = initial pressure absolute in pounds per square foot,
F! = the initial volume (in cubic feet) absolute,
TI = the initial temperature in degrees Fahr. absolute,
P2 = the absolute pressure at any other instant in pounds per
square foot,
V 2 = the absolute volume in cubic feet at that instant,
T 2 = absolute temperature Fahr. at that instant,
then, whether the gas was heated or cooled, whether it did work
or work was done on it,
T 1 T 2 '
In the equation PV = WRT there are five quantities : if any four
are known, the fifth can be found. Similarly in the equation
P 1 V 1 P 2 V 2
JJP = ~nn > there are six quantities; if any five are known, the
LI i 2
sixth may be obtained. Note that P is a rate or intensity of
pressure.
Ex. 47. A cylinder 1 square foot in area and 4 feet long contains
oxygen at 139 F. and 100 pounds per square inch pressure absolute.
What is the weight of the oxygen?
Ex. 48. A cylinder contains 1/10 of a pound of an unknown gas.
The volume of the cylinder is 3.2 cubic feet, and the absolute pres
sure is 100 pounds per square inch, and the temperature is 139 F.
What is the gas?
Ex. 49. What volume will 1/2 pound of dry air occupy at 39 F.
and 50 pounds per square inch pressure?
Ex. 50. A spherical balloon, 30 feet diameter, is to be inflated
with hydrogen gas at 70 F., with the barometer standing at 29.8
inches. What will be the weight and volume of the gas that should
be run in, if none is to be lost when the balloon has risen to such
height that the barometer stands at 20 inches and the thermometer
stands at 36 F.?
Calculate the liftingpower when the balloon starts to rise.
Ex. 51. Find the temperature at which one kilogram of air will
MEASURING THE EFFECTS OF HEAT. 137
occupy 3 cubic meters under a pressure of 5000 kilograms per square
meter.
Ex. 52. A cylinder 1 square foot in area and 3 feet in height con
tains air at 100 F. under a piston weighing 576 pounds, exclusive
of the atmospheric pressure. What is the weight of the air?
p l V l P 2 V 2
Boyle's Law. Taking the equation = ^ for a constant
1 1 i 2
mass of gas, it is evident that certain relations hold if any one
of the three factors, pressure, volume, or temperature, is kept
constant, allowing the other two to vary. If heat be added
or subtracted so that the temperature is kept constant, we have
P V
Boyle's Law; for if T L = T 2 , then we have P^ =P 2 V 2 or ^ = ^.
T2 V 1
Since the temperature is kept constant, P\Vi =P 2 V 2 must be the
law of isothermal expansion. If V 2 is greater than V\ the gas has
expanded; if it is smaller, then there has been isothermal com
pression. The law then expresses the fact that if the temperature
is kept constant, the volumes will be inversely proportional to the
pressures. It is generally much easier to deal with ratios thus:
if the volume is doubled or trebled, the pressure is halved or is one
third of the original pressure; or if the volume is one third or one
fourth the original, the pressure is three or four times the original.
Charles' Law. If the volume is kept constant, the equation
P P
becomes ^ WT If a gas be heated or cooled in a closed vessel
1 I 2
so that there is no change of volume, then the pressure is directly
proportional to the absolute temperature. Put in the form of a
P T
ratio, =p = m~ t we see that doubling the pressure requires double
"i * i
the absolute temperature.
Similarly if the pressure is kept constant the equation becomes
L^ZH YJh
Ti T 2 V 2 T 2 '
and we see that the volume is directly proportional to the AB
SOLUTE temperature under those circumstances.
Joule's Law. For engineering purposes we may say that if a
perfect gas expands and does no external work, the temperature
138 THE STEAMENGINE AND OTHER HEATMOTORS.
remains constant. Let us examine the effect of this on the general
equation
_
T 7 ! T 2 '
By supposition TI = T 2 , therefore
p,F 1 =P 2 F 2 .
But this is the law of expansion of a gas at constant temperature.
As T 2 is practically equal to TI, we shall assume the law to hold.
Ex. 53. The area of a piston is 2 square feet; the pressure of the
air against it when it is 1 foot from the beginning of its stroke is 50
pounds. The temperature of the air is 100 F. If the air expands,
doing work as the piston moves to the end of its stroke, find the final
pressure of expansion, if the stroke is 4 feet and the final temperature
of expansion is 100 F.
Ex. 54. The cylinder of an aircompressor is 3 square feet in area
and 2 feet stroke. If this cylinder is filled with air at 15 pounds
pressure and at a temperature of 60 F., what will be the final pres
sure of compression if the air is compressed at a constant tempera
ture to one fourth its original volume?
Ex. 55. A cylinder contains dry air at 100 pounds pressure per
square inch and at 75 F. If the area of the cylinder is 3 square feet
and its length is 2 feet, find the number of B.T.U. that it will take to
double the pressure, if the volume remains constant.
Ex. 56. A cylinder with a movable piston contains one half pound of
oxygen at a pressure of 100 pounds per square inch absolute. If the
volume of the gas under the piston is 1 cubic foot, required the num
ber of B.T.U. to double the volume under the above pressure. What
is the increase of intrinsic energy of the gas?
In using these formulas it is convenient to express the pressures
in pounds per square inch. This can be done by expressing the
area of the piston in square inches. All stroke dimensions must
be in feet.
The formulas for the net work done and the mean effective pres
sure are very much simplified by making the clearance equal zero
and closing the exhaustvalve at the end of the stroke. These
simple formulas will not apply to a cylinder that has clearance,
and most cylinders have clearance.
MEASURING THE EFFECTS OF HEAT.
139
Curves of Expansion of a Gas in General. When the volume of
a gas varies either increasing or decreasing in volume doing
work (or the reverse) and either receives or loses heat in some
regular way, the relation that exists between the pressure and
the volume at any instant may generally be expressed by the
equation
For example, if be, Fig. 93, represent the expansion curve
\
FIG. 93.
PV n = C, from the point 6 draw other curves above or below be.
It is evident that some relation such as
PV n = C,
or, in general,
might exist between the absolute pressure and its corresponding
volume at any instant of the expansion.
To find an expression for the work done during expansion when
the expanding gas either receives or loses heat in such manner
that the relation between the varying pressures and the varying
volumes is PV n = C.
140 THE STEAMEXGINE AXD OTHER HEATMOTORS.
Work done during expansion = J PdV;
This is readily reduced if F 2 ~ n+1 is multiplied by P 2 F 2 n (which
is equal to PiF^) rather than by PI TV
n+1 n1
This gives the work done during expansion of W pounds of
gas (determined by PI, FI) expanding from I^ to T 2 and mean
while receiving or losing heat so that the law of expansion may
bePF = C.
p TT _ p y
To express the work  t 2 in thermal units. From the
n1
general equation PF = WET we have
The w r ork done during expansion in footpounds is therefore
W(K P K V )(T 1 T 2 )
nl
or, expressing this directly in thermal units, is
W(C P C V )(T 1 T 2 )
nl
The change in intrinsic energy is WK V (T 2 TI), since the gas
has changed from Tf to T 2 .
MEASURING THE EFFECTS OF HEAT 141
The total heat required is that necessary to produce the change
in intrinsic energy and do the external work, viz.,
WK V (T 2 T 1 )
Tr(gpg.)(rir 8 )
nl
The equations just derived are general and any value of n
may be used except unity, and that value gives isothermal ex
pansion, which has already been discussed.
Since we may suppose heat added or subtracted in any way
we choose, a very important special case is that in which the
supposition is made that no heat is added to the gas from any
external source while it is expanding, neither does it lose heat
AS HEAT by radiation nor conduction to any outside body. If
the gas expands and does work, it must lose some heat. As we
have made the conditions such that it is impossible to lose or
gain HEAT as HEAT, it is evident that the external work done
must be the sole measure of the heat that the gas has lost. This
is adiabatic expansion.
For Adiabatic Expansion the formula for the total heat re
quired niay be equated to zero, since no heat is added or sub
tracted. Therefore
nK v (T 2 ~T 1 )K v (T 2 T l )+K p (T 1 T 2 )K v (T i T 2 )=0,
Since the temperature decreases T 2 cannot equal T\, therefore
(nK v K p ) must be the zero factor. Hence
T? C 1
L* P ^ P
An adiabatic expansion is a particular kind of expansion and
hence the general value n cannot be used. For this kind of
C
expansion n has the definite value ^, which is constant for
142 THE STEAMENGINE AND OTHER HEATMOTORS.
any gas but varies with different gases. For simplicity ? is
C
generally used for the value of ^ for any gas.
o v
The equation for adiabatic expansion is then
PVr = C.
The work done during adiabatic expansion is
ri
The total work of admission and expansion is
ri
The net work done per stroke when there is no clearance and
the back pressure = the final pressure of expansion
WK v r(Ti  T 2 ) = WK P (T 1  T 2 ) footpounds
C 2375
for perfectly dry air is  = ~ = * '
Y for moist air has some value between 1.4 and 1.2.
The equation PV r = C may be easily derived from the two
fundamental equations of thermodynamics derived on page 152:
H = K p dTVdP,
H = K v dT+PdV.
When the expansion is adiabatic H = Q:
K p dT=VdP,
K v dT= PdV,
K^ = VdP
K v ~ r ~ ~PdV
dV = dP
r v  p
MEASURING THE EFFECTS OF HEAT.
Integrating, C f log V = log P,
143
To Draw the Curve PV n = C (Fig. 94). Suppose the curve and
a tangent at any point m is drawn.
FIG. 94.
Differentiate PV n = C.
7 n  l dV = Ois the equation of the tangent.
dP
or
From the figure,
md
'* ~efe
From similar triangles,
d_P_md
'dV = ~d^'
md cd
n ~j > ' ~j~
cd ' de
&
r = n also.
be
The minus sign shows that the angle, 0, that the tangent makes
with the X axis, if measured from the X axis to the tangent, is
greater than 90 degrees. Given one point on the curve and n, the
value of C may be calculated. For any assumed V, the corre
144 THE STEAMENGINE AND OTHER HEATMOTORS.
spending P may be calculated, and then if be and cd be assumed
to be those values, de and ab may be laid off so that the tangent
may be drawn. Having a series of points and the tangents, the
curve may be drawn through the points and tangent to the tangents.
Logarithmic Crosssection Paper and PV n Curves. Loga
rithmic crosssection paper is invaluable in work dealing with
equations of the form PV n =C. By the use of this kind of cross
section paper we find that the drawing of curves is replaced by
the drawing of straight lines. Hence in hydraulics and in air
or steam compression or expansion, it not only facilitates work
immensely but it also serves as a guide to indicate any variation
in the law of expansion as the variation of the exponent n becomes
immediately apparent.
The curve PV n =C has many disadvantages:
1. It has to be laid out for each different initial P and V.
For superheated steam the curve is rather complicated, as it will
consist of two curves meeting at the point where saturated steam
is converted into superheated steam.
2. The areas in the lowpressure zone are very inaccurate,
the PV n = G curve being there nearly parallel to the axis of V.
It does not show at a glance what happens when the initial
pressure is lower than the boiler pressure; what happens when
the initial pressure is raised or lowered; what happens when
the exhaust pressure is raised or lowered; what happens when
both of these pressures are changed simultaneously.
3. The whole diagram is not flexible and transparent, so
permitting changes in the layout to be made rapidly and their
effects to be visible instantly.*
These troubles disappear when the curves PV n =G are plotted
on logarithmic crosssection paper. (Fig. 95.)
If we take the logarithm of both sides of the equation PV n = C
we still have a true equation. Hence
log P+n log V =log C or log P= n log F+log C.
In this form, we have the equation of a straight line as it is
evidently of the form y=mx + b.
Hence, if we plot the logarithms of the various values of
P and V and the logarithm of the constant C, we shall have a
* See Steamturbine Characteristics, Holzworth, Trans. A. S. M. E., Vol. 28.
MEASURING THE EFFECTS OF HEAT.
145
straight line whose intercept on the axis of Y is log C and which
makes with the X axis an angle whose tangent is n. It is
readily seen how simple it is to plot a straight line and how easy
it is to see if its inclination to the X axis varies.
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
9.9
9.8
9.7
9.G
9.5
9.4
9.3
9.2
9.1
9.0
X
Lc
o.U
f5 ft
4 ft
^'
^
q A
/
b
1
B
9
0^
^
i
/
1.5
 1.0
0,8
0.7
0.6
 0.5
0.4
0.3
 0.2
" 0.15
0.10
* x
s
X
X "
/
S E
<4.
^
^
A
z
/
f
^ x
i^
/
N ^
I
G
X
^ N
. .Cl
/
^ x
^
X
/
X N
N
F y
1
y
K
^
i
\
y
r
a
H to ot eo^oooo
3 20 00000
i f i i 1 i i 7 t
9 too o oooo c
^ C* * 00 C
i f I I I ~i i I i 1
% e d S o
FIG. 95.
o* o_^i4
Those who have used the slide rule know that it is la'.d off
to a logarithmic scale but that the divisions are marked with the
numbers themselves rather than with the logarithms of the
numbers. The divisions hence appear very irregular. In this
way one multiplies or divides with the aid of the slide rule by
the addition or subtraction of logarithms and yet never looks
up or knows the logarithms of the quantities multiplied or divided.
146 THE STEAMENGINE AND OTHER HEATMOTORS.
Similarly, if the subdivisions on the logarithmic crosssection
paper are marked by the numbers instead of their logarithms
the straight line form of the curve may be laid off without look
ing up the logarithms. Nevertheless, it is essential to keep
in mind that we are really dealing with logarithms. Hence
(1) The origin on logarithmic scale paper is at the inter
section of the lines 1 and 1 since the log (1) = 0.
(2) Multiplying or dividing a number by ten changes its
logarithm by 1.0, hence the logarithmic scale paper is divided
into squares of a unit (logarithmic) each.
(3) The logarithm of numbers between 1.0 and 0.1 would
lie between and 1.0. It is better to mark the intermediary
subdivisions 9.9, 9.8, etc., meaning 9.9 10, 9.8 10, etc. (as in
logarithms) and so avoid the use of negative quantities. The
tenth division line would be 9.0 and the eleventh 8.9.
(4) The intercept on the Y axis will be log C, since if log 7=0
we would have log P = log C.
(5) The " unit " or " base " of the logarithmic scale cross
section paper is 5 inches. On a large paper these units may
be repeated a number of times to the left or right of the Y axis
and above or below it. On the right of the Y axis the first line
at unit distance is marked 10, the second is marked 100, etc.,
since the logarithmic markings would have been 1, 2, etc. At
unit distances to the left of the Y axis the first line would be
marked 0.1, the second 0.01, etc., as the logarithmic markings
would have been 1, 2, etc. When an origin has been selected,
it cannot be changed during the calculations. Decimal points
must not be disregarded. To lay off the line, P=0.15F 2 or its
equivalent PF 2 = 0.15.
The logarithm of 0.15 is negative or less than zero, hence
we find the intercept below the origin, Z, at some point A. The
tangent of the slope is 2. This must not be measured by an
irregular scale such as the actual numbers appear to have. From
A lay off any distance, Aa f and at a erect a perpendicular ab
of twice the length of Aa. Through the point b so found, draw
the line AbB', it will be the required line.
The converse is apparent. Given the line AB, what is its
equation? The intercept on the Y axis is 0.15, which is there
MEASURING THE EFFECTS OF HEAT. 147
fore the constant. The value of any intercept divided by its
abscissa such as r is 2, which is therefore the exponent. Hence
the required equation is Y = 0.15X 2 or P7 2 = 0.15.
To lay off the line Y=2X' 5 or its equivalent PF~* = 2. The
logarithm of 2 is more than zero, hence the intercept on the
Y axis is above the axis of X and is found at c. The tangent
of the angle is positive and, by laying off to the left of the origin,
Z, an abscissa, Zd = 2Zc the point d is found. The required
line is dcD.
To lay off the line PV' = 0.3 or F = 0.3X 66 . Lay off
any distance Ze\. Then lay off Ze 2 and Zfo equal to twice and
three times that distance respectively. Through an intercept
on the Y axis = 0.3 draw a line EF parallel to a line joining / 3
and 62 It will be the required line.
Keep in mind that the subdivisions are logarithmic and are
unequal. Note the position of 1.5 and 0.15.
Relations between Temperature, Volume, and Pressure for a
Perfect Gas Expanding Adiabatically.
T 1 T 2 >" P
The general equation is always true and is therefore true in adia
p
batic expansion. These simultaneous values of p may therefore
be equated.
V 2 TI /V 2 \ r TI /V 2
Vi P 2 TI
Similarly V~ = p~ T~'
P 2 Vi /P 2
Hence we see that ^ =
148 THE STEAMENGINE AND OTHER HEATMOTORS.
r~i r^i
/. T l :T 2 ::P l ' :P 2 ' ,
TV TV: TV' 1 : TV' 1 ,
Ex. 56. The area of the piston of an aircompressor is 4 square
feet, the stroke is 2 feet. A cylinder full of dry air at 14 pounds per
square inch pressure, temperature 60 F., is compressed adiabatically
till the volume is reduced to 1/4 the original amount. The air is
then rejected at constant pressure. Compressor is doubleacting,
without clearance, and makes 100 double strokes per minute. Find
the final pressure of compression, final temperature of compression,
heat added to the air, and horsepower to effect compression.
Ex. 57. Find the same quantities on the supposition that the air
is damp and the law of compression is PV l  2 =C.
Ex. 58. A cylinder of indefinite length contains 3 cubic feet of
air under a pressure of 200 pounds per square foot and at a tempera
ture of 300 F. The pressure is varied so that the gas expands ac
cording to the law PVt=C till the volume is 9 cubic feet. How
much heat is added or subtracted, what is the work of expansion, and
what is the final temperature?
Ex. 59. A cylinder of indefinite length contains 4 cubic feet of
air at 539 F. and at a pressure of 400 pounds per square foot. The
volume expands to 16 cubic feet, the pressure varying in accordance
with the law PV~*=C. Find the heat added and the work of ex
pansion.
Ex. 60. Assume any gas at any pressure, volume, and tempera
tuie. Let it be heated or cooled irregularly, and let it do work or
have work done on it. The curve of expansion, which may be a wavy
line, is given, viz., all the ordinates and abscissa can be measured to
known scales. At any point of this curve find how much heat has
been expended and the increase ( f or ) of the heat in the gas above
the original amount in the gas when at the original pressure, volume,
and temperature.
Heat Energy Represented by Areas. (Fig. 96. ) Assume any
volume of any perfect gas, at any temperature, volume, and pres
sure, in a cylinder whose envelope is impervious to heat. Let the
stroke of this cylinder be indefinite in length. Let the gas expand
adiabatically (expending its internal heat in doing external work),
the resistance gradually reducing to zero pounds absolute. When
this is done it is evident that all the heat in the gas has been con
verted into external work.
MEASURING THE EFFECTS OF HEAT.
1. The work of adiabatic expansion is
149
When P 2 = the work is =
If the pressure is reduced to zero, it is evident that the absolute
temperature of
the gas is re
duced to zero
*
and all of its
heat has been
expended. The
total expendi
ture of heat
equals the in
trinsic energy
of the gas at
< i
^
FIG. 96.
the beginning of expansion =WK V T\.
Ex. 61. Treating air as a perfect gas, what is the total intrinsic
energy in 5 cubic feet of dry air at 10 pounds per square inch pressure
absolute and 75 F.?
2. (Fig. 97.) Let the gas in the preceding problem be heated
at constant volume, V\, until the pressure becomes P 2 and the
temperature T 2 .
As in the preced
ing problem, re
duce the resist
ance of the piston
in such manner
that the curve of
expansion is ad
iabatic, and con
tinue it until
both temperature
FIG. 97.
and pressure are reduced to zero.
The work done during expansion will be
P 2 7i
The increase
150
THE STEAMENGINE AND OTHER HEATMOTORS.
of work in this case over that in the preceding one is the area
OO&&QO between the two adiabatics. This increase of work must
equal the heat added to the gas. Therefore
In this case
The area *>BE*> =
Ex. 62. If the dry air in the preceding example is heated to
1000 F. absolute, at constant volume, how many footpounds of
work could be obtained from it if it were expanded infinitely?
FIG. 98.
3. Let the gas at PI, Vi, T l gain or lose heat so that the
expansion line BE is formed. Draw the adiabatics through the
points B and E. Then the total heat added (positively or nega
tively) to the gas to do the external work and change the intrinsic
energy from that which it possessed at PI, Vi, T l is &BEoo.
For if to the heat in the gas at PI, Vi, 7\ (area <*>AB<x>) we add
heat equal to the area <x>BE& (or subtract it) we obtain the
area <x>ABE<x>. Now of the heat equivalent to this latter area
we have expended the area A BEG in external work and hence
that heat is not in the gas and must therefore be subtracted.
This leaves the area ccGEoo as the heat in the gas at P 2 , V 2 , T 2 .
As this is correct the total heat added to change the state of a gas
MEASURING THE EFFECTS OF HEAT.
151
from PI, Vi, TI to P 2 , V 2 , T 2 is equal to the area enclosed by
its PV curve and the two adiabatics of the two states.
FIG. 99.
Ex. 63. If the dry air in Ex. 61 were heated, the temperature
being kept constant, and its volume doubled, show that its final
energy is the same as its initial energy.
4. Suppose the gas in the preceding case neither gains nor
loses heat. The heat in the gas remains constant and the curve
B
FIG. 100.
BE is isothermal. If the gas does work, it must receive heat as
fast as it loses it in doing external work. If work is done on the
gas, then the heat in the gas would increase unless it were cooled,
the loss of heat being measured by the work done on the gas.
By supposition oo AB oo = <*> GE oo ;
but oo ABE oo = nAB + oo BE oo = wGE<x> +ABEG.
152
THE STEAMENGINE AND OTHER HEATMOTORS.
If B represents the initial state, then the gas expands, receives
heat as heat and loses it in doing external work. If E represents
the initial state, then work is done on the gas in compressing it to
B and heat must be taken from the gas to keep its temperature
constant.
Ex. 64. If the air in Ex. 61 were expanded adiabatically till its
volume was trebled, what would be the external work done and what
would be its loss of heat?
The preceding demonstrations enable us to give graphic solu
tion to the two fundamental equations of thermodynamics:
dH = K v dT+PdV,
dH = K p dTVdP.
The first of these was written by Clausius.
dH = K v dT+dL+dU.
In this equation K v dT represents, as before, the increase in
the intrinsic energy of the gas, whilst dL represents the work of
molecular separation and dU represents external or visible work.
Some heat must be expended in separating even the molecules of
perfect gases, since they must have some attraction for one another
because they have mass. In practical work this is small enough
to be neglected.
MEASURING THE EFFECTS OF HEAT.
153
Let a d e . . . represent the path of the gas. Through the points
a, d, e, . . . pass both an isothermal and an adiabatic. The area
between the adiabatic and the base is in each case equal to the heat
in the gas. At a the heat in the gas is K v Ti ; at d the heat in the
gas is K v (T!+dT). The work done badc = PdV. Let d# = heat
added. Then
K V T 1 +dH = K v (T 1 +dT) +PdV
dH=K v dT+PdV.
To derive the formula dH = K p dTVdP.
Let ade ... be the path of the fluid. Through a draw an
isothermal TI and an adiabatic. Let the next higher isothermal
Ti +dT be df. The heat in the gas at a = K v T^
The heat in the gas at f = K v (T l +dT). The heat added
FIG. 102.
in going from a to f={bafg+K v (T 1 +dT)} I^T^I^dT +bafg
= K p dT.
The path of the fluid is from a to d, however. The heat in
the ga? at d and / is the same since those points are on the
same isothermal. To reach the point d from / the gas must be
cooled or heat must be subtracted equal to the area dcgf.
Since df is an isothermal, (dc) X (dk) = (fg) X (fh) . Subtract
the common area (hm) X (me) and we have kdmh = mfgc. Adding
the common area dfm to each side and we have kdfh = dcgf, but
kdfh = VdP; therefore the heat expended, dH, =K p dTVdP.
154 THE STEAMENGINE AND OTHER HEATMOTORS.
Carnot Cycle. The term cycle may be used to indicate a period
of time in which a series of events repeat themselves; a closed figure
that may be a graphic description of a recurring series of events,
or a series of operations bringing the thing operated upon to its
original state. The Carnot cycle is a cycle of operations per
formed on a perfect gas working in an engine of perfect mechan
ical efficiency, and it will be proved that the thermodynamic
heat converted into mechanical work efficiency of this engine
is the highest that can be obtained by the use of any substance or
combination of substances in any engine working in any other
cycle between the same limits of temperature. The practical engine
as it improves approaches this efficiency, but can never attain
it. In other words, the nearer the efficiency of any heatengine
is to that of the Carnot cycle efficiency (between the same tem
perature limits) the nearer it is to its highest attainable perfection.
Note carefully in the Carnot cycle that
(1) All the heat received as heat is at one temperature and
that is the highest.
(2) That all the heat rejected as heat is at one temperature
and that is the lowest.
(3) In order that (2) may be so the heat of the substance
must be lowered by an adiabatic expansion in which the
heat that disappears does so in doing mechanical work.
(4) In order that (1) may be so the gas must be compressed
adiabatically, so that all the heat received as heat may be
received at the highest possible temperature.
In order that we may control absolutely the gain and loss
of heat, let us imagine a cylinder (Fig. 103) made of a material
that is absolutely impervious to heat and has zero specific heat.
In other words, it takes the temperature of the gas inside imme
diately without requiring any heat therefor. The piston is to
be made of the same material. Let there be three separate
heads that may be applied, at will, to one end. One head, H, con
tains an indefinite amount of heat at a temperature TV Since
the amount of heat is infinite the withdrawal of any finite amount
will not lower its temperature. Let the other head, C, contain
an infinite amount of heat at T 3 . Since the amount is infinite,
MEASURING THE EFFECTS OF HEAT.
155
the addition of a finite amount will not raise its temperature.
Let the other head, N, be a nonconductor of similar material
to the cylinder. Let us imagine that we may change heads in
any desired way without losing gas, that the engine is single
acting (there being no head in the right side of the cylinder), and
that the back pressure against the piston is zero pounds.
H
Heat at T,
N
Non
conduc
tor
\
c"'
c
a d b c
Cold at F
O V, V 4 v, v 3
FIG. 103.
Let N be applied at the end e, the piston to be at a; the
volume ea to be filled with a perfect gas at PI, FI, 7\, and hence
W may be calculated if the kind of gas is known. The resistance
is PI.
1. Replace N with E\ reduce the resistance gradually; motion
will ensue as soon as the pressure is an infinitesimal amount less
than that called for by the law PI FI = const. The temperature
will be constantly T l . The pressures will be represented by the
ordinates of the isothermal curve ai6i. The work done will be
. The ratio of expansion, r, will be
The external
156 THE STEAMENGINE AND OTHER HEATMOTORS.
ivork will be PiVi\og f r, or its equal, P^z log r. The heat
received will be equal to the work done, or WRTi log e r.
2. At 6 replace H by N. Allow adiabatic expansion till the
end of the stroke. The pressures will vary in accordance with
the ordinates of biCi . The work will be the area of biCi V 3 V 2 , which
E> T/ P T/"
is equal to 2 . No heat has been received and the tem
perature has been reduced to T 3 , the temperature of the head, C.
The loss of intrinsic energy equals WKy(T 3 T 2 ). To accomplish
this, however, we now see that the point 61 in the stroke must be
T 2 /Vi\ r ~ l
chosen in accordance with some law. We know that  = ( TT~ ) ,
1 I \ V 2'
T 2 /OFsV 1
or in our case ^ = I KTT ) Knowing T 2 , T 3 , and 07 3 , we can
readily find OV 2 .
3. The returnstroke must be made by the action of some
outside force tending to compress the gas. Replace N with 0.
Compressing the gas (by doing work on it) tends to heat it and
therefore increase the pressure that now acts as a resistance.
The presence of C keeps the back pressure down, as it keeps the
temperature down to T 3 . Since C is at the lowest possible tem
perature T 3 , it is evident that this resistance is the least possible.
It is evident that c\d\ is the curve of back pressures and that
CidiV^Vs is the backpressure work up to the point d\. The heat
equivalent to this work is wasted. But we have made the waste
as small as possible by using the lowest TV This wasted heat is
0V*
4. The point d\ of the stroke must be chosen so that, if is
replaced by N and the gas is compressed into its initial volume,
its temperature will be increased from T 3 to the initial tempera
T /V \ r ~ 1
ture TI. Since r= (r 1 ) we have
T 4 (ovj
'*
but 7 7 4 =2 7 3 and 7 7 i = 7 7 2 ; therefore
T 3 '
MEASURING THE EFFECTS OF HEAT. I7
or the ratio of adiabatic compression must equal that of adia
batic expansion. From the above ratio of volumes we may
write
OV 3 OV 2 '
or the ratio of isothermal expansion equals the ratio of isothermal
compression. The work of adiabatic compression is
or the work of adiabatic expansion. The gain of the gas in in
trinsic energy during compression is WK v (Ti T 4 ).
Summing up results we have the work done in adiabatic
expansion balanced by the work of compression, and the heat
or intrinsic energy lost in adiabatic expansion equals that gained
in adiabatic compression. The net work must then be the differ
ence between that done in isothermal expansion and that re
quired for the isothermal compression. This is
PiV l loge rP 3 V 3 log, r = log r(P l V 1 P 3 V 3 ),
or
The efficiency is then measured by the ratio of the work done to
the heat expended or
This efficiency is independent of the gas and the mechanism j
since it contains no terms dependent on the gas or the mechanism^
it depends upon T 3 , as the efficiency evidently increases with a
decrease of T 3 . The lowest practical limit of T 3 is the temperature
of the atmosphere. Practically, then, increase of efficiency is to
be sought in increasing the initial temperature of the heat transfer
agents. That this is correct is seen in the increased efficiency of
the steamengine with increase of pressure and temperature in the
boilers. Gasengines, utilizing gas at still higher temperatures, are
even more economical.
158 THE STEAMENGINE AND OTHER HEATMOTORS.
The above cycle is reversible. With the nonconducting cover
in place, permit the gas to expand adiabatically to d, replace
N by C and allow the gas to expand isothermally, drawing heat
from C. Exchange C for N and compress the gas adiabatically
to b, and then, using the cover H in place of N, compress at 7\
until the original volume is reached. In this cycle instead of the
gas doing work it is evident that work has been done on the gas.
As before, the adiabatic areas will balance one another, as will the
gain and loss of heat in the gas WK v (Ti T 3 ). The quantity of
heat, WRT 3 log r, has been taken from the cold body, and
WRTi log.r has been added to the hot body. Work equal to
WR log* r(Ti T 3 ) has been done on the gas, the required energy
being supplied from an outside source. The efficiency of this
second engine running backward is the same as that of the first
running forward. If there is any cycle more efficient than the
Carnot cycle let a third engine F, using that cycle, taking heat
h'" from the source H and rejecting heat c'" into C, drive the
second engine which takes heat c" from C and rejects heat h"
into H.
' In some respects this is like a waterwheel driven by water
from a height, h, driving another waterwheel that takes the water
running from the first and restores it to the original height h.
If the power of each engine is the same h'" c'" = ft" c", but
according to supposition
W"c'" h"c"
which will only be true when h'"<h". That, is, this system is
taking more heat from the cold body and forcing it into the hot
body than is coming from the hot body into the cold one. This is
a selfacting system, since each drives the other (the amounts of
work of each being equal) and, neglecting friction, could theoret
ically go on forever. We thus have heat transferred from a cold
body to a hot one by a selfacting apparatus. This is contrary to
human experience. Since our premises bring us to an untrue
conclusion they must be incorrect. Hence engine F cannot have
a cycle more perfect than the Carnot cycle.
Ex. 65. Suppose the thermal efficiency of the furnace = 50% and
MEASURING THE EFFECTS OF HEAT. 159
the mechanical efficiency of the hotair engine = 65%. Let the fuel
contain 14,000 B.T.U. per pound, and the engine make 100 cycles
per minute. Find the B.H.P. and I.H.P. per 100 pounds of fuel for
the following cycle. One pound of dry air at 14.7 pounds per square
inch pressure at 60 F. is drawn in per stroke. It is compressed
isothermally and then adiabatically to 1200 F. absolute, receives
heat at that temperature, and expands adiabatically to the starting
conditions.
CHAPTER VI.
MEASURING THE EFFECTS OF HEAT ON WATER AND
STEAM.
WE have seen that when heat is added to a substance a careful
analysis will show only three elementary effects are accomplished.
The first two are ideal since they are always accompanied by the
third. We have found, however, that in the case of heating solids
and liquids so long as the former are not brought too near their
meltingpoint and the latter too near their point of vaporization
the heatequivalent of the internal and external work is practically
negligible, and hence all the heat is expended in raising their
temperature.
If the specific heat of ice is .5, how many B.T.U. would be
required to raise 3 pounds of ice from 43 F. to 32 F.?
3 X.5X75 = 112.5 B.T.U.
The above number of thermal units would be absorbed by a piece
of ice weighing 3 pounds that had been cooled artificially to
43 F. and then placed in open air whose temperature was 32 F.
Melting of Solids. When solids melt and become liquids the
variation in volume is slight, and we may say that all the heat is
spent in overcoming certain molecular attraction forces. To melt
the above quantity of ice or convert 3 pounds of ice at 32 F. to
water at 32 F. would require, since the latent heat of water is
144 B.T.U.,
3X144 = 432 B.T.U.
Boilingpoint of Water. If we heat the 3 pounds of water
at 32 F. we have seen that there will be a slight and slow forma
tion of vapor at the surface of the liquid at various temperatures.
160
MEASURING EFFECTS OF HEAT ON WATER AND STEAM. 161
Rapid boiling, where the steam is formed at the heating surface
and rises through the liquid to its surface,* will always take place
at the same temperature, in the open air, at the same locality. (It
is well known that the presence of gases and salts in the water and
the roughness and character of the containinig vessel may change
the boilingpoint by one or two degrees.) Hence the vapor tension
equals the pressure on the surface of the liquid. If the atmos
pheric pressure is 14.7 pounds per square inch, the water will boil
at 212 F.
Let us put 3 pounds of water in a cylinder 13.54" in diameter,
so that the area will be exactly 1 square foot. The height of the
3
water will be , =.0483'. This calculation is only made to
D^.4ZO
show that the volume of the water may be neglected in future
calculations.
The pressure of the atmosphere on the water may be replaced
by a piston weighing 14.7X144 = 2116.8 pounds. To the actual
weight of any piston that we might use, if exposed to atmospheric
pressure, this weight must be added to obtain the absolute pressure
on the water.
If we determine the temperature at which the water boils
under a series of pistons of different weights, we shall find that the
temperature increases with the weight, but, in no simple propor
tion. Regnault has done this work for us in a most careful way,
and given us the following empirical formula connecting the pres
sure and the observed temperature at which boiling took place :
where A, B, m, n are determined constants and t is the temperature
of the boiling water in degrees Centigrade.
Rankine's formula is equally difficult to apply :
7? C
where A, B, and C are constants and T is temperature of the boiling
water in degrees Fahr. absolute.
Practically, then, it is essential to refer to a set of tables to find
*For an extended discussion, see Rowan's Modern Steam Boilers.
162 THE STEAMENGINE AND OTHER HEATMOTORS.
the pressure corresponding to any boilingpoint or to find the
boilingpoint corresponding to any pressure.
Heat of the Liqiid. If we assume that the specific heat of
water is unity throughout its range from 32 F. to the boiling
point, we do not need tables to find the quantity of heat necessary
to raise W pounds of water from one temperature, ti, to another, t 2 ,
as it is simply Wxi X(t 2 ti).
When considerable accuracy is necessary we must refer to the
tables, as the specific heat of water is not constant. The actual
number of B.T.U. that are required to heat water from 32 F.
to any other temperature which is a boilingpoint at some pressure
have been calculated and tabulated. The increase in the specific
heat at high temperatures is due to the increase of internal work
as the water approaches the condition of steam. If the pressure is
high enough the molecular condition of the water at the boiling
point does not differ from that of steam; in other words, the latent
heat has become zero. This temperature is called the critical
temperature.
Problem. How many B.T.U. does it take to heat one pound
of water from 62 F. to the boilingpoint under a pressure of 400
pounds per square inch? If the specific heat is assumed to be
constant, the boilingpoint (by the tables) being 445 F.,
(445 62) =383 B.T.U.
If the tables are used, for variable specific heat,
419.8  30.12 = 389.68 B.T.U.
In this calculation 30.12 measures the heat of the water above
32 F. initially, and 419.8 measures the heat in the liquid above
32 F. finally. Hence, in general, if
qi = heat in the liquid above 32 F. initially,
52 = heat in the liquid above 32 F. finally.
Heat added =(g 2 9i) B.T.U.
The above difference of 6.68 B.T.U. is about 2% of the total.
The error per degree at 400 pounds pressure in using the first
method is 5.5%, hence particular care must be used at high pres
sures.
MEASURING EFFECTS OF HEAT ON WATER AND STEAM. 163
Expansion of Water when Heated to the Boilingpoint. We
have seen that the volume occupied by water at 32 F. is negligible,
and we shall now indicate the importance of
the external work that is done when water is
heated under pressure up to its boilingpoint.
Fig. 104 represents a cylinder 13.54" diam
eter or 1 square foot in area containing 3
pounds of water at 32 F. under a piston, P,
that is to take the place of the atmospheric
pressure, and therefore weighs 2116.8 pounds.
Let us put on this piston a shaft of wrought iron
12" in diameter and some 23' long. Heat is
added till the water is brought to the boiling
point, which, by trial, is found to be 307 F.
How much heat was added? and show how
much was spent in doing the external work, i.e.,
raising the shaft by the expansion of the water.
The absolute pressure corresponding to a
boilingpoint of 307 F. is 74.5 pounds per
square inch. The total weight of shaft and
piston will be 74.5X144 = 10,728 pounds.
By formula, the heat added is 3 X 1 X (307 
32)=825B.T.U.
By the table, the heat added is 3qi or 3 X
276.9 = 830.7 B.T.U.
The increase in volume of the water will be about 10% of the
original volume.
.0483 X.I = .00483 cubic feet.
FIG. 104.
The external work will be
10728 X. 00483
778
= .07 B.T.U.,
which may be neglected.
Vaporizing a Liquid at its Boilingpoint. Let heat be added
to the boiling water. We note two effects, (6) and (c) :
1. Notwithstanding the addition of heat, the temperature
of the water remains constant at 307 F.
164 THE STEAMENGINE AND OTHER HEATMOTORS.
2. The piston and shaft rise until they are 17.28 feet above
the original position, or, to be more accurate, the bottom of
the piston is 17.28 feet above the bottom of the cylinder.
If we experimented with shafts of different weights we might
ultimately discover Rankine's formula connecting pressure and
volume, viz., P7" = 475. Practically, however, it is easier to use
the table, and we there discover that one pound weight of steam at
74.5 pounds pressure per square inch absolute will occupy a volume
of 5.76 cubic feet, and hence 3 pounds of water converted into
steam will, at that pressure, occupy 3X5.76 = 17.28 cu. ft. The
actual rise of the piston is therefore 17.28 .0483 = 17.2317 feet.
As the temperature of the liquid does not change, but a liquid
is changed into a gas and external work is done, we see that all
heat is expended in doing two things only :
(b) Separating the molecules of the liquid.
(c) Doing external work.
The purely theoretical value of (b) may be obtained by measur
ing the sum of 6 and c and subtracting the value of c, which may
be measured directly. The sum of b and c is called the latent heat
and is found in the tables under that title. (See Table VIII.)
Latent heat of evaporation at 74.5 pounds per square inch
= 898.6 B.T.U. = Li.
.'. Latent heat of 3 pounds weight of steam at that pressure
= 3X898.6 = 2695.8.
The heatequivalent of the external work is
10,728X17.28
778
= 239.1 B.T.U.,
239 i
or ~ = 79.7 B.T.U. per pound of steam = Apu.
6
The value of the (b) event per pound would be
2695.8239.1^^
O
This value will be found tabulated under the head of Heat Required
to Overcome Internal Resistance =p.
MEASURING EFFECTS OF HEAT ON WATER AND STEAM. 165
We may now tabulate all our results per pound of steam.
^ = Heat in the
the '
Let
Total heat required
to produce one
pound of steam
from water at
32 F.
Heat in
steam
p = Internal
+ work heat
4
External / A pu = External
work I work heat
Latent heat
L,
A +819+79.7,
where A = 1 / 77 s' ) pi ^pressure in pounds per square foot; u= volume
in cubic feet of one pound of steam.
If the water were originally at some temperature t 2 so that it
contained q 2 thermal units above 32 F., then if
F. and q 2 = 30 B.T.U.,
276.930+819 + 79.7,
Heat in Steam and Heat Required to Produce Steam. Many
students and some authors confuse these terms. Steam cannot
be continuously made at a constant pressure without the per
formance of work, as the continuous formation of steam leads
either to an increase of pressure or an increase of volume. The
condition of uniform pressure then necessitates increase of volume
under a pressure, and therefore work. When steam blows off
from a weighted safetyvalve, the heat thrown away is the heat
required to produce steam, since that steam was formed at con
stant pressure. The heat that is required to RAISE steam in a
closed boiler is not the heat required to produce steam at the
highest pressure, since the pressure has varied from that of the
atmosphere to that of the highest pressure.
In our experiment with a cylinder one square foot in area,
let the piston, weighing 100 pounds per square inch, rest on a
pound of water, at 60 F. The heat required to produce one pound
of steam from this water is 1091.7 +.305 (327.6 32) (60 32).
If the piston is fixed at the top of its stroke and the steam is
cooled off till the water at the bottom is 60 F., how much heat
has been taken away? Evidently it is not the quantity put in,
as the piston is at the top of its stroke. Further, the water at the
bottom of the cylinder does not weigh one pound, as the cylinder
must be filled with steam at a temperature of 60 F. If we drop
166 THE STEAMENGINE AND OTHER HEATMOTORS.
the piston on this steam and then bring the temperature down
to 60 F., the cycle will be complete and we will then have ab
stracted the total heat put in.
To obtain the heat IN steam, subtract from the heat required
to produce the same weight of steam the heat equivalent of the
external work done.
The engineer ordinarily has no need for steam and water
temperatures below 32 F. As change of state occurs at that
temperature it is wisely used as an origin in the following formula
devised by Regnault:
Total heat required to produce steam = 1091.7 + .305(T 32)
(*32);
where t = temperature of the feedwater;
T = temperature at which the steam is formed at constant
pressure.
If the temperature of the feed water is 32 F., the last term
disappears, and it is evident that if the feedwater is at a higher
temperature than 32, less heat will be taken, and hence the
last term should be negative.
Modifications of Regnault's Results. After the student has
used different steam tables he will notice slight variations in
the values assigned to the same quantities. The recent accu
rate and extensive experiments to determine the specific heat
of superheated steam has disclosed the inaccuracies of the steam
tables based on Regnault's formulas. These experiments have
shown that it is extremely difficult to produce and maintain
steam in an exactly dry and saturated condition. Small globules
of water may float around even in highly superheated steam and
thorough mixing is essential to its production. Hence the diffi
culties experienced in the attempts to produce continuously
exactly dry saturated steam may be imagined.
Fig. 105 and Table A will show the variations from the Reg
nault table as deduced by Dr. Davis. The formula which he
deduces is not accurate below 212 F. Its best range is from
212 F. to 400 F.
Total heat required to produce one pound of steam is
H = 1150.3 + 0.3745(^212)  0.000550 (T212 ) 2 .
The tables given in this book, however, are based on Regnault's
MEASURING EFFECTS OF HEAT ON WATER AND STEAM. 167
formulas. In the middle range of temperatures they are in error
onehalf of one per cent which is unimportant to engineers.
B.t
u.
16
Ifc
8
4
^
\
\
\
\
/
\
J
jr
4
\
X,
s
/
V
>~ "
^~
(
) 100 200 *300 400 50
FIG. 105. Deviation in B.T.U. (from values given in Peabody Tables).
TABLE A.
DIFFERENCES BETWEEN PROPERTIES OF DRY SATURATED
STEAM AS GIVEN BY DAVIS FORMULA AND PEABODY
TABLES (MODIFIED IN EIGHTH EDITION).
Temperature,
Pressure,
Total Heat.
Specific Volume.
Fahrenheit.
Absolute.
Davis.
Peabody.
Davis.
Peabody.
32
0.089
1073.4
1091.7
3294
3395
100
0.949
1103.6
1112.4
349.7
354.7
212
14.7
1150.3
1146.6
26.76
26.66
327.8
100
1186.3
1181.9
4.412
4.409
358.5
150
1193.4
1191.9
2.998
3.016
381.9
200
1198.1
1198.4
2.27
2.299
401.0
250
1201.5
1204.2
1.837
1.858
417.4
300
1204 . 1
1209.3
1.540
1.558
426.3
330
1205.3
1211.9
1.403
1.417
Use of Formulas. In textbooks formulas are ordinarily given
for latent heat and internal latent heat, as well as other forms for
the total heat, such as
1082 + . 305 T(t 32),
1146.7 + .305(T 212)(32).
The constant repetition by the student of one fundamental
formula, in different phases, will result in a better comprehension,
by him, of the meaning of each of the items of heat expenditure
than he will obtain by the use of separate formulas.
168
THE STEAMENGINE AND OTHER HEAT MOTORS.
The student should have a few rough guides as to the relative
importance of heat quantities and their variation with pressure.
For instance, let him examine the amount that externalwork heat
varies from 80 B.T.U. for pressures between 80 and 250 pounds per
square inch. Similarly note, for the same range of pressures, the
variation of the total heat from 1190 B.T.U. (Fig. 106) Table VIII.
Quality of Steam. Steam formed in a steamboiler is always
saturated steam, as the space over the water contains nothing but
the vapor of water, i.e., the SPACE is saturated. This steam
may be either dry saturated or wet saturated steam. If it con
aoiibs.
Pounds Pressure
250!lbfl.
FlG. 106.
tains per pound the number of thermal units called for by the
above formula of Regnault, it is dry saturated steam; if it
contain a less number, it is wet saturated steam. If this dry
steam passes through pipes or tubes and has more heat added
to it, then it is called superheated steam. Hence dry steam
may be either saturated or superheated steam; usually, however,
the term dry is restricted to dry saturated steam.
Ex. 68. How many B. T. U. are required to convert feedwater
at70F. into steam at 327.6 F., pressure 100 pounds absolute? If
MEASURING EFFECTS OF HEAT ON WATER AND STEAM. 169
the volume occupied by 1 pound weight of this steam is 4.4 cubic feet,
find the internal latent heat.
Ex. 69. A 10"X10" steampump using steam full stroke at 100
pounds gage pressure makes 40 double strokes a minute. If half
the steam that enters the pump is condensed, find the work done
per minute in footpounds, the number of pounds of steam used per
hour by the pump, and its efficiency.
Ex. 70. The thermal efficiency of an engine is 14%. How many
pounds of feedwater will it require per horsepower hour if the boiler
pressure is 150 pounds and the temperature of the feed is 70 F.?
Ex. 71. Boiler pressure 125, gage: feed 65 F.; engine uses 20.5
pounds of feedwater per horsepower. What will be the gain in
efficiency if there is installed a feedheater that uses only waste heat
and raises the temperature of the feedwater to 212 F.?
Ex. 72. A tank 8'X8'X4' is filled 3 feet deep with water at 50 F.
How many pounds of steam at 324 F. will be condensed in a steam
coil in the bottom of the tank in bringing the tankwater to the boil
ingpoint? (The condensed steam in the coils does not cool below
324 F.)
Ex. 73. A certain boiler uses 12,000 pounds of water per hour.
From a catalog pick out a feedwater pump. If it uses per stroke
165% of the volume of its steamcylinder, find the number of pounds
of water pumped per pound of steam.
When steam is formed slowly and carefully in a welllagged
vessel, such steam is always dry saturated steam. If the steam
be formed rapidly and there are violent steam currents it is easy
to see how small vesicles of water may be swept along by the
current of the steam. More heat must be spent on these minute
drops of water to convert them into steam. This extra heat is
evidently a percentage of the latent alone, since the drops have
the same temperature as the dry steam by which they are carried.
Wet Steam. As wet steam does not contain the same number
of heatunits as dry steam and is much less efficient for use in
steamengines, it is necessary to have instruments to measure its
degree of wetness or its quality. Whether the boiler formed wet
steam, or the wetness arose from condensation due to radiation
losses from the steampipe, there is little excuse for allowing wet
steam to enter the engine since an efficient form of separator near
the engine should remove all the moisture. In measuring the
170 THE STEAMENGINE AND OTHER HEATMOTORS
evaporation of water per pound of coal, impossible results have
been reported by experimenters through neglecting the measure
ment of the quality of steam produced. As the moisture is only
water at the boilingpoint and requires onequarter or onefifth
as much heat as an equal weight of dry steam, it is easily seen
how the presence of only a small percentage of moisture will ma
terially alter the results.
Let =the per cent of dry steam in 1 pound of a mixture of
steam and water, then
100 x = the per cent of water present.
If hi = the heat in 1 pound of water above 32 F., then h 2 hi
will be the number of B.T.U. required to heat this water to the
boilingpoint, t 2 , corresponding to h^.
If only x per cent of this water at t 2 is evaporated, the total
expenditure of heat will be
xL 2 + h 2 hi, or less accurately, xL 2 +t 2 ti.
Problem. If the quality of steam issuing from a boiler is 97
per Cent, temperature of feedwater is 120 F., boiler pressure
100 pounds, gage, how many B.T.U. are expended per pound of
steam?
The temperature corresponding to 115 Ibs. abs. is 337.9 F,
L = 1091.7+ .305(337.9 32)  (337.9 32) = 877 B.T.U.
.97 X877 +337.9  120  1068.59 B.T.U.
From the tables
.97x876.3+308.788 = 1070.7 B.T.U.
Superheated Steam. The specific heat of steam at constant
pressure was determined by Regnault to be .4805, and at con
stant volume to be .346. These values have been accepted as
correct for pressures and temperatures higher than those used
by Regnault in his experiments. Recent experiments show that
these specific heats vary with the temperature and with the press
ure of the superheated steam. See Fig. 228 and Table XV.
Equivalent Evaporation from and at 212 F. To say that one
pound of a certain coal will evaporate ten pounds of water does
not convey exact information, as the amount of heat required to
evaporate the water would vary, not only with the initial tern
MEASURING EFFECTS OF HEAT ON WATER AND STEAM. 171
perature of the water and the temperature at which it was evap
orated but also with the quality of the steam. Otherwise ex
pressed, the same number of B.T.U. would evaporate different
weights of water as the circumstances differed. Hence it is
usual in boiler trials to reduce the rates of evaporation actually
obtained to those that would have been obtained under certain
adopted standard circumstances. These are :
1. That the feedwater should be at 212 F.
2. That the abovementioned feedwater should be con
verted into dry saturated steam at 212 F.
The heat then would be expended in converting water into steam
from and at 212 F. By reducing the results obtained in all
boiler trials to this standard, a result is obtained that expresses
the combined efficiency of the coal, the boiler, and the method
of firing. It is desirable to separate these factors, but experience
will prove that it is difficult to do so.
Problem. What is the equivalent evaporation if, on a trial,
a certain coal evaporated 9 pounds of water from feed at 120 F.,
the quality of the steam being 97%, boiler pressure 100 pounds
per gage?
All the water is raised from 120 to 337.9 F., and then 97%
of it is converted into steam at 337.9. Latent heat = 876.3.
91.97x876.3+337.91201=1067.9X9;
96111
966
9.95.
Ex. 74. Find the heat required to produce one pound of steam
at 324 F. from feed at 60 F. The quality of the steam is 97%.
What will be the equivalent evaporation from and at 212 F.?
Ex. 75. The efficiency of a boiler is 70%. If coal is burned whose
composition is C = 86, H = 8, = 4, how many pounds of steam,
quality 98%, will be made per pound of coal from feed at 180 F.?
What is the equivalent evaporation?
Ex. 76. Given one pound of wet steam at 358 F., quality 97%,
how many B.T.U. will be required to superheat the steam 75 F.?
Ex. 77. What is the equivalent evaporation per pound of com
bustible if, on a test, there is 10% ash and one pound of coal is found
to evaporate 9 pounds of water from feed at 100 into superheated
steam at 400 F., boiler pressure being 120 pounds, gage?
172 THE STEAMENGINE AND OTHER HEATMOTORS.
Methods of Determining Dryness of Steam.
1. By the Barrel Calorimeter. This method is theoretically but
not practically accurate. The steam to be tested is conveyed
by a pipe (the lower end of which is perforated with small holes)
to the bottom of a barrel that rests on platform scales. The
perforations in the pipe prevent bursting the barrel by a too free
admission of steam. The water on being heated by the steam must
be stirred, if necessary, to obtain water of uniform temperature.
Let Wi = the initial weight of cool water and ti its temperature.
If t 2 is its final temperature,
Wi(t 2 ti) = increase of heat.
If z=tne quality of
the steam added,
W 2 = final weight of mix
ture,
W 2 Wi = weight of wet
steam added,
L 3 = latent heat of steam
at given pressure,
is = temp3rature of steam at given
pressure,
lest by
the steam,
The quality of the steam,
or more accurately, use
\, h 2 , h 3 for t v t2, and 3 ,
FIG. 107. The Separator Calorimeter.
For example, suppose steam is run into a barrel of water
weighing 200 pounds at 60 F. The final weight is 208.5 pounds
at 105 F. Boiler pressure is 85 pounds gage, and the corre
MEASURING EFFECTS OF HEAT ON WATER AND STEAM. 173
spending temperature is 327.6 F. What is the quality of the
steam?
200(10560) = (208.5  200) (z884 +327 105).
x = 94.8%.
2. Carpenter's Separating Calorimeter (Fig. 107). The amount
in pounds of dry steam (at P pounds per square inch absolute)
that will flow through an orifice of A square inches area is
PA
~= (Napier's formula).
The amount of dry steam that will
flow through a given orifice in a given period ten minutes,
for instance can be determined by trial or can be calculated and
tabulated for various pressures. If wet steam flows through a
separator for a period of ten minutes the amount of dry steam
escaping through the orifice may be taken from the table and the
amount of water that was separated from the steam may be
weighed or calculated from its volume. The Carpenter calorim
eter depends upon the above principles.
3. Barrus Continuous water Calorimeter. If the wet steam is
made to flow through a surface condenser it will give up all its
heat to the coolingwater. The
weight of the coolingwater, Wi,
multiplied by (h 2 hi), corre
sponding to its rise of tempera
ture (t 2 ti), must equal the heat
lost in the same time by the W$
pounds of wet steam at 3 F.,
that flowed through the calorim
eter and issues as water at U.
Therefore
4. The Throttlingcalorimeter
(Fig. 108) was invented by Prof.
C. H. Peabody. As will be seen
below it is the only form recom
mended by the Committee on
Standards. Steam at high pressure contains more heat than an
equal weight of steam at low pressure. When steam is allowed
FIG. 108. Carpenter's Patent
Throttlingcalorimeter.
174
THE STEAMENGINE AND OTHER HEATMOTORS.
to expand suddenly from a high to a low pressure, forming eddies
and doing no useful work, the excess of energy or heat must be
taken up in some manner. If the steam at high pressure contains
any moisture the first effect is to convert the moisture into steam
at the lower pressure. If there is still an excess of heat, then all
the steam at the lower pressure will be superheated until the excess
is absorbed.
In Fig. 108 the steam passes through the samplingnozzle
MEASURING EFFECTS OF HEAT ON WATER AND STEAM. 175
(screwed into the main steampipe and the valve C) into the
chamber A. Ordinarily the exit to A is so great that the pressure
therein is that of the atmosphere. If the exit be throttled in any
way the pressure is shown on the U tube or manometer, which is
filled with mercury to the zeropoints before attachment to A.
In preceding discussions we let x = the quality or dryness of
the steam. In this case we shall let
y = per cent of moisture present;
TI = temperature of the moist steam;
hi and LI = heat of liquid and latent heat corresponding to T\;
T 2 = temperature corresponding to manometer pressure;
h 2 and 1/2= heat of the liquid and latent heat corresponding to T 2 ',
T s = temperature of steam as shown by the thermometer in
the well screwed in the chamber A, where the steam
is expanding freely.
Then hi + (1 y)L\ =heat to produce the moist steam.
f heat in the steam after expansion
fi 2 +L 2 + A8(l o 1 2) = i ,1 n
[ in the well.
If T s is not greater than T 2 the instrument cannot be used, as it
does not give utilizable readings.
1091.7 + .305(7 7 1 32) yLi = 1091.7 + .3Q5(T 2 32) +A8(T,T 2 ).
.305(7*1  7%)  .48(7*.  7 7 2 )
Ordinarily T 2 is taken from the tables by finding the tempera
ture corresponding to the sum of the atmospheric and manometer
pressures. The Standard Rules given below do not permit this,
since T s is taken with a thermometer that is subject to radiation
and other errors, and further it does not allow for the radiation of
tho chamber A, which may be considerable even when well covered.
To correct for these errors a Normal Reading is necessary.
Either before or after the test, take steam through the end hole
of the nozzle only, from a horizontal pipe, containing quiescent
steam at constant pressure. This steam is, in all probability, dry
176 THE STEAMENGINE AND OTHER HEATMOTORS.
and the calorimeter should give such a value for T that the value
of y should = 0. Instead of this it gives some other value, T n . We
know that y should = 0, therefore .3Q5(T 1 T 2 )AS(T n T 2 )=Q.
Therefore the true value of y corrected for indicator errors and
radiation errors is
A8(T n T 2 )  A8(T.T 2 ) _ AS(T n T s ) _ T n T.
LI L I LI
AS
Determination of the Water Equivalent of the Calorimeter.
All instruments have to be calibrated to determine their error
under the conditions in which they are used. They absorb heat
if they are heated, and they radiate a part of the heat that they
absorb. There are three ways of allowing for these effects :
A. Compute from the known weights of the apparatus and
the specific heats of the materials the quantity of heat absorbed.
Let Ci, C 2 , C 3 be the specific heats, and W 1} W 2 , W 3 be the
weights of the component materials of the apparatus and K the
water equivalent per degree variation,
\? K = C 1 W 1 +C 2 W 2 +C 3 W 3 .
B. By drawing into the apparatus that has acquired a con
stant temperature by being exposed to water at a definite
temperature, a certain amount of weighed warm water and
measuring the resulting temperature after equilibrium has been
established.
Let Wi = the weight of the apparatus;
W 2 = the weight of the water;
7 7 3 = the original temperature of the apparatus;
TI = temperature of the warm water drawn in;
T 2 = the final temperature of water and apparatus.
Then W z (T l  T 2 ) = C1F, (T 2  T 3 ) =K(T 2  T 3 ) .
K W (T * T>) '
A = W 2~7n  7fT~*
1 2 1 3
MEASURING EFFECTS OF HEAT ON WATER AND STEAM. 177
C. By taking steam from a boiler under steampressure, but
at rest. The steam is therefore dry. The variation of the cal
culation will therefore be due to the instrument. (See Normal
Reading.)
Ex. 78. What is the quality of steam shown by a Carpenter calo
rimeter if 4.45 pounds of dry steam escape from the orifice and 1.15
pounds of water are separated out? What is the diameter of the
orifice if the run is 25 minutes long and the pressure is 81.5 pounds
gage?
Ex. 79. An experiment with the Carpenter calorimeter gave the
following data: Duration of run, 25 minutes; gage pressure, 78.2
pounds; water separated out, 0.15 pound; dry steam escaping,
5.20 pounds. Find size of orifice and quality of the steam.
Ex. 80. If the steam escaping from the two preceding examples
gave readings 281 F. and 281.3 F. as the temperatures in a Peabody
throttlingcalorimeter, find the quality of the exhauststeam.
Quality of Steam. * "When ordinary saturated steam is used,
its quality should be obtained by the use of a throttlingcalorimeter
attached to the main steampipe near the throttlevalve. When
the steam is superheated, the amount of superheating should be
found by the use of a thermometer placed in a thermometer
well, filled with mercury, inserted in the pipe. The samplingpipe
of the calorimeter should, if possible, be attached to a section
of the main pipe having a vertical direction, with the steam
passing upward, and the samplingnozzle should be made of a
halfinch pipe having at least twenty oneeighth inch holes in its
perforated surface. The readings of the calorimeter should be
corrected for radiation of the instrument, or they should be
referred to a "normal reading/' as pointed out below. If the
steam is superheated, the amount of superheating should be
obtained by referring the reading of the thermometer to that of
the same thermometer when the steam within the pipe is satu
rated, and not by taking the difference between the reading of
the thermometer and the temperature of saturated steam at the
observed pressure as given in a steamtable.
"If it is necessary to attach the calorimeter to a horizontal
section of the pipe, and it is important to determine the quantity
* Standard Rules. A. S. M. E.
178 THE STEAMENGINE AND OTHER HEATMOTORS.
of moisture accurately, a samplingnozzle should be used which
has no perforations, and which passes through a stuffingbox
applied to the bottom of the pipe, so that it can be adjusted up
and down, and thereby draw a sample at different points ranging
from the top to the bottom. By this means the character of the
steam in the lower portion of the pipe, where it contains the most
moisture, can be determined, and especially that at the very
bottom, where there is usually more or less water being carried
along the pipe. If, by preliminary test, water is found at this
point, we recommend that a drippipe be attached a short dis
tance in front of the calorimeter, the end of the drip being below
the level of the bottom, and a sufficient quantity of steam be
drawn off, while the trial continues, to remove the water and
cause the calorimeter to show dry steam at whatever height the
samplingnozzle is adjusted. The quantity of water and steam
thus drawn off should be determined by passing it under pressure
through a separator, weighing the water after cooling it, and
the steam after condensing. If the amount of water on the
bottom of the pipe is so excessive that it cannot be removed by
this means, or in cases where the main pipe is vertical and the
calorimeter shows that the percentage of moisture varies widely,
sometimes exceeding three per cent, we recommend that a separator
should be introduced before making a test, so as to free the steam
of all moisture that it is possible to remove, the calorimeter being
attached beyond the separator.
"To determine the ' normal reading' of the calorimeter, the
instrument should be attached to a horizontal steampipe in
such a way that the nozzle projects upwards to near the top of
the pipe, there being no perforations and the steam entering
through the open end. The test should be made when the steam
in the pipe is in a quiescent state, and when the steampressure
is constant. If the steampressure falls during the time when
the observations are being made, the test should be continued
long enough to obtain the effect of an equivalent rise of pressure.
When the normal reading has been obtained the constant to be
used in determining the percentage of moisture is the latent heat
of the steam at the observed pressure divided by the specific heat
of superheated steam at atmospheric pressure, which is .48.
MEASURING EFFECTS OF HEAT ON WATER AND STEAM. 179
To ascertain this percentage, divide the number of degrees of
cooling by the constant and multiply by 100.
"To determine the quantity of steam used by the calorimeter
in an instrument where the steam is passed through an orifice
under a given pressure, it is usually accurate enough to calculate
the quantity from the area of the orifice and the absolute pressure,
using Rankine's wellknown formula for the number of pounds
which passes through per second; that is, absolute pressure in
pounds per square inch divided by 70 and multiplied by the area
of the orifice in square inches. If it is desired to determine the
quantity exactly, a steamhose may be attached to the outlet
of the calorimeter and carried to a barrel of water placed on a
platform scale. The steam is condensed for a certain time and.
its weight determined, and thereby the quantity discharged per
hour."
Ex. 81. The mean boiler pressure during a test was 155 pounds
by the gage, the barometer reading was 29.5 inches of mercury, the
mean thermometer reading of boiler steam was 367.1 F. The pres
sure in the manometer was equal to 6 inches of mercury and 3 inches
of waterpressure. The same thermometer that was used in determin
ing the temperature of the boiler steam read 272 F. in the expansion
chamber. What was the quality of the steam?
Ex. 82. Assume the data for calibrating the thermometers used
in determining the quality of steam.
CHAPTER VII.
MEASUREMENT OF HEAT LOSSES.
Quality of Steam in the Cylinder. The amount of dry steam
in a cylinder of a steamengine at the point of cutoff is only 50
to 90 per cent of the steam actually admitted. It is extremely
important to account for the differences between the amount of
steam admitted and that present at cutoff, because the economy
of a steamengine is fairly well measured by the number of pounds
of feedwater that are required per horsepower. Commencing at
the boiler, we may have
A. Wet steam delivered by the boiler.
B. Condensation in the steampipes.
C. Leaky steam valves.
D. Condensation of the steam in the cylinder.
E. Leaky piston.
F. Condensation due to radiation of heat from the cylinder.
G. Condensation due to the performance of work during
expansion.
A. Quality of Steam Supplied by the Boiler. A boiler is said to
give wet steam when there is an intimate mixture of the water
and steam. The boiler is said to be foaming or priming when the
water is carried into the steampipe in solid masses. A boiler may
furnish dry steam for months and then start foaming. This may
be due to
1. Bad feedwater. Feedwater containing soap, oils, salt,
mucilaginous matter, or certain vegetable ferments will foam.
2. The heatingsurfaces of the boiler may become coated
with oil from too free use of oil in the engine. This applies,
of course, only to surfacecondenser engines from which the
180
MEASUREMENT OF HEAT LOSSES. 181
condensed steam is returned to the boiler. New boilers and
boilers using condensed steam from recently erected steam
heating systems will foam till the oil is worked out of the
system.
3. Sudden reductions of pressure in the boiler. These
may be caused by the engine taking larger volumes of steam
per stroke than the boiler can properly supply. If the steam
pressure falls greatly and the engine cutoff is proportionally
lengthened to keep up the number of revolutions, foaming may
result.
4. A change in the boiler design, so that a bad circulation
of the water in the boiler is obtained instead of a good one.
If a new boiler continues foaming after the oil has been
worked out of it, the trouble is generally due to faulty design.
The trouble may be due to
a. Bad circulation of the water. This may be due to
faulty placing of the tubes or faulty movement of the hot
gases. Retarders were placed in the central tubes of a ver
tical boiler that had always given dry steam, and it foamed
till they were removed.
6. Improper method of collecting the steam for the
steampipe. Where the steampipe opening is only a foot
or so above the water in a boiler, the surface of that water
will not be level, but will curve up towards the opening.
The lessening of the static pressure at that point, owing to
the high steam velocity, will cause the presence of more
steambubbles in the water at that point than elsewhere.
The bursting of rising steambubbles will cause the spray
to be carried by the rapidly moving steam into the steam
pipe. A welldrained collectingpipe, nearly as long as the
boiler and having its upper surface perforated for its entire
length with numerous small holes whose total area is con
siderable in excess of the crosssection of the steampipe,
should be used.
All the causes of foaming may be reduced to
1. The water temperature is too high for the pressure that
exists in the boiler at that instant. To check foaming, cool
182 THE STEAMENGINE AND OTHER HEATMOTORS.
the water by opening furnace or connection doors; by putting
on a heavy feed; by increasing the pressure by partially closing
the throttle or the stop valve on the foaming boiler in a battery
of boilers. If the water disappears from the glass gage, start
the foaming again by raising a safetyvalve or opening the
throttle to keep the tubes cool and put on a heavy feed.
2. Formation of Steambubbles of Abnormal Size. Any in
gredient in the water that adds strength to the bubbleenvelope,
or any mechanical formation that allows the bubble to grow in
size before its detachment from the heatingsurface, is con
ducive to foaming. Feed and blow till the ingredients are
washed out of the boiler, or add other ingredients that will
reduce the envelope strength. In boiling sugar solutions, tallow
is added for this purpose.
B. Condensation in the Steampipe. The amount of heat lost
by an uncovered steampipe is considerable. It varies with
1. The extent of the uncovered area.
2. The temperature and rapidity of movement of the outside
air.
3. The temperature of the steam.
4. The character of the steam.
Ordinarily the number of B.T.U. lost is expressed by the formula
CA(T l T 2 ) )
where C is a constant = 2.5 B.T.U. per hour per square foot (approxi
mately), TI and T 2 are the temperatures of the steam and air
respectively, and A is the exposed area of the pipe in square feet.
Perfectly dry steam is a very poor conductor of heat, and it has
been found that pipes carrying superheated steam do not lose the
same amount of heat that they would lose if carrying saturated
steam of the same temperature. The presence of a slight film of
water on the inside of the pipe is an active agent in the transfer of
heat and therefore affects the value of the constant C in exact
determinations.
Whilst the loss of heat in small pipes is less in amount than in
pipes of large diameter, the percentage loss is enormously greater.
This arises from the fact that the exposed area varies with the
MEASUREMENT OF HEAT LOSSES.
183
diameter, whilst the amount of heat passing through the pipe
varies with the crosssection of the pipe or the diameter squared.
The value of nonconducting covering depends upon
1. Its nonconducting quality.
2. Its permanence.
3. Its inflammability or heatresisting qualities.
4. Its solubility or waterresisting quality.
5. Its corrosive effects upon the pipe.
6. Its bulk and general appearance.
TESTS OF COMMERCIAL STEAMPIPE COVERINGS.
The following results were obtained by G. M. Brill, and were reported in the
Trans. A. S. M. E., Vol. XVI. The heat loss was determined by the condensa
tion in an 8" steampipe GO' long. Steampressures varied from 109 to 117 pounds
gage, the airtemperature varied from 58 to 81 F. The difference in tem
perature at the two sides of the heatingsurface varied from 263 to 286 F.,
averaging 272 F.
Kind of Covering.
1
ti f
Scr
K
JL
M
H mw
rt o
ii
Thickness <
ing, Inc]
Pounds of
densed p
per Hou
P
&*
ffi
pll
Ratio of H
Bare to
Pipe in ]
.+.' *
M
Bare pipe
.846
12.27
2.706
100.0
2 819
Magnesia ....
1.25
.120
1.74
.384
.726
14.2
400
Rock wool . .
1.60
.080
1.16
.256
.766
9.5
.267
Mineral wool
Fire felt. ... ....
1.30
1.30
.089
.157
1.29
2.28
.285
.502
.757
.689
10.5
18 6
.297
.523
Manville sectional
1.70
.109
1.59
.350
.737
12.9
.564
Manv. sect, and hairfelt. . .
Manv. woolcement
2.40
2.20
.066
.108
0.96
1.56
212
.345
.780
.738
7.8
12.7
.221
.359
Champion mineral wool. . . .
Hairfelt
Riley cement
1.44
0.82
75
.099
.132
.298
1.44
1.91
4.32
.317
.422
.953
.747
.714
.548
11.7
15.6
35.2
.330
.439
.993
Fossil meal. ... ....
75
275
3 99
.879
.571
32.5
.916
The nonconducting quality depends upon the porosity and
not upon the material of the nonconductor. In other words, the
more air there is entrained in the pores of the material the better
the nonconducting qualities. If from any cause the covering
becomes more dense its nonconducting quality becomes less.
For instance, wetting ruins some nonconductors that otherwise
are excellent. Glass wool after a time breaks up into a dense
powder and so loses in value. The situation of the steampipe
184
THE STEAMENGINE AND OTHER HEATMOTORS.
to be covered is a prime factor in the choice of the covering. The
intense heat in the confined space over a boiler would prevent the
use of a covering that would be suitable for pipes that are subject
to occasional wetting. The chemical action of the constituents of
the covering when damp must be considered to prevent pipe
corrosion. On p. 183 ara tabulated some tests of commercial
steampipe coverings.
The following results were obtained by C. L. Norton of the
Mass. Manufacturer's Mutual Fire Insurance Co.:
Temperature Cor
responding to 10
Temperature Cor
responding to 200
Pounds Steam
Pounds Steam
Weight
pressure.
pressure.
Name of Covering.
Thick
ness in
Inches.
in Ounces
per
Square
Foot.
B.T.U.
Loss per
Sq. Ft.
Ratio of
Heat
Loss to
B.T.U.
Los per
Sq. Ft.
Ratio of
Heat
Loss to
of Pipe
Loss from
of Pipe
Loss from
per
Bare
per
Bare
Minute.
Pipe.
Minute.
Pipe.
Nonpareil cork
0.90
1.12
21
24
1.44
1.59
0.232
.262
3.04
3.40
.254
.284
Magnesia
Aircell No. 1
1.12
23
3.58
.300
Aircell No. 2
1.25
36
1.58
.261
3.40
.284
Magnabestos
1.12
1.00
48
46
2.32
2.4
.383
.395
3.84
3.99
.321
.333
Fire felt
Caleite
1.25
29
5.02
.423
Bare pipe
6.06
1.000
11.96
1.000
>2.3 45.8 33.9 27.3
1.53 1.46 1.40
When the difference of temperatures is small the B.T.U.
transferred per degree difference of temperature is also decreased.
COOLING OF WATER ix PIPES EXPOSED TO AIR.
4" Castiron Pipes.
Difference of tempera
ture 103.7 49.4 25.'
Heat emitted per 1 F.
difference of tempera
ture per hour 2.25 2.11 1.83
All steampipes should drain in the direction of the moving
steam and should be free of pockets where water may lodge.
It is almost impossible to prevent leakage from pipejoints if
water lies in the bottom of the pipes. Moving steam will carry
water against a very considerable adverse pitch. Notwith
standing the fact that the water should drain towards the engine,
none should be allowed, under any circumstances, to enter the
engine, as it is certain to lower the economy (see p. 187). Simi
larly, all receivers in multipleexpansion engines should be drained
MEASUREMENT OF HEAT LOSSES. 185
and the water wasted rather than let it enter the following cylin
der. To separate the water and steam, use may be made of any
efficient separator. The essential principles of a good separator
consist in giving a whirling motion to the steam to throw the
water outwards by centrifugal force and then preventing the
water so thrown out from entering into the moving body of steam
again. Fig. 5 shows one form of separator. The steam enters
at A, whirls in the direction of the arrows and passes out at B.
The amount of entrained water is shown by the sightglass C.
This water may be automatically trapped out and sent to the
hotwell with the rest of the feed water.
It is necessary to afford the same support to a hot pipe as
to a cold one. Frequently the expansion of the vertical part
of a pipe will lift parts of the horizontal portion of the pipeline
from intended supports. All movement of the pipe should be
calculated and proper allowances made.
Ex. 83. What will be the probable saving per annum, if coal is
worth $3.00 per ton, in covering (with magnesia 1.25 inches thick) a
6inch pipe 300 feet long; boiler pressure 100 pounds gage; average
outside temperature 50 F.; boiler used 14 hours per day, 300 days
in the year?
Ex. 84. Assume that any given covering will last five years, how
much may be paid without loss for a covering 2 inches thick (al
lowing 8% for repairs and interest and 15% for depreciation) on a
12inch pipeline 1000 feet long, carrying steam at 150 pounds pres
sure; average outside temperature = 50 F.; plant runs continuously;
coal $3.00 per ton, labor 50 cents per ton of coal?
Ex. 85. Sketch a pipeline connecting five compound engines of
1000 H.P. each to a battery of boilers of 300 boiler horsepower
each. The nearest boiler is 15 feet below and 300 feet distant from
the nearest engine. Steampressure 165 pounds gage, engines use
15 pounds water per H.P. Assume other quantities needed.
C. Leaky Steamvalves. The steam may leak directly into the
exhaust cavity and so tend to raise the back pressure and thus
produce a double loss, or, in some constructions, it leaks into the
cylinder during expansion. The leakage, of course, will be greatest
when the piston is near the end of its stroke and the steampressure
is lowest. It is easy to see that there will be a loss, but the magni
186 THE STEAMENGINE AND OTHER HEATMOTORS.
tude of such loss is only appreciated by those who know the
amount of steam that will pass through an almost insignificant
opening.
D. Condensation of the Steam during Admittance. By the use of
a drypipe to collect the steam in the boiler for the steamnozzle,
and by the use of welllagged steampipes, the amount of condensa
tion may be reduced, ordinarily to a small percentage of the feed
water, and this amount is readily taken out by an efficient separator.
We can therefore easily give dry steam to the engine. Leaky valves
and pistons present mechanical difficulties that are not difficult to
overcome. We now come to a problem of different character.
For clearness, let us deal with the events that take place on one
side of the piston only and we shall call the stroke in which the
steam drives the piston the forward stroke and the stroke in
which the piston drives the steam out of the cylinder the return
stroke. To be concrete, let us take an engine exhausting into
the atmosphere, using steam at 80 pounds absolute, temperature
312 F. As the piston starts on its forward stroke, steam at a
temperature of 312 F. is entering a volume the walls of which
were exposed during the whole of the previous stroke to steam
at a temperature of 212 F. The difference of 100 in tempera
ture is greater than the ordinary difference between a hot summer
day and a cold day in winter.* The immediate result of the
contact of the hot steam and relatively cool walls is the condensa
tion of enough steam to heat the walls (to a depth that probably
does not exceed 1/50 of an inch) to the temperature of the in
coming steam. The thickness of the film of water may not exceed
a few thousandths of an inch, but the detrimental effect on the
engine economy is very considerable. From 20 to 50 per cent
of the weight of the entering steam is condensed to form this
apparently inconsiderable film and to heat the inner wall to such
a small depth.
Let us make a few rough calculations for a 20"X24" cylinder
without clearance, steampressure 80 pounds per square inch
absolute, cutting off at onequarter stroke, and suppose the steam
* Later we shall show, however, causes that will prevent the walls from
sinking in temperature, in this case to 212 F.
MEASUREMENT OF HEAT LOSSES. 187
shown by the card at cutoff is 75 per cent of the steam actually
admitted :
Volume at cutoff 6X3.14x100 = 1884 cu. in.
Weight of steam present 1884/1728 X .1843 = .201 pound
Weight of steam admitted 201 X4/3 = .268 pound
Weight of steam condensed 268  .201 = .067 pound
Volume of condensed steam 067/.036 = 1.86 cu. in.
Area of internal surface 314 + 314 + 376.8 = 1008.8 sq. in.
Thickness of film 1.86/1008.8 = .0018 in.
Heat given up by cond's'd steam . 895 X .067 = 60 B.T.U.
Assume weight of cast iron .26 pound per cu. in.;
specific heat of cast iron .13;
rise in temperature 100 F.;
" thickness of metal affected = d.;
Then (1008 XdX. 26) (.13 X 100) =60 B.T.U. ;
hence d = l/55 inch approx.
For reasons given hereafter the assumed range of 100 is
probably too high and we have only considered the area up to
cutoff. The calculations are only intended to give approximate
values, as other variables will be found to enter the problem.
After cutoff the temperature of the expanding steam decreases
with the decreasing pressure. Therefore after cutoff the part of
the cylinder that is being uncovered by the moving piston does
not have to be heated to the same temperature that was required
for the part exposed before cutoff. At some point after cutoff,
then, condensation ceases and reevaporation starts, since the v/alls
are now hotter than the steam. If we have an accurate card from
an engine whose clearance volume, diameter, and stroke are known,
we may easily find the weight of steam present at cutoff and for
various points on the expansioncurve. The reevaporation, while
not considerable, is greatest near the end of the stroke where its
usefulness in driving the piston amounts to little. But the moment
that the exhaustvalve opens and there is a considerable drop in
pressure (and the corresponding temperature), reevaporation and
the consequent cooling of the walls proceeds rapidly. It may
probably be taken for granted that steam of any degree of wetness
(short of actual foaming) on entering a cylinder will be exhausted
188 THE STEAMENGINE AND OTHER HEATMOTORS.
as practically dry steam. The heat so taken from the walls must
be returned by the condensation of an appropriate amount of the
dry steam that enters for the next stroke. Hence the economy of
separating the steam and water before the steam enters the
cylinder.
Considering only the facts brought out in this article, we note
that:
1. The condensation and reevaporation would go on in a
cylinder clothed in a perfect nonconductor.
2. With an imperfect nonconducting covering there would
be an additional loss of heat and consequent increase of con
densation to supply the heat flowing to the outside of the
cylinder, and thence carried away either by conduction or
radiation.
3. In any practical case we may consider the cylinder
shell as made of two parts. In the inner (of greater or less
thickness in accordance with circumstances yet to be consid
ered) there is a rapid fluctuation of heat from and to the steam,
and a regular flow of heat to the outside surfaces of the
cylinder.
4. The water of entering wet steam will be reevaporated
at the expense of the dry steam of the next stroke, and that
this reevaporation takes place on the returnstroke and serves
only to tend to increase the back pressure. In the case of
compound engines, however, this steam does some work in a
following cylinder if there is one.
5. In the case of the loss of heat from steampipes it was
remarked that steam was a poor conductor of heat, and that
the presence of a film of water on the surface of the walls had
an extremely important influence on the loss of heat. We
shall find that, in this case also, the presence or absence of this
film modifies results materially. If, by evaporation during
exhaust, the walls become free of the film of water, then they
cease to fall materially in temperature and may remain at a
considerable temperature above that of the exhauststeam.
Their range of temperature is thereby lessened.
At the point of exhaust closure the steam remaining in the
MEASUREMENT OF HEAT LOSSES. 189
cylinder is not only dry, but may be slightly superheated. If this
point be late in the returnstroke the whole compression curve
may show evidence of superheating by rising more rapidly than
an adiabatic. With a heavier ratio of compression the first part
of the curve may rise higher than the adiabatic, owing to the recep
tion of heat from the hotter cylinder walls. With the rising tem
perature of the steam (from compression) the temperature differ
ence between the walls and compressed steam becomes smaller, the
rate of pressure increase is lower, and the compressioncurve crosses
the curve of dry saturated steam. Further compression raises the
temperature of the compressed steam above that of the cylinder
walls and condensation ensues. Heat is now lost rapidly by the
steam and further compression follows the laws governing the
compression of vapors in contact with their liquid. The curious
hook EVG is produced. In Fig. 110, taken from Thurston on Heat
Exchanges within the Steamengine, let GVETD'CA be the com
pressioncurve, CDH the adiabatic from any point (7, SEI the
saturationcurve from any point E, LM the temperaturecurve
if the compression were adiabatic, MNPR the actual temperature
as shown by calculation from the diagram, and MPR the probable
temperature of the metal.
The statement has frequently been made that there would be
no loss from clearance if compression were carried to the initial
pressure. Accurate experiments have shown a slightly increasing
water consumption per horsepower with increasing compression
when all other quantities were kept constant in the same engine.
Theoretically, increasing compression should produce a loss of
economy for the following reason. The steamengine is a mechan
ism for the conversion of heat into work. No economy can result
by changing the expensively obtained work back into heat, since
all changes of energy from one form into another are accompanied
by loss. As a practical result, in engines designed for economy,
clearance surface is reduced to the minimum by placing the valves
in the cylinderheads and only a moderate amount of compression,
conducive to smooth running, is used.
6. The amount of condensation will be affected by the size
and proportions of the cylinder. Comparing two cylinders (the
190 THE STEAMENGINE AND OTHER HEATMOTORS.
linear dimensions of one being twice that of the other), the
larger one could perform eight times the work of the smaller,
but its internal exposed area would only be four times as great,
hence the percentage of condensation would be reduced.
Similarly for engines of the same volume, by proper choice of
FIG. 110.
dimensions there would be one of minimum exposed internal
surface.
7. Other variables also affect the result. We may men
tion steampressure, revolutions, ratio of expansion, and jack
eting.
Range of Temperature. The amount of initial condensation
depends upon the range of temperature of the cylinder walls, and
MEASUREMENT OF HEAT LOSSES. 191
economy follows a reduction of this range. The range is de
creased
1. By a late cutoff. By studying the conditions we note
that the part exposed to the initial steam was exposed to the
exhaust conditions for a short time only, and more of the sur
face is at the highest temperature.
2. By the reduction of the amount of water present at cut
off. The walls part readily with their heat to a film of water
and less readily to dry steam. Therefore the lower tempera
ture is raised by reducing the amount of water to be evaporated.
3. By reducing the time of exposure. The element of time
always affects the amount of heat that may be transferred. By
increasing the number of revolutions the time of exposure is
diminished.
To Find the Weight of Steam Accounted for by the Indicator
card. At any point in the stroke, the steampressure is due to
the amount of dry steam present. At any point between admis
sion and cutoff all the steam has not yet entered the cylinder,
and after the exhaust opens a large percentage of the steam has left
the cylinder. In any case, however, we can determine the weight
of dry steam present in the cylinder at any piston position. From
cutoff to exhaustopening and from exhaustclosure to steam
opening we are dealing with a closed volume and approximately
with a constant mass of dry steam. . At all other points of the
stroke we are dealing with a variable mass of steam and care
must be taken in the interpretation of results.
The amount of dry steam present between cutoff and exhaust
opening differs materially from the amount of steam that entered
the cylinder before cutoff. The reasons for this become evident
when we consider not only the conditions that exist when steam
is admitted, but also the exceedingly small volume occupied by
the water formed in the condensation of steam. Two cubic feet
of steam may readily enter a cylinder whose volume up to the
point of cutoff is only one cubic foot. One cubic foot of the
steam may condense and form a film about 1/500" thick on
the walls. The volume of this film is, of course, practically neg
ligible.
192 THE STEAMENGINE AND OTHER HEATMOTORS.
To obtain the weight of the dry steam present in the cylinder
at any point of the stroke we need
1. The absolute steampressure at that point.
2. The absolute volume of the clearance and of the cylinder
up to the point considered.
3. Steamtables that show either the weight of one cubic
foot of steam or the volume occupied by one pound weight
of steam at the various pressures.
Then to obtain the weight of dry steam present at any point
of the stroke either multiply the absolute volume in cubic feet
by the weight of the steam per cubic foot, or divide the absolute
volume in cubic feet by the volume in cubic feet of one pound
weight of steam. Table VIII.
For example, find the weight of dry steam in a 20"X24"
cylinder at 16" from the beginning of the stroke, the pressure
at that point being 42 pounds absolute, clearance 10 per cent.
(16+2.4)X314
Volume =
1728
18 4x314
Weight = . 32 pound,
18.4X314X.10179
or weight =  1 _ OQ  = .32 pound.
1 / o
Analysis of Indicatordiagrams. Steam accounted for by the
indicatorcard assumes the following data :
Clearance ............................ =E =2%
Stroke ............................... =L ____
Number of strokes ..................... =N ....
Cutoff pressure above zero ............. 75.6 Ibs.
Weight per cubic foot at cutoff pressure =W e = .1773 Ibs.
Proportion of stroke completed at cutoff =C = .172L'
Compression pressure .......... . ....... 3 Ibs.
Weight per cubic foot at compression pres
sure .............................. = W h = .0085 Ibs.
Proportion of stroke uncompleted at com
pression .......................... =H .048L'
Mean effective pressure ...... , ......... =M.E.P. =37.17 Ibs.
MEASUREMENT OF HEAT LOSSES. 193
The weight of steam as shown by the indicatorcard would be
per hour per horsepower :
A " ;.172 + .02) (L X .1773)  (.048 + .02) (L X .0085)]# X60
33,000
Hence the general formula is
The symbol C may also refer to the proportion of the stroke com
pleted at release, and W c would be the weight of one cubic foot of
the steam at release pressure.
Method of Finding the Drysteam Fraction. Let us imagine
that we have a boiler of ample capacity in which the steampressure
is kept absolutely constant. Let us have two engines driving a
common shaft whose load is always too great for the engine that
is to be used as an experimental engine. Block the cutoff of the
latter engine at constant cutoff. The other engine takes steam
from a separate boiler and its cutoff varies with the load. The
experimental engine may easily be run at constant pressure, load
cutoff, revolutions, and so will give a constant card.
If the experimental engine has a surface condenser the feed
water per stroke may be calculated by weighing the condensed
steam. By keeping the waterlevel constant in the steamboiler
a less accurate measure of the feed per stroke is obtained by weigh
ing the feed water.
The drysteam fraction
Weight of dry steam at any point of the stroke
"Amount of steam and water present at that point
The method of finding the numerator was shown (page 163).
To obtain the denominator we must start at the piston position
when the exhaustvalve closes. All authorities agree that the
steam in the cylinder at the point of exhaustclosure is perfectly
dry. Knowing its volume and pressure, its weight can be calcu
t Standard Rules. A. S. M. E.
194
THE STEAMENGINE AND OTHER HEATMOTORS.
lated. At the end of the compressioncurve this steam may be
either wet, dry, or superheated. Knowing the pressure and volume
at that point, the weight of dry steam present can be calculated
and if that is less than the amount present at exhaustclosure, it
is evident that some steam has been condensed. If the pressure
is higher than that called for by the law, PV = C, the steam has
been superheated. In any case, the amount of steam and water
present when the steamvalve opens is equal to the amount of dry
steam present at the instant the exhaustvalve closes. If to the
amount so found we add the weight of steam and water admitted
per stroke (as found by weighing the condensed steam or the feed
water), we obtain the amount of steam and water that is present
at any point between cutoff and exhaustopening.
Hirn's Analysis. Mons. G. A. Him published his Thermo
dynamics in 1876. In that work he developed a theory of the
real engine that has served as the basis for nearly all subsequent
work on that subject.
O O'
FIG. 111.
In this analysis we endeavor to account for every thermal unit
of the steam that passes through the engine. To make such an
analysis we must know accurately the volume of the clearance and
of the cylinder at the important points of the stroke. The quality
of the steam at admission, the pressures, revolutions, and work
should be known and must be kept practically constant. All the
indicatorcards would then be precisely alike, so that the expendi
ture of heat and water per stroke multiplied by the number of
strokes per hour will give the actual expenditure per hour.
MEASUREMENT OF HEAT LOSSES. 195
Let Vb = volume of clearance in cu. ft.;
V c = volume at cutoff in cu. ft.;
V d = volume at exhaustopening in cu. ft. ;
V f = volume at exhaustclosure in cu. ft.;
V g = final volume of compression = 7 & ;
m = pounds of (mixture) steam and water;
x = quality of mixture;
xm = pounds of steam in the mixture;
(1 x) m = pounds of water in the mixture;
g = heat of the liquid above 32 F.;
p= internal latent heat;
E = external latent heat;
I/= internal latent heat + external latent heat.
As before, a subscript added to a letter limits its value to the
piston position shown by the letter. Thus m/ indicates the weight
of steam and water in the cylinder at the instant that the exhaust
valve closes.
The analysis will start at the instant the exhaustvalve closes
or at / on the indicatorcard. In all ordinary cases all the water
that may have been in the cylinder when the piston is at e will be
evaporated by the time the piston reaches /. Knowing p f and
Vf we may calculate m/. We know x = 100%.
At g we know that m g = mf, as we are dealing with a closed
volume. We do not know the condition of the steam, however.
Knowing p g and V g , we can obtain the amount of dry steam
present. This is (x g m g ). The water at g is then m f x g m .
Therefore x g = ~. In a preceding paragraph it was shown
that compressed steam may be either wet, dry, or superheated.
This would be shown in the above by x g m g being <, =, or (appar
ently) > than m { .
At g the steamvalve opens and the lines gb and be are made
Calling the weight of steam and water admitted per stroke m t
(found from the measurement of the condensed steam), we knov*
that the total weight of steam and water present at c is m a +m/=m c .
As before, the amount of dry steam present (x c m c ) can be calcu
lated, as we know p c and V e . The value of x c is . The
196 THE STEAMENGINE AND OTHER HEATMOTORS.
quality of the steam admitted x a must be determined by calorim*
eter experiments at some point just before the enginethrottle.
The weight of steam and water present at exhaustopening is the
same as that at cutoff, and its quality x^ is determined as before.
Heat Interchanges.
Let 7 c = the work of compression o'gjo" in B.T.U.;
U e = ihe work of expansion in B.T.U.;
7 r = the work of rejection of exhaust = o"feo r " in B.T.U.;
7 = the heat given to the cylinder walls in B.T.U.;
H = the heat required to produce one pound of steam.
In discussing heat interchanges we must start at the point of
exhaustclosure, as we assume that the steam is dry at that point.
This is a very safe assumption, for even if the quality of the clear
ance steam were only 75%, the amount of steam in the clearance
is so small that the percentage effect on final results would be
negligible. The amount of heat IN the steam at / on the assump
tion of dry steam is m f (q f +pj).
The amount of heat in the steam and water at g is ing(q g + Xgp g ).
Adding the heatequivalent of the work of compression to the heat
at /, we obtain the heat at g plus the heat given to the cylinder
walls. Therefore
whence the heat given to the cylinder walls, 7 C , may be found.
We must discriminate between the heat required to produce
m a pounds of steam and the heat in m a pounds of steam. The
heat required to produce the m a pounds of steam that enters the
cylinder is
For wet steam, H a = m a (q a + x a L a ) .
11 superheated steam, H a s = m a \q a + L a +QA8(t t t a )},
where t a t a is the rise in temperature due to superheating.
If we add the heat IN the steam and water at the beginning of
admission (at g) to the heat required to PRODUCE the steam (wet
or superheated) admitted, we obtain the heat in the steam at
MEASUREMENT OF HEAT LOSSES. 197
cutoff + the admission work (in B.T.U.) 4 the heat given to the
cylinder walls during admission. Hence
H a (or H a s ] + m g (q g + x g p g ) =m c (q c +x c p c ) + U a +I a .
As I a is the only unknown it may readily be found.
The weight of steam and water present at cutoff is the same
as that present at exhaustopening. The difference between the
amounts of heat in the mixtures at cutoff and exhaustopening is
equal to the work of expansion + the heat given to the cylinder
walls. Hence m c { (q c +x c p c ) (qa + xapd) } = U e + I e . If I e is nega
tive, then the walls have given more heat to the steam during
expansion than they have received.
If tests are accurately made on an engine with a surface con
denser, the amount of heat sent to that vessel per stroke may be
calculated by multiplying the rise in temperature of the cooling
water (more accurately the difference of the corresponding q's) by
the weight of that water used per stroke. While it is easy to cal
culate approximately the exhaustheat quantities sent to the con
denser, it is impossible to give directly an exact measure for the
following reason. The water that is in the cylinder is evaporated
in varying quantities in the time that the lines de and ef are made,
that is, at varying temperatures. If the fall of pressure, de, is not
great, it is probable that most of the water is evaporated during
the formation of the line ef. A check to any calculation is found
in the fact that the heat admitted the work done (B.T.U.) must
equal the heat sent to the condenser (neglecting radiation or heat
received from a steamjacket). This is an indirect but exact
measure of the heat sent to the condenser or to the atmosphere.
Or, H a (or H a 8 )  the net area of the indicatorcard in B.T.U.
=H r} the heat rejected = w(qi q^ +m a q a ,
where w = the pounds of cooling or injectionwater per stroke;
g e = the heat of the coolingwater above 32 F. as it en
ters the condenser;
198 THE STEAMENGINE AND OTHER HEATMOTORS.
qi = the heat in the cooling or dischargewater above 32F.
as it leaves the condenser;
q a = the heat in the feedwater above 32 F.
In the case of a jet condenser the amount of water leaving the
condenser includes the condensed steam as well as the injection
water.
Heat Interchange, I r , during Exhaust. We know the weight of
steam and water that is present at d, we can calculate its quality
x d , and therefore can calculate the amounts of heat. We have
already calculated these quantities for piston position, /. The
difference between these two quantities of heat is the heat given
to the cylinder walls (negative) + the heat given to the cooling or
injectionwater + the heat, q t , given to the condensed steam above
32 F. Or,
m c (q d + x d p d )  m f (q f +p f ) = I r + w(qiq e ) +m a (q 9 ).
As all quantities but I r are known, it may be found.
Jacketsteam. Each pound of jacketsteam, try, gives up L
thermal units, as the steam is condensed at constant pressure to
its liquid at the boilingpoint. The heat given up, WjLj, must be
added to the heat that is required to produce the m a pounds of
steam admitted. From this sum, subtract the heatequivalent of
the work done to obtain the heat sent to the condenser.
The thermal efficiency is obtained by dividing the net work done
per stroke in B.T.U. by the total heat expended to produce m a
pounds of steam (from the temperature of the feedwater) plus the
heat given up (WjLj) per stroke by the jacketsteam.
Hirn's Analysis. Work out Hirn's analysis for the following
data:
Area of piston, 3 sq. ft.
Stroke, 3 ft.
Clearance, 3.33%.
Steampressure, 100 pounds absolute.
Cutoff, 6" from beginning of stroke.
Exhaust opens at 98% of stroke.
closes" 95% " "
Back pressure, 15 pounds absolute.
MEASUREMENT OF HEAT LOSSES. 199
From a test it is found that the dry steam at cutoff is
composed of the steam saved by compression and 80% of the
steam mixture admitted. Quality of steam at the throttle,
98%. Fig. 111.
Clearance volume, 3 X3 X .033 = .3 cu. ft.
Volume at /, 3 X (3 X .05) + .3 = .75 cu. ft.
.75X15
Pressure at g, ptVt = p g v g ,  5  = 37J pounds.
.o
V/ = .75 cu. ft., p/ = 15 pounds.
Weight of dry steam at / = . 03868 X. 75 =ra/ = . 029 pound
dry steam.
F<, = .3 cu. ft., p g = 37.5 pounds.
Weight of dry steam at g = x g m g = . 09151 X. 3 = .02745.
Weight at /weight at g = weight condensed = .029 .0274
= .0016.
02745
x g = the per cent of steam =
To find m a , the steam and water admitted.
Volume at c = .3 cu. ft.+3X.5 = 1.8 cu. ft.
Weight of dry steam present at c, 1. 8 X. 2303 = .41454 pound.
" " the above dry steam that was admitted on this stroke
= .41454  .02745  .38709 pound.
38709
" " dry steam and water actually admitted, ^ Q = .483862
pound.
" " water in mixture admitted, .02 X .483862 = .00968 pound.
" "dry steam actually admitted, .483862  .00968 = .47418
pound.
" " steam condensed on admission, .47418 .38709 =
.08709 pound.
" " " and water present at cutoff, .483862 + .029 =
.512832 pound.
Heat Exchanges. Heat at /, the heat actually contained in 1
pound of dry steam at p f pressure multiplied by the weight of
steam:
1074.1 X. 029 = 31. 1489 B.T.U.
200 THE STEAMENGINE AXD OTHER HEATMOTORS.
Heat at g ......... 029 X232.46 + .0274 X853.48 = 30.1693 B.T.U.
Work of compression, U c = ' !L
7o
15Xl44x.75xloge2.5
778
Heat given to walls, 7 C = 31.1489 + 1.908 30.1693= 2.8876
Heat admitted = .4839 X298.09 + .47418 X 883.773 = 563.1840 "
Adding heat at g = 30.1693 "
593.3533 "
Subtracting heat present at c
= .5128X298.03 + .41454x803. 108 = 485.7478 "
107.6055
Subtract external work .......... 100X144x1.5 = ^ ^
778 . __
Heat given to the walls, I a ................... . . 79.845 "
1.8X100
Pd= Q .. =19.35 pounds.
9.3
Weight of dry steam present at d =9.3 X. 0495 = .46035 pound.
100X144X1.8,
Work during expansion =  log* 5.17= U e
= 54.735 B.T.U.
Heat at d = . 51286x195.28 + .46035X882 .36 = 506.3535
506.3535 + 485.747854.735=  76.3407 = / e = heat
OIVEX UP by the walls during expansion.
The data of this problem were assumed. The student will find
the heat that is wasted and determine if any change should be
made in the data.
MEASUREMENT OF HEAT LOSSES.
201
Steam Consumption. The actual consumption of steam by
engines is a very variable quantity. It varies with the style
of engine, its load, its speed, and a number of other quantities.
As important as any cause is the amount of leakage past worn
valves or pistons. Much that is called initial condensation is
really leakage. In an engine in good condition probably one
third of its so called initial condensation is leakage. For com
parison, we give two tables and their corrections, as given by
Helm in The Engineer, and the results of actual tests on engines
as they were in daily use. (Paper by Dean and Wood, A.S.M.E.,
June, 1908.)
The ideal consumption of steam per horsepower (S.P.H.) for
noncondensing engines of the fourvalve and Corliss types, with a
back pressure of 16 pounds absolute is given in Table C. To this
must be added the following corrections for initial condensation:
For 80 pounds initial pressure the following amounts should
be added to those given in Table C for noncondensing engines :
TABLE A.
For 2 expansions 3 . 65 pounds
" 3
" 4
" 5
" 6
" 8
" 9
" 10
" 12
" 15
" 16
For condensing engines increase the quantities given in Table
D by the following quantities based on an initial pressure of
125 pounds.
TABLE B.
For 2 expansions 3 . 28 pounds
3
4
5
6
7
8
9
10
12
15
16
18
20
4.10
5.45
tt
6 70
7 90
9 80
11 20
12.35
14.80
18.60
. 21.50
3.60
4.62
5 . 57
6 35
7 35
7.45
8.25
9.75
9 80
10 80
11.70
12 60
. 13.30
((
202 THE STEAMENGINE AND OTHER HEATMOTORS.
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MEASUREMENT OF HEAT LOSSES.
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204 THE STEAMENGINE AND OTHER HEATMOTORS.
If the initial pressure is increased above the amounts on
which the above tables of corrections are based, the cylinder
condensation will be increased by J pound for each 10 pounds
of increase in initial pressure. For instance, in noncondensing
engines if the pressure is 100 pounds instead of 80, then to the
amount in the correction Table A an additional .4 pound must
be added. In the case of condensing engines, if the initial pressure
is 165 pounds an additional amount of ^~X.2 = .S pound
must be added to the amount in the correction Table B.
Example. What is the steam consumption of a noncon
densing engine, initial pressure 100 pounds, five expansions.
From Table C, 16.42 pounds; condensation 6.70 pounds at
JAQ QQ
80 pounds, pressure, hence at 100 it would be 6.7 H ^ X.2
= 7.1. Total consumption = 23.52 pounds.
In Tables C and D the mean effective pressure, M.E.P., is a
little greater than would be realized owing to the effects of com
pression, release, and clearance.
Compare results obtained as above indicated with the results
given below. See Power, July 14, 1908.
(1) 15 in. by 14 in.; 240 r.p.m.; horizontal, single, flat
valve engine with 100kw. d.c. generator on the shaft. Average
steam pressure 83 pounds; back pressure 4.8 pounds; cutoff
30.7%; water per I.H.P. per hour, observed pounds, 44.7.
(2) 16 in. by 15 in.; 240 r.p.m.; vertical, singleflat valve
engine with two 50kw. d.c. generators on the shaft. Average
steam pressure 75 pounds; average back pressure, 1.6 pounds;
average cutoff, 46.85 and 29.3%; water per I.H.P. per hour
observed pounds, 37.3 and 39.7.
(3) 14 in. by 12 in.; 300 r.p.m.; horizontal, single flatvalve
engine with two 40kw. d.c. generators on the shaft; average
steam pressure 91 pounds; average back pressure 6 pounds; aver
age cutoff, 45.3 and 25.1%; water consumed per I.H.P. per hour
observed, 37.5 and 37.3 pounds.
(4) 16 in. by 14 in.; 270 r.p.m.; horizontal engine with four
"flat valves and having a 125kw. d.c. generator on the shaft;
tested at J, f, and full load; steam pressure, 114 pounds; back
MEASUREMENT OF HEAT LOSSES. 205
pressure, 3.5, 5, and 8 pounds; cutoff, 16.5, 27, and 40%; water
per I.H.P. per hour observed, 45.7, 43.4, and 42.7 pounds.
(5) 12 in. and 19 in. by 14 in.; 230 r.p.m.; vertical, cross
compound condensing piston valve engine with a 100kw. d.c.
generator on the shaft; steam pressure, 114 pounds; average
cutoff, H.P. cylinder 33 and 21%; average cutoff, H.P. cylinder,
38 and 25%; water per hour observed, pounds, 25 and 20, at .8
and .7 full load.
(6) 18 in. by 18 in.; 220 r.p.m.; horizontal piston valve
engine with a 100k.w. d.c. generator on the shaft; approximate
loads 1J, f, J; average steam pressure, 114 pounds; I.H.P.
273, 170, 122; water per I.H.P. per hour observed, pounds, 29.7,
34.8, 39.89.
(7) 15 in. by 16 in. ; 250 r.p.m. ; horizontal single piston valve
engine with a 100kw. d.c. generator on the shaft; loads, full,,
f, J, and J; steam pressure 87 pounds; I.H.P. 137, 102, 69,
36; water per I.H.P. per hour observed, pounds, 34.1, 37,,
42.3, 56.3.
(8) 12 in. by 18 in.; 190 r.p.m.; horizontal engine with two
flat inlet valves and two Corliss valves, and having a 75kw. d.c.
generator on the shaft. Loads, 1J, 1, and J; average steam
pressure 90 pounds; I.H.P., Ill, 74, 43; water I.H.P. per hour
observed, pounds, 34, 36.8, and 44 pounds.
While it would be unfair to draw general conclusions from
isolated tests such as the above it is nevertheless proper to call
attention to the great loss in economy due to improper seating
of valves and of pistons. Poorly made fourvalve highspeed
engines will not compare in economy with well made singlevalve
engines. The latter should have valves for which the wearing,
process should be a tightening process. Balanced valves in
which this process does not take place showed up badly in the
above test. The economical loads are the heavy loads. D. K.
Clark in the early fifties showed that the economical load for
locomotives was that due to a cutoff at onethird stroke.
Ex. 86. Assume data from Engine Tests by Barrus, and work out
the analysis.
Ex. 87. Assume card and other required data, and work out the
analysis.
206 THE STEAMENGINE AND OTHER HEATMOTORS.
Ex. 88. Corliss engine, area piston 8 square feet, stroke 4 feet,
clearance 2 inches, cutoff 1/6 stroke, initial pressure 100 pounds
gage, exhaust opens and closes at end of the stroke, expansion ac
cording to the law PF = C, revs. 100 per min., 20% of dry steam
that was admitted is condensed, quality of steam admitted = 98%.
Give Hirn's analysis.
CHAPTER VIII.
ENTROPY.
Definition. Every term on either side of an equation must be
of the same degree. An area cannot equal a volume, and a foot
pound cannot equal any number of feet, pounds, or degrees of
temperature. When the chemical energy of gunpowder is con
verted, through an explosion, into work, heat, light, and sound,
all of these must be compound and of like degree. As work is a
compound of two factors, heat must also be a compound of two
factors.
An area is a product of two dimensions, and, just as we have
heretofore represented work by areas, we shall now show that
heat may be represented in a similar manner. In so doing we
shall be able to illustrate easily certain facts that are difficult to
understand. Let it be clearly understood from the beginning that
as in the construction of the work diagram or PV diagram no
thought was given to the variation of heat quantities, so in the
construction of the heat diagram ; or <j>T diagram as it is often
called, we must lay off heat quantities and ignore variation of
pressures and volumes.
As work in footpounds is equal to Wh or PV= (pA)U, similarly
heat in thermal units will be found to equal <j>T, where <, or en
tropy, represents one factor of heat, and T, or absolute tempera
ture, represents the other. As the work diagram is a rectangle
if P is constant, similarly the heat diagram is a rectangle if T 7 is a
constant. The word entropy is derived from two Greek words en
and t~ope, meaning a turning in or transformation, referring to the
heat per degree which is transferred to another body or trans
formed into another form.
As we must resort to calculus in PV calculations when the
pressures vary according to some law, so we must resort to the
same instrument if the temperatures vary in the <f>T diagram.
4s work is made up of the sum of the infinitesimal rectangles,
207
208 THE STEAMENGINE AND OTHER HEATMOTORS.
abed, =pdV, Fig. 113, so the heat added is made up of the sum
of the infinitesimal heat changes Td$, Fig. 115. During these
\
a
\b
pdv
d c
FIG. 112.
FIG. 113.
changes T is kept constant as P was kept constant in the work
diagram. Hence (Fig. 115) we have
Td(j> or d<p = . We
can easily integrate this expression, when we can express Q in terms
of T. It is essential to remember that T is absolute temperature.
V
v
\
FIG. 114.
d<t>
FIG. 115.
The proper interpretation of many facts already given will
show that absolute temperature is one of the factors of heat. The
heat in a body increases or decreases as we increase or decrease its
temperature. If a perfect gas is expanded adiabatically to absolute
zero of temperature, it has lost all its heat. In other words, the
total heat of a perfect gas is a function of its absolute temperature.
ENTROPY. 209
If we agree that heat is made up of two factors and that absolute
temperature is one of them, we may call the other factor anything
we please. It is not possible at present to give an absolute con
crete meaning to entropy. It is said to be analogous to pressure
in a PV formula, or analogous to a variable thermal mass in the
WV 2
formula for energy, . For the present the student will find
^Q
the mathematical definition sufficient. In addition he should keep
in mind that change in entropy depends upon a change of heat as
heat. When heat is transformed into available work there is no
change in the entropy, since there has been no loss of heat as heat.
The student must remember that exact processes are theoretic
ones. In adiabatic expansion there must be no friction, conduc
tion, nor radiation. In other words, the process is reversible.
Evidently these assumptions are not absolutely obtained, then,
in any practical case.
In representing heat by an area, absolute temperatures are
represented by ordinates, and variable entropy by variable ab
scissas. Further, whilst temperature must be laid off from absolute
zero of temperature, entropy is never so laid off. We are only
interested in the increase or decrease of the entropy of a substance,
and not in the total amount of entropy that it may possess above
the absolute zero of entropy. In other words, by the formula
d(f> = 7F we mean that the addition or subtraction of the quantity
of heat dQ at T produces a change of entropy d(f>. The starting
point for measuring entropy is taken at 32 F., as we are not in
terested in the entropy of ice above some lower temperature.
In drawing a PV diagram, we assume one scale for pressures
and a different one for volumes. Similarly in entropy diagrams,
we may assume any convenient quantity, as \" or }", to represent
100 degrees of temperature, and 1" or 2" to represent a unit of
entropy. Assuming 200 degrees =1" and unity of entropy = 1",
then 1 sq. inch area = 200 B.T.U.
If dQ thermal units raise the temperature of any liquid dT
degrees, we know that dQ = cdT, where c is the specific heat of the
liquid. For water we may assume c = 1.0 for all temperatures.
Hence, for water, dQ = l.QdT, and therefore the equation d(f> = ^
210 THE STEAMENGINE AND OTHER HEATMOTORS.
1
becomes d$= ' , or jr. The student should remember
that the numerator dT now represents an infinitesimal quantity
of heat and not an infinitesimal difference of temperature.
Taking our origin for entropy at that possessed by water at
32 F., we have for the increase of entropy, when water is heated
from TV = 32 +461 to 3V, any other temperature in degrees Fah
renheit absolute,
Construction of the Waterline. To illustrate the use of the
above formula, let us draw the line that shows the variation of
absolute temperature and entropy when one pound of water is
heated from 32 F. to 350 F.
As this line will be slightly curved, let us find the abscissa and
ordinate for one pound of water heated to
The ordinates are
TO = 493; ^1 = 561; 7 7 2 = 673; T 3 = 8ll.
The abscissas are
.313; and
Qj I
.5042.
Having the abscissa and ordinate for each of the four points, they
may be plotted as in Fig. 116, where to, ti, t 2 , t% represent the points.
The heat required to raise the water from 32 F. to 350 F. is
the area eotot 3 e 3 . To show this approximately multiply the mean
ordinate by ^ or 4B3+561 ^ fl73 + 811 XJSM2319 B.T.U..
or 35032 = 318 B.T.U. These results would be equal if we had
laid off the figure accurately and used a planimeter.
As the curvature of the line t Q t^ is so slight, the entropy may
be obtained directly by dividing the known area by the mean
ENTROPY.
211
ordinate. For example, the area of e /o^i^i^?i <?o = 68 = 68
B.T.U. Dividing this by the mean temperature we have
68
493 +561 = .129 as the entropy or abscissa
'4931
T,
To
FIG. 116.
The reason for choosing an arbitrary startingpoint for entropy
T
may now be shown. In the expression < = log ^r let T = Q
absolute, .'. < = oo. This shows that entropy measured from an
absolute zero of entropy is infinite, so that it is absolutely necessary
to start at some finite point.
In the construction of the waterline it must be distinctly
understood that the pressure on the water increased with the
addition of heat in such manner that there was no steam formed.
Ex. 89. On a scale of 1" = 200 Fahr. abs. and 3" = unity of en
tropy, lay off the waterline for 32, 100, 150, 200, 250, 300 from
the entropy table; measure the area with a planimeter. Table VII.
212 THE STEAMENGINE AND OTHER HEATMOTORS.
Steamline at Constant Pressure. Having reached any de
sired pressure and the corresponding boilingpoint, let any further
addition of heat go to the conversion of some of the water into
steam. The volume increases in proportion to the steam formed
and the temperature will remain constant.
The heat added is the sum of the internal and external latent
heat. Ordinarily this sum is called simply the " la tent heat." As
the temperature remains constant, it is evident that the ordinate
in the diagram will be constant, and that the entropy will vary
directly with the amount of heat added or the amount of water
converted into steam.
If L 3 = latent heat of one pound of steam at TV Fahr. absolute,
the increase of entropy over that of water at the boilingpoint T 3 is
T rrt T
7;?. The total entropy above water at 32 F. is log, ^ +^. If
1 3 ^0 t 3
the water was initially at some temperature TI higher than T , the
T
increase of entropy above TI will be less by log e ^r, or the entropy
* o
required to raise one pound of water at a temperature TI to T$
(m \ T
jr) + jT
Tz . T, T 3
since log. ^rlog. ^r = log t TFT.
1 tQ ^ 1
T is / 3 + y +JT*
If we consider the diagram (Fig. 116) to be made by a point
travelling along the waterline, its vertical movement being due
to increase of temperature and its horizontal motion being propor
tional to increase of entropy, we know that after water reaches the
boilingpoint there is no further increase of temperature. On
further addition of heat the point must then change direction
abruptly and travel parallel to the horizontal axis. The distance
travelled along this line will be directly proportional to the amount
of water evaporated. For instance, if t 2 s 2 is the entropy added to
one pound of water at the boilingpoint to form one pound weight
of steam at that same temperature, then t 2 m 2 is the entropy of
~  pounds of steam. And, of course, represents the fraction
t 2 s 2 * t 2 s 2
An approximate value for log. +jT is + y +JT
ENTROPY. 213
of the pound of water that has NOT been converted into steam, or,
in other words, is water.
Expansion Curves. Draw the steamlines due to the forma
tion of steam by the addition of heat to water at the following
boilingpoints: 3 =350 F.; * 2 = 212 F.; and ^ = 100 F.
We may substitute in the formula
Latent hea t = 1091 .7 + .305fe  32)  (fe  32) ,
or from the tables obtain
QAQ
Latent heat at 350 F. = 868 B.T.U., .'. e 3 e 4 = 359+461 = 1 ' 07 '
212 F.= 966 " e 2 e s = =1.44;
1044
100 F. = 1044 " 6i6 6 = ~^r =186.
561
Evidently the area of the rectangle 63*35364 = 3= 868 B.T.U.
e 2 t 2 s 2 e5 = Lj 2 = 966
6iMi6e = LI = 1044
Ex. 90. From the values in a table of entropy, lay off the entro
pies for 1 pound of steam at the temperatures and on the same scales
as in Ex. 89.
The lines 3 s 3 , t 2 s 2 , Mi are lines of constant temperature or iso
thermal lines. If the points s 3 , s 2 , i, are joined, the curve so
obtained is called the saturation curve. This is a short way of
expressing the fact that as 3^2*1 limits the entropies of one pound of
water at varying temperatures, so s 3 s 2 Si limits the entropies of
one pound of dry saturated steam at various temperatures in a
similar way.
In discussing the expansion of steam it is easy to propose
theoretical conditions that could not be carried out in practice.
The information gained is of great value, however, as practical
conditions may lie between supposed ideal conditions.
Theoretically we may suppose the steam to expand
1. Adiabatically.
2. To expand receiving heat in just sufficient quantities as
to prevent the formation of any water by the loss of heat in
any way. The steam is kept dry, and therefore contains the
2H THE STEAMENGINE AND OTHER HEATMOTORS.
tabular number of B.T.U. for one pound of steam at each
temperature.
3. To expand and meanwhile receive heat so that the
steam becomes drier or perhaps superheated.
CASE 1. What course will the tracingpoint that described the
waterline tMs and the line t 3 s 3 take (Fig. 116), if the steam is
supposed to expand adiabatically? Keep in mind that this dia
gram is not concerned in variation of volume and pressure, but
solely in the reception and rejection of heat as heat. The tracing
point must radically change its direction and follow the line S 3 e 4 .
That this is true is indicated by the equation d^ = ^r, for if the
amount of heat added, dQ, is zero, the change of entropy d$ is
zero; therefore a line of adiabatic change is one that is parallel to
the axis of temperature, OF.
As the tracingpoint follows the line s 3 e 4 it cuts the isothermal
line 1282 in some point m 2 . The significance of this is important.
The position of ra 2 , in accordance with a previous explanation,
shows that if a pound of perfectly dry steam at a temperature of
TS expands adiabatically to T 2} only   will remain dry steam,
1282
as will be condensed to furnish heat to do work. With
t 2 s 2
greater expansion there is greater condensation, as is shown by the
,
increased value of
Ex. 91. At cutoff, the volume is 4 cubic feet, pressure is 100
pounds per square inch absolute, and the card shows 80% of the steam
admitted. If it were possible to expand the steam adiabatically to
15 pounds per square inch, how much water would be present?
If the steam is condensed at constant pressure, the temperature
will remain constant. This is not so if the condensation takes
place at constant volume, for then both pressure and temperature
change. If, then, after expanding adiabatically to temperature
t 2 the steam is condensed at constant pressure, our tracingpoint
will follow the isothermal line m 2 t 2 , and will reach t 2 if. all the
steam is condensed at t 2 . If the water at t 2 is cooled, the tracing
point will follow the waterline t 2 ti to the temperature h of cooling.
ENTROPY. 215
Work Done per Pound of Steam during Admission and Adiabatic
Expansion We shall discuss the case of wet steam, since that of dry
steam is easily found by making the quality of the steam mixture
100% instead of a less quantity Fig. 116). If the whole pound of
water at t$ is not converted into dry steam, lay off x% so that 
equals p^ the quality of the steam. Then the position of x% indicates
the entropy of the mixture. If this mixture expands adiabatically
to any lower temperature t 2 , the intersection of the vertical with
t 2 s 2 or x 2 marks the quality of the steam at that time. Calling
this quality of the steam p 2 , we see that
TV T 3
' t 2 s 2 t 2 s 2 L 2 '
T 2
since 1/3 = area 63^3^4 and L 2 = area e 2 t 2 s 2 e 5 .
Example. If one pound of water at 100 F. is converted into
steam, quality 95%, at 350 F., does work during admission and
adiabatic expansion to 212 F., what will be its quality at the
end of expansion? If the pressure during exhaust is constant and
equal to the final pressure of expansion, find the theoretical heat
expended, heat rejected, heat utilized, and the efficiency.
811 .95X867.3 966
Log. 573, 18, gjj =1.016, 731.435,
.18+1.016
P2=
Heat expended from ti = 100 = area eitit 3 x 3 e x
= 350 100 + .95X867.3 = 1074 B.T.U.
Heat rejected must be measured down to feedwater tempera
ture = eitit 2 x 2 e x = 212  100 + p 2 L 2
= 212 100 +.833X966 = 916.7 B.T.U.
Heat utilized 1074916.7
Efficiency ==  =15%.
This of course neglects initial condensation, friction, wire
drawing, etc.
216
THE STEAMENGINE AND OTHER HEATMOTORS.
In Fig. 117 we have a theoretical indicatorcard representing the
conditions of the last example. The line ab corresponds to
and at b there is present one pound of wet steam, quality ~.
This steam expands adiabatically to c, the adiabatic be correspond
ing to 03X2. The exhaust opens and the steam is forced out at
FIG. 117.
constant back pressure equal to the final pressure of expansion,
the line cd corresponding to x 2 t 2 .
Velocity of Steam Passing Through a Nozzle. The above for
mulas apply to steam flowing through nozzles as used in steam
turbines. The sum of all the different forms of energy on one side
of a section must equal the sum of all the energies on the other
side of that section. In the case under consideration there are
FIG. 118.
three different forms of energy, viz., heat or intrinsic energy, E }
external work, , and kinetic energy or energy of motion; hence,
Fig. 118, at any two sections, AB and CD,
w
The velocity of approach, Vi, in a large vessel is inappreciable and
may be neglected. The equation becomes, per paund per second,
V2 2
 (E 2 +p 2 y 2 ).
ENTROPY.
217
Inspection shows that the righthand member of this equation is
the difference of the total heats of one pound of steam. Calling
Hi and H 2 the total heats of one pound of the steam, differing
according as the steam is wet, dry, or superheated, we have, omit
ting the subscript,
= (Hi H 2 ) 778 footpounds.
From theoretical conditions and experiment, it is known that
the weight of steam flowing through an orifice increases as the
back pressure decreases to a limit which is reached when the
back pressure is .57 of the forward pressure (see page 445).
Initial Pressure,
Pounds
Absolute per
Square Inch
Pi.
Orifice
Pressure
P 2 =.57P,.
Weight of Fow, Pounds per Second.
Calculated
Velocity, Feet
per Second, at
smallest Cross
section of
Orifice.
Observed.
Calculated.
By Equation
Given
By Napier's
Formula.
132.3
117.6
102.9
75.2
67.0
58.7
.063
.057
.050
.0629
.0572
.0500
.0671
.0596
.0522
1470
1495
1490
* Table from Thomas's Steamturbines (Wiley).
If dry saturated steam at 132.3 pounds absolute flows through
an orifice whose crosssectional area is .0355 square inch, against
a back pressure of 75.2 pounds absolute, what will be the
velocity of discharge per second, volume and weight discharged
per second?
Draw the entropy diagram, Fig. 119. Then the area TiT 2 s 2 mi
72
represents H 2  HI in the formula = 77S(H 2 Hi).
We may obtain that area by either exact or approximate
methods If TiT 2 is assumed to be a straight line, the area of the
trapezoid TiT 2 s 2 mi is=(T 2 7 T 1 )J5, where
B
_,
r,
218 THE STEAMENGINE AND OTHER HEATMOTORS.
\ would be the
(If the initial steam were wet, the area
area.)
... ^^(809768)
=45.1 B.T.U.
= 64.32X778X45.1.
= 1500 feet per second.
FIG. 119.
The more exact method would give 1470 feet per second. If
the steam expands adiabatically, its quality is
T l m l
T lSl
_ 1.5731 .4465
1.6155 .4465 ** A/0 '
ENTROPY. 219
At 75.2 pounds the volume per pound weight of dry steam
is 5.68 cubic feet. The volume per pound of wet steam is
96.4X5.68 = 5.47 cubic feet.
The volume discharged = area orifice X velocity.
144
The weight discharged = ^^ = ^0637 pound.
Ex. 92. If steam of an initial absolute pressure of 117.6 pounds
flows through an orifice whose crosssectional area is .0355 square
inch, against a back pressure of 67 pounds absolute, find the velocity
of discharge and volume and weight of steam discharged per second.
Condensation or Expansion at Constant Volume. Fig. 120 illus
trates a series of events similar to those given in the example on
FIG. 120.
page 214 and illustrated in Fig. 117, up to the point of exhaust
opening, c. The line cf is made while the piston is theoretically
stationary. Therefore the volume of the cylinder is not being
diminished by the movement of the piston, and the steam is said
to be condensing or expanding at constant volume. It is evident
that the volume of the steam in the cylinder at / is precisely the
volume that was present at c, the weight, of course, being different.
We must therefore distinguish between the lines cf and fg in draw
ing our entropy diagram. The latter indicates condensation at
constant pressure and, since that occurs at constant temperature,
the corresponding entropy line will be parallel to the entropy axis.
When our tracingpoint described the line from t% to 3 (Fig.
116), its position at any moment indicated the weight of steam
formed and, therefore, its volume, since we can take from tables
the volume of one pound of steam at any temperature and, by
220 THE STEAMENGINE AND OTHER HEATMOTORS.
multiplication, obtain the volume of any fraction of a pound. Or,
reversing the conditions, if we have the volume of any unknown
weight of steam at any known temperature or pressure, by dividing
this volume by the volume of one pound of steam at that tem
perature we obtain a fraction that determines the weight of the
steam, and also the proportional part of the entropy of one pound
of steam, measuring from the waterline.
To illustrate a method of drawing the curve of constant volume,
let us draw the line corresponding to cf (in Fig. 120) in the entropy
diagram (Fig. 116). We know that x 2 indicates the conditions that
exist when one pound of steam, quality 95%, temperature 350 F.,
has been expanded adiabatically to 212 F. We have found that
its quality  is 83.3%. From the tables we find that one pound
1282
of steam at 212 F. occupies 26.64 cu. ft. Hence t 2 x 2 marks the
entropy of .833X26.64 = 22.19 cu. ft., or approximately 22 cu. ft.
Taking from the tables the temperatures corresponding to volumes
which are multiples of 22 cu. ft. per pound of steam, we obtain the
following series:
Volume in Degrees. Relative Entropy
Cubic Feet. Fahr. Abs. of 22 Cu. Ft.
44 .......... 186 647 1/2
66 .......... 167 628 1/3
88 .......... 154 615 1/4
111 .......... 144 605 1/5
132 ........ '.. 137 598 1/6
354 .......... 100 561 1/16
Hence the entropy of 22 cu. ft. is easily laid off at 1/2 the
entropy of one pound of steam at 186 F., 1/3 of that at 167 F.,
etc., thus obtaining the curve x 2 m^. The backpressure line fg of
the indicatorcard is given by mt\ of the entropy diagram.
Second Method of Drawing the Constantvolume Curve. Let
383 and t 2 S2, Fig. 121 7 represent two of any number of entropy
lines of steam at constant pressure.
Let OT and OE be the absolute temperature and entropy axes.
Prolong TO and lay off on the prolongation OF a scale of volumes.
The scale must be so chosen that OF is at least equal to the volume
of one pound weight of steam at the lowest pressure. Since the
ENTROPY.
221
diagram deals with one weight of steam only, it is convenient to
take the volumes from the tables for one pound, since it is easy
to change the scale to give the volumes for any other weight.
In the quadrant TOE, ordinates represent absolute temperature
and abscissas represent entropy; in the quadrant VOE, the ab
scissas represent entropy as before, but the ordinates repressnt
volume.
The line t 3 s 3 gives the increase of entropy due to the formation
of one pound of steam. At t$ the volume of the steam is zero, and
FIG. 121.
the entropy is found by dropping the perpendicular 2 3 e 3 . Simi
larly, dropping a perpendicular s 3 e 4 from s 3 and laying off on the
prolongation e 4 F 3 equal to the volume of one pound weight of
steam at temperature t$ (in accordance with the scale laid off on
OF), we obtain the point F 3 . Draw e 3 F 3 . This is a straight line,
as the entropy measured from the waterline is directly propor
tional to the volume of steam formed. Suppose e 4 F 3 = 3.324 cubic
feet. If we wished to find the entropy corresponding to any other
volume, as three cubic feet, find that number on OF; draw a
parallel to OE. At the intersection, i 3 , erect a perpendicular to
OE. The intersection of this perpendicular with 3 s 3 at c 3 gives
the required entropy 3 c 3 . In a similar manner draw ezVz, e\Vi,
222 THE STEAMENGINE AND OTHER HEATMOTORS.
and find c 2 and c\. Draw the curve CiC 2 c s . The line so found will
represent the entropy at constant volume of 3 cubic feet of steam.
We may now modify the data of the example on page 181.
Example. One pound of water at 100 F. is converted into
steam, temperature 350 F., quality 95%, under constant pressure,
and is then expanded adiabatically to 212 F. The exhaustvalve
then opens and the pressure drops to that corresponding to a tem
perature of 100 F.; at this pressure the remaining steam is re
jected to the condenser. Find the theoretical heat expended,
.heat rejected, heat utilized, and the efficiency. See Fig. 116.
The heat expended will be the same as in the preceding example
The heat rejected will be that of the preceding example less
the heat equivalent to the area t 2 x 2 ni4ti. By means of a planim
eter this can be obtained in square inches and the corresponding
B.T.U. obtained by multiplying by the heat scale..
The value of the area t 2 x 2 mti may be obtained from the indica
torcard, Fig. 120, as it is evidently equal to the area cfgh.
c/= 14.69 .94 = 13.75. Vol. of cyl. = 22.19 cu. ft.
Heat rejected =916.756.4= 860.3 B.T.U.
Heat expended = 1074 "
heat utilized 1074  860.3
Efficiency = heatexpended = ^ = 20%,approx.
CASE 2 (Fig. 116). If one pound of water at ti is heated to t a
and converted into dry steam at 3, the heat added will be e\ tit^s^e^.
Similarly if water at t\ is heated to t 2 and evaporated into dry
steam at t 2 , the heat added will be eitit 2 s 2 e 5 , and similarly with
other points. The curve 352$! expresses the relation between the
temperature and entropy of one pound of dry steam expanding
and meanwhile receiving heat in sufficient quantity as to prevent
liquefaction entirely. The heat taken from the jacket to do this is
4838^5 between temperatures t 3 and t 2 . In adiabatic expansion
the weight of steam was constantly changing on account of the
condensation of part of the steam. This curve, on the other hand,
is called the curve of constant steam weight for obvious reasons.
ENTROPY. 223
The total heat added is the area 61/1/3533265. This area may be
integrated by a planimeter or it may be divided up into the areas
61/1/262, 62/2^265, and /2/3S3S2 The last area may be obtained as
follows: The length of any elementary strip at temperature T (ab
solute) is , and, if the width of the strip is dT, its area is 
This may be integrated if we express L in terms of the absolute
temperature T. But
L = 1091.7 + .305 (t s  32)  (f.  32)
= 1091.7.7(/ s 32 )=1114.7/8
= 1114.7 (T 481) = 1437 .7 T.
' r /1437  .7 T r T *U37 dT
area
\
/'/1437  .7 \ l r*U37 dT r*
/  ~  )dT = / ^  / .7dT
' J L ^ J ^
This equals the net work done if the back pressure is constant and
is equal to the final pressure of expansion. If the back pressure
is less, the increase can be obtained from the indicatorcard as in
the preceding case.
CASE 3. The law connecting the pressure and volume in
Case 1 is PV^ = Ci, in Case 2 it is PV& = C 2 . Owing to the large
amount of initial condensation in steamengines, the steam at
exhaustopening is only superheated in exceptional engines, with
high superheat at cutoff. In the case of steamturbines the
exhaust, in certain cases, has been found to be superheated.
This is undesirable and is a source of loss. In such engines the
energy of the steam is converted into kinetic energy by allowing
the steam to expand. The curved buckets of the turbine are
designed to reverse, to a greater or less extent, the motion of a
mass (of steam) moving at very high velocity. The work done on
moving blades by the steam is at the expense of its heat energy,
and some steam should condense. It is not desirable that any of
this steam should reevaporate. It does so, however, and for the
following reason. Whenever two masses of considerable density
move past one another, friction is almost inevitable. With super
heated steam in a turbine the friction is considerable, and it is
224 THE STEAMENGINE AND OTHER HEATMOTORS.
greater with wet steam, as a very slight film of water increases
the surface friction greatly. This friction heats the buckets, and
this heat in turn reevaporates the condensed steam or, at low
temperatures, if the steam be dry, tends to superheat it. The low
pressure steam formed in this way does some work on the following
vanes before it goes to the condenser.
The conversion of frictiofial resistance into heat may occur in
another way, which forms the basis on which the theory of the
Peabody calorimeter rests. Steam flowing through a simple
orifice in a diaphragm forms eddies. The high kinetic energy of
the steam in the orifice is converted back into heat in the chamber
of the calorimeter. As no external work is clone, the heat in the
steam at the final temperature contains as much heat as it did at
the initial temperature. This curve of expansion may be called
the Constantheat Curve. If the steam at the initial tempera
ture was nearly dry, at the final temperature the steam may con
tain more heat than is required by saturated steam and the excess
is used in superheating the steam.
Constant Heat Curves are hyperbolas since (j>T = C. The con
/ \
/ \
/ \
\
\
\
\
\
FIG. 122.
stant heat curve x 3 a, Fig. 122, has the following data : Steam at
350 F., quality 97%, expanding in a Peabody calorimeter to 14.7
pounds; the superheat will be 35 F., approximately. The point
ENTROPY. 225
where the curve crosses the saturated steam line indicates the
temperature at which one pound of dry saturated steam contains
the same number of B.T.U. as an equal weight of wet steam,
quality 97%, at 350 F.
In the case of the constantheat curves a definite law is fol
lowed ,and intermediate points may be found and plotted. In
the case of steam expanding in an enginecylinder or in a turbine,
it is far from easy to find the values of the variable quality of the
steam. Let SsWs, Fig. 122, be the curve of expansion followed by
steam initially dry. The increase in the external work done, if the
final pressure of expansion is equal to the back pressure, is S 3 m 8 m3.
The additional amount of heat carried to the condenser, as com
pared to the case of adiabatic expansion, is m&e&emz. The heat
utilized always equals the heat received minus the heat sent to the
condenser. To make a comparison, let the heat received in two cases
be the same; in one the expansion is adiabatic, in the other some
curve, such as s 3 ms, is followed. The total heat received in each case
is eititsSse^ the heat sent to the condenser is e\t\m^e^ in the case of
adiabatic expansion, and is eitimses in the other case. In the case
of adiabatic expansion the efficiency is  In the other
case we must convert the area e 4 s 3 m 8 e 8 into some area x'
the area x fff s 3 m 3 x r being a measure of the extra heat sent to the
condenser and is therefore wasted. The efficiency in the second
case is then  . These results point out a source of ther
mal loss in the steamturbine.
Ex. 93. Compare the theoretical efficiency of a steamengine and
that of a steamturbine, both taking steam at 150 pounds pressure;
the expansion in the steamengine is adiabatic to 3 pounds back pres
sure absolute, and that in the steamturbine is adiabatic to 1/2 pound
back pressure absolute, the initial condensation being 15% in the case
of the engine and zero in the case of the turbine.
Deriving a Temperatureentropy Diagram from the Indicator
diagram. The two diagrams above mentioned involve four vari
ables, P, V, T, <j>. If, by graphic means, we can pass from the
PV or indicatorcard diagram to a PT diagram, any T correspond
ing to any P is obtained. If from the PV diagram we can pass to
226 THE ^TEAMENGINE AND OTHER HEATMOTORS.
a <f>V diagram, any < is at once obtained for any V whose P we
already have. Having and T the <j>T diagram may be con
structed.
As in Fig. 123, draw two axes at right angles to one another.
On OF volumes are to be laid off from zero volume.
On OP pressures are to be laid off from zero pressure.
On OT temperatures are to be laid off from zero absolute tem
perature.
ENTROPY. 227
On OE entropy is to be laid off in excess of the entropy of
water at the assumed temperature, 32 F. in the above case.
If, in the given indi:a torcard, the hyperbolic curve is con
tinued through the point of exhaustclosure to the line of steam
admission, we have seen that RS is the measure of the steam that
goes through the cycle, and RT can be laid off to measure the
actual steam admitted per stroke. The indicatorcard is to be
placed in the POV quadrant with R in the line PO at such a point
that RO measures the absolute pressure. It is convenient to lay
off the entropy diagram as for onepound weight of steam in this
manner. From the tables we find that an even pressure of 27
pounds corresponds to an even volume of 15 cubic feet for one
pound of steam. Through 27 pounds draw a line parallel to OF,
intersecting the hyperbolic curve at some point a. From a drop
a perpendicular on 0V and call the intersection 15 cubic feet,
thus determining the scale of volumes for a cycle of one pound of
steam. After constructing the complete diagram, by merely
changing the scale the dimensions for entropy or volume will suit
the corresponding steam weight. For instance, if the actual
weight were onethird of a pound, then on the new scale, three
times as large as the present one, the volume corresponding to a
would be 5 cubic feet.
From steam tables take the temperatures corresponding to con
venient pressures and so plot the PT curve in its proper quadrant.
From entropy tables or an entropy diagram, the water and satu
rated steam lines may be laid off in the TOE quadrant.
The diagonal (j>V lines in the VOE quadrant should be dr^wn
as required to avoid confusion, as there will be one of them for
each point, a, etc., in the hyperbolic curve.
Project any point, a, in the hyperbolic curve vertically to the
PV curve, obtaining b and c at the intersection of the projecting
line with the indicator curves, and d the zero of volume point;
project e on the entropy curves, thus determining / and g. Project
/ and g vertically and d and a horizontally, thus locating the <j>V
line hi. Project b and c horizontally and obtain j and Z; project
the latter vertically and obtain the required points k and m on the
steam line fg. Find other points of the <j>T diagram in a similar
manner. (See Fig. 124.)
228 THE STEAMENGINE AND OTHER HEATMOTORS.
Carnot Cycle. The conditions of this cycle are:
1. All heat to be received at one temperature, the highest
possible.
2. All heat to be rejected at one temperature, the lowest
possible.
3. Working substance cools from highest to lowest tempera
ture through loss of heat equal to external work performed by
it, i.e., expands adiabati^ally.
4. Working substance is heated from lowest to highest tem
perature by gaining heat equal to the external work done on it:
adiabatic compression.
On the entropy diagram (Fig. 116) t^s^m 2 mQ would represent a
Carnot cycle between temperature limits t 3 and t 2 . In the case of
a steamengine, assuming one pound of steam as going through
the cycle, we should have one pound of water at the boilingpoint,
Z 3 , receiving heat equal to the area 3536463 at a temperature fe,
expanding adiabatically, as shown byline s 3 ra 2 , to tempera ture = t 2 ,
then losing heat = e^e^mzniQ in the condenser at temperature 1%.
The abstraction of heat must stop when conditions indicated by
the position of m^ are attained. In some way work would have
to be performed on the mixture of steam and water, so that it
would all be converted into water at temperature 3. " This
cannot be practically accomplished, but a system of feedwater
heaters has been suggested and exemplified in the Nordberg engine,
which is theoretically a close equivalent to it. Where steam is ex
panded in, say, three cylinders, the feedwater may be successively
heated from the receiver intermediate between each pair, the
effect of which is illustrated in Fig. 116. The expansion line follows
the heavy line, being carried over to y by the first feedwater
heater and to y' by the second feedwater heater. With an infinite
number of such feedwater heaters, the line yy r would be parallel
to 2^3 and the cycle would be equivalent to that of Carnot.*
" Rankine Cycle. This differs from the Carnot cycle in that the
condensation does not stop at ra 6 , but is made complete by carrying
it to t 2 . We therefore have a pound of water at t 2 . The second
difference is that the water is heated by external heat from t 2 to 3.
* Trans. A. S. M. E.
ENTROPY. 229
*' Efficiencies of Ideal Engines. The efficiency of the Carnot
cycle is
T 3 T 2
the efficiency of the Rankine cycle is
t " Ratio of Economy of an Engine to that of an Ideal Engine.
The ideal engine recommended for obtaining this ratio is that
which was adopted by the committee appointed by the Civil
Engineers, of London, to consider and report a standard thermal
efficiency for steamengines. This engine is one which follows the
Rankine cycle, where steam at a constant pressure is admitted into
the cylinder with no clearance, and after the point of cutoff is
expanded adiabatically to the back pressure. In obtaining the
economy of this engine the feedwater is assumed to be returned to
the boiler at the exhaust temperature. Such a cycle is preferable
to the Carnot for the purpose at hand, because the Carnot is theoret
ically impossible for an engine using superheated steam produced
at constant pressure, and the gain in efficiency for superheated
steam corresponding to the Carngt efficiency will be much greater
than that possible for the actual cycle.
" The ratio of the economy of an engine to that of the ideal
engine is obtained by dividing the heat consumption per indicated
horsepower per minute for the ideal engine by that of the actual
engine."
Temperatureentropy Diagram of a Real Engine. In Fig. 124
let ABCD be the ideal diagram, or Rankine cycle, of an engine
between temperature limits, as shown by the positions of the
points A and D. As shown in this diagram the temperature at A
is the temperature of the steam as it enters the engine. If the
temperature at the throttle had been chosen the line AB would have
greater ordinates, and if the boiler temperature had been chosen
the ordinates would have been still greater.
t Trans. A. S. M. E. Standard Rules.
230
THE STEAMENGINE AND OTHER HEATMOTORS.
The point B represents the theoretical point of cutoff, but the
real point of cutoff is represented by b and the real admission line
by Ab. The heat lost by initial condensation is represented by the
area between AB, Ab, and the full length of the ordinates through
b and B.
Keeping in mind that the gain or loss of heat through doing or
receiving external work produces no entropy change, and that
therefore decrease of entropy means loss of heat as heat and in
crease of entropy means the reception of heat as heat, we see that
the inclination of W to the left indicates the loss of heat to the
FIG. 124.
walls, and the inclination of &'c' to the right shows that the walls
are returning heat, but at lower grade, i.e., lower temperature.
The line c'd indicates the changes in temperature and entropy
due to expansion at constant volume. Had the cylinder been
large enough in volume, adiabatic expansion from cf would have
added an additional amount, c'34d, to the work done.
The line dd f indicates condensation at constant pressure and
temperature. The fact that it does not coincide with Z)4 indicates
ENTROPY, 231
that there are resistances between the engine and the condenser,
so that a higher pressure and temperature are required in the
former to overcome the combined resistance of the condenser and
passageways.
The departure to the left of d'e from d', the point of exhaust
closure, indicates that the compression is not adiabati3 and heat
is given to the cylinder walls. The point e may be taken as the
beginning of compression, and the cylinder clearance steam is dry
saturated steam. The line eA may be considered as the water
line for the new charge of steam. It must be borne in mind that
in the part of the cycle Abc'ddf we are dealing with a constant
mass, as the condenser may be assumed to be part of the cylinder.
The part d'fA, on the other hand, deals with the much smaller
clearance mass, so that steam and water at / may have less entropy
than a weight of water equal to th$ full cylinder charge at the
same temperature.
Ex. 94. A steamboiler contains 5000 pounds of water and 50
cubic feet of steam at 100 pounds gage pressure. The barometer
reading is 29.3 inches. What number of footpounds of energy will
be developed by the water and by the steam if the boiler explodes?
What volume of steam will be formed?
Ex. 95. Draw the Rankine cycle for the expansion of one pound
of steam at 150 pounds per square inch pressure absolute to 1 pound
per square inch pressure absolute and determine the efficiency.
Ex. 96. If the steam in the preceding problem had a quality of
80% (due to initial condensation) and expanded to 27 inches of mer
cury vacuum, barometer 29.5, find the efficiency.
Ex. 97. The steampressure on a steampump is 100 pounds ab
solute during the entire stroke. If the exhaust is at atmospheric
pressure, 30.02 inches mercury, what is the efficiency?
CHAPTER IX.
CONDENSERS AND AIRPUMPS.
A BRIEF description of two forms of condensers has been given
already, but the influence of this vessel on the economy of steam
turbines and other engines using the highest possible grade of
expansion is so great that a more detailed description of its
requirements is necessary
Two divisions may be made :
1. Condensers giving a vacuum ranging from fair to excel
lent.
2. Condensers giving little to no vacuum.
In the first class we have :
(a) Jet condensers.
(b) Barometric condensers.
(c) Ejectorcondensers.
(d) Surface condensers.
In the second class are:
(a) Aircondensers.
(b) Evaporative condensers.
It is well known that the temperature of gases or vapors is
some function of the rate of vibration of their molecules, and
that the pressure exerted by the gases is some function of the rate
of bombardment of their molecules on the containing vessel.
When vapors condense there is an enormous decrease in both the
amplitude and the rate of vibration, hence there is a great reduc
tion of pressure. In the case of noncondensible gases, such as air,
the reduction of pressure on cooling, of course, is riot so great.
Jet Condensation. In the jet, barometric, and ejector con
densers the water and steam are brought into the most intimate
232
CONDENSERS AND AIRPUMPS. 233
contact. The cooling or injection water is sprayed by some
appropriate form of nozzle, and the steam is forced to travel one
or more times through spraying cascades.
Both the coolingwater and the steam carry large quantities of
air with them into the condenser. All this air being incondensible
expands enormously in volume on reaching the condenser, on
account of the reduction of pressure and the increase of tempera
ture therein.
The condensed steam and water, in jet condensation, form a
mixture. In some cases 2% to 5% of this mixture may be used as
feed water for the boilers and the rest runs to waste. If the injec
tion water contains anything injurious to the boilers, all the water
may be wasted.
Jet condensers were in common nse in marine practice until
186570. It was common usage to feed the boilers with part of
the discharge water from the condensers. As the injection was
salt water containing 1/32 of its weight in common salt, calcium
carbonate, magnesium carbonate, etc., it is evident that a large
weight of solids would be left in the boiler water, the density of
which would rapidly increase, as steam contains no solids. Some of
these solids would be deposited as scale. The density of the water
would be reduced by " blowing off " at a fixed high density and
replacing the water " blown off" with water of the lowest obtainable
density. The loss of heat in the water blown off was considerable.
The main differences in the three types of jet condensation are:
1. The air and water must be pumped from the jetcondenser,
and it may or may not be necessary to pump the water in.
2. It is necessary to pump the air out of the barometric
condenser, and the water must be pumped into an elevated
tank.
3. In the ejector type the water is forced into the condenser
at high velocity. This water in descending with high speed
past a series of gills entrains or syphons air and steam from the
main body of the condenser. The mixture of air and water
passes away by gravity.
Jet Condensers. This type is used in freshwater navigation,
in places where water is cheap and a vacuum is wanted either on
234 THE STEAMENGINE AND OTHER HEATMOTORS.
the score of economy or from the gain in power, but oily feed
water is feared. The sprayingnozzles clog at times with leaves,
fish, and other debris; hence the design should provide for their
ready removal. The diameter of the sprayingholes may be J" ',
and their total area may be three or more times the area of the
injectionpipe.
The end of the suctionpipe should have a strainer and a foot
valve and be immersed in deep water. In rivers heavy cribbing
is necessary to protect the pipe from ice and an accumulation of
logs floating on the water surface. The suctionpipe should rise
at a uniform grade without a single bend or dip. The water in
this pipe is under less than atmospheric pressure, and the air
therefore separates from the water and lodges at the highest bends.
When enough air accumulates the " water will not lift " and the
pump becomes inoperative. When the bend cannot be avoided a
small pipe should be tapped in the top of the bend and then be
connected to an airpump or condenser.
Air Leaks. It is exceedingly important to prevent the leakage
of air into a condenser, as pumping out highly expanded air throws
much unnecessary work on the airpump. As the vacuum affects
the net pressure on the L.P. piston, a loss of one or two inches of
vacuum will reduce the economy of the engine materially.
The principal sources of air leakage are the stuffingboxes of
the L.P. pistonrod and of the airpump rod; the various joints
of the condenser, exhaustpipe, and L.P. cylinder; the dripcocks,
or drain valves, on the main or auxiliary engines which exhaust
into the condenser. Absolute air tightness of joints is difficult to
secure. Even soldered joints will leak. Metal to metal joints are
the best. To test the tightness of a condenser wafoh the needle
move backward the moment the engines and auxiliaries are shut
down.
Dimensions. As is shown in Fig. 18, jet condensers are often
made pearshaped, the maximum diameter being twice the diameter
of the exhaustpipe leading into it. This shape tends to conserve
the velocity of the water entering the condenser and causes the
delivery to the airpump of a mixture of air and water. Under
these conditions the water absorbs considerable air, and in any
case this mixture can be handled with greater uniformity of pump
CONDENSERS AND AIRPUMPS. 235
motion than is possible when the air and water separate from one
another. The volume of the condenser may be from onefourth
to onehalf that of the L.P. cylinder.
Weight of Injection Water for Jet Condensation.
Let W = pounds of injection water per minute;
ti = initial temperature of injectionwater;
* 2 = final
then W(t2 t\) is the heat absorbed by the injection water per
minute and must therefore equal the heat lost by the steam per
minute. Now the total heat received by the steam per minute
from all sources minus the external work done in the engine per
minute is the heat above 32 F. sent to the condenser per minute,
I.H.P.X 33,000
= wH t = wH e ,
where H t = total heat received from all sources above 32 F.;
# c = heat (above 32 F.) per pound of steam as it goes to
the condenser;
w = pounds weight of steam sent to the condenser per
minute ;
w(H c  (t 2  32)) = W(t 2  h), or, more accurately,
The diameter of the injectionpipe may be calculated by allow
ing a velocity of 600 to 800 feet per minute to the injection water.
A velocity in excess of this may be obtained when the condenser is
much below the level of the surface of the watersupply. The
pressure of the atmosphere then supplies the power to force the
water into the condenser. Knowing the static head and assuming
any velocity, the corresponding velocity and friction heads may be
calculated. The sum of all the resistance heads should be less than
the head that is equivalent to the difference of the pressure of the
atmosphere and that in the condenser.
Ex. 98. Design a jet condenser for a 1000 horsepower engine
using 15 pounds of steam per horsepower. Make a sketch showing
size of injectionpipe, form of sprayer, number and size of holes in
sprayer. Assume other conditions.
236 THE STEAMENGINE AND OTHER HEATMOTORS.
Ex. 99. Design a jet condenser and airpump of type shown in
Fig. 8 for a Corliss engine of 40 horsepower, using 25 pounds of steam
per I.H.P. Assume other conditions.
Ex. 100. Design the suctionpipe line for Ex. 98. This pipe
line must cross a levee 15' above mean low level of the river. Maxi
mum and minimum river heights 10' above and below mean low level.
River bottom soft mud to a depth of 10 feet.
Barometric Condenser. In many operations, steam must be
condensed at some elevation above the ground. If this be over 35'
it is evident that the dischargewater would flow away by gravity.
All that is necessary is to seal the end of the tailpipe (discharge
pipe) in a tank or barrel of water. Fig. 125 illustrates a counter
current barometric condenser, so called because the coolingwater
is flowing in one direction and the air in flowing to the vacuum
pump is moving in the opposite direction. In this case it is evi
dent that only the air moves to the vacuumpump, as all discharge
water flows away through the tailpipe. It should be noticed in
Fig. 125 that the final temperature of the air on its way to the
vacuum pump is that of the incoming water, whilst in Figs. 17
and 18 it is the temperature of the discharge water. The weight
and volume of the air to be handled in barometric condensers is
very much less than in jet condensers. Serious accidents have
happened by the use of improperly designed condensers. For
instance, cases have occurred in which the water inside of the con
denser acquired a gyratory motion and then, rising over 34' high
in the condenser, flooded through the engine exhaustpipe, causing
the breakage of the cylinderhead. When this type receives a
larger amount of steam than usual, the current of steam and water
may reverse and flood the airpump. If the bottom of the dis
chargepipe becomes uncovered, air enters and, forming ascending
pistons, lifts the water (as in the Pohle airlift in wells) and may
cause the flooding of the cylinder. As the passageway for the air
to the pump may be very much constricted by water, ample
passageway should be allowed. The spraytubes are very liable
to become choked, and the injectionpipe should deliver into a tee
on the sprayer, so that by the removal of two blank flanges the lat
ter may be easily cleaned (Fig. 262). Condensers of tlds character
are used in connection with vacuumpans and multiple effects in
CONDENSERS AND AIRPUMPS.
FIG. 125. Heisler Induced Circulation Countercurrent Condenser.
238 THE STEAMENGINE AND OTHER HEATMOTORS.
sugarhouses, condensedmilk factories, and in chemical industries
where there is much boiling done at pressures less than atmospheric
pressure.
FIG. 126. Alberger Barometric Condenser.
Syphon, Ejector, or Injector Condensers. A remarkable degree
of vacuum may be obtained, without the use of an airpump, by
means of condensers of the form shown in Fig. 127. Its most im
portant and essential feature is a suctiongill, so arranged that
the steam, vapor, and air may be drawn into the discharge
CONDENSERS AND AIRPUMPS.
239
water. This action is due to the high velocity of the water entering
the contracted orifice above the gill, and since the sum of the
static, velocity, and friction heads must be constant, it is evident
that if the velocityhead is increased the static head will be de
creased.
In tests made with an injectorcondenser of this type in winter
in New York the condenser pressures varied from 0.82 pound to
FIG. 127.
1.25 pounds absolute, the engine varying from 340 to 1004 I.H.P.
An objection to this condenser, when used with variable loads, is
that the same volume of water is required to fill the throat regard
less of the load.
Surfacecondensers. The Alberger condenser (Fig. 128) has
several unique features. The exhauststeam enters either at the
bottom or at the side near the bottom. The coolingwater enters
at the top and leaves at the bottom. The object of this arrange
ment is to obtain a full countercurrent transfer of heat. The
steam as it rises is condensed, and the water thus produced falls
down against the incoming steam and is removed by a hotwell
240 THE STEAMEXGINE AND OTHER HEATMOTORS.
pump. On account of this intimate contact the feedwater acquires
the same temperature as the steam. The air left after condensa
tion, before being withdrawn by the dryair pump is cooled by
passing over the tubes containing the coldest circulation water.
In the lower part of the condensershell is a diaphragm to dis
tribute the steam to all parts of the condenser. The method of
changing the direction of flow of the coolingwater is similar to
that shown by the arrows in Fig. 10.
FIG. 128. Albarger Surfacecondenser.
A high vacuum may be obtained by the use of a surface
condenser. Such a vacuum is not necessarily economical in prac
tice. The vacuum that gives the best economy will vary with the
ratio of expansion of the engine. When there is a big drop in the
pressure between the engine and the condenser, increasing the drop
by an excessively high vacuum may be very uneconomical. In
other words, the extra gain in work does not compensate for the
increased loss in heatunits caused by the increase in initial con
densation, colder feedwater, increased cost of pumping greater
quantities of coolingwater, and the interest on the increased size
of air and circulatingpumps, condenser, et3.
On the contrary, if the steam can be expanded in the engine
CONDENSERS AND AIRPUMPS. 241
to any back pressure, however low, theoretically there would be an
enormous gain in reducing the condenser pressure to the lowest pos
sible amount. In the steamturbine there is no trouble with initial
condensation, and it was expected that there would be a great
advance in economy from the greatly increased ratio of expansion
possible. As a consequence machinery for the production of a
vacuum of 29" + has been devised. The entropy diagram will
show that if steam is expanded adiabatically to 40 or 50 times its
original volume, theoretically some 20% of it would be converted
into water. As it is the province of the steamengine to convert
heat into work, the above effect would be very desirable. Unfor
tunately, from causes explained under the head of turbines, much
of this water from friction is converted back into steam. It is evi
dent that this causes a loss in the external work done, since the
latter is the difference between the heat entering the turbine and
that going to the condenser.
Amount of Coolingwater. The amount of coolingwater per
pound of steam entering a surfacecondenser is somewhat greater
than it is in the case of jet condensation, as the range of tem
perature of the coolingwater is less. As an engine converts into
work only 10 to 15% of the heat it receives, in practical design,
it is not important to be particular about the pressure at which
the heat is sent to the condenser since H does not vary greatly
with the pressure. Evidently ^ is not only indeterminate in such
cases but is also variable and a variation of three degrees in its
assumed value has a material effect on the value of W.
Let ti = the initial temperature of the coolingwater;
2 = the final temperature of the dischargewater ;
3 = temperature of the condensed steam;
He = heat in the steam entering the condenser above 32 F.;
w = weight of steam entering the condenser per minute;
W = weight of injection water per minute.
Then w\He(t 3 32)}=W(t 2 t 1 ) ) or, more accurately,
The outside diameter of condensertubes is 1/2", 5/8", or 3/4";,
thickness of metal, .049"; the spacing is 1 1/2 diameters; length
from 6' to 16', but supported at 5' spaces; composition Cu, 70,
Zn, 29; Sn, 1, or Admiralty metal; packed by screwed glands
7/8" diameter and cotton tape.
242 THE STEAMENGINE AND OTHER HEATMOTORS.
In ordinary land service the coolingsurface is 1 sq. ft. for every
10 pounds of steam the engine uses : with high vacua, as with tur
bines, 1 sq. ft. for 4 to 8 pounds of steam is allowed. The velocity
of water through the tubes is from 150 to 200 feet per minute.
Heat Transfer through Metals. Many experiments have been
made on the rate of heat transfer through heatingsurfaces.
When the difference of fluid temperatures at the two surfaces is
very high, as in steam boilers, the rate of heat transfer probably
varies with some power, probably the second, of the difference in
the tw r o temperatures. In surface condensers the difference of
fluid temperatures at the inside and outsidetube surfaces is so
small that the rate is generally taken as varying with the difference
of the temperatures only.
Motion only ensues when there is a difference of pressure, and
heat only passes when there is a difference of temperature and the
rapidity depends upon the temperature gradient, or, in other
words, the latter depends Upon the rapidity with which the heat
is taken away. The temperature fall in the metal itself is always
very small. The principal falls occur in the soot, grease, scale,
inert gases or liquids adjacent or attached to the two metal surfaces.
We note that
1. As the water passes along a tube and increases in tem
perature the efficiency of the heatingsurface gradually dimin
ishes; therefore
(a) the cooler the injection the greater the efficiency.
(6) Long tubes must be inefficient compared to short
tubes and disregarding the amount of water used.
(c) The higher the vacuum the lower the steam vapor
temperature, therefore the efficiency of heat trans
fer is low and the necessity of cold injection for rec
ord tests is greater.
2. If the tubes are coated with any nonconductor of heat
the efficiency will be lowered. Grease and scale are evident
examples, but there are others of equal importance. Air in a
condenser acts as a nonconducting blanket, and whilst it is
important at condenser temperatures ranging from 140 to 120
F. ; at 80 F. the presence of air having a pressure of .2" mer
cury is prohibitive of all heat transfer.*
* London Engineering, 1906.
CONDENSERS AND AIRPUMPS. 243
3. Increasing the rapidity of motion of water through the
tube increases the efficiency of heat transfer. The rise in
temperature of the water will be less, but at high velocities the
product of the weight of coolingwater and its rise in
temperature will be greater than that same product at low
velocities.
Professor Perry's Theory. This theory is given as applied to
a boiler tube, but it applies in a measure to condenser tubes as
the steam takes the place of the hot gases and the water is the
quantity heated in both cases. According to this theory the
rate at which heat is imparted to a boiler tube is propor
tional to :
1. The difference of temperature between the hot gases
and the metallic surface.
2. The density of the gases.
3. The velocity of the gases parallel to the metallic surface.
4. The specific heat of the gases at constant pressure.
The heat transmitted per second per unit of heating surface is
H=Cpv(T l T 2 )' )
where #=the amount of heat transmitted;
(7= the specific heat multiplied by a constant:
v= velocity of gas parallel to the metallic curface;^
p = density of the gas.
That the heat imparted should depend upon the difference
of temperature is selfevident. Experiments seem to show that
it does not depend upon a higher power of the temperature differ
ence than one. Weiss, for instance, makes it depend upon the
square of the temperature difference, but Josse's experiments
do not favor this exponent. ,
Heat is imparted by molecular impact and the greater the
number of these impacts per unit of area and per unit of time
the greater the molecular vibration of the metallic surface. As
the number of impacts is proportional to gas density, it is
evident that density should be one of the factors in the transfer
of heat.
The effect of a blow is lessened if there is a cushion between
the striking and the struck object. If we imagine a number of
244 THE STEAMENGINE AND OTHER HEATMOTORS.
inert gas molecules entangled in the spaces between the metallic
molecules and holding other gas molecules by attraction at the
metallic surface we have such a cushion. (See Fig. 129.) If
the heating gas passes with a strong current so that these inert,
nonmoving, cold gas molecules are swept away it is evident
that a stronger blow will be struck on the metallic surface and
hence more heat will be conveyed. That the value of H will
depend upon v is the more evident when we remember what
poor conductors of heat all gases are. In all forms of steam
condensation, it is noticeable how violent the boiling action is
directly opposite the induction steampice if baffles or deflectors
FIG 129.
are not placed in front of it. A strong steam current over the
entire cooling surface is necessary for a high mean rate of con
densation per square foot of cooling surface. As gas currents
take the lines of least resistance it is evident that their direction
of flow must be compulsory to avoid short circuits, air pockets,
and dead ends in which there is no circulation.
All gases at the same temperature, pressure, and volume
contain exactly the same number of molecules. (Avogadro's
Law.) But they require and give up different amounts of heat.
The latter depends upon the specific heat of the gases, hence the
heat given up should vary with the specific heat. In the case of
condensers this factor is merged in other empirical factors.
CONDENSERS AND AIRPUMPS. 245
Heating or Cooling Surface. The value of any one of the
four factors in the equation below is easily deduced after we
have obtained the proper value of the other three.
H=FAT m .
This equation is applied to surface condensers, feedwater
heaters, multiple effects, vacuumpans, or any form of apparatus
where heat is given up by a hot fluid and absorbed by a cooler
one through some metallic surface.
In this formula,
HihQ total heat transmitted in B.T.U. per hour through the
entire heating surface, A ;
J^=the number of B.T.U. transmitted per square foot of heat
ing surface per degree difference in temperature in
degrees F. between the heating and cooling fluids per hour;
A = area of the heating surface in square feet;
7^ = the mean difference in temperature in degrees F. between
the hot and cold surfaces for one hour;
TF=the pounds of cold water passing through the heater per
hour;
7\. = temperature of steam to be condensed (at constant pres
sure) ;
th= temperature of the hot liquid (if other than steam) at any
point;
tin an d tfo are initial and final temperatures of the hot fluid;
t c = temperature of the cold fluid at any point;
k, and tc 2 are initial and final temperatures of the cold fluid;
th tc = ihe difference in degrees F. between the hot and cold
fluid at any point.
The Mean Temperature, T m . In an endeavor to find the mean
temperature between the heating and cooling sides we see that
four cases may occur:
Fig. 130. The hot fluid maintains a constant temperature
and there is a continuous rise in temperature in the cold fluid ;
Fig. 131. The cold fluid has a constant temperature but
the hot fluid varies in temperature;
Fig. 132. Both fluids change in temperature and both flow,
in the same direction, in currents parallel to the heating surface.
246 THE STEAMENGINE AND OTHER HEATMOTORS.
T"T
r
*
..I.
"T
J.
FIG. 130.
FIG. 131.
FIG. 132.
FIG. 133.
1
r
HO
CONDENSERS AND AIRPUMPS. 247
This would occur in concentric tubes, one carrying the cold
and the other the hot fluid ;
Fig. 133. Both fluids change in temperature but both flow
in opposite directions parallel to the heating surface.
The following discussion is limited to the case of feedwater
heaters, as is illustrated by Fig. 130. Steam at constant tem
perature, Ts, gives up heat to water, raising its temperature from
tc t tO tc r
Formula for T m . Case I. In a time dt the temperature of
the water will rise an amount dd where 6 = T s t c .
Wdd=heat transferred in time dt,
FA C'dt =
*A)
Let = 1 hour,
As FA = the number of B.T.U. transmitted by the heating
surface per hour for one degree difference in temperature,
FAT m =W\og s ^"^.7^ = total heat transmitted =W(T Cl  Tc z ).
Is tc 2
T C1 T C2 (T s t C2 )(Tst Cl ) d 2 di
TsT c ~ Tst Cl di'
lOgs 7p  TFT lOgc ~  log r
1 s JL C2 JL s lc2 U2
where d\ = difference in temperature between the hot and cold
fluids initially,
d 2 = difference in temperature between the hot and cold
fluids finally.
In fact, according to Grashof, Theoretische Maschinenlehre, 1,
the mean temperature in each of the four cases is given by the
formula,
For example, in an opposite current condenser, the cold
liquid enters at 50 F. and leaves at 176 F. ; the hot liquid
248 THE STEAMENGINE AND OTHER HEATMOTORS.
enters at 212 F. and leaves at 122 F. What is the mean tem
2fi 2
perature. Here di=36 F., d 2 = 72 F. Hence
51.9 F. This is a case of the cooling of water coming from
condensed steam.
When vapors are cooled the operation should be divided
into two parts. In the first part the vapor is cooled and con
densed at constant temperature and in the second the resulting
liquid is cooled at a varying temperature to some lower tem
perature. During these two operations the factor F is quite
different, as will be seen. The mean temperature difference, T m ,
should be obtained for each operation.
Feed Heaters. Feed heaters should accomplish much more
than heating the feedwater important as that is. It is only
in recent years that proper attention has been given to the
steamboilers and, owing to the high development of steam
engine economy, it is often possible to obtain greater economy by
attention to boiler management than to refining the engine
room economics. For high boiler efficiency it is absolutely essen
tial to obtain a supply of feedwater free of salts or scaleform
ing substances, oil, gases, acids, alkalis or organic matter. In
brief, feedwater should be pure and as hot as it is possible to
get it.
The thermal efficiency of an injector used as a boiler feeder
is 100%, but that does not make it necessarily a better feeder
than a boiler feedpump whose thermal efficiency may be only
1/50 of that of the injector. If the exhaust from the steam
pump is sent to an open feed heater the thermal efficiency of
pump and heater becomes 100% approximately if radiation is
neglected. The injector using live steam from the boiler is there
fore far less efficient than the pump, as its steam pumps and purifies
the feedwater. Injectors are unreliable with hot water and are
unreliable as pumps if the resistance is liable to fluctuation.
Injectors cannot be used to pump water that has been heated
in a heater nor can they be used as pumps to send water through
heaters, since the water has been so heated in the injector as
to make the heater inoperative. Injectors do not remove any
foreign matter whatever from the feedwater, and the decrease
CONDENSERS AND AIRPUMPS.
249
FIG. 134. The Cochrane Heater and Purifier for use in connection with Engines
or Pumps exhausting freely to the atmosphere.
250 THE STEAMENGINE AND OTHER HEATMOTORS.
in economy due to the formation of scale, the destruction of the
boiler due to acids or alkalis must be charged to the injectors.
Feedheaters may be divided into three classes:
1. Openfeed heaters;
2. Closedfeed heaters*
3. Feed purifiers.
Choice of a Feed Heater. In choosing a feed heater it is
essential to keep in mind all the requirements of the situation.
FIG. 135. A conventional illustration showing the general method of con
necting up a Cochrane Feed Water Heater and Purifier, where all of the
exhaust is passed through heater engine exhausting free to atmosphere
at all times. Pump exhaust entered into main line ahead of heater.
Direct and free feed line from heater to pump. Heater foundation as high,
or preferably higher than pump foundation. Live steam drips saved
by returning to heater through steam trap. Direct connection to cold
water supply. Waste piped direct to sewer or other convenient point not
higher than bottom of heater,, and without any valves in the line.
In practically all cases the oil must be removed. Once water
and oil are mixed it is almost impossible to separate them, hence
the oil should be removed from the steam by the use of a sepa
rator. The other requirements are fixed by the composition of
the feedwater. Volatile gases should be driven out. Some
salts are precipitated around 212 F. but others are precipitated
only at high temperatures. Some feedwaters form scums and
some do not. Hence scum removers, settlingchambers, cham
CONDENSERS AND AIRPUMPS. 251
bers holding chemicals to cause precipitation may or may not
be necessary.
OpenFeed Heaters (Figs. 134 and 135). Openfeed heaters
are simple in construction, are exposed only to one or two pounds
pressure, are efficient as the steam is brought into direct contact
with the feedwater, neither deteriorate nor lose their heat
transfer capacity and being of ample capacity serve as hot wells.
All the volatile gases are expelled, thus enormously reducing
the work of airpumps; they are equipped with means of purify
ing the water of oil and various salts, carbonates of lime, and
magnesia for instance; have settling and filtering chambers in
addition to oilseparator.
Exhaust steam in condensing will give up enough heat to
raise six to ten times its own weight of water from ordinary
temperature to 203 F., which is about as high as openfeed heaters
can heat. Hence they cannot utilize the entire exhaust from
the main engines for feed heating. But the exhaust from a
few pumps will supply this heat and therefore a condensing plant
should turn their exhaust into feed heaters. In so doing they
far exceed the main engines in economy.
Closed Feed Heaters (Fig. 136). Closedfeed heaters are those
in which the heat is transferred through some form of heating
surface to the water in a vessel which is closed, so that the water
may be heated above 212 F. This heater is best suited to
water which is free from scaleforming deposits and volatile
gases. For instance, carbonates are precipitated when the C02
is driven out of the water. In closed heaters if the C02 is not
driven off these salts will be deposited on the boiler tubes. This
will happen if the valve placed for this purpose on the heater
is not opened to permit the gases to escape.
The closed type of heater is subject to boiler pressure and the
corresponding strains and accidents; it is not as economical as
the open heater, and becomes less so as the tubes become covered
with scale; it is difficult to remove the scale from its tubes; a
coating of oil on its tubes renders them less efficient; the con
densed steam is ordinarily wasted; the precipitate does not
settle owing to the agitation of the water.
It is extremely desirable to reduce the amount of gases passing
252 THE STEAMENGINE AND OTHER HEATMOTORS.
FEED
\WATER OUTLET
EXHAUST
STEAM OUTLET
WHEELER CON DENSER \ ENGINEERING CO'S
FEED WATER HEATER
FIG. 136.
CONDENSERS AND AIRPUMPS. 253
into the condenser when high vacua are desired. These gases
interfere with the economy of the condenser and increase mate
rially the load on the airpump. In the open heaters these
gases are driven out automatically.
In the design of a closed heater, in addition to the properly
arranged heating surfaces to abstract all the heat possible from
the steam, other requirements arise from the necessity of main
taining that efficiency with the least amount of trouble. Being
under boiler pressure the heads must be stayed if not thick
enough to withstand expected pressures. Grease may be re
moved by gentle boiling in a strong alkali and scale by subse
quent boiling in a weak acid solution. Do not mix the acid and
alkali.
Percentage Gain in Using Feed Heaters. The theoretical gain
in percentage by the use of feedwater heaters is easily shown.
Let #=B.T.U. in one pound of steam at boiler pressure;
gi=B.T.U. in one pound of water as delivered from the
heater;
g 2 =B.T.U. in one pound of feed water before being heated;
p = percentage gain.
P*.
Suppose one pound of unheated feedwater at 60 F. is raised
to 202 F. in an open heater and is then forced into a boiler at
100 pounds gage, what is the percentage gain? From the tables,
H= 1184.9,
Theoretically, then, the gain is 1% for every 12% gain in
feedwater temperature. There are, however, a number of gains
that cannot be calculated easily in percentage. The heater
drives air and carbonic acid out of the water and so lessens oxida
tion in the boiler and makes the airpump work much lighter
if a condenser is used. The circulation of the water in the boiler
is undoubtedly improved and the economy of the boiler from
that cause is improved. An undoubted gain is the furnishing
254 THE STEAMENGINE AND OTHER HEATMOTORS.
of pure soft water to the boilers thus reducing the formation of
scale and prolonging the life of the boiler. Most heaters are
provided with means to remove oil from the steam where the
water is used to feed boilers. The percentage gain then varies
from 1.2 to 1.4% for each increase of 10 in the feedwater.
Relative Value of Feedwater Heaters and Economizers.
Feedwater may be heated by the hot gases which would other
wise go to waste and it becomes a question as to which is the
better source to look for economy. In England, where the
FIG. 137. Hoppes Heater.
boilers have less heating surface than those in this country,
economizers are used extensively.
Economizers cannot purify the water, neither do they serve
to remove any of the absorbed gases. The purchaser has to
consider the relatively high initial cost; the high cost of upkeep;
a high rate of depreciation; the difficulty of keeping the appa
ratus in an efficient condition; the value of the space occupied;
its effect on the draft or the cost of forced draft. No hard and
fast rule can be laid down and each case must be considered on
its merits.
Closed Purifiers. Fig. 137 represents a closed purifier. The
purifier is generally placed over the boiler. The water is pumped
into the boiler and trickles over the pans. It then comes in
CONDENSERS AND AIRPUMPS. 255
contact with the steam from the boiler at boiler pressure and
temperature. Many salts are deposited at the high tempera
tures attained which would not be precipitated at lower tem
peratures. It is important to take the steam to run pumps
and other auxiliary machinery from the top of the purifier and
in that way remove gases arising from the feedwater. From
the purifier the water runs into the boiler, through the regular
gate and check valves, by gravity.
It is generally contended that there is an economic gain in
taking steam from the boiler to heat the feedwater, as is clone
in purifiers. There will certainly be a gain if salts are removed
which would scale up the boiler. Independent of this reason,
it is contended that the hotter feedwater causes an increased
circulation of the water in the boiler. Recently, however, some
experiments were made which seemed to discredit the above
theory. The question is still open.
Heating Surface in Feed Water Heaters. In the open heaters
and the closed purifiers there is no heating surface as the steam
and water are brought into intimate contact. In these vessels a
large volume must be used to divide the steam and water into
thin divisions to bring about the necessary intimate contact.
In the closedfeed heater the heating surface must be calculated.
Instead of finding the mean temperature by calculus the arith
metical mean is often used. In Case I, Fig. 130, for instance,
such a mean would be
Value of the Heattransfer Factor F. The ability of a heating
surface to transfer heat is far greater than the amount of heat
which is actually transferred. The resistance to heat transfer
does not lie in the molecular resistance of the metal but in the
resistances at the two surfaces, as is shown in the discussion of
Professor Perry's theory.
In surface condensers, for instance, the factor F is dependent
upon the density of the steam, its velocity of flow, the velocity
of the water squared (or perhaps cubed), the amount and charac
ter of the incrustation of the cooling surfaces, the position and
256 THE STEAMENGINE AND OTHER HEATMOTORS.
direction of the cooling surfaces, width and capacity of the con
denser space, and whether the tubes are drowned with water
from above or blanketed by air which is not driven off by the
current of the steam.
In closedfeed water heaters, receiving steam at atmospheric
pressure, the value of F is often taken to be proportional simply
to the velocity of flow of the water. This assumes all other con
ditions to be normal and at their best. For instance, if the
arithmetic mean of the temperatures be taken, practical results
are obtained if F is taken in B.T.U. per hour the same as the
velocity of flow of the cooling water in feet per minute. Thus,
if the cooling water flows at 200 feet per minute then F is 200
B.T.U. per hour per square foot per degree F. difference of tem
perature. If the logarithmic difference be taken, then an as
sumed value of .F=325 B.T.U. seems to give better results.
Example. What amount of heating surface is necessary to
heat 50,000 pounds of water per hour from 40 to 200 F. with
steam at 212 F.
50,000(20040)
200x92 = 435 sc l uare feet >
or using the logarithmic mean temperature and 325 for the
coefficient,
21240
325A  50,000 log, 212 _ 2QQ ,
^4. = 410 square feet.
Primary and Secondary Heaters. If the steam on its way
to the condenser passes through a heater we can raise the feed
water from 40 F. (winter conditions) to 110 F. if the vacuum
carried is 26 inches, corresponding to a temperature of 126 F.
The feedwater at 110 F. can be raised to 205 F. in another
heater where exhaust steam from pumps or other noncondensing
engines is used as the heating medium.
The preceding method may be used to find the amount of
heating surface in a primary and secondary heater to raise
CONDENSERS AND AIRPUMPS.
257
50,000 pounds of water per hour "from 40 F. to 205 F. if the
main engine carries a vacuum of 26 inches.
50,000(11040)
200 + 51
50,000(205110)
343 square feet;
200X55
432 square feet
775 total area in both heaters'
Factor F, according to Hausbrand. In finding the rate of heat
transfer Hausbrand divides the operation into two parts. In
the first part the factor F is large, as it is applied only to the
cooling surface at which steam is condensed. In the second
part a lower factor is used, as it is applied only to the cooling
surface at which the condensed steam is cooled below its boiling
point to some lower temperature.
In thermal units, B.T.U., per square foot per hour per one
degree difference, the factor is
F =
where V d is the velocity of the steam in feet per second and Vj
is the velocity of the cooling water in the same units.
The table below is for F at various velocities of the cooling
water in feet per second, but for a steam velocity of one foot
per second. For any other steam velocity, with any of the
tabulated velocities of the water, the proper F is determined by
multiplying the tabulated value of F by the square root of the
steam velocity in feet per second.
TABLE A.
V) of cooling
water in feet . .
0.003
0.026
0.066
0.5
0.75
1.00
1.5
2.0
3.0
5.0
7.5
9.0
10.0
Fin B.T.U
17
21
25
46
52
57
65
72
82
97
112
118
124
The Coefficient of Transmission of Heat, F, between two liquids
at different temperatures may be found from the equation
40
258
THE STEAMENGINE AND OTHER HEATMOTORS.
where v^ is the velocity in feet per second of one liquid and v/ 2
is the velocity of the other in the same units. For certain veloci
ties the value of F is tabulated below in B.T.U. per square foot
of cooling surface per hour per degree F. difference of tempera
ture:
TABLE B.
,,
./,
0.25
0.36
0.49
0.64
0.81
1.00
1.96
3.00
4.00
0.25
53
57
59
62
64
66
73
77
79
0.36
57
60
63
66
69
71
79
83
85
0.49
59
63
67
70
72
75
83
89
93
0.64
62
67
70
73
75
79
88
94
99
0.81
64
69
72
75
80
83
93
101
105
1.00
66
71
75
79
83
86
96
105
111
1.96
73
79
83
88
93
96
106
123
130
3.00
77
83
89
94
101
105
123
135
144
4.00
80
87
93
99
105
111
130
143
154
In endeavoring to apply these formulas to a condenser the
variety of conditions encountered therein will be made apparent.
The formulas show possibilities for future improvement, point
ing out surface efficiencies that ought to be attained but are
not and indirectly indicating the reason therefor.
Suppose that we are required to find the cooling surface per
100 pounds of steam, exhausted at 10 pounds absolute, 193 F.;
temperature of injection, 60 F. ; temperature of discharge,
90 F.; temperature of feedwater, 110F.; velocity of cooling
water, 200 feet per minute. Assume other data as required.
To condense the steam to water at its boilingpoint, 193 F.,
will require the absorption of its latent heat or 978.8 B.T.U.
per pound. To cool the water from 193 to 110 F. will require
the absorption of 83 B.T.U. or about 1/12 of the former quantity.
Ideally then the range of the injection from 60 to 90 F. should
be divided into twelve parts and one of those parts should be
devoted to cooling the condensed steam and eleven should be
devoted to condensing the steam. The range of temperature of
the injection would be 60 to 63 F. for cooling and 63 to 90
for the condensing.
CONDENSERS AND AIRPUMPS. 259
(193 63) (19390)
Tm== ~~ =117 K >
( 193_63)(11060) 00
130
= 83.
These temperatures do not differ materially from the arithmetical
means.
The velocity of steam as it strikes the tubes may be very
much less than its velocity in the exhaustpipe. Similarly the
velocity of the descending hot water on the tubes is indefinite.
We are not interested in its velocity in falling from tube to tube.
Let us assume 5000 feet per minute as the velocity of the steam
and 40 feet per minute for the velocity of the hot water on the
tubes. Hence F<* = 83.3, ^ = .66 feet, and iy a = 3J feet. F (from
Table A) =84; Vv d =9.1, F (from Table B) = 95.
Heat transmitted per square foot of cooling surface
Condensing=(9.1)(84)(117) = 89,400 B.T.U.,
Cooling = (83) (95) = 7,885 B.T.U.
1 DO V Q7$ 8
To condense 100 Ibs. steam requires  Qn , nn ' =1.1 sq. ft.;
To cool 100 Ibs. water requires  = 1.06 sq. ft.
/OOO
100
Hence ., fa . 1 1 =46 pounds of steam are condensed and
l.Uo H 1.1
cooled per square foot of cooling surface.
As this result is not secured in practice under the given cir
cumstances it is important to discuss the causes of the difference.
In the first place, it is seen that the transmission of heat in con
densing is ten or a dozen times that in cooling. If therefore any
of the condensing surface is water covered all the time, since its
rate of heat transmission is enormously reduced, it is evident
that a very great increase must be made in the cooling surface
to make up for the loss of the more efficient surface.
Suppose, for example, that onehalf of the condensing surface
is water covered. Then onehalf of 89,400 B.T.U. must be trans
mitted by watercooled surfaces.  Then  '   = 6.7 square
260 THE STEAMENGINE AND OTHER HEATMOTORS.
feet of cooling surface will be required As the condensing surface
100
is now .55 feet, we have ,, = 13.8 pounds of steam con
o. / T~ OO
clensed and cooled per square foot of cooling surface.
In the contraflo type of condenser an average of 33 pounds
of steam were condensed and cooled per square foot of cooling
surface. The rate for the upper tubes was much higher than
this. It is instructive to examine the tables and note the effect
that the velocity of steam and cooling water has on the coefficient
of heat transmission.
Contraflo Condensers. " A leading feature of this type of con
denser is a compartment draining of the feedwater (Figs. 138, 139).
The condenser is divided into three compartments by two dia
phragms somewhat inclined to the horizontal, and the water of
condensation in each of the three compartments is drained off
directly from that compartment, so that the surfaces in the lower
compartments are unimpeded in their condensing action by water
from the upper compartment flowing over them. As the major
part of the condensation, even at fairly high rates of condensa
tion, is completed in the highest sections of surface on which the
steam first impinges, the importance of this feature is apparent,
and its influence will be seen in the results.
" Surface Efficiency. Surface efficiency is at the root of all
efficiency in a surfacecondenser. That condenser is the most
efficient in which each square foot of surface transfers in given
time and conditions, as to watersupply, etc., from the steam to
the water, the largest number of heatunits. This will, moreover,
be the condenser which will not only register the highest vacuum,
but will maintain it at the least cost in condensing water, and
with the smallest surface a*nd cubical capacity per pound of steam
condensed. It will also, in given conditions, be the one to yield
the highest hotwell temperature. Now, in order that a surface
may act thus, it is necessary that the steam should have free access
to, and should pass over, sufficient surface on the one side, and
that all the condensing water should come into direct and efficient
contact with the surface on the other side. This clearly cannot
be the case if, on the steam side, practically the whole surface is
continually subjected to showers from the water of condensation,
or if the steam can shortcircuit any material amount of the sur
face; nor can it be the case on the water side if the condensing
CONDENSERS AND AIRPUMPS.
261
\\
U3BHVH3
Nou.naiaj.sia unodVA
773AI20H OJL
H3J.VM MV31S
262 THE STEAMENGINE AND OTHER HEATMOTORS.
water flows through the tubes in unbroken cylindrical streams,
peripheries of which streams alone come into actual contact with
the tube surface, and a greater or less proportion of watercore
passes through without efficient contact. Hence the augmented
efficiency of the surface as a whole, due to the early interception
and removal of the feedwater, the provision for promoting steam
circulation, and the adoption of a suitable ratio between the surface
and the watercarrying section of each tube element, by the intro
duction of a solid displacing core in the tubes or otherwise, as
shown in Fig. 139a. The effect of the use of cores, as against open
tubes, on economy in vacuum production will be dealt
with later on. The cores used on these trials were tri
angular laths of hard wood rough from the saw. They
IG. I39a. were a  DOut two inches longer than the tubes, and were
simply inserted in the tubes without any fastening whatever. The
annexed figure, 139a, shows a fullsized section of tube and core in
place.
" Let ti = temperature of injectionwater;
t " dischargewater;
t v = corresponding to the vacuum V.
"Then the index of relative surface efficiency is the ratio in
*v
relation to t it the heatunits absorbed per pound of condensing water
being (t 1<). The greater this quantity the less the condensing
water required per pound of the steam condensed. Hence economy
of condensing water is one very important result of enhanced sur
face efficiency. Economy of water is important from several
points of view. First, as in the case of land installations, water
may itself have to be purchased. Second, it has to be pumped
through the condenser; and any saving in water means, other
things being equal, power economy in vacuum production.
Third, water may have to be cooled for repeated use, and in this
case surface efficiency of condenser has a double effect. Not only
is there less water to be pumped, but owing to its higher outlet
temperature there will be a greater mean difference between the
temperature of the water to be cooled and the air which cools it;
and hence coolingtowers will be more efficient, and may therefore
be of smaller size for given power.
" Another important result of enhanced surface efficiency is, of
CONDENSERS AND AIRPUMPS.
263
course, economy of condensing surface. Owing to steam space
being dispensed with in this type, a given surface is contained in
less capacity of condensershell. These two features conduce to
economy of weight and capacity. From the point of view, there
fore, of weight and space occupied, this type of condenser has
important advantages, which would seem to render it peculiarly
adapted for use aboard ship, and specially so for all classes of war
vessels, in which both weight and space are of supreme importance.
In the case of marine condensers, economy of condensing water is
of itself of secondary importance; but economy of pumping power,
of weight and space occupied, degree of vacuum maintained, and
hotwell temperature are all of great importance.
"The table gives results obtained under similar conditions by
two Contraflo condensers and one old type condenser attached to a
quadrupleexpansion engine 7"XlOJ"Xl5i"X23", stroke 18",
using steam at about 210 pounds, superheated 50 F.
Condens
Surface
Condenser.
Surface.
Capacity.
Steam
Condensed
perSq. Ft.
per Hour.
Vacuum.
ing Water
per 1 Lb.
Steam .
Inlet
Temp.
perH.P.,
allowing
12 Lbs.
Steam
perH.P.
Relative
Capacity
per H.P.
(No.3 = l).
= 50F.
Hour.
Sq. Ft.
Cu. Ft.
Lbs.
Ins.
Sq. Ft.
No 3
62
6
33
28
32
.36
1
" 2
100
9 6
20
28
24
.6
i.ea
Old type. . .
170
18
10
28
43
1.2
3.6
" Thermal Efficiency. The higher hot well temperature and the
smaller amount of condensing water and surface are both due, the
former entirely and the latter partially, to the same cause, viz.,
the compartment drainage of the condenser. At all, except very
high rates of condensation, or with very small quantities of con
densing water per pound of steam, the greater proportion of the
condensing work is done by the surface situated in the uppermost
compartment. The great mass of the feedwater is therefore with
drawn from the condenser at a temperature sensibly equal to that
obtaining in the top compartment of the condenser and without
passing over the cooler compartments lower down, and specially
escaping the lowest compartment of all, which is thus reserved as
an efficient aircooling section. The hotwell temperatures of the
old type are from ten to fifteen degrees lower than those for cor
264 THE STEAMENGINE AND OTHER HEATMOTORS.
responding conditions in the new type for all degrees of vacua
exceeding 26 inches.
"The absolute pressure in these condensers is practically uniform
throughout the interior; but the temperature is not uniform
throughout. It is always higher at the top than at the bottom.
The absolute pressure, therefore the vacuum must be a com
promise between that due to the top and that due to the bottom
temperatures. As a matter of fact, in airtight systems the vacuum
recorded is generally somewhat higher than that corresponding to
the top temperature, but is not so high as the bottom tempera
ture would indicate, especially at high vacua.
" Economy in Vacuum Production. Conditions are conceivable
in which a given vacuum might be too dearly purchased. Leaving
out of account for the moment all question of the first cost or
weight of the vacuumproducing appliances, including condenser
and pumps, as well as any commercial value attached to the con
densing water, we have on one side of the account the power ex
pended in maintaining the vacuum and on the other side the
power realized from it. Obviously, if a given vacuum should cost
more in power for its attainment than it returns in the shape of
power due to it in the engines, it would be bad policy to work at
such a vacuum. On the above basis, the power cost of a vacuum
will comprise the power required to drive the air and circulating
pumps. The power absorbed by the airpump will clearly depend
upon its size and speed, but so far as degree of vacuum is concerned
the power seems practically independent of the vacuum, at least
for the Edwards type of pump and for vacua ranging between
26" and 29". If there is any effect at all, it is so small, in a com
parative sense, as to be negligible in practice. (For proof, see
page 270.)
"As regards the power absorbed by the circulatingpump, this
will, of course, depend upon several factors, according to the cir
cumstances of each individual case; but so far as the essential
circumstance is concerned, viz., the production of different degrees
of vacua in a given condenser the power will depend on two
factors only the quantity of condensing water and the head or
pressure against which it is propelled through the condenser.
" The speed of the circulating water in the tubes varied from
\y to 4}' per second with no cores, and from If to 6J' with cores,
CONDENSERS AND AIRPUMPS. 265
the corresponding maximum resistances being those due to heads
of 10' and 32' respectively."
Surfacesection Ratio. If L is the length of one tube and the
water circulates 4 times, the length of one element = 4L. Calling
s the exterior surface of one element and a the crosssectional
area of one tube, then the surfacesection ratio = ( ). The numer
W
ator of this ratio indicates proportional heatabsorbing capacity,
and the denominator proportional condensing watercarrying
capacity; and it might therefore be expected to have a determining
influence upon the efficiency of condensers on the water side. In
this type of condenser surface efficiency is independent of rate of
condensation up to 37 Ibs. per sq. ft. per hour but it is materially
dependent upon the value of the surfacesection ratio.
The sole advantage of cores in these trials consisted in the
fact that they afforded a ready means of changing the surface
section without the necessity of structural alterations in the con
denser. In new designs the same end can, of course, be attained
by the adoption initially of suitable proportions and without cores.
Maximum efficiency will occur when dischargewater tempera
ture is equal to the temperature at the condenser top. This is
practically attained when the surface section has a value of some
thing like 2900 or 3000." *
Coolingtowers. In many places water is either unobtainable
in large quantities, expensive, or, if abundant, contains elements
such as mud, salts, or acids that are objectionable. Some appli
ance that will reduce the amount of water necessary to operate
condensers is desirable. Evidently if the coolingwater could be
cooled and used repeatedly, a very great saving would be effected.
Fig. 140 represents the Alberger coolingtower for this purpose.
It consists of a thin cylindrical steel shell, open at the top and
supported on a suitable foundation, and having fitted on one side
a fan, the function of which is to circulate a current of air through
the tower and its filling. This filling consists of layers of cylindrical
6inch tiles 2 feet long, breaking joints. The hot water passes
up through a central pipe to four perforated arms that are made
to revolve by the discharge reaction. The water is thus sprayed
over the tiles, down which it runs in thin layers, exposing an enor
* Lordjn Engineering.
266
THE STEAMENGINE AND OTHER HEATMOTORS.
mous surface to the air rising from the fan. The area of floor
space occupied varies from 1 to 2 square feet per hundred pounds
of steam used by the engine.
FIG. 140.
The fans must be large and run at low speed. The speed of the
fans must vary with the temperature and humidity of the atmos
CONDENSERS AND AIRPUMPS.
267
phere, and a direct enginedrive proves economical. The water
lost per hour by evaporation in the tower = .8 of the feed water
used per hour. Hence the total water required by a condensing
plant with a tower is .8 of the feedwater instead of 30 to 50
times the feedwater. The power to run the fans varies from 2%
to less than 1% of that of the main engine.
The following data show the effect of changes in the season :
Temperature of atmosphere .
' ' condenser dis
cl.arge to coolingtower. . .
Temperature of injection re
turned from tower
30 F.
110
65
36 F.
110
84
78 F.
120
84
96 F.
130
93
85. F.
118
88
59 F.
129
9
Degrees of heat extracted by
tower
45
26
36
37
30
37
Speed of fans at tower
R P M
36
145
162
150
148
Vacuum at condenser, inches
Strokes of airpump
Boiler pressure
25i
30
110
26
30
110
25
37
120
24i
44
120
25i
43
120
25
28
112
Temp, boiler feed
212
212
210
211
213
213
The gain by condensing is shown in the following table : *
Type of Engine.
Feedwater per I.H.P. per Hour.
Per Cent
Gained by
Condensing.
Noncondensing.
Condensing.
Probable
Limits.
Assumed
for Com
parison.
Probable
Limits.
Assumed
for Com
parison.
Simple high; peed
" low " ...
Lbs.
35 to 26
32 " 24
30" 22
Lbs.
33
29
26
24
24
Lbs.
25 to 19
24 18
24 16
20 12
23 14
18 12
Lbs.
22
20
20
18
17
33
31
23
25
29
Compound highspeed. . . .
' ' low ' '
Triple highspeed
27 to 21
" low "
Correct Absolute Condenser Pressure. The vacuum on a con
densingengine is usually expressed in inches of mercury, whether
a mercury column or the ordinary Bourdon gage is used. The
latter is seldom correct enough for accurate work and ther
mometers properly placed give more accurate results. If the
* See A. S. M. E., Vol. XVII.
268 THE STEAMENGINE AND OTHER HEATMOTORS.
mercury column is used, care must be taken in interpreting its
reading. If the barometer reads 29.6 and the corrected mercury
column reads 27.5, the absolute pressure in the condenser is 2.1
2 1
inches, or 14.7^^ = .491 X 2.1 = 1.032 pounds per sq. in., corre
sponding to 102.5 F. If, however, the barometer stood at 30.5
the pressure would then have been .491 X (30.5 27.5) = 1.473
pounds per sq. in., corresponding to 114.5 F. This would make a
serious difference, for example, in the adiabatic expansion of
steam in a steamturbine.
Wet Vacuumpump Design. Let us state a few laws that are
demonstrated in books on physics :
1. The temperature of ebullition, or the boilingpoint, in
creases with the pressure.
2. For a given pressure ebullition begins at a certain tem
perature, which varies in different liquids, but which, for equal
pressures, is always the same in the same liquid.
3. Whatever the source of heat as soon as ebullition begins,
the temperature of the liquid remains stationary.
4. The tension and consequently the quantity of vapor
which saturates a given space are the same for the same tem
perature whether this space contains a gas or is a vacuum.
5. The tension of the mixture of a gas and a vapor is equal
to the sum of the tensions which each would possess if it occupied
the same space alone.
In engineering problems none of these laws is absolutely true be
cause the requirements of the law are not fulfilled. The conditions
existing in the vaporspace of a jet condenser are very complex.
The injection and feed waters bring into the condenser from
5% to 7% of their volume of air when reckoned at atmospheric
pressure and temperature. The volume that this air will occupy
in the condenser depends upon its tension or pressure in the con
denser, and not on the total pressure in the condenser as shown
by a vacuumgage. The latter, as shown by law 5, indicates
the sum of the pressures due to the steam tension and the vapor
tension.
The five laws given above, governing a vapor and its liquid,
CONDENSERS AND AIRPUMPS. 269
when there is temperature equilibrium in both vapor and liquid
(which occurs in experiments when vapor and liquid are quiescent),
must not be applied too rigidly to masses moving with cyclonic
velocity. The temperatures of the vapor and its liquid are not
the same, and the temperature of both differs throughout their
mass in enginecondensers.*
For our purposes it is close enough to take the mean tempera
ture of the vapor and liquid and find the corresponding pressure.
This is approximately the pressure due to the steam ; and the
difference between this quantity and the pressure as calculated
from the vacuumgage reading is the pressure due to the incon
densible gases, such as air, carbonic acid, etc. If the mean tem
perature of the water and steam were 126 F., we know that the
pressure due to the steam vapor is 2 pounds per sq. in. If the
vacuumgage shows 24", the barometer reading being 30", the
total pressure in the condenser would be 2.94 pounds, and the
pressure due to the air alone would be .94 pound per sq. in.
The importance of distinguishing between the air and steam
pressures will become apparent if we attempt to obtain high degrees
of vacua in any system of jet condensation where the air is allowed
to separate from the water.
Airpump. f "It is sometimes thought that a large airpump
is a very inefficient machine for handling comparatively small
amounts of air, and the reason given is that the piston of the
pump is drawing against the vacuum all the time, and there is 14
pounds pressure on every square inch of the piston to be overcome
by the motor. This idea is wrong, however. The work on the
pump is nearly proportional to the amount of air handled regard
less of the size of the pump. If the amount of air is less than the
pump is capable of delivering, the pressure on the atmospheric
side of the piston itself is balanced, or nearly so, for a good portion
of the cycle. This can be demonstrated mathematically, and has
been demonstrated by actual measurements on these airpumps.
The maximum load on the pump occurs when the vacuum is about
18J", varying with the clearance. If the vacuum is less than that,
* Expts. Surface Condensation. J. H. Smith, Engineering, March 23, 1906.
f Engineering Mag., April. 1906.
270
THE STEAMENGINE AND OTHER HEATMOTORS.
the load falls off because of the decreased difference in pressure.
If the vacuum is greater, the load falls off from the decrease in the
mass of air handled. The curve on page 271 (Fig. 142) is a record of
FIG. 141.
a trial made on a pump to demonstrate this, and the analytic dem
onstration is also given. The record of the trial of the pump does
not present a perfect and uniform curve, because the pump valves
are mechanically operated, and for the low vacuum they can be ad
justed only by the sound which the mechanism gives out; but the
curve in general is correct and demonstrates the point. The read
ings were taken down to 18J" of vacuum. Below that point only
one reading was to be had, i.e., that at inches.
Analytical Proof. (Fig. 141.)
A = area of card = piVi + I I2 pdv (piv c +P2V 2
t/i'i
log, v 2 pivi log* vi piVc
dA
piv c
.
The area = a maximum when log v\ =log* v 2 1 + .
1'2
Let p l =14.7, v 2 = l, r c = .03, log. i?i =01 +.03= .97.
(Add 2.3025 and we obtain 2.3025 .97 = 1.3325, or the logarithm
of ten times the required number, .*. Fi = .379.) Hence the
area is a maximum when V\ = .379. The corresponding value of
CONDENSERS AND AIRPUMPS. 271
Amperes of Current
n pi Vi = p 2 v 2 is 5.6 pounds, or a vacuum of 14.7 5.6 = 9.
^
,
.
/
/
/
/
/
/
/
/
A
/
(
/
) * . 4 G 8 10 12 14 16 18 20 22 24 _ 26 28 30
" Vacuum in Inches
FIG. 142.
FIG. 143.
"Edwards' Airpump. The condensed steam flows continu
ously by gravity from the condenser into the base of the pump
272 THE STEAMENGINE AND OTHER HEATMOTORS.
and is there dealt with mechanically by the conical bucket working
in connection with a base of similar shape. Upon the descent of
the bucket the water is projected silently and without shock at
a high velocity through the ports into the working barrel.
"However slowly an airpump with foot and bucketvalves
may be running, the pressure in the condenser has to be sufficiently
above that in the pump to lift the foot valves, overcome the inertia
FIG. 144.
of the water, and drive the water up through the valves into the
barrel. The higher the speed of the old type of pump the greater
is the pressure required to overcome these resistances owing to the
very short space of time available, and as any increase of pressure
in the condenser is accompanied by a corresponding increase of
back pressure in the L.P. cylinder, it"' will be seen that in an air
pump fitted with foot and bucketvalves, increase of speed means
loss of efficiency.
"Under ordinary working conditions, when the bucket descends
and the ports are open, there is absolutely no obstruction between
the condenser and the pump; the air has a perfectly free entrance
into the barrel (Fig. 142), while immediately afterwards the water
CONDENSERS AND AIRPUMPS. 273
is injected into the barrel at a high velocity. Thus, instead of
obstructing the entrance of the air, the water tends to compress
that already in the barrel and to entrain or carry in more air
with it.
"In the old type of pump the clearance between the bucket and
head valveseat is necessarily large, due to the space occupied by
the bucketvalves, the ribs on the under side of the valveseating,
etc. Before an airpump can discharge, all the air in the working
barrel above the bucket must be compressed to a pressure slightly
in excess of the atmosphere. Immediately the bucket descends,
the airbubbles remaining in the clearance water expand and
occupy a space in the pump which should be available for a fresh
supply of air from the condenser. In this type of pump the top
clearance is reduced to a minimum."
To obtain high vacua we should utilize one or more of the follow
ing:
1. Cold injectionwater.
2. Have low discharge water temperature.
3. Control the amount of injection water.
4. Increase the speed of the airpump.
5. Reduce the back pressure on the airpump.
6. Prevent the separation of air and discharge water and
sweep both out together by gravity.
7. Use an airpump that does not require suctionvalves.
8. Have the minimum possible clearance in the airpump and
fill that clearance with cool water.
9. Cool the gases to the temperature of the injection water.
10. Use a dryair pump.
11. Use a surfacecondenser, pump all air out of the system,
and absolutely prevent airleakage.
Airpump for Surfacecondensers. At first sight it would seem
that airpumps used with marine engines could be of very mod
erate size, as the same feedwater is used continuously, and after
it has circulated a few times it ought to be freed from all of its
contained air. And yet on large transatlantic steamers we find
an airpump capacity of .23 cubic foot per pound of steam con
densed, the vacuum ranging from 26 to 27 inches. When dealing
274 THE STEAMENGINE AND OTHER HEATMOTORS.
with high vacua, as required in steamturbine work, much higher
pump capacity is required.
5 1. 1.5 2. 2.5 3. 3.5 4. 4.5 5. 5.5 6. 6.5 7.
jUr Jump Capacity in Cubic Feet
fer pound of Steam
FIG. 145.
Professor Weighton, in experiments illustrated in Fig. 145,
found
1. That when the system is fairly airtight .7 cu. ft. per
pound of steam condensed is as good as anything larger.
2. When airleakage exceeds a certain amount, larger pump
capacities are required. This ranged from .7 cu. ft. per
pound of steam, condensed when the engine was running under
full power and airleakage was consequently slight, up to 6.5
cu. ft. at onequarter power when the receiver pressures were
below atmospheric pressure.
3. That there is no apparent advantage in working pumps
on the compound principle.
Dimensions. When airpumps are directly connected to the
engine so that they make the same number of strokes, the follow
ing dimensions have been used :
For jetcondensing engines having vertical, singleacting air
pumps the area of the airpump piston or bucket multiplied by
its stroke may be from 1/5 to 1/10 the capacity of the L.P. cylinder;
if the pump were horizontal and doubleacting its capacity may
be from 1/8 to 1/16 of the L.P. cylinder.
For surface condensing engines the singleacting airpump
capacity may be 1/10 to 1/18 of that of the L.P. cylinder, and
the capacity of the doubleacting pump would be 1/15 to 1/25 cf
the volume of that cylinder.
On torpedoboats with main engines making 330 revolutions
per minute the ratio of directly connected airpump volume swept
through per revolution is from 1/36 to 1/30 of that swept through
CONDENSERS AND AIRPUMPS.
275
AIR PUMP ORDINARY.
A.Line
TW^PICCM c^ {Tension Hnch= 9.874
M.E.P. 1.894 Spnng, \ Comp , , n l inch=8 . 7
Cooley
0.Line = 14.334
FIG. 146.
AIR PUMP OCCASIONAL.
A.Line
V.Line= 12.549
0.Line= 14.324
A.Line
Cooley
FIG. 147.
0.Line = 14.324
276 THE STEAMENGINE AND OTHER HEATMOTORS.
per revolution by the lowpressure pistons. On the battleships the
corresponding ratio of independent airpump piston displacement
per revolution to the displacement of the lowpressure pistons per
revolution was 1/25, but the pumps only made 1/4 to 1/5 the
number of revolutions made by the main engines.
Bauer gives
I.H.P.
L.P.Cylinder
Airpump
Directly
Connected.
Independent.
Small cargo boat
700
2,000
4,200
9,000
33,000
40,000
20,000
1,300
10,000
19,000
16,000
21.1
15.5
18.5
19.6
41.2
17
17.6
19.5
17
8.2
11.4
Medium cargoboat
Large cargo boat . ....
Mail steamer .
Dcutschland
KdisGT 'Wilhclm II
Russian cruiser Booatiir
Navy gunboat
Small cruiser
Large cruiser
Battleship
Definitions of Airpumps. If we refer to Fig. 16 we see that
this pump draws from the condenser the condensed steam and
a mixture of air and vapor. The injection water, however, is
forced by the circulating pump through the tubes and out of
the condenser without coming into contact with the condensed
steam. If we examine Fig. 17 we see that that airpump has
to handle a mixture of injection water and condensed steam as
well as the mixed air and vapor. Airpumps which must handle
both water and a mixture of air and vapor are called wet vacuum
pumps. On the other hand, a vacuumpump attached to the
barometric type of condenser, Figs. 125 and 126, would draw
off only the mixture of air and vapor as the mixture of condensed
steam and injection water flows off by gravity at the bottom
of the discharge pipe. An airpump working in this manner is
called a dryair pump. The ejector type of condenser needs no
airpump.
Action of an Airpump. Comparing the airpumps in Figs.
16 and 144 we notice that one is horizontal, with large clearance
spaces and with inlet valves, S, which must be lifted. The other
pump is vertical, with no clearance spaces and with no inlet
CONDENSERS AND AIRPUMPS. 277
valves. On the suction stroke the difference between the abso
lute pressure in the pump cylinder and that in the condenser is
the force which moves the water and mixture of air and vapor.
That this difference may be as small as possible so that the con
denser pressure will be a minimum it is evident that anything
causing resistance to movement, such as valves, narrow passages or
sharp bends, should be removed. That the pressure in the pump
should be as low as possible there should be no pockets in which air
is compressed on one stroke only to reexpand on the following one.
To understand the action of the airpump the student should
have a clear idea of the sequence of events as they occur in the
pump during a revolution. At the beginning of the compression
stroke of the airpump piston (see Figs. 16, 144, and 146), the
airpump chamber contains more or less water and some air and
water vapor at the same temperature as the water and at a certain
pressure absolute.
Returning to Figs. 16, 144, and 146, we note that in the
early part of the compression stroke that the curve of pressure
rises very slowly. This is due to the fact that the water vapor
cannot be compressed as the vapor is converted into water. Hence
the air alone is compressed. After all the water vapor is con
densed, the curve of air pressures rises very rapidly to something
over the pressure due to the atmospheric and valve resistances.
On the return stroke, the pressure drops very rapidly if only
water is present, but, if any air is present (at full atmospheric
pressure) the curve drops rather slowly. (Fig. 147.)
Designing Airpumps. The design of an airpump consists in
finding the volume which the airpump piston must sweep through
per minute to remove all the air and water intended from the
condenser. This amount will vary greatly. For example :
1. If the condenser is thirty or more feet from the ground,
it may be made selfdraining. A surface condenser of that
sort would use a dry airpump whose volume would depend
principally on the amount of air leakage and the degree of
vacuum required.
2. A barometric condenser has a dryair pump but it must
remove not only the air from the condensed steam but also
the air from the injection water and the air leakage.
278 THE STEAMENGINE AND OTHER HEATMOTORS.
3. The wet vacuumpump attached to a surface condenser
removes the condensed steam and the air that leaks in.
4. The wet vacuumpump attached to the ordinary jet
condenser has to remove the discharge water, the condensed
steam and the air which the feed and injectionwater con
tained.
Design of Airpump for Surface Condenser. Assume the
following data: Compound engine, 300 I.H.P.; 15 pounds of
water per I.H.P.; injection, 70 F.; discharge, 90 F.; feed,
110 F.; vacuum, 26 inches; barometer, 29.90 inches.
The unit of volume generally used is the volume of one pound
of feedwater. Let us assume that feed and injection water
contain 1/20 or .05% of their volume of entrained air at atmos
pheric temperature and pressure. As soon as the water con
taining this air gets into the condenser the air increases in volume
in proportion to the decrease in pressure and to the increase of
PV
absolute temperature according to the law, ==C.
As the vacuum gage is affected by the atmospheric pressure
we see that the absolute pressure in the condenser is 29.90 26
= 3.90 inches. As the temperature of the water vapor is 110 F.
we see from the tables that the pressure due to it is 2.58 inches
or 1.29 pounds absolute. Then, from Dalton's law, we know
that the difference, or 3.90 2.58 = 1.32 inches, is the pressure due
to the air.
NOTE. If over a little water at 110 F. we had a cubic foot of
space filled with water vapor alone at 2.58 inches pressure abso
lute, we could take a cubic foot of air at 1.32 inches pressure and
110 F. and force it into the cubic foot of vapor. At the end of
the operation there would be only one cubic foot of the mixture
of vapor and air but the pressure would be the sum of the former
pressures. The volume occupied by a certain weight of air in
the condenser is determined by the absolute temperature of the
air and the air pressure and not by the condenser pressure. If
the vapor in a condenser were at 126 F., it would be impossible
to obtain a vacuum over 26 inches, or if the temperature of the
vapor were 141 F. it would be impossible to secure a greater
vacuum than 24 inches, no matter what the volumetric displace
CONDENSERS AND AIRPUMPS. 279
ment of the air pump might be. Hence to obtain a high vacuum
it is necessary to have the air and vapor as cool as possible.
If F 1= =the volume of the feedwater in cubic feet per minute,
then .05Fi is the volume of its entrained air at 29.90 inches of
pressure and 460 + 70 = 530 F. A. From the equation,
PV P 2 V
22
rfi rfi )
JL 1 JL 2
we can find its volume at 1.32 inches of pressure and at
460 + 110 = 570 F. A. Hence,
29.90 X.057i_ 1.327 2
460 + 70 "460 + 110
The theoretical volume of the airpump would thus be
Vi + 1.2Fi = 2.2Vi. As the volume of the feedwater is generally
taken as the unit, we may say then that the volumetric displace
ment of the airpump in cubic feet per minute is, in this case,
2.2 times the volume of the feedwater in cubic feet. The above
makes no allowance for air leakage or pump efficiency. On the
other hand, the factor 2.2 is too large if the condensed steam is sent
to the boiler continuously since such feedwater will not contain
.05% entrained air. Neither is it true if new feed water is used
continuously if this feedwater is sent through an open heater
and brought to the boilingpoint approximately. The entrained
. 460 + 70 53
air would be then only 4590 . 210 = 67 = ; as mucn as ^ was
in water at 70 F.
Manufacturers of condensing apparatus are in the habit of
calling for piping free from air leaks and then supplying air
pumps that are entirely too large if there are no air leaks. In
the present case a reliable index of the amount of leakage ex
pected is obtained from the size of airpumps supplied. Manu
facturers of vertical twin airpumps will guarantee '26 inches of
vacuum with injection at 70 F. with an airpump displacement
of 13 times the volume of the feedwater. This allows practically
ten or eleven volumes, at condenser pressure and temperature,
for air leakage and pump inefficiency. Horizontal pumps are
280 THE STEAMENGINE AND OTHER HEATMOTORS.
furnished with a displacement of 20 times the volume of the
feedwater, thus allowing 18 volumes for leakage and inefficiency.
A 300 horsepower engine would use
625X60 = 1>2 CU * ft ' ^ water P er mmute 
The theoretical displacement of the required airpump would
be 2.2 times and the practical displacement would be 13 or 20 times
1.2 cu. ft. per minute, according as the airpump is vertical or
horizontal.
Bauer states that the principal dimensions of singleacting
airpumps are determined from the equation
Here /= sectional area of airpump in square inches;
s = stroke of pump piston in inches;
I. H. P. = indicated horsepower of the main engine;
C = constant, equal to volume delivered by the airpump
per I.H.P. per minute.
n= number of effective strokes of airpump piston.
The coefficient C=86 to 111 in surface condensers of triple
or quadruple engines, with separatelydriven engines.
C=185 to 245 in surface condensers of triple or quadruple
expansion engines, the airpumps being driven by the main engine.
C=300 to 365 in surface condensers of compound engines, the
airpump being driven by the main engine.
If jet condensation is used as well as surface condensing, or
if the former alone is used, (7=610 to 730. If instead of one
airpump, two pumps are fixed to and driven by the main engine,
the volume swept through per stroke in each may be about .6
of that above. The piston speed varies from 200 to 350 feet
per minute in cargo boats and from 300 to 500 feet per minute
in warships.
The student may discuss the following data of the Glasgow
Electric Power Station (Power, 1905): Steam handled, 60,000
pounds per hour; vacuum, 25 inches in the condenser and 23
inches in the engine; injection, 78 F.; discharge, 94 F.; con
CONDENSERS AND AIRPUMPS. 281
densers, 7000 square feet; cooling surface (2690 tubes), 1 inch
diameter; Edwards' threethrow electricallydriven airpumps;
diameter of cylinder, 16 inches; stroke, 12 inches; revolutions,
150.
Wet Vacuumpump for Jet Condenser. Assume the following
data: Compound engine, 300 I.H.P; water rate, 15 pounds per
I.H.P.; injection, 70 F.; discharge, 110 F.; vacuum, 26 inches;
barometer, 29.90 inches.
As the amount of heat per pound of steam to be absorbed in
the condenser is practically constant and is about 1050 B.T.U.,
we can assume that the amount of injection water required is
1050 Kl 10 70) = 26 pounds. The total water is then 27 pounds
and the volume of air is
29.9 X .057i (29.90  26  2.58) 7 2
460 + 70 460 + 110
Hence V% is equal to 1.27:. As V\ is 27 times the volume of
the feedwater then the volume of the entrained air is 27X1.2
or 32.4 times the volume of the feedwater. The amount to be
allowed for air leakage is largely guess work. If we allow 10
times the volume of the feedwater we shall have the following
allowances :
Volumes : 1 .... Feedwater
26 Injection water
32.4 . . . .Air in feed and injection water
10 Air leakage at condenser pressure and temp.
69.4
Hence the displacement of the airpump in cubic feet per
minute will be 70 times the volume of the feedwater. The
required displacement is therefore
300X15X70
62.5X60 =84 CublC feet '
The required airpump may now be chosen from a catalogue.
282 THE STEAMENGINE AND OTHER HEATMOTORS.
Cooling Air in Condensers. To cool the air In its passage to
the airpump a large cooling surface is necessary, as the heat
transmission coefficient is very low. Efficiency depends upon
the air velocity, the water velocity in the pipes being of little
importance. In Josse's experiments (Power, Feb., 1909) it
varied from 0.172 to 0.955 B.T.U. per square foot per hour per
degree Fahrenheit difference of temperature.
Dry Airpumps for Countercurrent Barometric Condensers.
If Fig. 125 is carefully examined it will be seen that the air is
drawn off at the top of the condenser. To reach the eduction
pipe the air has to pass in intimate contact with " cold fingers "
containing injection water at initial temperature. The tendency
of these cold fingers is to deprive the air of its last remnant of
vapor and to cool the air down to (theoretically) the injection
temperature. If the vapor is condensed, there is a marked ten
dency for the vapor pressure to decrease and the air pressure
to increase as the total pressure must be very nearly uniform
through the condenser. It is evident that the lowest total
pressure must be at the mouth of the aireduction pipe, as
the gases are flowing in that direction and all flow is from
the greater to the less pressure. But in gases so light as these,
a very high velocity is secured by a very slight difference in
pressure. At condenser pressures air is lighter than steam, but
practically the velocities in the condenser are so great that it
is easy to see that ideal conditions cannot be carried out. Hence
in the design of an airpump for this style of condenser the volume
of the pump displacement is materially reduced, as it does not
care for the feed and discharge water and receives the air not
only at much higher pressure but also colder.
Design a dryair pump for a 300 I.H.P. compound engine,
using 13 pounds of water per I.H.P. The injection is at 70 F.;
the discharge at 110F.; vacuum is 28.5 inches; barometer,
29.90. Countercurrent condenser.
We shall assume that the air is drawn off at 85 F. (the cor
responding pressure is 1.2 inches of mercury) and that the air
leakage at condenser pressure is 15 times the volume of the feed
water.
The pressure corresponding to 110 F. is 2.58 inches of mer
CONDENSERS AND AIRPUMPS. 2S3
cury and, if the steam vapor were not brought below that tem
perature, no vacuum pump however large would give the
required vacuum. The difference, 29.90 28.5 = 1.4 inches, is the
maximum possible pressure of the air and could only occur if
all the vapor is condensed. The air may be lower than 85 F.,
the minimum 70 F. being possible. Assume then 1.2 inches as
the absolute pressure of the air.
Assuming each pound of steam going into the condenser loses
1050 B.T.U the amount of injection per pound of steam will be
= 26 pounds.
For each cubic foot of feedwater there will be 26 + 1 = 27 cubic
feet of discharge water. The volume, V 2 , of the air in this injec
tion and feedwater (assuming both to have been originally at
70 F. and 29.90 inches pressure) after reaching the condenser
and passing the cold fingers of the injectionpipe will be, since
29.90 X.057i 1.2F 2
460 + 70 "460 + 85'
1.3Fi, where Vi represents the volume of the discharge in any
unit of time.
The number of cubic feet of feedwater per minute will be
300X13
60X62.5
The volume of the discharge, per minute, will be
27X1.1 = 29.7 cubic feet.
The volume of air to be discharged per minute will be
29.7X1.3 = 38.6 cubic feet.
If the air leakage is 15 cubic feet per minute the total dis
placement of the dryair pump, per minute, will be
38.6 + 15 = 53.6 cubic feet.
284 THE STEAMENGINE AND OTHER HEATMOTORS.
Ex. 101. Design a surface condenser for a 100 horsepower high
speed engine using 18 pounds of steam per I.H.P. Assume other
conditions. Vacuum 27".
Ex. 102. Design a contraflo condenser for a 2000horsepower
engine using 13.5 pounds of steam per horsepower. Vacuum ex
pected = 28".
Ex. 103a. Design a wet vacuumpump for the jet condensers;
26.5 inches of vacuum required.
Ex. 1036. Design a dry vacuumpump for the surface condensers.
CHAPTER X.
SMALL AUXILIARIES.
Steampumps (Fig. 4). The wastefulness of the ordinary
steampump is not recognized by the ordinary steam user. It
uses steam at full boilerpressure; the clearance is inordinate when
the piston makes a full stroke and there is no adjective strong
enough to express its wastefulness in case it does not make its full
stroke. The initial condensation depends upon range of tempera
ture which, in the case of a steampump, is from the boiler tem
perature to 212 F. As a result, the initial condensation is very
great. In case the pump is used only occasionally and the steam
pipe fills with water from radiation losses, the percentage loss for
the actual work done is very great. The ordinary steampump will
use between 80 and 300 pounds of water per I.H.P. A simple
pump will require one pound weight of steam to pump 40 pounds
of water during the time actually employed in pumping.
This waste may be reduced by compounding, and a still greater
saving will be made by the use of a compound condensing pump.
For instance, a duplex 6"X4"X6" may be replaced by a single
compound with high and lowpressure steamcylinders of 6 inches
and 10 inches diameter, water cylinder 5 inches in diameter and
10inch stroke.
The greatest saving can be made by using the exhauststeam
in a feedwater reheater. Great care should be used not to increase
the back pressure unduly.
Wasteful as they are, however, they are far more economical
than ejectors when the heat in the water ejected is thrown away^
as in the case of (bilge) syphons.
To economize, auxiliaries have been beltdriven from a shaft:
285
286
THE STEAMENGINE AND OTHER HEATMOTORS.
which was driven from the main engine. This arrangement has a
number of difficulties to overcome :
1. The need of regulating each pump to an exact speed
depending upon requirements. In an emergency an excessive
speed of one pump may be needed for a few moments, or for
long intervals no speed at all may be needed.
FEED PUMP 30 REVS. BYEPASS CLOSED.
M.E.P. 134.15
Spring, 1 inch 84.905 Ibs.
A.Line
O.Line
M.E.P. 141.79
Spring, 1 inch =84.905 Ibs.
Cooky
O.Line
FIG. 148.
2. The friction of heavy shafting is a large part of the power
required, hence the arrangement is wasteful if only a few aux
iliaries are running.
If the steam from the main engine is sent to a condenser, this
arrangement is less economical in heat and less convenient than
separate auxiliaries if the latter send their exhauststeam to feed
water heaters.
There is a practical limit to the amount of exhauststeam that
can be used in this way. Moreover, the use of any heater is not
economical unless it is using heat that would otherwise be neces
SMALL AUXILIARIES.
287
sarily wasted. As in many other things, heating economies are
possible in a large plant that are not practically possible in a small
one. Similarly plants that are run for short intervals only cannot
use apparatus on which the interest and depreciation charges
would counterbalance the economy gained by their use for a short
FEED PUMP 42 REVS. BYEPASS OPEN.
M.E.P. 132.28
Spring, 1 inch =83.19 Ibs.
A.Line y
O.Line
M.E.P. 144.75
Spring, 1 inch =83. 19 Ibs.
A.Line
Coo ley
O.Line
FIG. 149.
period of time. Hence with a uniform load and good feedwater an
economizer may pay for itself.
The amount of feed water required per horsepower varies
from
40 to 25 pounds for simple engines,
25 to 15 pounds for compounds,
20 to 11 pounds for triples.
Each pump should be designed to supply 1.5 to 2 times the
theoretical quantity of water required. This allows for slip or
imperfect filling of the pump with water.
288 THE STEAMENGINE AND OTHER HEATMOTORS.
The velocity of the water in the suctionpipe should not exceed,
normally, 450 feet per minute, that in the dischargepipe being
600 feet per minute. The net area of the valve passageway
should be calculated at 400 feet per minute. The diameter of the
steamcylinder is 1.4 to 1.6 times that of the watercylinder, thus
affording a pressure of 2 to 2.5 times that of the boiler.
In duplex pumps the steamvalve on one cylinder is driven by
the reciprocating motion of the other pump. In the simplex
pumps it is necessary to employ an independent valve.
Suction
FIG. 150.
Reciprocating Circulating Pumps (Fig. 18). The piston speed of
these pumps may reach 475 feet a minute; their volume may be
obtained by allowing
9 to 10.5 cubic feet per hour per H.P. for compound engines:
7 to 9 cubic feet per hour per H.P, for triple or quadruple
expansion engines.
This allows 80% efficiency for the pump.
The number of strokes per minute made by a steampun: p is
generally calculated on the basis of 100 feet of piston speed per
minute. For continuous boiler feeding and running under heavy
SMALL AUXILIARIES.
289
pressure the speed should not exceed 50 feet per minute. The de
livery is also frequently given in gallons. If the diameter of the
watercylinder is squared and then multiplied by 4 ; the result is
the delivery of the pump in gallons per minute on the basis of
100 feet of piston velocity.
On most pumps it is deemed advisable to place an airchamber
on the delivery side of the pump. In most cases it is even more
j Suction
FIG. 151.
essential to put an a^rchamber, as in Figs. 150, 151, on the suction
side. Fig. 152 is added to show how not to apply the airchamber.
On long suction lines this airchamber takes up the inevitable
surging of the water in the suctionpipe due to the irregular taking
of water by the pump. It stops the hammerblow noise heard in
pumps that are " pumping dry," as in pumping bilges dry.
Ex. 104. A compound engine of 1000 I.H.P.; cylinder ratio, 1:4;
19 expansions; steam at 165 pounds absolute on the piston; revolu
tions, 94; vacuum, 26"; using 14.5 pounds of water per I.H.P.; injec
tion, 70; discharge, 110 F.; jet condenser; feedwater, 70 F. in
rivermains. Find the size of the feedpump by calculation or from
catalog. Assume positions of machinery and other data that may be
required. Use handbooks or other aids.
290 THE STEAMENGINE AND OTHER HEATMOTORS
Ex. 105. Find the size of airpump for Ex. 104.
Ex. 106. Find the size of reciprocating circulating pump.
Ex. 107. Find the size of centrifugal circulating pump.
Ex. 108. Find the size of a feedwater heater to take care of the
exhauststeam from the steamcylinders of the above pumps if the
dischargewater be unfit to use.
Ex. 109. Design a reheating receiver to superheat exhauststeam
50. See page 297.
Suction
FIG. 152.
Centrifugal Circulating Pumps (Fig. 153). The inner diameter
of the driving vanes should be 1.1 to lAd, where d = the diameter
of the single suction or deliverypipes, and the outside diameter is
2 to 2.6U The width of the vane at its inner diameter is .23
to Ad. The width of the vane at its outside diameter may be
reduced in proportion to the increase in velocity of the water,
Notice proportions in the cut showing double suctionpipes.
If the water enters from one side there is an axial thrust which
is avoided by having the water enter on both sides.
The shape of the vanes is such that the water may enter with
out shock (see steamturbine calculations). The velocity at the
periphery must be 25 to 40 feet per second for a frictionhead of 5
SMALL AUXILIARIES.
291
to 8 feet, the revolutions varying in general from 150 to 350 per
minute.
The engines to drive these pumps must have a horsepower
where Q = pounds of water delivered,
h = head in feet.
292
THE STEAMENGIXE AND OTHER HEATMOTORS.
These engines should develop this power with a pressure equal to
.75 boilerpressure.*
Steaminjector. Fig. 154 is a diagrammatic sketch of an in
jector. We owe this invention to M. Giffard, a French engineer.
The original invention has been much improved and many care
fully worked out devices have been added to make the device reli
able and automatic. Its use is practically confined to boiler
feeding, as its efficiency as a pump is very low. As a boilerfeeder
its thermal efficiency approaches 100%, as all the heat that it
takes from the boiler is returned, but at a lower temperature.
FIG. 154.
The device consists essentially of a steamnozzle, A ; a combin
ing tube, B; and a deli very tube, D. C is an overflow and E is
the suctionpipe.
On page 216 we found that if steam is made to expand adia
batically in a properly proportioned nozzle, the heat lost in
expansion was converted into energy of motion, or, in other words,
the steam acquired a high velocity. The amount of thermal energy
wV 2
converted into kinetic energy = ^~ =wh is more than sufficient to
do the work required in forcing W pounds of feedwater = (12 to 22) w
into the boiler against the boilerpressure, or wh>(W+w) 
.4o
(W +w)hb, where hb is a head of water in feet equivalent to the
boilerpressure P&.
* See Bauer, Marine Engines.
SMALL AUXILIARIES. 293
When steam is turned on the injector, the first effect is to drive
all air out of the system through the overflow which is open. The
partial vacuum allows the atmosphere to force water through the
suctionpipe, E, into the combining chamber, B. The steam, issu
ing from A at high velocity (as soon as the reduction of pressure
occurs due to the condensation of the steam), possesses sufficient
energy to move a large mass of water with considerable velocity.
The combined mass in slowing down can overcome a higher static
pressure than its own, and can therefore enter the boiler.
Weight of Feedwater per Pound of Steam. Assume the steam
to be dry, and measuring all heatunits from 32 F. :
Let qi HZ/i =heat required to produce one pound of steam;
#2= heat contained in the feed before entering the
injector;
#3 =heat contained in the feed after leaving the injector;
w = number of pounds of steam used in any given time;
W = pounds of feed water lifted by the injector in the
same time;
W+w = pounds of water delivered by the injector;
W(qzq2) =heat gained by feed water;
+qi qs) =heat lost by the steam;
V 2 1
The last term (W +w) ~~ X ^= is the heatequivalent to the kinetic
energy of the delivered feedwater entering the boiler. As it is
very small it may be neglected, hence
/. =  = weight of feed water lifted per pound of steam
w qs~q2
used by the injection.
Efficiency of the Injector. A large portion of the kinetic
energy of the steam is converted back into heat, as the impact
must be that of nonelastic bodies.
Let MI = the mass of the steam and Vi its velocity;
M 2 = " " " " lifted feed and 7 2 its velocity;
V c = " common velocity of the mass MI +M 2 .
291 THE STEAMENGINE AND OTHER HEATMOTORS
We know that the sum of the momenta before impact equals the
momentum of the combined mass after impact, or
(1) MM +M 2 V 2 = (M 1 +M 2 )V
Let EI = %M i Fi 2 + %M 2 V 2 2 = the sum of the kinetic energies be
fore impact;
E 2 = %(Mi+M 2 )V c 2 =t'he energy of the total water after
impact. Then from (1)
/M 1 7 1
\ M l
>
+M 2 /> 2(M l+ M 2 )
The initial velocity of the lifted feed is so small that it may be
neglected. M 2 V 2 2 = approximately, hence EI = \M\ Vi 2 approxi
mately. The energy converted back into heat is
AW M 2
E 2 =Wit i  = '
In a locomotive injector one pound of steam is required for
every 12 pounds of water lifted; therefore from the above formula
12/13 of the energy of the steam must be converted back into
heat.
Disregarding V 2 we have
13'
w
Similarly, E 2 = ^ .
If from the entropy diagram we find the velocity of the steam
is 2400 feet per second,
1X2400X2400
EI =  2^32  =90,000 ft.lbs.
The Hancock Inspirator, " Stationary " Type.
Directions for Connecting.
Steam, water, delivery, and overflow connections are as illus
trated.
Si earn. Take steam direct from the dome or highest part of
the boiler and not from a pipe furnishing steam for other purposes,
SMALL AUXILIARIES.
295
Place a globe valve in the steampipe for a startingvalve, and
before connecting the inspirator blow it out thoroughly to remove
any red lead, iron chips, etc.
Suction. A TIGHT SUCTION is absolutely necessary, especially
on a high lift and for the smaller sizes of inspirators.
STEAM
FIG. 155. Hancock Inspirator.
The size of the suctionpipe should be in proportion to its
length. For a high lift or long trail, use pipe one or two sizes
larger than the suction connections. The suctionpipe should be
as nearly straight as possible.
Never use a footvalve, as the water should be allowed to drain
from the suctionpipe when the inspirator is not in service.
296 THE STEAMENGINE AND OTHER HEATMOTORS.
Place a globe valve in the suctionpipe to regulate the supply
of water to the inspirator, and KEEP IT WELL PACKED.
Delivery. Place a checkvalve in the deliverypipe, between the
inspirator and the boiler, also a globe valve between the check
valve and the boiler, so that the checkvalve may be examined and
cleaned when necessary. If the inspirator is to feed through a
"heater," there must be a check valve between it and the in
spirator.
Overflow. The overflowpipe must be as straight as possible
and the full size of the connections. The end of the overflowpipe
must be opened to the air and not piped below the surface of the
water.
We do not recommend the arrangement for an inspirator to
take water under a head, but the use of a tank fitted with a "ball
cock," so that the inspirator may lift the water from it. If it is
necessary to connect the inspirator direct to waterworks pressure,
the suctionpipe must be large enough to secure a uniform pressure.
Never take water from a pipe which supplies water for other pur
poses, as the watersupply may be reduced so much at times as to
make it unreliable.
Directions for Operating.
Open the overflowvalves Nos. 1 and 3, close forcer steamvalve
No. 2, and open the star ting valve in the steampipe.
When the water appears at the overflow, close No. 1 valve,
open No. 2 valve onequarter turn, and close No. 3 valve. The
inspirator will then be in operation.
NOTE. No. 2 valve should be closed with care to avoid damag
ing the valveseat.
When the inspirator is not in operation both overflowvalves,
Nos. 1 and 3, should be open to allow the water to drain from the
inspirator.
If the suctionpipe is filled with hot water, either cool off both it
and the inspirator with cold water or pump out the hot water by
opening and closing the startingvalve suddenly.
No adjustment of either steam or watersupply is necessary for
varying steampressures, but both the temperature and quantity
of the deliverywater may be varied by increasing or reducing the
SMALL AUXILIARIES. 297
watersupply. The best results will be obtained from a little
experience in regulating the steam and watersupply.
To locate a leak in the suctionpipe, plug the end, fill it with
water, close No. 3 valve and turn on full steampressure. Examine
the suctionpipe and the water will indicate the leak. If the in
spirator does not lift the water properly, see if there is a leak in
the suctionpipe. Note if the steampressure corresponds with
the lift, and if the sizes of pipe used are equal to the size of the
inspirator connections.
If the inspirator will lift the water, but will not deliver it to
the boiler, see that the checkvalve in the deliverypipe is in work
ing order and does not stick. Air from a leak in the suction con
nections will prevent the inspirator from delivering the water to
the boiler even more effectually than it will in lifting it only. If
No. 1 valve is damaged or leaks, the inspirator will not work
properly. No. 1 valve may easily be removed and ground.
To remove scale and deposit from the inspirator parts, discon
nect the inspirator and plug both the suction and delivery outlets
with corks. Open No. 2 valve and fill the inspirator with a solu
tion of one part muriatic acid and ten parts water.
Reheaters. There is little use in drying steam passing from
the high to the lowpressure cylinders, but it is economical to.
superheat steam that has been dried by passage through a separa
tor. Figs. 156 and 157 show two such reheaters, in which the
extent of heatingsurface provided is at the rate of 1.25 square feet
to the horsepower. The principal data are shown on the cuts. ,,
Oil and Water Separators. The thermal efficiency of an
engine is increased by removing water from the steam before
they enter the high, or any succeeding cylinder, or a surface
condenser. The thermal efficiency is also increased by removing
the oil before it enters any condenser or boiler or any succeeding
heating system. Water or oil interferes with the transfer of
heat through condenser tubes. It is better to have a solid clean
scale a quarter of an inch thick on a boiler tube than an amount
of oil that could be placed there by rubbing the tube with a greasy
rag. Water carrying oil should not be used as boiler feedwater
and steam carrying oil should not be used in radiators or other
heating systems.
tl
S I
II
II
iVV
bb
^
i
1
l
SMALL AUXILIARIES.
299
Fig. 5 represents a separator depending upon centrifugal
force. Figs. 157 and 157a represent separators in which a ribbed
baffle plate is placed at right angles to the current of steam.
The ribbing prevents the oil or water from being brushed off by
the deflected steam current. The water drains down and out
away from all entraining currents.* The vacuum oilseparator
is placed on the exhaust pipe of the engine and in addition to
the baffle plates it has a circumferential lip to catch the oil that
End Section
Side Section
FIG. 157. Vacuum Oil Sep
arator for Horizontal Pipes
18 inches and larger.
FIG. 157a. Separator.
creeps along the interior surface of the exhaust pipe in the direc
tion of the steam current.
If oil is to be removed from exhaust steam it should be
done before condensing the steam. It is almost impossible
and generally impractical to remove oil from condensed steam.
The reason arises from the fact that the oil becomes oxidized on
the surface. The, oily particles lose all tendency to coalesce
and only break down when they are subjected to the high heat
of the boiler. In the boiler, the oil unites with the metal of the
boiler, forming oleates of iron which has the consistency and
strength of graphite.
* By enlarging the lower cylindrical body a separating receiver is formed
which may be used between the various cylinders of multipleexpansion engines.
CHAPTER XI.
MULTIPLEEXPANSION ENGINES.
THE heat in the steam exhausted from a simple or single engine
is wasted, as far as the engine is concerned. In some cases this
exhauststeam is sent to a heater and its heat is saved, but the
resulting economy may be considered as belonging to the engine
plant rather than to the engine. If this steam is exhausted at
considerable pressure above zero, more work might be obtained
from it by further expansion. This would necessitate a second
cylinder of much larger volume than the first to accommodate the
proposed increased expansion of the steam incident to the lowering
of its pressure before rejection.
In no case is it economical in simple engines to lower the tem
perature by expansion below that which may be obtained with con
siderable ease by utilizing the temperature of natural substances
around us. If water be expensive, then it is nojt economical to
expand below the atmospheric pressure. If water is cheap, then
we may expand the steam to a pressure not lower than three or
four pounds per square inch above the pressure corresponding to
the temperature of the water aS shown in steamtables. The back
pressure should be as close to the pressure corresponding to the
temperature of the injection water as possible.
Advance in the design of economical engines had to wait on
advance in knowledge of methods of manufacturing better mate
rials for use in boiler and engine construction. Lack of proper
lubricants for highpressure steam prevented its use for one or
more decades. Failure to experiment restrained advance in all
sciences till the middle of the last century. Watt advanced the
theory that the water consumption of an engine per horsepower
would decrease with increased ratios of expansion, the maximum
300
OF THE
UNIVERSITY
OF
.SALIFQSJJP'
'ULTIPLEEXPANSION ENGINES. 301
expansion, however, being that which gave a final pressure equal
to the back pressure. In 1840 a Cornish pump was accurately
tested, and the water consumption was found to be 24 pounds at
1.5 expansions and 16.5 pounds at 3.5 expansions. This was
assumed to prove Watt's theory, and enginebuilders gave all the
expansion that their form of valvegear would admit. Gradually
it began to be felt that " expansionengines were expensive engines."
From 1840 to 1860 no authoritative experiments were made. At
the latter date, Chief Engineer Isherwood, U. S. Navy, pub
lished his accurate and elaborate experiments on the U. S. Steam
ship Michigan, and the losses from initial condensation were re
vealed. A more intimate knowledge of the facts demonstrated
that the Cornish engine experimented upon was working under
unsuspected advantages, which accounted for its economy. The
working end of its cylinder was not exposed to exhaust tempera
tures, the admission steam was superheated by excessive wire
drawing, and a livesteam jacket effectively reduced internal
condensation.
Rankine's analyses of Isherwood's results showed that the
initial condensation depended upon the range of temperature to
which the cylinder was subjected, and that by dividing this range
among two or more cylinders economy would result. In a double
expansion engine, for instance, all the steam condensed in the first
cylinder is reevaporated, and so is capable of performing work
in the next cylinder. The condensation in the second cylinder is
due to its own range of temperature, which is far less than it would
be in a simple engine having the same range of expansion as the
compound engine.
During the next forty years competition caused an interesting
struggle in the production of recordbreaking engines. Pressures
rose with the advance in the art of boilermaking and the advent
of mineral oils. Triple and quadruple expansion engines naturally
followed the advance in pressures. Highspeed engines showed a
marked economy over slowspeed engines. It was claimed that the
large clearance spaces of the former caused no loss, because the
clearance space was filled by recompressed steam to the boiler
pressure. It has only been, in recent years that proper considera
tion has been given to the large losses that may be expected from
302 THE STEAMENGINE AND OTHER HEATMOTORS.
high compression in engines having large ratios of expansion, large
clearance surfaces, and early release. With small clearance, a
slight degree of compression produces no considerable loss and is
conducive to smooth running.
The economy arising from enclosing the workingcylinder with
not only nonconducting material, but also with heatgiving fluids,
has been recognized. Hot waste gases in jackets caused unequal
expansion and trouble in lubrication, so that the use of hotair
jackets soon ceased. The use of steamjackets continues till this day,
but with more general use of steamsuperheaters they also will cease
to be employed. In the past, however, not only the cylinderbarrel,
but also the heads and even the piston have been jacketed. In
tests, a gain in economy is shown by their use, because they are
regulated properly; in practice, they cease to be economical (when
their high cost of installation is considered) if not kept properly
drained and the drainage returned at high temperature to the boiler.
We have already seen that the maximum fluctuations of tem
perature take place only in the innermost layer of the cylinder
walls. With a rapidly diminishing range of temperature these
fluctuations take place in successive layers till the outermost one
is reached. If this outside layer is kept at some constant tempera
ture by means of a jacket the less will be the range of fluctuation
the higher the temperature of the steamjacket, since the heat from
the latter is flowing inwardly. As the steamjacket practically
only affects the cylinder steam that comes in contact with the
cylinder walls, its value in the case of large cylinders is doubtful.
Reduction of clearance having been found to produce economy,
clearance was reduced more and more till the shortening and
lengthening of the pistonrod under stress became a subject of
consideration ( !) . It is now recognized that reduction of clearance
surface is more essential than reduction of clearance volume. To
obtain reduction of clearance volume, the valves are placed in the
cylinder heads to give the shortest possible ports, and separate
valves are used for admission and exhaust.
High speeds of rotation having proved economical, Corliss
speeded his engines up from 50 to 125 revolutions, and for a long
time his engine was considered a highspeed engine. A higher
speed with detachable valves is not practical, as the piston travels
MULTIPLEEXPANSION ENGINES. 303
too far during the time that the dashpot is operating the valve.
The shaftgoverned engines, running at speeds of over 200 revolu
tions per minute, have put Corliss engines with detachable valves
in the slowspeed list. Small engines rotating 400 to 600 times
a minute and large engines with a piston speed of 1000 feet per
minute are in general use.
We have seen that the second or lowpressure cylinder is larger
than the first or highpressure cylinder in a doubleexpansion or
compound engine; in a triple the third or lowpressure cylinder is
larger than the intermediate pressure cylinder, which is larger than
the first or highpressure cylinder. Ordinarily the lowpressure
volume may be taken at 3 to 4 times the volume of the high in the
compound system, and in the triple the relative volumes are fre
quently 7, 2f , 1. Rockwood designed a compound engine in which
the ratio of the low to highpressure volumes was 6J to 1, or
practically a triple with the intermediate cylinder left out. Other
data were: Engine room gage, 172.2 pounds: superheat at throttle,
46 degrees; cutoff, .278 stroke; clearance, 4.3 and 5%; revolu
tions, 80.25; vacuum, 27.7 inches; horsepower, 565.1; steam con
sumption, 11.22 pounds per I.H.P. A belief immediately arose
that high ratios between the cylinder volumes of compound engines,
combined with low clearance percentage, were essential to com
poundengine economy.
More recent compounds designed by Prof. Rockwood have given
better results. A 16 X 40 X 48 CrossCompound Cooper Corliss
Engine, designed by him, consumed 11.22 pounds of water per
I.H.P. including steam condensed in jackets and reheater coil.
The principal data were: Steam pressure, engine room gauge, 172.2
pounds; superheat at the throttle, 46 degrees; cutoff at .278
stroke: clearance 4.3 and 5%; revolutions, 80.25; vacuum 27.7
inches; horsepower, 565.1.
The following tests, made in the last five years, will demon
strate that, whilst all of the above are contributing, none of them
is an essential element to economy. A deficiency in one respect
may be more than replaced by an economy in some other direction.
On December 28, 1901, Jacobus on a Rice and Sargent cross
compound engine, cylinder ratio, 4 to 1; Corliss valvegear, 121.5
revolutions; steampressure, 151.3 pounds; pressure absolute in
condenser, .85 pound; live steam in cylinderhead jackets of
304 THE STEAMENGINE AND OTHER HEATMOTORS.
both cylinders and in a reheatingreceiver at 627.4 I.H.P. found
a water consumption of 12.10 pounds. The clearances were 4.7
and 7%; expansions, 33; initial condensation, 22%. This engine,
with ordinary cylinder ratios and ordinary clearances, gave a better
economy than the Rockwood engine. It had a better vacuum and
a larger ratio of expansion.
Schroter with a Van den Kerchove poppetvalve compound
engine, cylinder ratio, 2.97 to 1; 126 revolutions; steam pressure,
130 pounds; 27.6" vacuum; jackets on barrels and heads; no
reheater; 32 expansions; 23.5% of initial condensation at 117
I.H.P. found a dry saturated steam consumption of 11.98 pounds
per horsepower.
This result is slightly better than the preceding and on a smaller
engine.
Whitham, Andrew, and Wells on a Westinghouse compound
with twin L.P. cylinders; combined poppet and Corliss valve; cylin
der ratio, 5.8 to 1; 76 revolutions; clearances, 10.5% and 4%;
steampressure, 185 pounds; 27.3 inches of vacuum; 29 expan
sions; 32% initial condensation; no jackets, no reheater at 5,400
horsepower found a water consumption of 11.93 pounds.
This result is a trifle better than the preceding. We are dealing
with a large engine with a fairly large ratio of expansion, but, on
the other hand, the revolutions are low, the clearance high.
The only elements in common in the above engines are the high
ratio of expansion and a high boilerpressure. Jackets helped the
small engine, and the large one did not need them. Reheaters are
probably of little account unless they superheat from 30 to 100
degrees as a minimum limit. Very high expansion may overcome
initial condensation losses.
Laying out Theoretical Indicatorcards for Compound Engines.
The essential fact to keep in mind in laying out the theoretical
indicatorcards from a compound engine according to the following
method is:
The weight or mass of steam entering the highpressure cylin
der is the weight or mass that is rejected by the lowpressure
cylinder.
From this naturally flows the following assumptions :
The mass of steam in the highpressure cylinder at cutoff =
The mass of steam present in the highpressure cylinder at
exhaust opening =
MULTIPLEEXPANSION ENGINES. 305
The mass of steam in the lowpressure cylinder at the instant
of cutoff =
The mass of steam in the lowpressure cylinder at the instant
of exhaustopening.
We shall assume that the exhaust opens at one end and closes
at the oiner end of a stroke, and that there is no clearance in either
cylinder and no steam is lost in the cycle. We are not discussing
conditions that exist when the engine is first started up or when it
is stopping. The engine is supposed to be rotating uniformly and
taking regular charges; there is no initial condensation and, con
sequently, no evaporation. The weight of a mass of steam is known
when its pressure and volume are known, and if steam is supposed
to expand in accordance with the law PV = C the mass is desig
nated by its product PV.
The student will obtain a better knowledge of the sequence of
events in compound engines if he will draw the indicatorcards on
crosssection paper from direct calculations, using simple round
numbers, instead of substituting in derived formulas that become
meaningless from cancellation. After obtaining a full comprehen
sion of the cycle of events in a compound engine, he may derive his
own formulas.
Definitions, Figs. 159, 160, 191. When the high and low
pressure pistons are on one pistonrod, the engine is called a tandem
compound. In a crosscompound engine the pistonrods of the high
and lowpressure pistons are parallel to each other, and their cranks
are at right angles, or the pistonrods are at right angles to each
other in a plane, which is perpendicular to the crankshaft, and a
single cr^nk is used. There may be more than one lowpressure
cylinder. In triple and quadrupleexpansion engines the angle
between successive cranks is not necessarily the same in amount,
nor is there any compulsory sequence of cranks. In no case should
the opening of the exhaustvalve of one cylinder occur before the
steam cutoff of the next larger cylinder. As will be shown later,
we shouid avoid transforming energy (that should be available for
the production of work) into lowgrade thermal energy that cannot
be efficiently utilized.
The maximum volume occupied by the steam admitted to a
compound engine is the volume of the lowpressure cylinder
minus the volume of the piston, of course and the minimum
306 THE STEAMENGINE AND OTHER HEATMOTORS.
volume is the volume of the highpressure cylinder up to its point
of cutoff; therefore the total ratio of expansion is
Volume of L.P. cyl.
Volume of H.P. cyl. at cutoff"
Varying the cutoff on the H.P. cyl. varies the amount of heat
admitted, but varying the cutoff on the L.P. cyl. has no effect on
the amount of heat rejected. The final pressure of expansion in
the L.P. cyl. is governed by the H.P. cutoff and the relative sizes
of the high and lowpressure cylinders.
The work done per stroke by any engine depends upon
1. The mass of steam admitted.
2. The total ratio of expansion.
3. The back pressure at which the steam is finally rejected.
Therefore the w r ork done per stroke is independent of the posi
tion of the point of cutoff in the L.P. cyl. For in any given
engine the mass of steam admitted depends only on the high
pressure cutoff, and the other two quantities are independent of
the L.P. valve.
On the other hand, the percentage of the total power that is
developed in each cylinder does depend upon the position of the
L.P. cutoff. For it is evident that any cause that increases the
back pressure on the piston of an engine decreases the power of
that engine. If the cutoff on the L.P. cyl. is shortened, the pres
sure in the receiver is increased, since the same mass must be ad
mitted into the L.P. cyl. as before, and the volume in which it is
to be contained has been decreased. As the receiver pressure is
the back pressure on the H.P. piston, increasing the receiver pressure
decreases the work done in the H.P. cyl. As the total power of
both engines has not been altered, it follows that the work in the
L.P. cyl. has been increased. The only use of the L.P. cutoff valve
is, then, to regulate the percentage of the total power developed in
each cylinder.
Tandem Compound Engine Without a Receiver (Fig. 158).
Draw the cards for a tandem compound engine, initial pressure,
100 pounds abs.; back pressure, 3 pounds abs.; volume of H.P.
cyl., 4 cubic feet; volume L.P. cyl., 16 cubic feet; cutoff in the
H.P. cyl., 1/2 stroke.
MULTIPLEEXPANSION ENGINES. 307
Since there is no receiver there can be no cutoff on the L.P. cyl.
Practically there is always a small receiver, as the pipes leading
to the L.P. cyl. from the H.P. cyl. always form part of the receiver.
Theoretically, however, we may assume their volume as zero.
Lay off on A B the pressure 100 pounds abs.
Lay off on BC the volume of the L.P. cyl., 16 cubic feet.
Lay off AD = 2 cubic feet = 1/2 the volume of the H.P. cyl.
At steam cutoff in the H.P. cyl. P^i = 100x2 = 200, the con
stant mass passing through the system.
At exhaustopening in the H.P. cyl. P 2 V 2 = 2QO, but V 2 = vol
ume of H.P. cyl. = 4 cubic feet. .'. P 2 = 50 pounds, giving point E.
The mass in the L.P. cyl. at the moment the exhaustvalve
opens = 200.
The volume of the L.P. cyl. = 16. .'. P 3 = ~ =12^ pounds,
giving point F.
At the end of the highpressure stroke we have the H.P. cyl.
full of steam at pressure of 50 pounds. The opening of the exhaust
valve admits this pressure on the L.P. piston without change, as
the volume of the connecting pipe is zero. Therefore the admis
sion pressure in the L.P. cyl. is 50 pounds.
Lay off J9G = 50, thus giving the point G.
The pressure in the L.P. cyl. varies gradually from G to F,
hence draw a smooth curve, FG.
The back pressure of the H.P. cyl. is the same as the forward
pressure in the L.P. cyl.
308 THE STEAMENGINE AND OTHER HEATMOTORS.
Lay off HB = FC and draw curve EH.
Lay off CI = 3 pounds and draw //; it will be the back pressure
of the L.P. cyl.
The curves GF and EH are not hyperbolic curves. Inter
mediate pressures may be found as follows :
Suppose the pistons are at 1/4 stroke on the return. Then 3
cubic feet at the exhausting end of the H.P. cyl. would be con
nected to 4 cubic feet on the steam side of the L.P. cyl. This
mass in this case must = 200.
200
Hence y=28 pounds would be the required pressure to be
laid off, giving points K and L.
The cards from the ends of each cylinder are similar.
Cards from tandem compound steam pumps are similar to the
above.
Ex. 110. The diameter of the H.P. cyl. = 1'; diameter L.P. cyl., 2';
stroke, 3'; initial pressure, 120 pounds absolute; back pressure, 3
pounds absolute; 12 expansions. Draw the cards. Use relative in
stead of absolute volumes.
Tandem Compound Engine with a Receiver (Fig. 159) . Initial
pressure, 120 pounds abs.; volume of H.P. cyl. = 4 cubic feet;
volume L.P. cyl. = 12 cubic feet; volume of the receiver = 6 cubic
feet; cutoff in H.P. cyl. at 1/4 stroke; cutoff in L. P. cyl. at 3/4
.stroke; back pressure, 3 pounds abs.
Lay off A B = 120 pounds,
Lay off BC = 12 cubic feet and 7)' = 4 cubic feet,
Lay off AD = l cubic foot or 1/4 the vol. of H.P. cyl.,
then the constant mass = 120 X 1 = 120.
The volume occupied by the steam in the H.P. cyl. as the
exhaustvalve is about to open = 4 cu. ft. ; therefore the pressure
120
= j = 30, giving the ordinate of point E. DE is an hyperbola.
When the exhaustvalve is about to open in the L.P. cyl. the
mass present = 120 and the vol. = 12 cubic feet, therefore the
120
pressure = ^ = 10 pounds, or the ordinate of point F.
At the instant of cutoff in the L.P. cyl. the mass present
= 120, and it will be the mass rejected, since there is no clearance
MULTIPLEEXPANSION ENGINES.
309
120
The pressure at cutoff or G will be <r = 13J pounds, because
the vol. of the L.P. cyl. at cutoff = f Xl2= 9 cu. ft.
Draw GF; it will be an hyperbola.
D'
FIG. 159.
We assume that the pressures in the L.P. cyl. at the instant
before its cutoff, at its cutoff, and the instant after its cutoff are
identical. The instant before cutoff in the L.P. cyl. the exhaust
from the H.P. cyl. was in communication with the receiver, and the
latter was in communication with the L.P. cyl. The pressures in all
three must have been identical and equal to that in the L.P. cyl. at
its cutoff.
As the L.P. piston is at 3/4 stroke, the H.P. piston must be at
3/4 of its stroke, so that the volume of the H.P. cyl. on the exhaust
end must be (1 f)4 = l cu. ft. This is open to the receiver with
a volume of 6 cu. ft. The back pressure at H on the H.P. piston
= 13J, and the mass must be 7X13J.
Since the cutoff valve on the L.P. cyl. is closed, further move
ment of the H.P. piston must compress this mass into the volume of
the receiver alone. The rise in pressure must be
pounds, or the ordinate of /. Draw HI.
6
= 15.55
310 THE STEAMENGINE AND OTHER HEATMOTORS.
The back pressure on one side of the H.P. piston is 15.55 pounds,
and the forward terminal expansion pressure on the other side of
this piston is 30 pounds. The next instant, the H.P. exhaust
valve opens, and these masses with these two pressures form one
mass. A common pressure will be attained immediately. The
masses joined are 30x4 and 6x15.5, or 120+93.3 = 213.3. As the
volume of the combined mass is 4 +6 = 10, the common pressure is
21.33 pounds, which is the value of the ordinates of K and J.
Join K and G, it will be the admission curve of the L.P. cyl.
Join / and H, it will be the corresponding back pressure line of
the H.P. piston.
Lay off CM = 3 pounds and draw MN, it will be the back
pressure line of the L.P. piston.
Ex. 111. Data same as in preceding example, except that there is
a receiver whose volume is twice that of the H.P. cylinder.
Crosscompound Engines. In crosscompound engines the
cranks of the high and lowpressure engines are at right angles
to one another. There must be a receiver between the two engines,
as the highpressure exhaust occurs when the lowpressure piston
is at halfstroke. In addition to the work in the preceding case
we have to find the positions of one piston when the other is at
critical points, such as cutoff, exhaustopening, etc. It is essential
to decide on the character of rotation, whether clockwise or the
reverse, and also fix on the crank that is leading. Much help will
be found in diagrammatic sketches for each critical position, show
ing piston positions and the volumes that are in communication
at such critical positions (Figs. 159 and 160).
Crosscompound Engines. Draw the cards from a crosscom
pound engine, L.P. crank leading; rotation clockwise; initial pres
sure H.P. cyl., 180 pounds abs.; number of expansions, 30; ratio
of cylinder volumes, 6 to 1 ; volume of H.P. cyl., 5 cu. ft. ; volume
of receiver, 10 cu. ft.; cutoff on L.P. cyl., 1/3 stroke; back pressure
in L.P. cyl., 1 pound abs.
Volume of L.P. cyl. = 6 X 5 = 30.
30
Volume of H.P. cyl. at cutoff = == 1 cu. ft.
oU
Ratio of expansion in H.P. cyl. == = 5.
MULTIPLEEXPANSION ENGINES.
311
30
The volume of L.P. cyl. at cutoff = ^ = 10 cu. ft.
The constant mass passing through the cycle or PiV l = 180 X 1
180.
180
The pressure at cutoff in the L.P. cyl. must equal
lcu.ft.: their
pounds = H.
Lay off AB= 180 pounds; AC=30 cu. ft.;
180 180
EF = = 36 pounds and CV2 = = 6 pounds, and the ordinate*
o oU
at H is laid off for 18 pounds. Join H and G by an hyperbola.
Diagrammatic Sketch at
Low Pressure CutOff
FIG. 160.
Check. The pressure at H is three times that at G.
We must now find the volume of the H.P. cyl. that is exhaust
ing into the receiver at an instant before L.P. cutoff takes place.
If the length of the connectingrod is to be considered, graphic
construction will be found easier than by analysis. For simplicity
we shall assume infinite rods and obtain our results analytically.
Draw the circular diagram (Fig. 160) in accordance with the
data. It is evident that ce represents the desired volume if ef
represents the volume cf the H.P. cyl.
ed = ^, od= 2 ^=
312 THE STEAMENGINE AND OTHER HEATMOTORS.
hence
da=oc=efV (1/2) 2 (l/6) 2 = . 47 ef,
The required volume is therefore .03 X5 cu. ft. = .15 cu. ft.
Hence the pressure in .the L.P. cyl. at cutoff, in the receiver
and in the H.P. cyl. when the piston of the latter has .15 cu. ft. of
exhauststeam behind it is 18 pounds.
Lay off AJ = .l5 cu. ft. and lay off an ordinate = 18 pounds,
thus finding point I.
As the H.P. piston moves to the end of its stroke all the steam
in the H.P. cylinder on the exhaust side and in the receiver will be
compressed into the receiver volume alone, as the L.P. valve has
cutoff steam admission. The pressure in the receiver whose
volume is 10 cu. ft. when the H.P. piston reaches the end of its
stroke will be ~Tn~ ~~ = 18.27 pounds or the ordinate at K.
There is assumed to be no exhaust lap on the highpressure valve.
The next instant the exhaust from the other side of the H.P.
piston is opened to the receiver and the two masses must come to
a common pressure. The sum of the two masses is proportional
to 5X36+18.27X10 = 362.7, and the common volume is 5+10 cu.
ft., or the sum of the volumes of the H.P. cyl. and receiver.
The pressure at L is then 362.7^15 = 24.2 pounds. On this
diagram there is no corresponding point on the L.P. diagram, as
its valve is closed.
The pressure having dropped from F to L at the opening of the
exhaustvalve, the H.P. piston now starts on its returnstroke,
sweeping steam into the receiver. This continues till the H.P.
piston reaches halfstroke. No steam is taken from the receiver
during that interval, as cutoff on the L.P. cyl. took place before
halfstroke.
A mass of 362.7 is forced into a volume of 2+10 = 12.5, and
362 7
the resulting pressure will be ^  =29 pounds, which is not only
the back pressure on the H.P. piston at the middle of its stroke at
M, but is also the initial pressure on the L.P. piston at N. Join
MULTIPLEEXPANSION ENGINES.
313
L and M , M and /, N and #. These curves are not hyperbolic
curves and may be sketched in. Intermediate points can be found
by calculating volumes and pressures.
Draw the backpressure line for the L.P. cyl. at 1 pound above
the absolute zero line.
Ex. 112. Diameter of the H.P. cyl. is 20"; stroke, 40"; cutoff
H.P. ryl., 1/4 stroke; total expansions =16; initial pressure, 160 abs.;
back pressure, 3 pounds abs.; volume of the receiver, 3/2 that of
H.P. cyl.; cutoff in L.P. cyl., 3/8 stroke. (Assume volume of H.P.
yl.4.)
Crosscompound with L.P. Cutoff after Halfstroke (Fig. 161)
FIG. 161.
If the cutoff on the L.P. cyl. has not taken place before half
stroke, it is evident that, when the highpressure exhaust opens,
the common volume will be the volume of the H.P. cyl., the re
ceiver, and half the volume of the L.P. cyl. The result is a hump
in the middle of the L.P. card. This indicates a loss of efficiency,
for whenever highpressure steam is allowed to enter a space filled
with steam of a lower pressure, there is a transformation of energy
into heat that could have been converted into work. Keeping in
mind that the object of a steamengine or steamturbine is the
transformation of heat into work, any reversal of that process is
certain to produce a loss in the number of footpounds of work.
314 THE STEAMENGINE AXD OTHER HEATMOTORS.
In Fig. 160 the drop FL, known as receiver drop, is not economical
when excessive, and hence for best results thermodynamically LE
should be made to equal FE by cutting off shorter in the L.P. cyl.
If this results in making the L.P. card larger than the H.P. card,
the engines will develop different horsepowers, which will produce
;nonuniform rotation.
Take the same data as in the preceding problem and let the
cutoff on the L.P. cyl. be at 2/3 stroke.
The points B, D, F, and G will be in the same position as before.
At cutoff in the L.P. cyl. the volume is 20 cu. ft. and the mass
is 180X1 = 180, therefore the pressure = V<f = 9 pounds, giving #
.and h.
Check. Expanding 20 cu. ft. at 9 pounds to 30 cu. ft. the pres
sure becomes 6, as found.
Drawing the circular diagram and laying off crank positions in
^accordance with the data we find
df=& od = 4, da = oc = Al ef. .'. c/ = .97 ef.
o o
The volume of the H.P. cyl. exhausting into the receiver at this
cutoff of the L.P. cyl. is then .97x5 cu. ft. =4.85 cu. ft.
The mass in the H.P. cyl. and the receiver at the instant of
L.P. cutoff is then 9 X (4.85 +10) = 133.65.
Rotate the crankshaft till the L.P. is at the end of its stroke.
The H.P. piston compresses the above mass into the volume of the
.receiver and half the volume of the H.P. cyl. The pressure there
fore rises to ^ ^r =10.7 pounds, which is therefore the value of
&2 ~T 1U
the ordinate, 7, at the middle of the returnstroke of the H.P. cyl.,
and of /, which is the initial pressure in the L.P. cyl.
Rotate the crank till the H.P. piston reaches the end of its
stroke. During this period the volume of the H.P. cyl. exhaust is
rapidly diminishing, but the volume of the L.P. cyl. is increasing
more rapidly, so that the pressure in the receiver is falling till
9 X 14 85
halfstroke. At that time the pressure is in ' =5.34 pounds,
1U ~r 1)
which will be the value of the ordinates K at the middle of the
L.P. stroke and of L at the end of the H.P. stroke. Join 7 and L,
MULTIPLEEXPANSION ENGINES. 315
J and K. These curves represent the same change of pressure,
being the back pressure on the H.P. piston and the forward pressure
on the L.P. piston.
An infinitesimal movement of the crank produces the next
event, viz., opens the exhaust of the H.P. cyl. into the receiver and
the L.P. cyl. whose steamvalve is wide open.
The sum of the two masses united is 36x5+5.34 (10+15) =
313.65, and the common volume is 5+10+15 = 30 cu. ft., hence
313 65
the common pressure is ^' 10.45, which is therefore the
ordinate at M and N. Join N and h, h and 7, K and M, M and H.
Draw the backpressure line on the L.P. diagram.
Ex. 113. Data as in preceding example, but assume cutoff at 5/8
stroke.
Ex. 114. Alter the data of the preceding example to obtain equal
horsepower in each cylinder.
Ex. 115. Alter the data to obtain the same range of temperature
in each cylinder.
Ex. 116. Alter the data in the preceding example, giving clearance
and points of exhaust opening and closing in each cylinder, but use an
infinite connectingrod.
To Find the Sizes of Cylinders for a Compound Engine. The
power of any engine per stroke is determined by the mass of steam
admitted and its ratio of expansion. All the power of a compound
or other multipleexpansion engine could be developed in its low
pressure cylinder, disregarding for a moment the necessary strength
of parts and condensation, since, if we admitted into that cylinder
the same mass as was. admitted into the highpressure cylinder,
we may expand that mass in this cylinder the same number of
times as in the multipleexpansion engine against the same back
pressure.
Find the diameters of the high and lowpressure cylinders of a
crosscompound engine, gage pressure at the boiler, 150 pounds;
total ratio of expansion, 16; ratio of lowpressure cylinder area to
that of the high, 4 to 1; assumed diagram factor derived from
engines of about the same power and of the same general design,
83%; back pressure in the condenser is 1 pound absolute; revo
lutions, 120; horsepower, 1000, stroke, 42".
316 THE STEAMENGINE AND OTHER HEATMOTORS.
A B Boiler Pressure
Low Pressure Head End
Pressure in Coudenser
FlG. 162.
MULTIPLEEXPANSION ENGINES. 317
Expected mean effective pressure
Yg  1 F .83 = 31 .45 pounds.
L J
For cards, see Fig. 111.
The diameter of the highpressure cylinder is 20". Cutoff in
the highpressure cylinder is at a little less than 1/4 stroke.
Assume clearance in highpressure cylinder is 5%, and in the
low is 7%, and that the volume of the receiver equals the volume
of the L.P. cylinder.
To Combine Indicatorcards of a Compound Engine. "The
'Combined Diagram ' is a hypothetical figure, which in its essential
features represents an indicatordiagram which would be obtained
if the whole process of admission, expansion, and exhaust occurred
in one cylinder, viz., the lowpressure cylinder. It is a diagram
from which the pressure of the steam at any point in the stroke
of either cylinder, and the volume of that steam, can be measured
from one diagram in the same manner that it can be measured in
the case of a singlecylinder engine from the actual indicator
diagram.
"The general method of laying out a combined diagram is
shown in the appended cuts, Figs. 163 and 165, the first of winch
refers to a Corliss compound engine (receiver engine), in which the
ratio of volumes of the two cylinders is as 3.72 to 1, and the clear
ance of the highpressure cylinder is 4 per cent, and of the low
pressure cylinder is 4.8 per cent; and the second to a Westing
house compound engine (Woolf engine), in which the ratio of the
volumes is as 2.72 to 1, and the clearance 33 per cent and 9 per
cent respectively." f
In the single cards the high and lowpressure diagrams are of
approximately the same length. Since there is a radical difference
in the volumes represented by the lengths of the cards, there must
be a radical difference in their scale of volumes. Similarly the
scale of pressure in each card is different. In the combined dia
gram there is only one scale of volumes and one scale of pressure.
t Standard Engine Tests.
318 THE STEAMENGINE AND OTHER HEATMOTORS.
COMBINED DIAGRAM.
RECEIVER ENGINE.
ATMOSPHERE
p. j 00  *<C.04
CLEARANCE
100 .
H. P. CYL.
1 13(7
120
110
100
30
70
60
50
40
30
MULTIPLEEXPANSION ENGINES.
319
To Draw the Combined Diagram. Draw any line to represent
the clearance line as in Fig. 163. Perpendicular to it, at any given
point, erect a line, called the zero line, whose assumed length will
represent the volume of the lowpressure cylinder plus the clear
ance. Lay off this clearance. Divide the remainder into any
number of parts and divide the atmospheric line of the lowpressure
diagram (limited by the end ordinates of the diagram) into the
same number of parts. Draw ordinates through these points and
lay off in the combined diagram (in accordance to its assumed
H. P. CYL.
120
100
 80
 60
40
 20
L. P. CYL.
30
15
 10
5
 5
10
Standard Engine Tets
FIG. 164.
scale of pressures) the pressures as determined by the length of the
corresponding ordinates in the single card.
To the same scale of volumes lay off the volume of the high
pressure cylinder and its clearance from the clearance line or line
of zero volume. As before, after laying off its clearance, divide
the remainder into any number of parts and divide the length of
the highpressure card into the same number of parts. Convert
the ordinates of the highpressure card into pressures and lay off
these pressures (to the chosen scale for the lowpressure card) in
the combined diagram.
Practical Diagrams. In the formation of the theoretical dia
grams just described many assumptions were made that are
impossible of attainment in practice. There is
320 THE STEAMENGINE AND OTHER HEATMOTORS.
1. The loss due to drop of pressure between the steam
boiler and the piston. This includes loss in the pipe, bends,
valves, and separators. It varies from 5% of the boiler
pressure upwards, depending upon conditions.
2. The steam valve opens the port gradually, and there
must be a considerable difference in pressure between the steam
in the chest and that inside the cylinder to generate the high
velocity demanded when the port is nearly closed. The corner
at cutoff is rounded off.
3. The loss due to drop when the H.P. exhaust valve opens.
4. The corresponding losses of pressure in the steam entering
the L.P. cylinder or cylinders.
5. The reduction of the mass of steam in the cycle. The
steam from the H.P. cylinder should pass through a separator
and the water separated out should be returned to the boiler,
and hence passes out of the cycle.
6. A loss due to deficient vacuum. One or two inches of
vacuum make considerable difference in the total pressure on
a L.P. piston. This amount is frequently lost through allowing
avoidable airleaks, greasy tubes, defective airpump, etc. The
loss of one inch of vacuum on an 80inch piston would cause
the continuous loss of over a ton of force.
7. The exhaust opens gradually instead of instantaneously
at the end of the stroke. This causes a small loss.
8. Clearance space and clearance surface cause much loss.
Ratio of Expansion. The rounding of the corners necessitates
a definition of tne ratio of expansion in a compound engine.
"In a multiple expansion engine it is determined by dividing
the net volume of the steam indicated by the L.P. diagram at the
end of the expansion line, assumed to be continued to the end of
the stroke, by the net volume of the steam at the maximum pres
sure during admission to the highpressure cylinder.
"For a compound engine, referring to the combined diagram
(Fig. 166), the ratio of expansion is the distance CD divided by
the distance AB, in which E and F are points on the compression
and expansion lines respectively of the highpressure diagram, the
latter being near the point of cutoff, and H and G points on the
compression and expansion lines of the lowpressure diagram, the
Atmos. Line*
14.7
632.
1.72
FIG. 165
i21
322
THE STEAMENGINE AND OTHER HEATMOTORS.
latter being near the point of release, and the curves EA, FB, HC,
and GD being hyperbolic. If it is desired to determine the ratio
without laying out the combined diagram, it can be done by draw
ing on the original diagrams the hyperbolic curves referred to
above and multiplying the ratio of volumes of the cylinders,
Maximum pressure
during admission.
Ratio of Expansion
Com.on Eng. Tetti
FIG. 166.
first by the ratio of the length of the highpressure diagram to the
distance AB, and then by the ratio of the distance CD to the
length of the lowpressure diagram.
" Diagram Factor. The Committee's definition of the ' Diagram
Factor ' was given in the case of simple engines. In Fig. 167 the
diagram factor is the proportion borne by the area of the two
determined for the highpressure diagram in the
game way as 3 in Fig. 50.
Bo.ler Pressure
^ Zero Line of Pressure
Line of Pressure
in Condenser
FIG. 167.
323
324 THE STEAMENGINE AND OTHER HEATMOTORS.
combined diagrams to the area CNHSK. In Fig. 167 the distance
CN for the highpressure cylinder is found in the same manner as
in the case of the simple engine. . . . The mean effective pressure
of the ideal diagram can readily be obtained from the formula
p
^(1 4 hyp. log ft) p,
where P is the absolute pressure of the steam in the boiler, R the
MJ
ratio '^jr, and p the pressure of the atmosphere or in the con
denser."!
Diagram factors for compound engines:
Highspeed, shortstroke, unjacketed 60 to 80%
Slower rotational speeds 70 " 85
" jacketed 85 " 90
Corliss 85 " 90
Tripleexpansion 60 ' ' 70
(See Vols. XXIV and XXV, Trans. A. S. M. E.)
Jacketing, reheaters, and superheaters modify the diagram
factor considerably.
In marine engines these factors are much lower. Bauer and
Robertson, "Marine Engines and Boilers," give:
Expansion in a singlecylinder :
Large slowspeed engines 70 to 75%
Small highspeed engines 65 " 70
Expansion in twocylinder or compound engines:
Large engines up to 100 revolutions per minute 60 " 67
Small engines with a higher number of revolutions . . 55 " 60
Tripleexpansion in three cylinders :
Warvessels with a high number of revolutions 53 ' ' 54
Mercantile vessels up to 100 revolutions per minute. . 56 " 61
In multipleexpansion engines the weight of authority is in
favor of expanding in all cylinders but the lowpressure to a pressure
equal to the backpressure, i.e., there will be no drop in the re
f Standard Engine Tests.
MULTIPLEEXPANSION ENGINES. 325
ceiver. The explanation of the difference lies in initial condensa
tion.
"The reason why condensation effects this change is not that
some steam is condensed in the cylinder each stroke, but that the
condensation is not in proportion to the steam admitted and the
work done, but is nearly a fixed amount per stroke for a given set
of conditions. If more steam is admitted, the amount condensed is
practically the same, but the proportion which is condensed becomes
less; and for this reason it is economical to throw away some work
by free expansion at each end of each stroke, for in so doing the
total amount of work done per stroke is increased and the con
densation, which is a total loss, becomes smaller in proportion." *
This reasoning is applicable to expansion in the lowpressure cylin
der, where condensation should be reduced to a minimum.
Terminal drop or free expansion tends to heat the steam. In
other words, a loss of work is converted into a gain in heat. The
highest economy is opposed to such a transfer. The required heat
should be obtained from reheating coils placed in the receiver.
Further, the heat so obtained should be applied to superheating
dry steam, all water having been previously removed and sent to
the boiler with the feedwater.
Ex. 117. Initial pressure 120 pounds absolute, clearance H.P.
cyl. 2J%; cutoff J stroke; clearance L.P. cyl. 5%; diam. of
L.P. cyl. is twice that of the H.P. cyl. Vacuum 24"; piston speed
800 feet per min. Find the following quantities for a horizontal,
crosscompound condensing engine of 2000 horsepower capacity:
(1) Give dimensions of each cylinder.
(2) Number of revolutions per minute.
(3) Size of pulleys on engine and shaft. {
(4) Initial pressure in each cylinder.
(5) Terminal pressure in each cylinder.
(6) Mean effective pressure in each cylinder.
(7) Give the point of cutoff for economy.
(8) Draw cards from each cylinder for economy.
(9) Draw some cards with admission late ^ of the stroke. f
* Trans. A. S. M. E., Vol. XXI, p. 1006.
t See Power, page 622, 1907.
t See page 386.
CHAPTER XII.
REVOLUTION CONTROL.
THE work done by some machines is dependent on the irregu
larity of motion of some one of their parts. In a punchingmachine,
for instance, the rather constant and small pull of a belt is utilized
to store up energy in a flywheel by increasing its revolutions. At
the instant the punch commences to penetrate a plate, the demand
for the pressure and work of detrusion is supplied instantly by the
flywheel. The consequent loss of speed is made up in the time
elapsing between the commencement of the rise and the com
mencement of the penetration of the punch.
The degree of uniformity of rotation exacted of steamengines
varies with their use. In the case of engines for certain electrical
purposes and for cottonmills, for instance, the closest possible
approach to perfect uniformity is desirable.
Uniformity of rotation may be considered under two heads:
1. Uniformity in the number of strokes per minute.
2. " of rotation during the stroke.
It is evident that any governor controlling the pressure or
volume of steam entering an engine has no control of the speed
between the point of cutoff and the end of the stroke. The speed
of an engine having badly set valves or a poorly designed governor
may be incessantly changing, one stroke being made too fast and
the next too slow, although the revolutions in a minute may be the
required number. If the work done during one stroke is the same
in amount as that done during the following one, then the amount
of energy received (measured quite approximately by the weight
of steam admitted) should be identical on each stroke. Uniformity
of rotation requires the same mean effective pressure on both
326
REVOLUTION CONTROL. 327
strokes of the piston for a fixed position of the governing mechan
ism. The valves of an engine are not properly set until indicator
cards simultaneously taken from each end of the steam cylinder
on the same revolution show the same mean effective pressure*
In vertical engines this pressure must be corrected for the weight
of the reciprocating parts.
No practical means of anticipating variation of speed have
ever been devised. Hence momentary variation of speed has been
used to actuate mechanism, that governs the incoming energy, to
give practical uniformity of rotation within the limits set by tha
designer.
The principal methods of governing steamengines are :
1. Throttling. By regulating the pressure, but not the vol
ume of the steam admitted to the engine.
2. Variable Cutoff. By regulating the volume, but not the
pressure of the steam admitted.
3. Flywheels. By storing up surplus energy in such form
that on demand it will be returned.
FIG. 168.
Throttling (Fig. 168). If a circular disc be pivoted at any
crosssection of a pipe, a more or less efficient and easy means of
regulating the weight of steam that passes will be secured. A.
disc of this character arranged in a practical manner is called a
butterfly valve or throttle. As the valve approaches its closing
position the difference in the pressure of the steam on the two
sides of the valve will be a considerable quantity. This difference
of pressure is necessary to produce the high velocity of the steam
in the contracted area of the pipe, and to overcome losses pro
duced by friction and eddymaking. By placing a valve of this
character close to the engine and moving it by some kind of auto
328 THE STEAMENGINE AND OTHER HEATMOTORS.
ma tic mechanism we obtain a means of governing the speed of
the engine under changing load.
Variable Cutoff. We have already seen that, by changing the
throw of a valve, the volume of steam admitted may be altered
to comply with variations, either in the load or the boilerpressure.
The different mechanisms for doing this automatically will be dis
cussed in this chapter.
Flywheels. We shall find that the flywheel has very little
influence on the constancy of the number of revolutions made in
a minute. We must distinguish carefully between a rate and an
actual quantity. When an engine has no governor, as in marine
engines, if the load decreases (as it does when the ship pitches and
the propeller rises in the water), there is an immediate increase in
the velocity of rotation. Whilst a flywheel might absorb some
of this energy, yet the amount absorbed would be trivial compared
to the surplus energy constantly coming into the engines. In
marine engines, if the increase of speed becomes dangerous the
supply of energy is controlled by regulating the throttle by hand.
In land engines the revolutions in a minute are controlled either
by a throttlinggovernor or by a variable expansiongovernor.
The duty of the flywheel is then almost li mi ted to securing uni
formity of rotation during a revolution.
Fundamental Equations. We must distinguish carefully be
tween tangential and centripetal or centrifugal forces in revolving
masses. If a mass is revolving uniformly it can neither exert any
tangential force nor can any tangential force act on it unless such
force is balanced by an equal and opposite force. Any unbalanced
force means an accelerated or nonuniform speed. If there be any
change of speed there is, on the contrary, a tangential acceleration
that may be utilized in the production of force. On the other
hand, in cases of uniform motion there is developed a force along
the radius, called centrifugal force, that is utilized in nearly all
forms of steamengine governors. As we cannot have a pull on a
string without the presence of two equal and opposite forces, so
centrifugal stress (causing tension on the arms of the flywheel)
requires two equal and opposite forces. A pull to the center is
necessary to draw the particles from the straight line, that they
tend to follow, into the curve of the circular path. The particles
REVOLUTION CONTROL.
319
exert an outward pull, and the arm exerts a stress in the opposite
direction. Centrifugal force then is not a force acting along a
tangent, but is the outward radial pull exerted by the particles,
and produces its equal and opposite centripetal force acting
inwardly. The EQUALITY of centripetal and centrifugal forces only
exists when there is NO motion along the radius. In the shaft
governor, for instance, the weight moves outwardly till the tension
on the spring representing centripetal force overcomes the cen
trifugal force and tends to cause motion inwardly of the weight.
This demonstration is limited to the centrifugal force exerted
by a particle revolving at uniform speed in a circle.
Let be the center, R the radius, and ds
the length of arc described in the time dt. Q
If dd is the length of the arc at unit radius,
Rdd ds
j~ = r = F, the uniform speed in a circle.
The acceleration along the radius may be
taken as the difference between two successive
velocities along two consecutive radii. If in
each sec' or the origin is taken at the end of the
left radius, we may take the velocity along the
light radius as the acceleration. For example, the veloc'ty along
the radius OA is zero and the velocity along radius OC (found by
d 2 R
drawing a tangent at A to intersect OC) is CB or , so marked
CLv
as acceleration is a second differential.
dsdO = d 2 R, since the triangles A C and CAB are similar.
But
ds ds
d 2 R,
R
ds 2 d 2 R
a,
Rdt 2 ~ dt 2 ~
V 2
~p = a R = acceleration alone: the radius.
330 THE STEAMENGINE AND OTHER HEATMOTORS
The force to produce an acceleration is equal to the product of
the mass and the acceleration. Therefore
WV
7~B'
A body weighing W pounds revolving at a speed of V feet per
second at R feet radius (gyration) will cause a centripetal force
,of F pounds per second.
Ex. 117. The student should show why F is elementary; is pounds
and not feet.
Kinetic Energy. If a body weighing W pounds is raise i h
feet, Wh footpounds of work are required. If this body is allowed
to fall, the instant that it has passed over h feet Wh footpounds
of work are stored in it. This energy of motion may also be ex
pressed in terms of the velocity that it possesses at the instant of
V 2
passing the point h feet below the startingpoint. As h = ~ we
WV 2
have Wh=f^ . It is immaterial how a particle acquires the
*9
velocity V whether by falling or by the action of forces other than
gravity. 'Hence if a particle in a flywheel is moving with a velocity
WV 2
of V feet per second, its kinetic energy is also ~ .
WV 2
29
It is essentially a compound quantity and is reducible to footpounds.
Note carefully that any equation containing g (gravity) must have
aU linear dimensions in feet, and all measurements of time must be
in seconds unless proper constants are used to effect the desired
variation.
Flyball Governor with and without Central Rotating Weight.
Let AC be a rotating spindle carrying revolving balls B
and BI and a heavy rotating weight of L pounds at C. Let the
balls B, BI, weighing w pounds apiece, be attached to links in such
manner that if C move vertically upward to C', the linkage will
now take the position AB'C'B'i, shown in dotted lines.
By the action of two equal forces, P, P ly exerted vertically at
B and BI, let the linkage attain the dotted position. Either analyt
yy y ~
Ex. 118. Separate ~ into its component parts, and show that
REVOLUTION CONTROL.
331
ically or graphically it will be found that if the balls B, B\ move
through a small vertical height (dh], the heavy weight L will move
a greater height, k(dh) . The work put in must equal the work done,
.'. 2P(dh) = 2wdh +Lk(dh) .
kL

If the upper and lower arms are of the same length, k = 2.
horizontal work will evidently be zero.
The
L Pounds
FIG. 170.
Let the mechanism shown be that of a loadsd highspeed
governor. Let centrifugal force F, acting along E'B f and E'Bi,
keep the balls in the dotted position shown. Then, for the reasons
above given, we have, taking moments around A, Pr=Fh, or
This equation contains apparently six variables, five of which
must be given to determine the remaining one. Suppose Z/ = 0,
332 THE STEAMENGINE AND OTHER HEATMOTORS.
This gives the equation of the simple pendulum governor,
yjV2 Y 2 T 2
wr = h or = r .
gr g h
In this equation the weight of the balls B and BI has entirely
disappeared. Hence, theoretically, if there were no such effects
as friction and inertia, and if certain very necessary parts had no
weight, we could use balls of any weight whatever. Practically,
as there is considerable friction in valvestem packing, as heavy
parts must be given motion quickly and as connecting links have
necessary weight, the balls are generally made of considerable
weight, depending on the size of the governor and on the condi
tions under which it is to act.
In the above equation V is the velocity of the governorballs
in feet per SECOND; a more convenient equation for use in practice
is one in terms of the number of revolutions that the governor
balls make per MINUTE =N. .'. V 2 =
or
HEIGHTS AND SPEEDS OF GOVERNOR.
Altitudes.
Altitudes.
Revolutions
Revolutions
per Minute.
per Minute.
Feet.
Inches.
Feet.
Inches.
60
.815
9.76
200
.073
.876 .
80
.457
5.48
300
.032
.39
100
.292
3.50
400
.018
.22
125
.187
2.24
500
.012
.14
150
.13
1.56
600
.0075
.09
An examination of the table and the figure shows that the
heights of the cones become very small and impractical at speeds
much exceeding 80 revolutions per minute. This becomes more
apparent when we remember that it is the difference in the height
of the cones that affords the motion of the mechanism for closing
the throttle. Thus, in changing from 80 to 85 revolutions a
REVOLUTION CONTROL.
333
minute, the difference in height of the cones is 1 inch ; at 200 revo
lutions the cone height is only .88 inch, and the speed would have
to reach 300 revolutions per minute to change the height .88
.39 = .48 inch. These dimensions are entirely too small for any
practical mechanism.
Referring to our fundamental formula, page 331, let k = 2.
This will be the case when the upper and lower arms are of equal
length. Then
(w+L)r>
gr
60V
or
 = N*h.
.'. 2936(1 +)=N 2 h.
\ /
The relation between this formula and that for the simple pendu
lum is at once apparent. For simplicity, let the heavy central
FIG. 171.
weight be nine times that of one of the balls, then the height of
the cone will be ten times that of the simple pendulum. This
makes this form of governor available in cases of governor revolu
tions ranging from 200 to 240 revolutions or higher.
Sensitiveness. If N\ is the highest and N 2 the lowest number
of revolutions permitted by the governor, the sensitiveness is
334 THE STEAMENGINE AND OTHER HEATMOTORS.
N N
expressed by ^ + ^ = the range of speed divided by the mean
2
speed. The smaller this fraction the more sensitive the governor,
If Ni~N 2 becomes 0, the governor ceases to act properly from
su persensi ti veness.
For convenience let 2936 = Ci 2 and (l +j =C 2 2 .
Then for the loaded governor 1 JJ = JVi,
Subtracting,
Adding,
i i
I ,
We would obtain the same expression for the sensitiveness of an
unloaded governor. It is therefore evident that their sensitive
ness is identical if their cone heights h 2 and hi are identical. The
greater inertia of the loaded governor makes it the more sensitive,
as it overcomes friction the more readily.
Practical Forms of Flyball Governors. The pendulum
governor takes many shapes and different qualities are possessed
in varying amounts by the different forms. Fig. 172 illustrates
a Proell governor. It consists of a hollow vessel, G, fixed to
the rotating shaft, R, and possessing two projecting ears, E, which
in turn provide pivots, D, for the bent leverarms L. The rotation
REVOLUTION CONTROL.
335
of the shaft is conveyed to the balls through G, E, and L. As
the balls, B, B' , fly out, the inner ends of the bent lever L press
downward on a plate resting on the spring S. The motion of the
balls results in the motion of the sleeve, C7, whose motion in turn is
used to actuate a lever or other mechanism.
It is evident that the centrifugal force of the balls increases,
as they fly out, on account of the increasing radius from the spindle
C
FIG. 172.
R, as well as from their increased revolutions. The compressive
resistance of the spring S opposes the outward motion of the
balls.
Three cases may arise :
1. The compressive resistance of the spring may increase in
exactly the same ratio that the centrifugal force exerted by the
balls increases.
2. It may increase less rapidly than the centrifugal force.
3. It may increase more rapidly than the centrifugal force.
In the first case it is evident that the balls will maintain their
lowest position until the spindle R attains some fixed speed. The
336 THE STEAMENGINE AND OTHER HEATMOTORS.
slightest increase over that speed sends the balls to their extreme
outward position, which shuts off steam entirely. The consequent
decrease in speed is followed by the return of the balls to the
lowest position and the steamvalve is opened wide. This con
tinual fluctuation is called hunting. The governor is said to be in
neutral equilibrium, unstable, astatic, or isochronous. Theoret
ically, the governor has only one speed (hence isochronal) for all
positions of the balls; the equilibrium is not stable, hence the
other terms. The sensitiveness is evidently too great.
If we substitute another spring whose resistance on compression
increases less rapidly than the centrifugal force, we have an arrange
ment that will not regulate at all not even badly for the balls
fly to their limit and shut off steam before, the engine reaches the
desired number of revolutions.
Let us substitute, then, a spring whose compressive resistance
increases with its diminishing length, only a trifle more rapidly
than the corresponding increase of the centrifugal force of the balls,
due to their increasing radii of action, the revolutions being kept
constant at the lower fixed rate. If the speed of an engine is to vary
from 180 to 182 revolutions, the spring is stronger than the centrif
ugal force at 180 revolutions for corresponding lengths of spring
and radius of action of the governorball. But at any speed higher
than 180 revolutions there are positions of momentary equilibrium.
These moments are followed by decreased speed, as the steam
supply has been diminished for the following stroke.
It is desirable that governors approach, but not arrive, at iso
chronism, since oversensitiveness practically produces more irregu
larity in the motion of an engine than that arising from a pre
determined variation from perfect uniformity of rotation.
There are other methods of obtaining isochronal motion.
/ kL\
N 2 h = 2936\l +o/ ^ or anv Si yen governor the only variables
in the above fundamental equation are N and h. If the governor
is so constructed that h is constant for different radii of action of
the balls, then N becomes constant also. For example, three dif
ferent simple pendulumgovernors having the same cone height AC y
but the leverarms of different lengths as shown, would all revolve
in the same time, for, in that case, N 2 h = 2936. Hence if in a
REVOLUTION CONTROL.
337
governor the arm AB could lengthen out as shown, the motion
would be isochronous.
A practical method of obtaining the above motion quite ap
\
\ s
\
0
Bl
FIG. 173.
FIG. 174.
proximately is found by crossing the arms of the governor balls
and making use of auxiliary arms, so that the balls in ascending
describe an approximate parabola instead of the circle.
fi,
FIG. 175.
On the axis XX' of Fig. 122 lay off a parabola as shown.
Draw the ordinates BE' and erect the normals BS and B'Si.
Draw a parallel ordinate BiBi' and erect normals as before to
338 THE STEAMENGINE AND OTHER HEATMOTORS.
intersect the other normals in some points S and Si. It is a prop
erty of the parabola that the subnormal ac = bd. The cone height
being constant, a governor operating on these lines would be iso
chronal.
A practical form of this governor is shown in Fig. 175. By
choosing the points Si, S f so that the subnormal slightly increases,
a stable governor is obtained; if, however, the subnormal decreases,
the governor would be unstable.
Power of a Governor. There is a certain amount of work done
in raising the weights of a governor, which is given out again on
the descent of the weights. This work is called the power of the
governor and is equal to the two vertical forces that are necessary to
raise the weights multiplied by the range of elevation in feet, or
twice the mean centrifugal force of each ball multiplied by the
difference between the maximum and minimum radius.
Pr = Pr
Vh lr, . . *= 
By laying off the values of F for various radii as ordinates
with the radii as abscissae, an area is obtained that expresses
graphically the integral of Fdr for one ball. For a Porter loaded
governor with equal arms, if L = 9w the power of the governor will
be ten times that of a simple governor for the same variation in
the height of the cone. Liability of the governor sticking as the
engine slows down is diminished by increasing the power of the
governor.
Friction of a Governor. Hitherto we have neglected friction
in the joints of the governor mechanism, friction of the valvestem
packing, unbalanced steam pressure, and the friction of the valve
itself. But little consideration is necessary to show that all these
resistances should be reduced to a minimum if a sensitive govern
ment of the steam is desired. It is better to let a little steam leak
from the valvestem packing than to tighten up the gland so tight
that the governor acts irregularly. A method of measuring the
total amount of these resistances in pounds will now be given.
REVOLUTION CONTROL. 339
In the general formula (page 331) Pr = Fh, if r and h remain
P F N 2
constant we have ^ = rr = Tfi; in other words, the centrifugal
* 2 ^2
force varies with the square of the revolutions and P varies with
the centrifugal force.
Supposing all parts of the governor mechanism are in their
proper position when NI revolutions are being made, but that
they do not move until additional centrifugal force due to .2
revolutions is generated, it is evident that the friction is meas
ured by F 2 FI or by Pz Pi. From the above equations we have
2 l = 2 2 l . Hence the frictional resistance of one ball
l? or the total friction = 2P l ^^.
Valves for Short Cutoff. The common slidevalve with a fixed
eccentric is not used to cut off steam at less than 5/8 stroke. On
constructing a valve diagram one sees at once that with a constant
maximum portopening the steamlap, and consequently the valve
travel, become impractically large if a shorter cutoff is attempted.
With simple engines the economical cutoff, using steam pressures
varying from 80 pounds to 120 pounds per square inch (gage),
varies from 1/4 to 1/7 stroke. To obtain this result the following
mechanisms have been used :
1. Adjustable eccentrics.
2. Links, by the use of which the greater or less valve travel
depends on two eccentrics, as in the Stephenson link.
3. An independent valve driven by a separate eccentric and
moving on an independent valveseat over the main valve. A
true representative of this type, the Ganzenbach or gridiron
valve, is no longer used. We shall describe a modified type
the Buckeye valve.
4. An independent valve riding on the back of the main
valve Meyer valve.
5. Tripped valves of the Corliss type.
6. Poppetvalves driven by cams used in connection with
superheated steam.
Adjustable Eccentrics. Instead of fitting and keying the
eccentric to the shaft, let us attach the eccentric to the arms of a
340
THE STEAMENGINE AND OTHER HEATMOTORS.
flywheel which is keyed to the shaft. Any rotation of the shaft
will then cause exactly the same movement of the center of the
eccentric as would have been caused if the eccentric had been
fastened directly to the shaft. It will be seen, however, that this
method of attachment allows us to change not only the angular
advance, but also the throw of an eccentric. Fig. 176 shows a
swinging eccentric with ears X and X' cast on the front edge ef an
'^ /
FIG. 176.
eccentric, leaving the rim to be encircled by the eccentricstrap as
usual. The flywheel is supposed to be in front of the eccentric,
and is omitted to avoid confusing the diagram. The eccentric,
reduced to a ringlike form, fits the shaft so loosely that it may
readily be swung around X as a pivot, thus causing the center of the
eccentric to swing through the arc AfF. If P is the center of the
crankpin, it will be seen that this increases the angular advance
DO A to DO/, and shortens the throw of the eccentric from OA to
Of when the center of the eccentric is moved from point A to
point /. If X' is held rigidly in this new position, then the valve
motion will be that due to an eccentric having the new throw
Of and the new angular advance DO/. In Fig. 176) S, P', and X are
REVOLUTION CONTROL
341
fastened rigidly to the flywheel, which is keyed to the shaft 0.
If B moves about P' (from centrifugal force), the eccentric center
A will move in the arc AfF.
Keeping the center of the crankpin as it is in the figure, it is
evident that the arc AfF will vary with the radius XA and the
position of the center X. If XA be made longer the arc becomes
flatter; if XA be infinite in length or a construction is used that
produces the effect of an infinite rod, the arc becomes a straight
line perpendicular to the line joining the center of the shaft and the
center of the crankpin. This may be called a shifting eccentric,
FIG. 177.
to distinguish it from one that swings. If X' is made the pivot
and X the moving center, the curvature of AfF is reversed. The
effect of these changes of the position of the center X and of the
length of the arm XA may be readily determined from the valve
diagram.
The student should draw a number of complete diagrams,
including the indicatorcards to scale, keeping in mind that the
steam and exhaustlaps are constant (Fig. 177). Lay off nega
tively an angular advance DO A. With the maximum throw of
the eccentric OA (4X(M, Fig. 176) as a diameter construct on
OA (and OA produced) valvecircles. With steamlaps OC and
exhaustlap OH construct steam and exhaustlap circles. With a
342 THE STEAMENGINE AND OTHER HEATMOTORS.
center on OX produced if necessary (to the right in this case) and
a radius X'A = 4XA (Fig. 176) construct an arc AffF. Join
and any point / and construct on Of and on an equal pro
longation valvecircles; they will be the valvecircles for the new
throw and new angular advance. Note the effect on
1. The crankangle of admission.
2. The amount of steamlead.
3. The point of cutoff.
4. The crankangle of exhaustopening and exhaustlead.
FIG. 178. FIG. 179.
FIG. 178. Diagram from a 12"X12" engine. 250 revs, per minute, width of
port 1", length of port 9", steamlap \" , exhaustlap 0, L/R=G; center
abou which the eccentric swings is distant 14" from the center of the shaft.
FIG. 179. Diagram from StraightLine engine 11 'X14". 275 revs, per
minute, width of port I", length of port, If" crank end, If" head end;
exhaustlap, crank end f", head end $"; eccentricity varies from l^f" to
2$"; steam lead .04 at quarter cutoff . (Klein's Steamengine.)
5. The crankangle and piston position of exhaustclosure.
6. The work of compression.
7. Note the effect of choosing the center X! above and
below the line OX'.
8. Note the effect of sliding the eccentric in guides so that
the center of the eccentric moves in a vertical line through A.
REVOLUTION CONTROL.
343
9. Note the position of the point X f in the diagram and on
the flywheel.
10. Note the effect of interchanging the position of the
fixed and moving pivots.
The general effect of increasing the angular advance and de
creasing the throw of the eccentric is to hasten all events, viz.,
steam opening and closing, exhaust opening and closing, and to
decrease the maximum portopening very materially. In high
FIG. 180.
speed engines cutting off at j or \ stroke this portopening re
ALN
quires the use of 360,000" for the factor F in the formula a = ^
b
(see page 109). The effect on the lead varies with the position and
distance of the center X f from the point A.
The Bilgram diagram may be equally well used for the deter
mination of the effects of swinging the eccentric center through an
arc. The center X' of the arc CC'C" is, in this case, at right
angles to its true position in the engine. (See Fig. 178.)
Shaftgovernors. As in the pendulum type of governor, there
is no action in the flywheel type of governor except with non
uniform rotation. As long as the engine is revolving uniformly the
344 THE STEAMENGINE AND OTHER HEATMOTORS.
centrifugal stresses are balanced by the pull of a spring of some
description, and there is almost complete static equilibrium, viz.,
there is no motion of the parts relative to one another. With the
slightest change in speed not only is there an unbalancing of the
centrifugal or radial forces, but new forces producing tangential
acceleration and angular acceleration may be brought into
existence.
In Fig. 180, if disc 1, representing a flywheel, rotate in the
direction of the arrow, being driven from a shaft, center at 0, the
weight W, center at C, exerts a radial or centrifugal stress along
OW that is resisted by the pull of the spring. If the speed increases
the radius OW increases until the pull on the stretched spring
equals the centrifugal force of W with its increased radius. The
movement of W outwardly or inwardly is utilized, by appropriate
leverarms not shown, to move the adjustable eccentrics already
described (Fig. 176).
Suppose the weight W were centered as in 2. No such radial
motion is possible, since the arm OW is not a spring. But suppose
that disc 2 is suddenly stopped. The weight W being pivoted at
is unimpeded and will continue its motion. To stop it a tangen
tial force must be exerted in a direction opposite to its motion in a
tangential direction.
In 1, as long as WC is perpendicular to OTF, all tangential
stress is taken by the pin C, and motion, due to tangential stress
alone, is impossible, but if the centrifugal force throws the weight
W so that the arm WC is no longer perpendicular to OW, as in
3 and 4, the motion will be due to a combination of the centrifugal
and tangential forces.
The tangential force may either increase or decrease the centrif
ugal force. In 3 the weight precedes the pivot, but in 4 the pivot
precedes the weight, hence, while the disc in each case is revolving
clockwise, the effects of the tangential force are opposite. If the
speed of 3 is increased, the inertia of the weight produces a force,
acting in the direction WB, which tends to increase the radius OW\
whereas if the disc slows down the tangential force then tends to
decrease OW. In both cases the tangential effect has aided the
centrifugal effect and hence made the governor more sensitive.
The opposite effect is seen in 4.
I
I
REVOLUTION CONTROL. 347
w
The amount of this tangential force is equal to Xthe tan
y
gential acceleration, and its moment is equal to the product of the
above force and its leverarm CA. Theoretical calculations give
an approximation to required quantities, but the final results are
obtained only by setting the engine up and running it at speed and
varying the tension of the springs by trial.
Angular Acceleration. Another method of using tangential
force is shown in 5. Suppose two weights are connected by a bar
pivoted in the middle to a fixed or component part of the fly wheel ..
If the latter slows down, the inertia of the revolving weights causes
them to set up a rotation around the pivot C in the direction of the
arrows. On the other hand, an increase of velocity of rotation of the
flywheel will cause rotation in the opposite direction. The rotation
around the pivot C is said to be caused by "angular inertia."
Springs. If to the above forces we add the force of gravitation,
we have the principal forces that are opposed in flywheel gover
nors by either leaf springs, as shown in Fig. 176, or helical springs,
as shown in Fig. 181. The strength of helical springs depends
upon a number of variables, among which are the modulus of
elasticity of the wire, diameter of the wire, the helical angle,
number and radius of the coils.
The springs may be wound so that their resistance is exactly
proportional to the stretch or to some increasing ratio. As in the
pendulum type, the centrifugal force increases directly with the
radius of the circle described by the center of gravity of the fly
weights, and if the stress in the spring increases exactly in the
same proportion, the flyweight will oscillate from its innermost
to its outermost positions. It is then truly isochronal and super
sensitive and therefore useless.
The tension of the spring must increase slightly faster than its
rate of elongation, more especially since, with a variation from
uniform velocity, other forces are brought into play and must be
counteracted. On the other hand, the variable friction of the
valve and its stem, the friction of all the joints of the governor
mechanism and the difference between the friction of rest and the.
friction of motion must be considered.
In Fig. 181 is shown the governor of the American Ballengine.
348 THE STEAMENGINE AND OTHER HEATMOTORS.
In this design are used two pivoted parts, both of which use angular
inertia. The smaller bar is pivoted wholly with regard to the best
location of the pivot for centrifugal force, and is controlled by the
help of the spring. The larger bar is located so that its center of
gravity practically coincides with the center of the shaft, and " is
pivoted at the most desirable point for determining the path of
motion of the valve actuating pin." The parts are so arranged
that a complete gravity balance exists in every position of the
wheel. "In many cases the total departure from normal speed,
with the whole load thrown on or off suddenly or gradually, does
not exceed the space between two arms of the wheel, or onesixth
of a revolution, which at 300 revolutions per minute is 1/18 of 1%."
Inertia Governor. The inertia governor designed by F. M.
Rites is used on the engines manufactured by over one hundred
firms. Originally designed for highspeed engines, it is now used
on mediumspeed four valve engines and is displacing the revolving
pendulum governor of the Corliss type.
A hollow, flattened, dumbbellshaped bar or weight (Figs. 212,
213) is fastened on one end of a spindle, s, that may oscillate
through a small angle in a bearing in the hub of the flywheel.
If an eccentric, E, is used it is fixed to the other end of the spindle.
The position of the latter must be such that the total allowed
rotation of the weight or bar from its position when the engine
is at rest will shift the eccentric from its position of maximum
throw at A to that of minimum throw (= steamlap) at B. In
stead of an eccentric (with its considerable weight, inertia, and
friction) an eccentric pin is used in many designs. Necessarily
this must be an overhung pin, so that its rod may clear the shaft.
The angle of rotation (in the arc gG) of the weight around
the axis of the spindle (through the action of centrifugal and
inertia forces) is governed by the action of the spring z. The
tension of this spring may be regulated by a nut at z', and the
length of its leverarm cd may be altered at z" .
While the weight is designed to look symmetrical with regard
to the shaft, as a matter of fact the end to which the spring is
attached is the heavier. The center of gravity of the rotating
weights (the barweight, the eccentric, eccentric strap, and the
strap end of the eccentric rod) is at some point G. To determine
REVOLUTION CONTROL. 349
the effect of the weight due to its inertia, consider it as two weights
concentrated at G\ and G 2 . If the engine slows down, these tend
to spurt ahead, rotating the spindle and therefore the eccentric in
the direction required to give increased travel to the vdve. The
diminished centrifugal force of the weight considered as a single
mass concentrated at G tends to produce a similar motion of the ec
centric. If the engine speeds up, the opposite effects are produced.
Hence we may say that in all cases the centrifugal and inertia
forces act together in increasing or decreasing the engine speed.
As the force of inertia acts only at change of speed, when
running at theoretical constant speed the forces acting on the
governor may be grouped under four heads:
1. Centrifugal force.
2. Tension of the spring.
3. Gravity.
4. Force exerted through the valverod.
Constant speed would only be possible if the sum of the moments
of these forces around the valvespindle was zero at all parts of a
revolution. A more exact analysis will be given later.
Practical Hints. If an engine runs unsteady, ascertain if it
ever ran satisfactorily or if the unsteady running occurred after
making repairs, overhauling, cleaning, or setting up any part
of the engine, such as the packing, journals, dashpot, springs, etc.
Examine the steamvalve for leakage or undue pressure, the steam
piston for undue leakage or tightness, the governor for misplaced
weights or undue friction.
By means of a brake or a waterrheostat run the engine at
onethird of its rated load. If the engine speed is steady but
too low, tighten the spring. If the spring has already been set
up to the limit, remove any attached weight from the short end
of the bar GI, or cut out one or two coils from the spring.
In making any alterations in the governor the following general
principles must be kept in mind :
Any alteration that increases the mass at G\ or increases its
radius tends to increase its centrifugal force and tends to slow the
engine down. The same results follow from weakening the spring
or decreasing its arm.
It is evident that fine adjustments are possible by changes
350 THE STEAMENGINE AND OTHER HEATMOTORS.
whose effects partially offset one another. The bes<t results in
steadiness are obtained when the noload speed is about 2%
higher than the fullload speed. Therefore the tension of the spring
must increase a trifle more rapidly th&n the increase in the cen
trifugal force of the mass due solely to its increase of radius,
i.e., at constant speed.
If at change of load the governor exhibits the phenomenon
called hunting, try the effect of adding a small weight to the lower
weight 6r?> if there is no trouble due to carelessness, such as stick
ing at the pin from dirt or scoring. Hammering at the slops
on starting and stopping may ordinarily be avoided by either
increasing or decreasing the attached weights either at the spring
end or at both ends.*
In order to operate successfully the modern highspeed shaft
governed valve it is necessary to reduce the friction of the valvd
and its stem to a small and constant quantity. The work of fric
tion is reduced by
1. Removing the pressure from the valve.
2. Diminishing its travel.
The first is accomplished by balancing the valve or using self
balanced valves. The valve is balanced by working it between
parallel scraped plates (Fig. 183), so that the steam does not get
to the back of the valve. In piston valves (Fig. 182) the pressure
due to the steam is balanced, leaving the friction of the packing'
rings to be provided for.
The travel of the valve is diminished by the use of double
ports or by the use of auxiliary passages in the valve. In the
Allen or Trick valve (Fig. 183) the steam enters the cylinder not
only directly past the valveedge, but also through a portpassage
in the valve itself.
Draw the Zeuner or Bilgram diagrams for the following examples.
Ex.119. Width of port, 5/8 in.; length of port, 12 in.; steamlap,
9/16 in.; exhaustlap: head end 1/8 in., crank end in.; L/R=6'.
eccentricarm infinite; engine, 14 // X20 // ; 210 revolutions, double
ported.
Ex. 120. Width of port, 1 in.; length, 9 in.; steamlap, 3/4 in.;
steamlead increases from 1/16 in. to 1/6 in. at maximum cutoff;
* See Power, Nov., 1906.
REVOLUTION CONTROL.
35
'C JV
\
352 THE STEAMENGINE AND OTHER HEATMOTORS.
length of eccentric or swinging arm, 14 in.; its center is on the line of
centers of shaft and crankpin when the latter is on a deadcenter.
Ex. 121. Width .of port, If in.; length, 8 in.; 9"X10" engine;
300 revolutions; steamlap, 1 in.; exhaustlap, 5/16 in.; throw of
eccentric varies from lf~J to 1 in.; length of swinging arm, 6J in., and
its center is 5/8 in. below the line of centers of the shaft and crankpin
when the latter is on its deadcenter.
Ex. 122. What change would be made if the valve took steam on
its inside edges instead of the outside?
Ex. 123. What changes would be made if the eccentric drove the
valve through a reverselever?
Ex. 124. Could this reverselever be designed to give equality of
cutoff and equal lead at the important point of cutoff with equal
steamlaps?
Link Motion. The Stephenson link is in common use in this
country and in England, whilst on the Continent the Gooch link is
preferred. The former will be the only one described (Fig. 184).
The Stephenson link is most generally used on locomotives and
marine engines, as it gives not only a convenient means of reversing
or running the engine backwards, but also affords, when carefully
designed, a fairly efficient means of economizing steam by affording
a variable cutoff (Fig. 185).
This link consists in a goingahead and a backing eccentric with
their rods and a link. The eccentrics as a rule have equal throws
and are placed at equal angles ahead and behind the crank. The
eccentricrods are attached by linkpins, P, P', to the link either
at or near its ends. The length of a rod is the distance from the
center of its linkpin to the center of its eccentric. When the link
is in full gear, either ahead or backing, the valve receives its motion
from one eccentric only. As the link is shifted from that position
to those nearer midgear, it receives less motion from that eccentric
and more from the other one. At midgear it is affected equally
by the eccentrics. As the gear is shifted towards the other full
gear, the influence of the first eccentric becomes less and less and
that of the second greater. It will be shown that the effects on
steam distribution caused by the change of valve motion produced
by this movement of the link are the same as those produced by a
swinging eccentric.
REVOLUTION CONTROL.
353
On locomotives, owing to the relative positions of the valve
(above the cylinder and outside the drivingwheels) and the eccen
trics (on the drivingaxle and inside the drivingwheels) a rocker
BTA is necessary (Fig. 185). To prevent the reversal of the
valve motion the eccentrics must follow the crank. Hence, if the
crank is at C the center of the goahead eccentric is at E, and the
FIG. 184. Marine Engine.
center of the backing eccentric is at E f . The linkpins P and P f are
behind the link; the saddleplate mo is dished to pass over the
linkblock, B, when the link is raised to bring the eccentric, E',
into full gear. The link is suspended on one side by the hanger
rwQ from the bellcrank RSn keyed to the reverseshaft S. The
reachrod, attached to SR at R, is actuated from a reversing lever
in the cab. The link shown is a slot link.
A lighter and better construction is shown in Fig. 186. In this
case the link receives and delivers centrally the stress due to driving
354 THE STEAMENGINE AND OTHER HEATMOTORS.
FIG. 185. Stephenson Link. (From Peabody's "Valvegears.")
REVOLUTION CONTROL.
355
t
p
p
__p_
in

Et
Fia. 186. Stephenson Link. (From Peabody's "Valvegears.")
356 THE STEAMENGINE AXD OTHER HEATMOTORS.
the valve. In other words, the axis of stresses in the valvestem
and in the eccentricrods coincides with the axes of those rods.
The figure also illustrates another form of link called the sidebar
link. The position of the linkblock is adjustable to vary the cut
off by means of the screw M actuating the bridle NP. This is
often desirable in regulating the distribution of power between the
cylinders of compound and tripleexpansion engines. By rotatirg
the reverseshaft, S, however, the link may be thrown over or
reversed independently of the position of the screw M.
To shift the link there are required (Fig. 185) a reverseshaft,
S; a bellcrank, RSn; and a suspensionrod, nwo (also called a
hanger or bridle), attached to the saddlepin, mo. The motion of
any theoretical point on the theoretical link arc (shown dotted) is
due to the motion received from the two 63centrics and from the
connection of the link to the suspensionrod, or hanger. The curve
made by any such point is generally some irregular form of the
figure 8, the loops differing in shape and size. To provide for
this motion a linkblock carrying a pivot pin B is used. We must
distinguish, then, between a point on the theoretical link arc and a
point on the axis of the pivotpin of the block, which coincide
exactly in position only at the time the crossingpoint of the loops
of the figure 8 is made. At other times the linkarc point has
slipped by the point in the block by the halfbread lh of the loop.
This motion of the link relative to the linkblock is called the
slipping or slotting of the block. In Fig. 186 the linkblock point
must move only in a straight line, since the block is directly con
nected to the valvestem; in Fig. 185 the linkblock pin moves in
the arc of a circle about T with a radius BT. A pivot connection
is necessary in each case, on account of the slight rotation of the
block about its axis.
Open and Crossed Rods. It is necessary to distinguish between
open and crossed rods. This is not so simple as it appears, since in
what is called openrod construction the rods become crossed
during a revolution and then open again. Similarly the crossing
apparently disappears in crossedrod construction. In taking an
engine apart, care must be taken, on reassembling the parts, not to
convert a crossedrod construction into an openrod construction,
or vice versa, as the steam distribution will be so altered that the
REVOLUTION CONTROL. 357
engine will not turn over. This mistake is frequently made in
overhauling steamlaunch engines.
To decide whether eccentricrods are crossed or open, we must
first determine whether the connection is direct or indirect. In
direct connection the linkblock must drive the valvestem directly
and the steam must be controlled by the outside edges of the
valve.
In indirect connection the valve is either driven by a rocker
or the linkblock drives the valvestem directly, but the steam
is controlled by the inside lap of the valve.
For direct connection (Figs. 187 and 188) put the crank on the
deadcenter away from the link. If the rods are open, the open
FIG. 188.
rod construction is used. If the rods are crossed, crossed con
struction is used.
For indirect connection put the crank on the deadcenter
toward the link. In openrod construction the rods will be open,
and they will be crossed in a crossedrod construction. By re
volving the crank through 180, the diagrams will show that open
rods become apparently crossed and vice versa.
Considerations Affecting the Design of a Linkmotion. The
design will vary in accordance with the importance of the following
considerations :
1. The linkmotion is to be used practically only for revers
ing, as in marine engines.
358 THE STEAMENGINE AND OTHER HEATMOTORS.
2. The linkmotion is not only to be used for reversing and
giving a variable cutoff, but is to be much used at an important
cutoff.
3. The linkmotion is to be used as frequently in the backing
as in the goahead position, as in hoistingengines, switch
engines.
4. The importance of reducing slip at an important point
of cutoff.
5. The importance of having equal cutoff on both strokes
at the important point of cutoff. Any inequality at short
cutoff affects the regularity of rotation more at short than at
long cutoff, as the percentage of power difference is greater.
6. The available places of locating the r ever singshaft.
7. The importance of reducing or increasing lead as the link
is shifted towards midgear.
The quantities affecting these considerations are:
1. The position of the axis of the saddlepin.
2. " " " " reverseshaft.
3. ' l length of the hanger, eccentricrods, suspensionrod.
4. ' ' use of crossed or open rods.
5. Whether or not rockerarms are used.
Whilst it may be easy to design a linkmotion that will work,
much care and skill is required in obtaining the best possible solu
tion. In locomotive works not only are fullsized drawings made,
but fullsized models are frequently used in the endeavor to obtain
the best design. In marine work the problem is simpler, but in
many cases that which is desirable cannot be obtained on account
of the interference of other practical considerations.
The Position of the Saddlepin. The position of the saddlepin
is generally determined with reference to the usual position of the
linkblock to prevent excessive slotting of the block at that position.
The saddle may be placed on the goahead end of the link. The
axis of the sa Idlepin will then be in a prolongation of the axis of
the linkblock when the link is in fullgear ahead position. This
construction is used in links of engines of certain types of vessals.
It may coincide with the axis of the linkblock when the latter is at
the important point of cutoff, as in p ssengerenginso. The center
of the saddlepin may be on the center of the link arc or before or
REVOLUTION CONTROL. 359
behind that position in engines that run much in both directions.
Offsetting the saddlepin to equalize cutoff is necessary when
the linkpins are behind the linkarc. A finite connectingrod
tends to reduce the offset as the latter increases with the length of
the connectingrod.
Position of the Reverseshaft. This shaft must be well sup
ported, and as a rule practical considerations bring it too clos2 to
the link. Small variations of position do not affect results greatly.
Length of Rods. In general, long arms tend to reduce inequali
ties and short arms to increase them. Advantage may be taken
of this fact and inequalities may, in some cases, be made to offset
each other.
Open or Crossed Rods. If the openrod construction is used,
the lead will increase as the link is shifted from full to mid gear;
with crossed rods the lead will decrease. The length of an eccen
tricrod should be at least twelve times the throw of the eccentric.
Linkarc. The length of the linkarc should be at least four
times the throw of the eccentric. The radius of the arc is
equal to the length of the eccentricrod if its linkpin is on the
linkarc. If the center of the linkpin is behind the linkarc, then
the radius of the arc exceeds the eccentricrod in length by the
distance that the linkpin center is from the linkarc measured
along the eccentricrod. The length of the linkarc radius just
given will give equal lead on both strokes if the valve has equal
laps. If unequal laps are given, so that the cutoff on the two
strokes may be equal or nearly so, then, of course, the leads will
be unequal. A somewhat greater or less length may be used, but
it will cause the leads to be unequal, and too large variation is not
advisable unless the effect is worked out on a diagram.
Equivalent Eccentric, Open Rods (Fig. 189). Suppose the
link in its midposition to the right of the figure, the crank on the
left center, the direction of rotation to be as shown, OC and OD
the positions and throw of the eccentrics. With a radius equal to
the length of the eccentricrod, viz., from the center of the eccentric
to the center of its linkpin, and with the centers of the linkpins
as centers, describe arcs cutting AB at c. Then with a center on
BA (produced) describe an arc through C, c, and D. Divide that
portion of the linkarc travelled by the linkblock into any number
360
THE STEAMENGINE. AND OTHER HEATMOTORS.
of equal parts, and also divide the arc CD into the same number of
parts. Then if 8 be the number of parts so chosen, and if the link
is moved 1/8 of the linkarc from full gear ahead, the motion of
FIG. 189.
the valve will be that due to an eccentric whose throw is Qc" r
and whose angular advance is LOc'", where Cc'" is 1/8 of CcD.
If the rods are crossed the construction is practically the same,
but the curvature of the arc CcD is reversed as in Fig. 190.
R L
FIG. 190.
Ex. 125. Design a Stephenson link for a tug of a vertical engine;
boilerpressure, 100 pounds; cutoff, 3/4 stroke; jet condenser, 26"
vacuum; 125 revolutions; lead, 1/16"; maximum portopening, 3/4".
Connectingrod = 5 cranks. Assume position of reverseshaft and
other required data.
Buckeye Engine. Fig, 191 is a crosssection of a tandem
compound engine of the Buckeye type. The valve mechanism
is composed of a main and a cutoff valve, the latter controlling
ports in the main valve. Both valves are of the piston type in
which steam is admitted in the central part, and exhaust takes
I
I
a
REVOLUTION CONTROL. 363
place at the ends. Admission of steam is practically controlled
by the cutoff valve, while exhaust is controlled by the main
valve alone. The main valvestem is hollow and the cutoff
valvestem works through the main valvestem.
Fig. 192 illustrates the valvegear diagrammatically. Let OB
represent the crank rotating anticlockwise, c" be the cutoff valve
riding on the top of the main valve m" '. In the position shown,
the live steam is passing through ports a and b into the cylinder
and the exhaust through the port b f is about to be closed by
the end of the main valve. The angular advance is negative,
since the exhaust is on the outside of the main valve. Therefore
the main eccentric is found at some point M and the cutoff at
some point C.
By an ingenious system of levers the cutoff valve receives not
only the motion due to its own eccentric, but also that due to the
FIG. 192.
main eccentric. Hence the motion of the cutoff valve relative to
the main valve is due to the cutoff eccentric alone. This motion
is similar to that of a man walking in a moving car. The motion
of the man relative to the ground is the resultant of his own and
the car's motion; relative to the car his motion is due to his own
movements alone, and the car may be considered stationary.
The main valve receives its motion directly through the eccen
trierod Mm' and valvestem m'm" . At m', however, it drives also
a lever .pivoted at p. This lever carries another lever that pivots
at /. The cutoff eccentric C by its eccentricrod Cc drives this
second lever at c. Suppose the cutoff eccentric stationary, then
c' and m' would have the same motion, since the point c' would
have twice the motion of the pivot / about the pivotpoint c (sta
tionary temporarily). Any movement of c will be given to c'
unchanged in amount, but reversed in direction.
If the cutoff valve is put in its midposition in Fig. 192, it will
be found to have a negative lap equal to about half the portopen
364
THE STEAMENGINE AND OTHER HEATMOTORS.
ing, a. To vary the point of cutoff the position of the cutoff
eccentric center is rotated (the radius, OC, being unchanged)
about 0. Its three principal positions are shown in Fig. 193.
Lay off the diagram for the main valve as usual, BOP being
the angular advance, Pe and Pi being the exhaust and steamlaps.
With a center C and a radius equal to the negative lap of the cut
off valve describe a circle tangent to OA. Draw any crank posi
tion 07. Drop the perpendicular C 8. Then from the construction
of the Bilgram diagram C 8 +C 9 is the distance that the cutoff
valve must move to close the port in the main valve, since we may
consider the latter stationary. At crank position OC , the port is
FIG. 193.
open, the negative lap, and at OA the port is clored. If the port in
the main valve is closed, it is a matter of indifference whether the
port in the cylinder is open or closed. If the eccentric center is
rotated to Ci, then the cutoff is in crank position 02. The latest
desirable cutoff point of the cutoff valve is 03, or at the point of
cutoff of the main valve.
The width of the cutoff blocks must be such that the blocks
will not overrun the port and open on the back edge when the
valve is set for the shortest cutoff. The greater the throw of the
cutoff eccentric the more rapidly the valve passes over the port
REVOLUTION CONTROL.
365
in the main valve and the quicker the cutoff. But this also in
creases the width of the blocks and the consequent friction.
Ex. 126. Make a diagrammatic sketch for a Buckeye valvegear
and its Bilgram diagram for a 20"X36" engine, making 125 revolu
tions per minute, lead of the main valve, 1/16 in.; maximum cutoff,
.8 stroke; minimum cutoff at the beginning of the stroke; exhaust
opens and closes at .9 stroke; connectingrod, 9 feet long; ports in
the main valve 2/3 of those in the cylinder.
Meyer Valve (Fig. 191). Consists of a main valve, C, with ports
through the valve, and two blocks, DD, forming a cutoff valve
Connects to Condenser
IUJJ
FIG. 194. Meyer Valve.
that rides on the main valve. The main valve governs the latest
point of steam cutoff and the points of exhaust opening and
closure. The earlier points of cutoff can be varied by adjusting,
by hand, the distance between the cutoff blocks. Means are pro
vided for rotating the cutoff valvestem that fits with right and
left threads of different pitches into corresponding nuts in the
blocks. One thread is necessarily larger in diameter than the
other, otherwise it would be impossible to put on one of the valves.
To make the valves cut off earlier they must be separated, to cut off
later they must be brought closer together. By giving the main
valve unequal laps equal cutoff may be obtained at the maximum
point of cutoff. By the unequal pitches of the right and lefthand
screws, equal cutoff may be secured at two points, as, for example,
the most important point of cutoff and the earliest point of cut
off. At all other positions the cutoff will be unequal. In revers
ing engines, the cutoff eccentric is direotly opposite the crank.
366 THE STEAMENGINE AND OTHER HEATMOTORS.
Ordinarily it has an angular advance of 75. Its throw is not an
absolute quantity, but is generally a little larger than that of the
main valve.
Corliss Engine. In this type there are two steam and two
exhaustvalves placed in separate chambers, either in the cylinder
heads or above and below the cylinder at its ends. The valves
oscillate about their axes, which are at right angles to that of the
cylinder. For proper drainage the exhaust valves are always the
lower ones. The lower or exhaust valves have an invariable
motion which they receive from a wristplate. The oscillating
movement of the latter about a heavy pivot symmetrically placed
in regard to the axes of the four valves is obtained as follows. The
eccentric, set ahead of the crank a little more than 90 degrees, as
the valve has very little lap, drives a rockerarm, which, in turn,
drives the wristplate B A (Fig. 195). The links, as BE, never drive
the valvestem directly, but indirectly, through a detachable mech
anism. In the figure, the governor, of the revolving pendulum type,
moves a cam xg through the linkage NMl. On the extreme throw
to the right of the link BE, the fork gTh is forced by the spring
hs to engage with the block shown just above y. On the stroke
to the left, the arm BE carries this block, whbh is rigidly attached
to the valvestem, with it until the arm gT of the fork comes into
contact with the cam. This causes the fork to rotate anticlock
wise and to let go of the block. A piston which had been lifted in
a dashpot by the previous motion promptly closes the valve.
SETTING SINGLEECCENTRIC CORLISSENGINE VALVES.
In the design of this valve mechanism advantage is taken of
the great variation in the rapidity of motion that may be produced
by an assemblage of links. It is desirable that a valve should
openand close rapidly; when wide open or shut the motion should
be as small and as slow as possible and the motion should be a
minimum when the maximum pressure is on the valve.
The student should note the variation in steam valve move
ment due to variation of position of the links Ob 2 , b 2 e 2 , e 2 v for the
movement of the wristplate through equal parts of the arc b 2 bi.
Similarly he should note the corresponding movement of the
REVOLUTION CONTROL.
367
FIG. 195. Corliss Engine. (From Peabody's "Valvegears.")
J68
THE STEAMENGINE AND OTHER HEATMOTORS.
exhaustvalve due to changes in the relative position of the links
Oa, aidi, diw for movement of the wristplate through equal parts
of the arc a\a^.
An examination of the automatic method of detaching the
steamvalves will show that it can only operate through a crank
^Exhaust
La?
FIG. 196.
FIG. 197.
movement of 90 degrees in each stroke, i.e., while Th is rising.
We are at liberty to choose the position of these 90 degrees in a
semirevolution if the steam and exhaustvalves are operated by
independent eccentrics. If, however, only one eccentric is used,
the necessity of having the exhaustvalve open and close at proper
points practically limits the detachment of the steam valve be
tween the deadcenter and 3/8 stroke positions of the piston.
With double eccentrics by giving the steamvalve negative steam
lap and its eccentric negative angular advance later points than
that above given may be obtained.
When the stroke is short compared with the diameter of the
cylinder the method of connection illustrated in Figs. 195 and 198
is used; if the stroke is long compared with the diameter of the
cylinder, the form shown in Figs. 196 and 197 may be used.
" The following method of setting the valves applies to single
eccentric engines of the following types: Reynolds, Twin City,
Hamilton, Murray Bates, Cooper, Monarch (old), Harris, Hardy
Tynes, Lane and Bodley, and all others of similar valve arrange
ment.
REVOLUTION CONTROL.
369
FIG. 198.
Table
" First. Place wristplate D in central position as shown in
Fig. 196, with both valves hooked on, so that mark on wristplate
hub will coincide with center mark on
stud; loosen studnut and place a piece
of cardboard between washer and wrist
plate and tighten so that wristplate will
not move.
" Second. Loosen locknuts on shackle
rods and adjust valves until they have
laps as found in table (which are given in
parts of an inch opposite size of cylinder) ,
after which set up locknuts securely.
" Third. Plumb rockerarm by hang
ing a plumbline over center of pins^
then adjust hookrod between rockerarm and wristplate.
" Fourth. Remove cardboards so wristplate and rockerarm
can oscillate; now connect eccentricrod to rockerarm and revolve
eccentric on shaft in the direction
the engine is to run, being careful
that mark on wristplate coincides
with side marks on stud when
making adjustments of the eccen
tric rod. Next adjust dashpot
rods H as follows (Fig. 198): When
rod is down as far as it will go, the
shoulder E on brass hook should
just clear the steel block F on valve
arm as shown in cut, leaving a
clearance of 1/16 inch between block and catchplate. Swing
wristplate to opposite side and adjust in same manner.
" Fifth. Place crank on exact deadcenter and revolve eccentric
in the direction engine is to run until valve on end nearest piston
shows amount of lead as given in table. Now fasten eccentric and
revolve engine in direction it is to run ; when opposite deadcenter
the opposite valve should show the same amount of lead.
" Sixth. Set governor on startingpin and adjust triprods so
that cams will just trip valves as wristplate coincides with travel
marks on stud when oscillated.
Diameter of
Cylinder
Lap of
Steam Valves
Lap of
Exhaust Valves
Lead of
Steam Valve*
8
>fc
y\6
Ym
10
y\a
y\*
Vxi
12
y\s
K S
y.',2
u
x
%
y,2
1G
x
X
Y,1
18
H
X
KJ
20
H
%
M2
22
x
y
&
21
%
%
26
5
k
JJM
28
%
y\s
pi
30
*i
g
1
&2
H
X
y\s
34
H
H
KB
36
%
g
Vffi
370 THE STEAMENGINE AND OTHER HEATMOTORS.
" Seventh. Now remove startingpin and allow governor to go
as low down as it will, then adjust safetytoes on tripcams so that
valves will not hook on when wristplate is swung to travelmarks
on stud.
"Caution. The adjustment of rod H is very important: if too
long something will break, if too short the valves will not hook on.
Adjust your dashpots so as to maintain a good working vacuum."*
FIG. 199.
FIG. 200.
Poppetvalves. Slidevalves give much more trouble than
pistons wh n steam is ueed that has been superheated to such
FIG. 201.
FIG. 202.
a degree, that it is still superheated on entering the cylinder.
This is probably due to the cooling received by the cylinderbore
Mechanics.
REVOLUTION CONTROL.
371
during exhaust, whilst there is no such effect on certain parts of
the surfaces rubbed by the valve.
As the steamvalve must have a variable cutoff it must also
be a balanced valve. Exposed to high pressures, it must be very
stiff to maintain the truth of its steamsurfaces, and it must also
be tight when highly heated. The valve that best satisfies these
372 THE STEAMENGINE AND OTHER HEATMOTORS.
requirements when superheated steam is used is a dropvalve
called the double poppetvalve. It may be balanced as closely as
desired, since the steampressure is made to act on the valve in
FIG. 204. Double Poppetvalve used as a Governor.
opposite directions at all times. Old forms are illustrated in
Figs. 199202. The valve of the Putnam engine is shown in Fig.
203. (See page 440.)
CHAPTER XIIl.
SPEED VARIATION CONTROL.
Turning Effort in the Crankshaft. The motion of a body is
uniform when the resisting forces of all kinds are exactly balanced
at each and every instant by the impelling forces. For some pur
poses it is desirable to have the crankshaft rotate absolutely
uniformly. Not many years ago it was usual to describe the uni
formity of rotation of an engine by specifying that its revolutions
per minute would not vary more than one or two from the mean in
changing from no load to full load. An uptodate engine for some
electrical purposes is now designed not to vary per revolution more
than a certain number of pole degrees eight, for instance from
the position that absolute uniformity of rotation would give it.
This would be a displacement in inches on the crankpin circle of
o
$" = o^n^oA X ^ 7rr if tne generator had 30 poles; i.e., a pole degree
ouU X oU
equals the degrees between two poles divided by 360. In cotton
mills uniformity is exceedingly desirable. Large capacity for cer
tain machines is secured by driving shuttles carrying cotton threads
so fast that the threads are on the point of breaking but do not
break. Calling this the economical speed, a lower speed would
produce less cloth; and a momentary higher speed, causing the
threads to break and the machine to be stopped to allow the
operator to tie the threads, would also reduce production. The
exactness required for various classes of machinery will be given
later.
Two different kinds of uniformity must be secured. If the
load should vary after the point of cutoff, it is evident that the
governor controlling the steamsupply can exercise no influence on
the speed until the next stroke. Hence the engine must change
373
374 THE STEAMENGINE AND OTHER HEATMOTORS.
speed to make the governor act, and it controls by regulating the
amount of steam or the pressure on the stroke following the change
of speed. The steamgovernor affords means of controlling the
number of strokes per minute, but it is also desirable to control
the speed of the crankpin during a stroke. If we suppose the
resistance is uniform, then uniform rotation will be secured by uni
form tangential pressure on the crankpin, since it is only the tan
gential pressure that is effective in the production of rotation.
Net Steampressure. The net steampressure on a piston at
any instant is the difference between the absolute driving steam
pressure on one side of the piston and the absolute back pressure
on the other side at the same instant. The amount of this net
pressure cannot be obtained from a single card, since the bottom
line on such a card is the back pressure on the same side of the
piston on the returnstroke. To obtain exact results we should
have two indicators, each taking a single card during the same
revolution of the engine.
In Fig. 204 let A and B be cards so taken. For convenience
of illustration both diagrams are shown on one card. Then the
net steampressure at any piston position b is ab bc=ac,
where ab= absolute forward pressure,
be = absolute back pressure,
ac=difference between drivingpressure of one card and
back pressure of the other card.
Draw a new card, 12345, whose ordinates represent the net forward
steampressure.
When the back pressure exceeds the forward pressure the
ordinates are laid off, as in the figure, below the baseline.
Variable Velocity of the Piston. If the crankpin revolves with
uniform velocity it will pass over equal arcs in equal periods of
time. The piston then necessarily passes over unequal distances
in equal periods of time. On page 73 it was shown that these
distances increased from the beginning to the middle of the strc ke
and then decreased to the other end of the stroke. The pisto^,
then, must have a positively accelerated motion from the beginning
of a stroke to near the middle and then a negative acceleration
to the end of the stroke. It was further shown that shortening
the connectingrod increased the amount of all irregularities.
SPEED VARIATION CONTROL.
375
Bodies at rest or moving uniformly are under the action of
forces that are absolutely balanced. Bodies having an accelerated
motion are storing up work represented by the increasing kinetic
. 205a.
energy of the moving masses. This energy will be given out again
if the moving masses slow down. At any point in the first half
of the stroke a part of the net steampressure (acting through
a distance) will be required to produce the necessary acceleration
376 THE STEAMENGINE AND OTHER HEATMOTORS.
of all parts of the engine having a reciprocating motion or a motion
of translation. On the other hand, the net steampressure during
the second half of a stroke will be augmented by the pressure
made available by the necessary slowing down of the reciprocating
parts.
Reciprocating Parts. These are the piston, pistonrod, cross
head, and half the weight of the connectingrod. (See Vol. XXVI,
Trans. A. S. M. E.) In the discussion of accelerations and .forces
on the assumption of an infinite rod we shall use the above propor
tion of the weight of the real rod in finding the forces, as the
change required by the use of a finite rod is then easily made.
Pressure Required to Accelerate the Reciprocating Parts (Figs.
205 and 206).
CASE I. Infinite Connectingred.
Let V= constant velocity of the crankpin in feet per second;
v= variable velocity of the piston in feet per second;
r= radius of crank in feet;
0=length of the arc, measured from the deadcenter,
swept through by a point on the crankarm at
unit distance from center of the shaft in t seconds;
TP=weight of the reciprocating parts.
Then rO = length of arc swept through by crankpin in t seconds
= Vt.
rdd = Vdt, hence j =
at T
( distance the piston moves in t seconds from a
r(l cos0) =s= J , , ,.! , ,, , Q
( dead center whilst the crankpin moves rd.
ds d(rrcosd) r sin 6d6 T _ . rdd T _
dt= ~dT ~dT ^ sin ^ since ^=7.
dv d 2 s d(Vsm0} V cos Odd F 2 cos#
But acceleration =rr =rz = T. = T; =
dt dt 2 dt dt r
The product of the acceleration and the mass that has been accele
rated gives the force required to produce the acceleration; or
W V 2 cos 6
F = =the total force required to produce the necessary
acceleration of the reciprocating parts at the piston position cor
SPEED VARIATION CONTROL. 377
responding to a crankangle, 0, if the crankpin revolves uni
formly.
As the indicatorcards show pressures in pounds per square
inch it is advisable to divide the total
pressure F by the area of the piston in
W V 2 cos0.
square inches. Hence / = r is the
loss or gain of pressure in pounds per
square inch of piston area arising from the
necessary acceleration, positive or negative,
of the reciprocating parts (at a piston posi FIQ 2Q6
tion corresponding to the crankangle 6).
Mass of Reciprocating Parts Considered as Concentrated at the
Center of the Crankpin. If the weight of all the reciprocating
parts could be concentrated at the center of the crankpin the cen
WV 2
tripetal force of such a weight would be  . The horizontal
WV 2 cos
projection of this radial force would be   or the above
force, F.
In the above equation for /, the only variables are / and cos 6.
As the equation is of the first degree, it is therefore the equation
of a straight line. This can be seen by giving 6 a few values such
as 0, j, ~> an d TT and plotting the results.
Hence it is only necessary to find the value of / for 0=0 and
6 = n and join the points so found by a straight line.
For example suppose the cards, Fig. 205, are from a horizontal
highspeed engine.* With the following data find the pressure per
square inch of piston area that will be required to accelerate the
reciprocating parts at the beginning of a stroke, neglecting the
angularity of the connectingrod.
Revolutions 300
Stroke 12 inches.
Diameter of cylinder 10 "
Length of connectingrod 36 "
* Trans. A. S. M. E., Vcl. XI.
378 THE STEAMENGINE AND OTHER HEATMOTORS.
Distance from wristpin (crosshead pin) to the
center of gravity of the connectingrod ........ 20. 15 inches.
Principal radius of gyration of connectingrod ..... 15 "
Weight of connectingrod ....................... 70 pounds.
Weight of piston, pistonrod, and crosshead ....... 90 ".
Weight of above and half connectingrod .......... 125 "
When 0=0 or TT
. 125X4X*
7 ' ;rX5 2 X32.16Xi fc 2X32. 16
(Fig. 205.) Lay off IE or 5^ = 24.42 pounds to the scale of
the indicatorcard pressures. Then any ordinate as, dc, represents
the pressure that is required to produce (or is produced by) the
instantaneous variation of velocity in the reciprocating parts.
Negative pressure is therefore indicated above and positive pressure
below the reference line 15. As these pressures are always modified
by the use of a finite rod, its effects will be discussed next. The
equation of / and 6, when the length of the rod is considered, will
no longer represent a straight line such as EF, but takes the form
of a complex curve HIJ.
CASE II. Finite Connectingrod. In general, sufficient accuracy
is attained if only three to five points on this curve are obtained.
The formula to be used for each of these five points may be ob
tained from the general formula by the substitution of the proper
crankangle.
Piston Position of Zero Acceleration. After reaching its maxi
mum velocity the piston begins to slow 'down. Evidently the
acceleration changes sign and passes through zero at the point of
maximum piston velocity. With an infinite rod this occurred at
halfstroke, the crank arm and rod being at right angles at that
point. With a finite rod this point will occur before half stroke,
and its position may be obtained graphically as follows:
(Fig. 207.) Draw a circle with a radius OA = r, the throw of the
crank. Perpendicular to OA draw AC and lay off AC equal to
the length of the connectingrod. If OAC is swung around till
C cuts the line OD, the required point E will be obtained. To do
this,_ measure the hypothenuse, OC, and lay off OD = OC. With
D as a center and a radius = AC = length of the connectingrod,
SPEED VARIATION CONTROL.
379
describe the arc EF. Then OE will be the crankpin position and
GF the distance the piston is from its deadcenter G when the
piston has its maximum velocity and its acceleration is therefore
zero, and hence f = 0.
FIG. 207.
Accelerations, Finite Connectingrod (Fig. 55). In general,
however, for any position of the crankpin 6 degrees from the dead
center, the piston has moved
x = r(l cos 6) +1(1 cos a).
I sin a = r sin 0, rd = Vt,
rdd = Vdt, sin a = sin 6,
cos a =
I Tr \ 2 / 1 r 2 \
a = vft ( j sin I = ( l  _ _ sin 2 6 , approximately,
V / \ & I ]
(By squaring the above quantity and neglecting sin 4 6 the quantity
under the radical is obtained.)
/. x = rl 1 cos 0n j s
dx rdd / . 1 r .
^ = v(sm6^sm26},
ctt \ 2i I
cos
cos
r \ V 2
jcos2dj=
= cos 6jcos 20
)
380 THE STEAMENGINE AND OTHER HEATMOTORS.
Forces to Produce Required Acceleration. As in the preceding
case
Force = mass X acceleration.
W V 2 / r \ WV 2 / r \
/. F =  (cos 6jcos2d] and f = ^ ~ { cos 0ycos 26 ).
The value of this equation for
W V 2
6=* 45 and 135, / = cos 45;
The value for 0=45 or 135 is the same as in Case I and
may therefore be used if the corresponding piston positions are
obtained.
/ W V 2 \
Substituting the value of ( : ) already found (24.42 pounds)
\i/ /
and the value of T = ^> we obtain /o = 24.42 (); / 180 = (24.42)
i 60
(); / 90 =(24.42)(J). Plotting these results and those ob
tained for zero and equal acceleration (45) we obtain the curve
HIJ.
Pounding of the Engine. It can be readily seen that the inertia
of the reciprocating parts may be used to equalize the pressure
that is exerted on the pistonrod during the entire stroke. At
first sight this might seem desirable, and it has been so enunciated
many times. On the contrary, it is not desirable, as it will cause
the engine to pound on the centers, due to the sudclen change from
positive to negative pressure. Smoothness of running is secured
by such weight of reciprocating parts as will cause the forward
pressure to increase gradually from zero to a maximum at the end
of the stroke. The sudclen cessation of pressure will not produce
a pound, but the taking up of lost motion under heavy pressure
will produce a destructive pound that should be avoided. In
SPEED VARIATION CONTROL. 381
shaftgoverned engines at cutoff shorter than the normal, the lead
is often made negative. This tends also to reduce the tendency
to sudden reversal of stress. Heavy compression also has the
same effect.
Determination of Tangential Pressures. Let the ordinates of
H2KU of Fig. 208 be the same as those of H234JK1H, Fig. 205,
the abscissas being reduced to onethird of their original dimensions.
With a radius equal to the length of the connectingrod (3XHJ)
lay off B and D from H and J and construct the circle BCD.
Divide it up into any number of equal arcs and let C be one of
the division points. With the length of the connectingrod as a
radius and C as a center, find A, the corresponding crosshead
position. Having taken out the pressures required to produce
acceleration of the masses, we may consider the forces that we
are now discussing as static.
The crosshead and crankpin are each under the action of
three forces produced by the action of one force acting in the
direction of HJ and of magnitude p. The pressure in the con
nectingrod is greater than p, since the component of the connect
ingrod pressure along HJ must equal p.
Prolong the crankarm OC till it intersects a perpendicular,
AI, erected at A. The tendency to rotate around the instan
taneous center, /, is zero, since the forces producing change of
velocity have been removed Taking moments about /, all forces
disappear from the equation except p and the tangential force
T acting on the crankpin.
On 01 lay off OP f = p and draw P'T' parallel to the connecting
rod position AC and intersecting OM, a perpendicular erected to
BD at 0.
The triangles OP'T' and CIA are similar, therefore
oF~ci m '' OT '=P x cJ'
Hence OT f is the reqiured tangential pressure at this crankposition.
382
THE STEAMENGINE AND OTHER HEATMOTORS.
It is evident that connectingrod positions will have to be
drawn for each crankposition in succession to determine a new
piston position and the corresponding net pressure, such as p. By
laying off this pressure from the center of the shaft on the crank
position, prolonged if necessary and drawing a parallel to the
new connectingrod position as P'T' was drawn, the tangential
pressure for the new crankposition will be indicated by the
distance between and the point of intersection of the parallel
and the line OM. It is not necessary to find the instantaneous
center, as that is only necessary to prove the construction.
The tangential pressures so found may be laid off in two ways;
1. (Fig. 208.) At each point of division of the crankcircle
FIG. 208.
lay off the tangential pressure radially at right angles to its
true position from the center of the crankpin. CT" 1 ', for instance,
is equal to OT'. Join the points so found. The area enclosed
by this line and the perimeter of the circle does not measure work.
2. (Fig. 209.) A much more useful diagram is formed by recti
fying the path of the crankpin thus giving actual linear distance
and at each point of division on the rectified perimeter erecting
a perpendicular equal to the tangential pressure at that point.
All areas then measure work and by means of a planimeter or by
SPEED VARIATION CONTROL.
383
the method of ordinates we can obtain the excess or deficit of
work variation from the mean that produces either positive
or negative acceleration.
The importance of dividing the semicircles into equal parts is
now apparent, as it facilitates the rectification of the arcs. Accord
ing to Rankine the following method is accurate to Tiror (Fig.
210.) To rectify the circular arc AEB prolong the chord AB to C,
making AC = %AB. With a center at C and a radius AC describe
an arc AD. At B draw a tangent, BD, limited by the arc AD.
Then 5D = arc AEB in length.
Fig. 209, has many important qualities. For instance, its area
is exactly equal to that of the original indicatorcard, thereby
FIG. 209.
FIG. 210
illustrating the fact that there is no loss of energy, friction
excepted, in the conversion of the " toandfro" work of the piston
into the work of rotation of the crankpin.
If we divide the area of the card, Fig. 209, by its length and
lay off a line parallel to the base with the resultant pressure as the
ordinate, we shall divide the card into two parts. The + area
indicates work in excess of the mean, the areas indicate cor
responding deficits. In every case the sum of the + areas must
equal the sum of the areas per revolution.
In the case of a single engine one of the + areas may be called
AE and its ratio to work per revolution or 2 (area of the rectangle)
A W
= 2 (the area of the indicatorcard) may be called
2/pds '
This
fraction is often called the fluctuation ratio or coefficient of un
steadiness. Its value ranges from 1/6 to 1/4 with singlecylinder
expansion engines, with a pair of engines of practically equal power
coupled at right angles its value is from 1/25 to 1/15; and for three
384 THE STEAMEXGINE AND OTHER HEATMOTORS.
engines coupled at 120 degrees apart it is 1/75 to 1/50. By
means of a flywheel, the effect of all of these variations from
the mean energy on velocity changes may be much reduced. The
absorption of energy by the flywheel in speeding up reduces the
highest velocity that would otherwise be attained and increases
the lowest velocity by returning the absorbed energy.
The following table gives an approximate value of allowed
coefficients of unsteadiness in velocity = =s =k.
For stamps, crushers, etc 1 / s
' ' sawmills and pumpingengines 1 / 20 1 / 30
' ' weavingmachines and papermills V 30 1 / 40
" spinningmachines for coarse to middlefine yarns. . 1 / 35 l / 50 ! /eo
" spinningmachines for finer yarns 1 / 50 . . 1 / IM
tl belt driven dynamomachines 1 / 150
' ' directly coupled dynamomachines 1 / 300 1 / 60Q l / 3000
Approximate Formula for a Flywheel.
W = weight of the flywheel.
Vi= maximum velocity of the rim, at radius R, in feet per
* second.
V 2 = minimum velocity of rim, at radius R, in feet per second.
V =mean velocity of rim, at radius R } in feet per second.
We shall assume that V = ~ . This is not true frequently,
as the maximum velocity may persist for a much longer or shorter
period of time than the minimum velocity.
The radius R is generally taken from the center of the shaft to the
middle of the rim. The proper radius is the radius of gyration,
as we are really dealing with the mean of the squared radii. In
dealing with thin rims in an approximate solution, the assumption
of the mean radius is sufficiently accurate.
W
The kinetic energy of a mass, moving Vi feet per second is
v7
W
~Vi 2 . If the velocity changes to V 2 feet per second the new
SPEED VARIATION CONTROL. 3S5
WV 2 2
kinetic energy is , . The change of energy is
This must equal
JE may be obtained in footpounds from the maximum + or
area in a diagram (Fig. 209) , or it may be obtained from an
assumed fraction of the work per revolution.
For example, find the weight of a flywheel for a 100 I.H.P.
engine making 100 revolutions per minute; fluctuation of energy
17? 1
= T,  = .2; fluctuation of speed = r^; mean velocity of fly
2/pds.
wheel rim = 50 feet per second.
100x33,000 2
1oo^ x io x32  18
*  .01X50X50  =849 P und& 
Another method of reducing the difference between V l and 2
is to reduce the amount of the + and areas. This can be done
by having the work done by two engines coupled at right angles,
or three engines at angles of 120 degrees apart.
I T7T
The formula W = ~TT^ is expressed in several forms :
Let N = number of revolutions per minute;
RI =mean radius of rim in feet;
R 2 = " " " " " inches;
R g = radius of gyration in inches;
/ =WR g 2 = moment of inertia;
=/ = jjjyvj inchpounds;
N 2 or .0000278TF# 2 2 N 2 footpounds.
386 THE STEAMENGINE AND OTHER HEATMOTORS.
In Fig. 222 the curve of tangential effort of the highpressure
engine of a compound is given in full lines, while the curve for
the lowpressure engine is given in dotted lines. From the posi
tions of the points of zerocrank effort it is readily seen that the
cranks of the engines are at right angles to one another. In
Fig. 223 the ordinates of the two engines have been added and
the variation from the mean ordinate MC is indicated.
Belt Wheels. For many purposes the belt wheel, if properly
proportioned so that it does not look weak, will be found suffi
ciently heavy to serve as a regulator. It will not serve where
very close regulation is required, as in parallel operation of A. C.
generators. Two per cent variation on either side of the normal
speed is close enough for steady burning of lamps and a belted
Corliss should run that close. If power and lamps are on the
same circuit a heavier wheel should be used.
Horsepower of a Belt. Authorities differ but common rules
are:
Single belts transmit one horsepower per inch of width per
1000 feet linear veloc ty;
Double belts transmit two horsepower per inch of width
per 1000 feet linear velocity;
At 3000 feet the effect of centrifugal force becomes per
ceptible and 5000 to 6000 feet is the economic limit if the life
of the belt is to be considered.
The Arc of Contact. This is supposed to be 180. Reducing
the arc increases slippage and causes less horsepower to be
transmitted. The maximum ratio that should exist between
driving and driven pulley should not exceed 5. With this large
ratio the axes of the pulleys should be well separated. The
bottom of the belt should be the tight side. The upper side
should run with a perceptible sag.
General Details. The face of a belt wheel should be crowned
at the rate of J inch to the foot. If over 40 inches wide, double
staggered arms are used. The rims of wheels under 13 feet in
diameter should be at least one inch in thickness and strength
ened at the sides and middle by ribs. The middle rib serves to
connect the thicker arms and rim and reduce shrinkage stresses.
The diameter of the hub is about twice that of the shaft and
SPEED VARIATION CONTROL. 387
the length of the hub is one and a half to twice the shaft diameter.
This width is necessary to prevent the wheel from rocking on the
shaft. The minimum weight of a belt wheel for good looking
proportion is given in column five, Table A, page 389.
Weight of Balance Wheels. In the analytical discussion it was
shown that the efficiency of a flywheel varied with WR 2 , where
R 2 is the squared radius of gyration. It is evident for economy
of material that the diameter of the wheel should be as large
as possible, yet, for good looks, it may become too large.
When engines are used to drive generators it is convenient
to express the weight of the balance wheel in terms of the revolu
tions of the engine and the kilowatts of the generator. To do
this, primary constants will be given for singlecylinder engines,
running at 100 revolutions per minute, the rim of the flywheel
moving with a velocity of 5700 feet per minute. These constants
will have to be modified in the case of multicylinder engines
and in case the revolutions are not 100. Two sets of primary
constants will be given, one for A. C. current generators running
in parallel, and another for D. C. current generators and for A. C.
current generators which are not in parallel operation.
The method then is as follows:
From Table A pick out the diameter of the wheel corresponding
to the given number of revolutions. From Table B (page 390)
pick out the constant K A or KD, according as the engine is to
drive A. C. generators in parallel or A. C. generators not in
parallel or D. C. generators. Obtain a new constant, K\ or K%,
depending on the number of revolutions from the formulas below :
100
K2=
In turn the constants K\ or K% must be modified in accordance
with the amount of variation of energy from the mean during a
revolution. As that of the single cylinder is a maximum it will
be assumed as unity and K\ and K 2 must be multiplied by the
decimals below corresponding to the type of engine:
388 THE STEAMENGINE AND OTHER HEATMOTORS.
Singlecylinder engine .............. ........ 1 . 00
Tandemcompound engine ................... 80
Crosscompound engine ...................... 60
This final constant, K/ t multiplied by the kilowatts will give
the weight of the wheel in pounds. The effect of the WR 2 of
the armature and rotors of the generators is only to ^ of
that of the wheel, except in very large sizes. They may therefore
be neglected.
Examples. A tandemcompound engine is direct connected to
a 500kilowatt 60cycle alternatingcurrent generator, running at
90 revolutions per minute. Find the diameter and weight of
the wheel.
From Table A we find that a wheel corresponding to 90
revolutions must have a diameter of 20 feet and from Table B
the primary constant, K A , is 145 for 100 revolutions per minute.
Hence for 90 revolutions,
For a tandem compound,
K/=220X.80 =
Total weight of wheel,
176X500 = 88,000 pounds.
After finding the weight, reference should be made to the
last column of Table A, as the weight should not be less than
the tabular amount. In the present case the tabular amount
for a 20foot balance wheel is 32,000 pounds, and hence the
weight found, 88,000, may be used. If less than the tabular
weight is used the wheels will appear out of proportion and look
light.
Example. A singlecylinder engine is direct connected to a
75kilowatt directcurrent generator running at 120 revolutions
per minute. Find the diameter and weight of the wheel.
If we used a rim speed of 5700 feet per minute we should
obtain a wheel with a rim section too light to look well. Even
SPEED VARIATION CONTROL.
389
at 4800 feet we shall lower the amount of the radius to obtain
a more substantial appearing rim.
From Table A, column 2, the nearest diameter is 12 feet and
from Table B, K D is 185.
For 120 revolutions per minute,
100\ 3
: I

1207
X 185 = 107.
Total weight of the wheel, 107x75 = 8025 pounds.
Referring to Table A we find that the minimum weight that
should be used for a 12foot wheel is 12,500 pounds. We must
therefore assume a 10 or 11foot wheel and recalculate.
For a 11foot wheel,
_/100\ 3
1207
X 225 = 130.
The weight of the wheel is
130X75 = 9750 pounds.
This is a trifle above the limit for a 11foot wheel and hence
may be used.
TABLE A.*
BELT AND BALANCE WHEELS.
Diameter of
Wheel in
Feet.
Revolutions
per Minute,
Rim Speed
4800 Feet
per Minute.
Revolutions
per Minute,
Rim Speed
5700 Feet
per Minute.
Fare Width
in Inches of
Belt Wheels.
Average
Weight of
Belt Wheels
in Pounds.
Minimum
Weight for
Balance Wheel*
in Pounds. J
8
191
227
12
4,000
4,500
9
161
201
15
4,500
5,000
10
152
181
20
8)500
8,000
11
139
165
24
9,400
9,500
12
127
151
27
12,000
12,500
13
117
140
30
13,250
15,000
14
109
130
33
14;500
18,000
15
101
121
35
16,500
20,000
16
95
113
37
18,500
24,000
18
85
101
42
25,000
27,000
20
76
91
50
42,000
32,000
22
69
82
60
52,000
65,000
24
63
76
26
58
70
28
55
65
30
51
60
* Power.
390
THE STEAMENGINE AND OTHER HEATMOTORS.
TABLE B.*
VALUES OF PRIMARY CONSTANTS.
K A
KD
i_^ameter 01
Balance Wheel
A.C. Current
D.C. Current
in Feet.
in Paralle
and
Operation.
K.C. Current
not in Parallel.
10
585
270
11
485
225
12
400
185
13
350
160
14
300
135
15
260
120
16
230
105
18
185
85
20
145
65
Analysis of the Rites Inertia Governor. The designing of
steamengine governors is the work of a specialist. It involves
FIG. 211. The numbers show variable positions of the eccentric center and
gravity center at variable cutoff. The dotted lines AO and OG are of
variable length. is the center of the shaft ; C is the center of the crank
pin; s is the spindle center; G is the center of gravity of the rotating
weights; M is an ideal center of mass placed at a distance equal to the
radius of gyration from G; zz" is the line of action of the spring; OG is
the ,line of action of centrifugal force; Gi is the line of action of tan
gential acceleration; I a is the angular acceleration couple around G.
* Power.
SPEED VARIATION CONTROL. 391
not only special knowledge of the action of such mechanism but
also shops and funds for experimentation of no mean propor
tions. The analysis here given gives not only an insight into
the action of this particular mechanism but gives an extended
application of various principles of mechanics. In this analysis,
there is; first, a rather long preliminary statement of principles;
next, the proof of an equation of static equilibrium; then, the
proof of an equation of work, or dynamic, equilibrium; and,
finally, some equations dealing with angular inertia.
In Fig. 211 let OC be the position of the crank; s, the position
of the spindle center; A is the center of the eccentric and the
dots indicate positions of A giving shorter cutoff; G is the center
of gravity of the rotating weights of the governing mechanism,
and the dots indicate positions of G corresponding to the different
positions of A; cd is the leverarm of the moment about the
spindle centers s, due to the tension in the spring z\ ef is the
leverarm of the moment of the centrifugal force of the rotating
weights' G about s, since it is equal to the perpendicular let
fall from s on OG. See also Fig. 213.
Division of Weights. The weights are placed in two main
divisions :
Reciprocating Parts valve, valve stem, slide, and the
eccentricrod up to the eccentric.
Rotating Parts the eccentric, its strap, strap end of the
eccentricrod, and the governor bar, GiG 2 .
The center of gravity of all the rotating weights is intended
when the center of gravity of the bar is used in the following
discussion. If the eccentric is heavy a material difference is
made if its weight be neglected.
Forces Acting through the Eccentricrod and their Leverarms.
The force acting in the eccentricrod at any instant is the
resultant of the following forces:
1. The inertia of the reciprocating parts of the valve
mechanism;
2. The friction of the valve;
3. The unbalanced pressure on the end of the valve stem,
since only one end of it is exposed to steam;
4. The weight of the reciprocating parts in vertical engines.
392 THE STEAMENGINE AND OTHER HEATMOTORS
The eccentricrod will be treated as if infinite in length.
Hence, at all parts of a revolution, it will be parallel to the center
line of the engine.
The resultant of all the forces in this rod, at any instant, will
pass through the center of the eccentric.
If in Fig. 215 the eccentric center is at the point, a\, the
moment of the force acting in the eccentricrod, at that instant,
about the spindle axis, 61, will be the product of that force and the
leverarm bid. At 120, the leverarm is almost zero; at the
next point, it is negative.
FIG. 212. RitesCarpenter Governor.
Algebraic Signs of Forces, Arms, and Moments. Forces, arms,
and moments may be either positive or negative. We shall
call positive all moments which tend to increase the eccentricity
of the eccentric, i.e., tend to move the center of the eccentric
away from the center of the shaft. Movement in the opposite
direction will be negative. Positive arms are those which com
bined with positive forces will produce positive moments. For
example, the moment of the spring, z, is positive and the moment
of the centrifugal force through OG is negative. Calling the
stroke of the valve toward the shaft its instroke and the stroke
from the shaft its outstroke, we have:
1. The inertia of the reciprocating parts of the valve mech
anism is positive during the first half of the instroke and the
SPEED VARIATION CONTROL.
393
second half of the outstroke. The inertia forces, therefore, produce
negative stress during the second half of the instroke and during
the first half of the outstroke.
2. When the steam pressure is on the outside of the valve
(exhaust inside) the unbalanced pressure on the end of the valve
stem will produce a negative stress in the eccentric rod.
3. Friction produces a positive stress on the instroke and a
negative stress on the outstroke.
4. The weight of the reciprocating parts (in vertical engines)
produces a negative stress during both strokes.
FIG. 213.
FIG. 214.
Gravity. The effect of gravity on the reciprocating parts:
1. Will be called zero in horizontal engines;
2. In vertical engines, will be classed as one of the forces
acting through the eccentricrod as above;
The effect of gravity on the rotating parts:
1. The attraction of gravitation being constant the force
due to the weight of the rotating parts is constant;
2. The leverarm of this force will vary from a maximum
positive, equal to the radius sG, through zero to a maximum
negative equal to sG and back again during the next semi
revolution. Its effect in a complete revolution is zero and
will not affect our static equation of equilibrium to be derived.
Its effect in determining the weight of the bar will be dis
cussed. (Figs. 213 and 214.)
394 THE STEAMENGINE AND OTHER HEATMOTORS.
Conditions of Static Equilibrium. If a body is at rest or is
moving uniformly, it is in a condition of static equilibrium;
hence, the sum of the vertical forces is zero, the sum of the hori
zontal forces is zero and the sum of the moments of all the forces
acting on it is zero. In the case of this governor it will be shown
that absolute static equilibrium for a number of consecutive
instants is not obtainable owing to the incessant variation of one
of the moments. An equation of static equilibrium for 'a revo
lution can be written by finding the mean moment of the forces
and arms that vary in amount and sign.
To find this mean moment we shall assume the engine to be
revolving at constant speed. In the case of the flywheel, we
found that it had no value in regulating the number of revolu
tions per minute but had very great value in regulating the speed
during a revolution. As the flywheel absorbs the excess or deficit
of work put into the crankpin through the connectingrod, so
the governor bar absorbs or gives out work through exceedingly
small variations of speed. These variations occur if the engine
is supposed to be rotating uniformly. In case the engine speeds
up or slows down an entirely different use of the bar arises through
its angular acceleration aiding centrifugal force in bringing the
eccentric center to a new position. This phase of the use of
the bar is discussed last.
The static equation of equilibrium for a revolution involves
three moments. These moments are taken around the spindle
axis and are as follows:
1. The tension of the spring is constant for a revolution,
its leverarm is constant, and, as the moment of the spring
tends to increase the eccentricity, the moment will be called
positive.
Let Z = tension of the spring,
cd = the lever arm.
Moment of the spring = +Z(cd).
2. At constant speed the centrifugal force of the revolving
parts concentrated at G and with an arm ef, would have a
constant moment,
Centrifugal moment Q.QW34WRN 2 (ef),
SPEED VARIATION CONTROL. 395
if W= weight of revolving parts;
# = distance of the center of gravity, G, from the center of
the shaft, expressed in feet;
N = number of revolutions per minute.
The negative sign is used as centrifugal force tends to decrease
the eccentricity.
3. The third force is the resultant force in the eccentricrod
passing through the eccentric center. Not only is this a variable
force but its leverarm about the spindle, s, is variable.
When we remember, however, that a point on the surface of a
crankpin revolves once around the axis of the crankpin in one
revolution of the latter about the axis of the shaft we perceive
that the center of the eccentric and the center of gravity of the
rotating weights revolve in circles about the axis of the spindle.
The radii of these circles are the distances of those centers from
the spindle axis.
To find the mean moment of the third force we shall divide the
path of the eccentric center in its revolution around the spindle
axis into equal parts, say, twelve. We shall find the amount of
the force in the eccentric rod when the eccentric center is at each
of these points and multiply the force so found by the perpen
dicular let fall from the spindle center on the axis of the eccentricrod
produced. The mean of the products found arithmetically is the
mean moment required.
To find the resultant pressure acting at each of the twelve
positions of the eccentric center, it is best to rectify the path of
eccentric center, 2na\bi, Fig. 215, and at each point lay off the
positive or negative pressures as follows (Fig. 217) :
The force due to the inertia of reciprocating parts is
/= 0.0000284 wrN 2 cos 0,
where w= weight of reciprocating parts of valve mechanism 4 ,
r = eccentricity in inches]
N = the number of revolutions per minute;
= angle swept through.
By laying off the values of / so found, some such curve as
A (Fig. 217) is obtained. Had valve positions instead of eccen
396
THE STEAMENGINE AND OTHER HEATMOTORS.
trie center positions been used two straight lines would have
replaced the double curve, A.
The friction of the valve is a variable quantity. It varies
with the construction of the valve, the amount of wear and the
lubrication. In the diagram, the unbalanced steam pressure on
the end of the valve stem, the friction and the weight of the
reciprocating parts is indicated by that part of each ordinate
included between the curves A and B so that the ordinates of B
indicate the resultant pressure in the eccentricrod at the corre
sponding positions of the eccentric center. From Fig. 217, we
FIG. 215.
see that these ordinates pass through zero value at 90 and 300
approximately.
The corresponding leverarms are shown in Fig. 215, b\c\
being the arm for the force in the eccentricrod when the eccentric
is on the dead center; b 2 C2 being the arm for the force in the
rod when the eccentric center is 30 from its dead center, etc.
The next step is to scale off each force and its leverarm and
find the arithmetical product. The mean of all the products is
the mean turning moment due to the forces in the eccentricrod
during a revolution. This operation is not performed in the
text. We can then write:
Constant centrifugal moment constant spring moment ^the
mean moment of the eccentricrod forces.
SPEED VARIATION CONTROL.
397
To Find the Weight of the Bar to Absorb Unbalanced Work.
The second part of the analysis is devoted to a discussion of a
method of finding the weight of the bar to absorb excess or
deficit of work caused by the unbalanced pressure in the eccentric
rod and by the weight of the rotating parts. As work is the
product of a mean pressure and the distance through which that
mean pressure is exerted, it remains to show the distance through
which the force in the eccentricrod and the weight of the rotating
parts is exerted.
Work of Eccentricrod Forces about the Spindle Axis. Refer
ring to Fig. 216, we see that if abi is the pressure in the eccentric
rod when the eccentric is at a\ then the turning effort of the
pressure, abi (about the spindle bi), is equal to that of a force
8i033030ff
2 10 1
\
FIG. 217.
\
FIG. 218.
ao acting normally to a radius, a i&i. Note that the forces and
their normal components in the figure are drawn at the spindle
centers instead of the eccentric centers to avoid confusion of
lines. By taking all the pressures normal to the line joining the
eccentric and spindle centers, it is evident that the mean normal
pressure multiplied by the circumference of a circle whose radius
is a\b\ would represent the work done by the resultant eccentric
rod pressure during a revolution. In Fig. 218 the line, ef, repre
sents 27rai&i and the ordinates of the full line curve marked aC
represent pressures in the eccentricrod resolved normally to
the lines joining the eccentric and spindle centers. The area
between the curve aC and the base 360 represents the work.
Work of Rotating Weights about the Spindle Axis. The
rotating weights are constant in weight, are concentrated at G,
398 THE STEAMENGINE AND OTHER HEATMOTORS,
and have variable leverarms, since the. perpendicular let fall
from the spindle axis on a vertical through G is variable. In order
to combine the work of the rotating weights with that of the
eccentricrod forces just found, it is best to lay off the work
diagram to the same base line as that of the eccentric rod forces
and to vary the pressures proportionately. Note that the radius
of the circular path of G about the spindle axis differs from the
radius of the eccentric centers' circle. Therefore take the moment
of the rotating weights concentrated at G about the spindle axis
for each 30 of revolution of the eccentric center and divide this
moment in each case by the distance between the eccentric center
and the spindle axis. Lay off the pressure so found at the corre
sponding degree position on the line 360 in Fig. 218 and
obtain the curve in full line marked D. The total work done
during a revolution is seen to be zero.
Combining the curves, C and D, we obtain the brokenline
curve, EHG, Fig .218. The mean ordinate of curve C is of. The
crosshatched area, GHE, is the fluctuation of energy which
must be controlled by the governor acting similarly to a fly
wheel.
gJE
GHI in inchpounds;
/ = moment of inertia of governor weights in inchpounds;
k = desired regulation, viz., greatest allowed variation of speed
= k times the mean speed;
N number of revolutions per minute;
V = velocity of the point at the end of the radius of gyration
in feet per second.*
Variation of Load. Inertia governors depend upon centrifugal
force, linear acceleration, and angular acceleration. Variation
in the type of governor is due to the variation in the amounts
* See Power, Nov. 1906.
SPEED VARIATION CONTROL. 399
of each of the above means of regulation. In one type, for
instance, a powerful centrifugal force is developed, aided at change
of speed by a powerful inertia effect which is largely linear. In the
Rites type, for instance, the centrifugal force action is relatively
small, the linear acceleration is also small as the center of gravity
G is close to the spindle axis s. The angular acceleration, how
ever, is very powerful and acts as a steadying influence.
Inertia Governor during Change of Speed. The centrifugal
force acts along OG and its moment about the spindle is
if W = weight of revolving parts concentrated at G',
R = radius OG (which is variable) in feet;
N = number of revolutions per minute.
While the speed of the shaft is changing, the above cen
trifugal force will be augmented by a small amount of linear and
by a considerable amount of angular inertia.
If the flywheel receives the angular acceleration, a), the center
of mass G receives the linear acceleration OGco, and the weight
W develops the inertia force I =OGa), acting along Gi with
u
an arm hi about the spindle center s. If this arm is small it
is evident that the turning moment will be small.
While the center of gravity of the rotating weights is at G
if we take the polar moment of inertia of the mass of the rotating
weights about G as a center we can find the polar radius of
gyration by dividing the polar moment of inertia by the mass
and extracting the square root. Let MG = k be the polar radius of
gyration. During change of speed an angular acceleration equal to
is developed about G, as shown by the couple marked 7 a . As
indicated in the figure this inertia effects acts with centrifugal
force to hasten the movement of the governor bar.
400 THE STEAMENGINE AND OTHER HEATMOTORS.
Counterbalanc.'ng. If the piston, pistonrod, crosshead, con
nectingrod, crankpin, and crankarms of an engine had no mass,
the engine would be in equilibrium under what we may call the
static pressures, or pressures not used in causing nonuniform
motion of the engine mechanism. As these bodies possess mass
and variable velocity, unbalanced forces exist that cause shaking
or vibration.
Those of the abovementioned bodies that have a motion of
rotation can be balanced by other rotating bodies of proper mass
and radii of action. On the other hand, it is impossible to counter
balance any reciprocating mass by any rotating mass. What can
be done, however, is this. Rotating weights can be so placed as
to transfer the direction of the unbalanced force from one plane to
another. If, for example, horizontal shaking forces are undesirable
(from lack of proper means of absorbing them) by means of rotat
ing weights, these forces may be made vertical.
If we consider the connectingrod as a beam supported at the
crankpin and crosshead pin, the support afforded by each will be
inversely proportional to its distance from the center of gravity of
the rod. This is true no matter what the inclination of the rod
may be. It therefore applies to vertical engines. Therefore (Fig.
55)
W = weight of the connectingrod;
L = length of the rod in inches;
a = distance the center of gravity of the rod is in inches from
the crosshead;
b = distance the center of gravity of the rod is in inches from
the crankpin;
Then Wj is to be considered as a rotating weight concentrated at
Ju
the center of the crankpin and Wj is to be considered as a recip
JL/
rocating weight concentrated at the crosshead. If this is done
the connectingrod may be considered as having no mass.
In discussing the effect of the inertia of the reciprocating parts
on the distribution of power we assumed that the connectingrod
would have its weight equally distributed between the crankpin
and the crosshead. When the inertia of the mass and not the
SPEED VARIATION CONTROL.
401
con
weight of the reciprocating parts is considered, the proper division
K 2
is Wj^j concentrated at the crankpin and considered as a rotating
/ K 2 \
weight, and (1 J 2 )^' concentrated at the crosshead and
sidered as a reciprocating weight, K 2 being the squared radius of
gyration of the rod about the crosshead axis. In most cases
K 2
~j2=%, and for all practical purposes may be so taken. If the
shaking forces are desired, it is a little more accurate to use Wj
and W as the two divisions. (Trans. A. S. M. E., Vol. XXVI.)
Equivalent Weight at the Center of the Crankpin. All the
various rotating weights with their leverarms may be reduced
to one weight at the center of the crankpin. For example, let
the crank shown in Fig. 219 have a connectingrod weighing 136
FIG. 219.
pounds with a center of gravity at 55% of its length from the
crosshead pin.
Weight of one arm(solid), { (10 2 X.78) + (10X10) }2 X .28= 99.68
of both arms =200
" . of crankpin, 9X 2 /X7X.28 = 55
Moment of all parts about the center of shaft, 200X5 + 55X10 =
1550. Dividing by 10", the distance from the center of the crank
pin to the center of the shaft, and we find that 155 pounds concen
trated at the crankpin would have the same moment. In addi
tion there is 55% the weight of the connectingrod to be con
centrated at the same point or a total of 155 and 75 = 230 pounds.
WV 2
The above weight would have a centrifugal force of p.
gti
402
THE STEAMENGINE AXD OTHER HEATMOTORS.
At 210 revolutions per minute this would be
230/4X22X22X5X210X210\
32 \ 7X7X6X60X60 /
2900 Ibs.
WV 2
The horizontal shaking force would be 5 cos 6 = 2900 cos
WV 2
and the vertical shaking force would be rr SU1
2900 sin 6.
A good counterbalance can be obtained by the addition of weights
formed by prolonging the crankarm in single or overhungcrank
engines and prolonging both arms in doublecrank arm engines.
The product of the added weight and the distance of its center
of gravity from the center of the shaft must be 1550 in the above
case, or in general the product of the weight and its gravity arm
equals the sum of the moments of all the rotating weights.
FIG. 220.
In general, rotating weights cannot be balanced by a single
rotating weight, as it is not practically possible to put the center
of gravity of the counterweight in the plane of revolution of the
center of gravity of the unbalanced weights. For equilibrium
it is essential that the moments of all the forces exerted by the
weights about any axis should be zero. In statics, the force
exerted by a weight is equal to the weight; in dynamics, the force
may be put proportional to the product of the weight and its lever
arm if the comparison is restricted to bodies having the same
number of revolutions; if the number of revolutions of the bodies
compared differed, then their forces would be proportional to the
product of their weight, their leverarm, and the square of the
number of their revolutions, as is apparent from the formula for
WV*
centrifugal force, ~ .
SPEED VARIATION CONTROL. 403
In Fig. 220, suppose that we wish to counterbalance equivalent
weights W h and W l concentrated at the crankpins of a compound
engine having two cranks at right angles to one another. Let
W h be balanced by the weights WI H and w 2 h placed opposite the
crankpin as shown. Since all parts of the shaft have the same
angular velocity the moment about the axis of the shaft is zero
when
But the moments of the centrifugal forces of Wi h and w 2 h about
the rotating axis X h X\ h must also be zero to prevent shaking
about that axis.
(wi h rfya = w 2 h r 2 h (b + c).
Similarly, W l R l = wfa 1 + w 2 l r 2 l ,
and w\ l ri l (a + b) = w 2 r 2 (c) .
The weights on each wheel may be combined into one weight.
Let W r be the desired resultant weight and R r its radius (distance
of its center of gravity to the axis of shaft). Then
The direction and magnitude of the product W r Rr can be easily
obtained by laying off wi h ri h and wi l ri l as the two sides of a
right triangle and WrRr will be the hypothenuse. The direction
in which W r is to be laid off on the wheel is shown by the angle
at the base of the triangle. In a similar manner a single weight
may be obtained for the two weights on the other wjieel.
Shakingforces. The following method may be used in find
ing the shakingforces due to the inertia of the reciprocating
masses . and the centrifugal force of the unbalanced rotating
masses as represented by an equivalent weight rotating at the
crankpin center.
In Fig. 221 the force required to accelerate the reciprocating
parts in Fig. 205 at every 30 degrees (to a different scale) has
been combined with an assumed centrifugal force. The direc
tion in which forces act is indicated by the order of the let
ters.
In any horizontal engine let Oa\, Fig. 221, be the centrifugal
404 THE STEAMENGINE AND OTHER HEATMOTORS.
force of all the unbalanced rotating parts. It produces a hori
zontal shakingforce Oc\ and a vertical shakingforce cia\ at
crankangle aoOai. Let a\A\ be the horizontal shakingforce
exerted against the left cylinderhead at this crankangle. It is
equal to 3(d'c), Fig. 205. Then OA\ indicates the shakingforce at
the crankangle a 0ai. Its horizontal component is evidently the
sum of Oc\ and a\A\. a^A^ and a^A^ are equal to HI and 5/
respectively to the new scale (Fig. 205.)
Suppose counterweights are added in such manner that their
centrifugal force is equivalent to a force b 2 acting at the crank
pin. This force not only counteracts the centrifugal force of the
unbalanced rotating parts Oa 2 , but also alters the horizontal
and vertical components of the shakingforces due to the recipro
cating parts. The amount of these alterations is evident when
we join 61 and A\, b 2 and At, etc. For the previous shakingforce
OAi is now to be combined with the introduced force bi 0, and the
result is a shakingforce b\A\, OA 2 is to be combined with b 2 y
giving b 2 A 2 . Lay off OB\, OB'2, etc., parallel to b\A\, b 2 A 2 , etc.
Join #o, Bi, B 2 , etc. It is accidental that A 2 falls on the line Obi.
It is well to note the peculiar direction taken by OB\ and OB 2)
etc., with reference to the crankpositions to which they belong.
The effect of increasing and decreasing the value of 61 should be
noted. In the addition of counterweights it must be remembered
that their effect varies with the square of the revolutions. If a
balance exists at one speed it will exist at all speeds ; the shaking
SPEED VARIATION CONTROL. 405
force only varies with some function of the square of the speed
of the parts out of balance.
It is evident that these circular diagrams may be laid off in
the following way also. Rectify the crankcircle; lay off the hori
zontal or vertical components of the shakingforces at right angles
to the rectified circle at the division point indicated by the crank
position.
For a singlecrank horizontal engine without counterbalance
the horizontal shakingforces are a maximum at the ends of the
stroke, and are zero just before and just after the 90degree position,
For two cranks 180 degrees apart, with infinite rods the inertia
of the reciprocating masses, if of equal weight, would balance one
another; with finite rods this is not the case, and there are two
maxima and two minima. The shaking, however, is much less
than in the singlecrank engine.
For a triple^crank engine of equal weights of reciprocating
parts for each engine the sum of the inertia effects, no matter
what the length of the connectingrod, is zero. This can be shown
by adding /j, / 2 , and / 3 in the following equations and showing
that the sum is zero.
7?
cos W +120)
(0+240) +y cos 2(0 +240) V
gAri\ L
The ordinary form of two engines with cranks at right angles
has smaller shakingforces than a single engine of equal size, but
greater shakingforces than any of the other types mentioned. The
shakingforce diagrams should not be confused with the tangential
force diagrams.
Determination of Angular Displacement. To insure the satis
factory operation of two alternatingcurrent generators when work
ing in parallel, the maximum amount of angular variation or dis
placement should not exceed 2.5 degrees of phase departure from
the. mean position (shown by a theoretical engine moving with
uniform velocity) during any revolution.
406 THE STEAMENGINE AND OTHER HEATMOTORS.
Having designed all the reciprocating and rotating parts and
their counterweights, and having determined their centers of grav
ity, it is necessary to calculate the phase departure of an engine
intended for work in the class described above.
At Top
FIG. 222.
Curve ol' Displacement
FIGS. 223, 224, 225.
The following description is taken from Vol. XXII, Trans.
A. S. M. E. The method of obtaining the crank diagram will be
omitted, as the only practical difference between the author's
method and our own is that he uses the total pressure on the
piston of each engine, and we used the pressure per square inch in
SPEED VARIATION CONTROL. 407
obtaining the diagram of crank effort. Twelve crank positions
are used as in Fig. 205. Fig. 222 represents the individual and
Figs. 223225 the combined cards, MM being the line of mean
effort.
"We will now consider the equivalent mass of the rotating
parts of the engine concentrated at the crankpin, and as having
no other velocity than that produced by the positive and negative
forces represented by those portions of the curve of crank effort on
either side of the line MM. For convenience in estimating we will
assume that the applied force is uniform within each of the twelve
spaces; i.e., this tangential force for each space, expressed in
pounds above or below the normal MM, is equal to the mean
height of each space above or below the line MM and is exhibited
in Table A, page 408.
" The velocity gained or lost during each twelfth of a revolution
is deduced as fellows :
" The equivalent weight of the revolving parts at crank radius
(2.5') equals 3,367,000 pounds. The velocity of the crankpin is
2.5' X2x3.1416x75 revs.
fi( .  =19.63 feet per second. As the number
of revolutions per second equals ^ = 1.25, the number of spaces
traversed per second equals 15, and the time for each space .0667
, W 3,367,000
second. The mass of the revolving parts equal ; = O IT^ =
g 6Z.4
T 06666
104,584. Hence ^ = ' g , = .000,000,637,4 equals the accelera
T
tion for a force of one pound. Therefore TT xF equals the velocity
gained or lost during each interval, as shown in column A, Table
A, page 408.
" Now, if the velocity of the pin be assumed normal at the begin
ning of the stroke, the velocity attained up to the end of the various
spaces will be equal to the algebraic sum of the velocities gained
during each of the preceding spaces. These velocities attained up
to the end of each space are shown in column V". As the actual
velocity of the crankpin at the beginning of the stroke was not
normal as assumed, it becomes necessary to correct the values of
408 THE STEAMENGINE AND OTHER HEATMOTORS.
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SPEED VARIATION CONTROL 409
V" accordingly. The integrated sum of the velocities above and
below normal attained during one revolution must be zero, there
fore the correction to be applied equals the algebraic sum of the
velocities V" divided by the number of spaces (twelve in this case) .
Thus the correction is .033, and this amount must be deducted
from the values of V" in order to arrive at the true velocity attained
up to the end of the successive intervals. With these true veloci
ties, given in column V of Table A, as ordinates, plot the curve
of velocity V (Fig. 224), where BB represents the mean velocity
of the pin.
"From the curve of velocity V (Fig. 224), ascertain the average
velocity above or below the mean velocity, BB, during each space,
shown in column V of the table. With these velocities given, the
space actually passed over during each interval can be readily
calculated by multiplying the value's of V by .0667, the time for
one space. The figures in column S" were deduced in this way.
" If the position of the pin be assumed normal at the beginning
of the stroke, its distance from normal up to the end of the respective
intervals will be equal to the algebraic sum of the spaces actually
passed over, ahead of or behind the mean position, during each
interval. Therefore the figures in column S' are equal to the
integrated sum of the preceding figures in column S". As the
position of the crankpin at the beginning of the stroke was not
zero, as assumed, a correction must be applied to the values of S'.
Since the integrated sum of the distances ahead of or behind the
mean position must be equal to zero, the value of the correction
is equal to the ratio of the algebraic sum of the values of S' to the
number cf spaces. The value of the correction is .0019, and is to
be added to the values of S' to get the true displacement or dis
tance from normal of the pin at the end of each interval, the figures
for same being shown in column S. Since one foot corresponds to
22.92 degrees of arc, measured on the crankpin circle, the number
of degrees of arc from normal equals the product of the true dis
tances in feet from normal (column S) by 22.92. The number of
degrees of arc from normal deduced in this way are shown in the
next to the last column of Table A. Finally, as there are 40
poles on the generator, there will be 20 cycles or changes of phase
per revolution, therefore one degree of arc equals 20 degrees of
410 THE STEAMENGINE AND OTHER HEATMOTORS.
phase, and the displacement (shown in the last column of table)
at the end of each interval may be calculated by multiplying the
corresponding degrees of arc by 20. With the values of the dis
placement in degrees of phase from normal as orclinates, the curve
of displacement (Fig. 225) was plotted, in which CC represents the
mean position of the crankpin."
CHAPTER XIV.
STEAMENGINE TESTS.
Rules for Conducting Steamengine Tests. Code of 1902 A. S.
M. E.* A large part of this code has been given in the text
(markedf). Such parts will not be repeated.
I. Object of the Test. Ascertain at the outset the specific ob
ject of the test, whether it be to determine the fulfilment of a
contract guarantee, to ascertain the highest economy obtainable,
to find the working economy and defects under conditions as they
exist, to ascertain the performance under special conditions, to
determine the effect of changes in the conditions, or to find the
performance of the entire boiler and engine plant, and prepare
for the test accordingly.
No specific rules can be laid down regarding many of the prep
arations to be made for a test, so much depends upon the local
conditions; and the matter is one which must be left mainly to
the good sense, tact, judgment, and ingenuity of the party under
taking it. One guiding principle must ever be kept in mind,
namely, to obtain data which shall be thoroughly reliable for the
purposes in view. If questions of contract are to be settled, it
is of the first importance that a clear understanding be had with
all the parties to the contract as to the methods to be pursued
putting this understanding, if necessary, in writing unless these
are distinctly provided for in the contract itself. The preparations
for the measurement of the feedwater and of the various quantities
of condensed water in the standard heatunit test should be made
in such manner as to change as little as possible the working
conditions and temperatures of the plant.
* Trans. A. S. M. E., 1903.
411
412 THE STEAMENGINE AND OTHER HEATMOTORS.
II. General Condition of the Plant. Examine the engine and
the entire plant concerned in the test; note its general condition
and any points of design, construction, or operation which bear on
the objects in view. Make a special examination of the valves
and pistons for leakage by applying the working pressures with
the engine at rest, and observe the quantity of steam, if any,
blowing through per hour.
If the trial has for an object the determination of the highest
efficiency attainable, the valves and pistons must first be made
tight and all parts of the engine and its auxiliaries, and all other
parts of the plant concerned, should be put in the best possible
working condition.
The method of testing the valves and pistons for leakage in a
Corliss engine, or one in which the admissionvalves can be operated
independently of the exhaustvalves, is as follows : Close the two
steamvalves, open the two indicatorcocks, and admit a full pres
sure of steam into the chest by opening the throttle valve. The
movement of the startingbar, first one way and then the other,
so as to close one exhaustvalve and then the other, causes the
leakage through the steam valves to escape from the open indicator
cock, where it becomes visible. The quantity of leakage is judged
by the force of the current of steam blowing out.
To test the exhaustvalves and piston, the best method is to
block the flywheel, so that the piston will be at a short distance
from the end of the stroke, and turn on the steam. The leakage
escapes to the exhaustpipe, and can be observed at the open
atmospheric outlet. If the outlet is not visible, and there is a
valve in the exhaustpipe, this can be shut and the indicator
cock opened, thereby deflecting the steam which leaks and causing
it to appear at the indicatorcock. In the case of a condensing
engine where no atmospheric pipe is provided, and there is no
opening that can be made in the exhaustpipe in front of the
condenser, some idea can be obtained in regard to the amount of
leakage by observing how rapidly the condenser is heated. It is well
to make these tests with the piston in different positions so as
to cover the whole range of the length of the stroke.
Another but more approximate method of testing leakage is
called the "time method." Instead of observing the steam that
STEAMENGINE TESTS. 413
actually blows through the valves or pistons to be tested, they are
subjected to full steampressure, and when the parts are thoroughly
heated, the throttle valve is shut and the length of time observed
which is required for the pressure to disappear. In testing the
piston and exhaustvalves, the flywheel is blocked as before, and,
preferably, an indicator is attached, and a line drawn on a blank
card at intervals of, say, onequarter of a minute after the valve
is shut, thereby making a record of the fall of pressure. In a tight
engine the fall of pressure is slow, whereas in a leaky engine it
is sometimes very rapid. The relative condition of the engine
as compared with a tight engine must be judged by an observer,
who must, of course, have had experience in tests of this kind on
engines in various conditions.
The leakage of a piston can always be determined by removing
the cylinderhead and observing what blows through the open
end with the pressure of steam behind it. The advantage of the
"time method" is that it saves the labor and time required in
removing the cylinderhead and replacing it, which, in cases of
large engines, is considerable.
Leakage tests of singlevalve engines cannot be made as satis
factorily as those of the Corliss type and other fourvalve engines.
The best that can be done as regards the valve is to place it at or
near the center of its travel, covering both ports, and then make
the test under full pressure. The valve and piston can be tested
as a whole by blocking the flywheel and opening the throttle
valve in the same way as in other engines.
In testing compound engines for leakage, the work is somewhat
simplified in case of any one cylinder as compared with a single
engine. For example, leakage of the highpressure cylinder can
be revealed by opening the indicatorcock on the proper end of
the lowpressure cylinder, the steamvalve of that cylinder being
open. The test of leakage of the lowpressure exhaustvalves
and piston when the "time method" is used can be based on the
indications of the receiver gage instead of using an indicator.
In that case the fall of pressure due to leakage is read from the
gage.
The tests thus far referred to are qualitative, and not quantita
tive. It is practical in some cases to determine the quantity of
414 THE STEAMENGINE AND OTHER HEATMOTORS.
leakage under any set of conditions by collecting the steam which
passes through, condensing it and weighing it. This can be readily
done when there is a surface condenser, and it can be done in the ab
sence of such a condenser by attaching a small pipe to the exhaust
and carrying the steam which escapes into a tank of water and
condensing it. How much dependence can be placed upon the
results of such a quantitative test as showing the actual quantity
of leakage which occurs when the valves and pistons are in motion
must be left to the judgment of the person who makes the test.
When full information is desired, it is well to test the valves
and pistons in several different positions, so as to cover the whole
range of action.
In Corliss engines the leakage of the piston with the engine
in operation can be observed by removing the cylinderhead,
disconnecting the steam and exhaustvalves at the head end, and
setting the engine to work with steam admitted at the crank end.
III. Dimensions, etc. Measure or check* the dimensions of
the cylinders in any case, this being done when they are hot. If
they are much worn, the average diameter should be determined.
Measure also the clearance, which should be done if possible by
filling the spaces with water previously measured, the piston
being placed at the end of the stroke. If the clearance cannot
be measured directly, it can be determined approximately from
the working drawings of the cylinder.
Measure also the dimensions of auxiliaries and accessories,
also those of the boilers so far as concerned in attaining the objects.
It is well to supplement these determinations with a sketch or
sketches showing the general features and arrangement of the
different parts of the plant.
To measure the clearance by actual test, the engine is caref illy
set on the center, with the piston at the end where the measurement
is to be taken. Assuming, for example, a Corliss engine, the best
method to pursue is to remove the steamvalve so as to have
access to the whole steamport, and then fill up the clearance space
with water, which is poured into the open port through a funnel.
The water is drawn from a receptacle containing a sufficient quan
tity which has previously been measured. When the whole space,
including the port, is completely filled, the quantity left is measured,
STEAMENGINE TESTS. 415
and the difference shows the amount which has been poured in.
The measurement can be most easily made by weighing the water
and the corresponding volume determined by calculation, making
proper allowance for its temperature. The proportion required
is the volume in cubic inches thus found, divided by the volume
of the piston displacement, also in cubic inches, and the result ex
pressed as a decimal. In this test care should be taken that no
air is retained in the clearance space when it is filled with water.
The only difficulty which arises in measuring the clearance in
this way is that occurring when the exhaustvalves and piston are
not tight, so that, as the water is poured in, it flows away and is
lost. If the leakage is serious, no satisfactory measurement can be
made, and it is better to depend upon the volume calculated from
the drawing. If not too serious, however, an allowance can be
made by carefully observing the length of time consumed in pour
ing in the water; then, after a portion of the water has leaked out,
fill up the space again, taking the time, and measuring the quantity
thus added, determining in this way the rate at which the leakage
occurs. Data will thus be obtained for the desired correction.
IV. Coal. When the trial involves the complete plant, embrac
ing boilers as well as engines, determine the character of coal to be
used. The class, name of the mine, size, moisture, and quality of
the coal should be stated in the report. It is desirable, for pur
poses of comparison, that the coal should be of some recognized
standard quality for the locality where the plant is situated.
For New England and that portion of the country east of the
Alleghany Mountains good anthracite egg coal containing not
over 10% ash, and semibituminous Clearfield (Pa.), Cumberland
(Md.), and Pocahontas (Va.) coals are thus regarded. West of the
Alleghany Mountains, Pocahontas (Va.) and New River (W. Va.)
semibituminous and Youghiogheny or Pittsburg bituminous coals
are recognized as standards.
V. Calibration of Instruments. All instruments and apparatus
should be calibrated and their reliability and accuracy verified by
comparison with recognized standards. Such apparatus as is
liable to change or become broken during a test, as gages, indicator
springs, and thermometers, should be calibrated before and after
the test. The accuracy of scales should be verified by standard
416 THE STEAMENGINE AND OTHER HEATMOTORS.
weights. When a watermeter is used special attention should be
given to its calibration, verifying it both before and after the trial,
and, if possible, during its progress, the conditions in regard to
waterpressure and rate of flow being made the same in the cali
brations as exist throughout the trial.
(a) Gages. For pressures above the atmosphere, one of the
most convenient, and at the same time reliable, standards is the
deadweight testing apparatus which is manufactured by many
of the prominent gagemakers. It consists of a vertical plunger
nicely fitted to a cylinder containing oil or glycerine, through the
medium of which the pressure is transmitted to the gage. The
plunger is surmounted by a circular stand on which weights may
be placed, and by means of which any desired pressure can be
secured. The total weight, in pounds, on the plunger at any time,
divided by the average area of the plunger and of the bushing
which receives it, in square inches, gives the pressure in pounds
per square inch.
Another standard of comparison for pressure is the mercury
column. If this instrument is used, assurance must be had that
it is properly graduated with reference to the ever varying zero
point, that the mercury is pure, and that the proper correction is
made for any difference of temperature that exists, compared with
the temperature at which the instrument was graduated.
For pressures below the atmosphere an airpump or some other
means of producing a vacuum is required, and reference must be
made to a mercury gage. Such a gage may be a U tube having a
length of 30 inches or so, with both arms properly filled with
pure mercury.
(b) Thermometers. Standard thermometers are those which
indicate 212 F. in steam escaping from boiling water at the
normal barometrical pressure of 29.92 inches, the whole stem up
to the 212clegree point being surrounded by the steam; and
which indicate 32 F. in melting ice, the stem being likewise com
pletely immersed up to the 32degree point, and which are
calibrated for points beyond and between these two reference
points. We recommend, for temperatures between 212 and 400
F., that the comparison of the thermometer be made with the
temperature given in Regnault's Steam Tables, the method required
STEAMENGINE TESTS. 417
being to place it in a mercury well surrounded by saturated steam
under sufficient pressure to give the desired temperature. The
pressure should be accurately determined, as pointed out in sec
tion (a), and the thermometer should be immersed to the same
extent as it is under its working condition.
Thermometers in practice are seldom used with the stems
fully immersed, consequently when they are compared with the
standard the comparison should be made under like conditions,
and practically under the working conditions, whatever those
happen to be.
If pyrometers of any kind are used, they should be compared
with a mercury thermometer within its range, and if extreme
accuracy is required, with an airthermometer, or a standard
based thereon, at higher points, care being taken that the medium
surrounding the pyrometer, be it air or liquid, is of the same uni
form temperature as that surrounding the standard.
(c) Indicatorsprings. See text.
(d) Watermeters. A good method of calibrating a water
meter is the following, reference being made to Fig. 226:
Two tees, A and B, are placed in the feedpipe, and between
them two valves, C and D. The meter is connected between the
outlets of the tees A and B. The valves E and F are placed one
on each side of the meter. When the meter is running, the valves
E and F are opened, and the valves C and D are closed. Should
an accident happen to the meter during the test, the valves E
and F may be closed and the valves C and D opened, so as to
allow the feedwater to flow directly into the boiler. A small
bleeder, (r, is placed between the valves C and D. The valve G
is opened when the valves C and D are closed, in order to make
sure that there is no leakage. A gage is attached at H. When
the meter is tested, the valves C, D, and F are closed and the
valves E and / are opened. The water flows from the valve /
to a tank placed on weighingscales. In testing the meter the
feedpump is run at the normal speed, and the water leaving the
meter is throttled at the valve / until the pressure shown by the
gage H is the same as that indicated when the meter is running
under the normal conditions. The piping leading from the valve
/ to the tank is arranged with a swinging joint, consisting merely
418
THE STEAMENGINE AND OTHER HEATMOTORS,
of a loosely fitting elbow, so that it can be readily turned into the
tank or away from it. After the desired pressure and speed
have been secured, the end of the pipe is swung into the tank the
1
B
\ f
* IG. 226.
instant that the pointer of the meter is opposite some graduation
mark on the dial, and the water continues to empty into the
tank while any desired number of even cubic feet are discharged,
after which the pipe is swung away from the tank. The tests
should be made by starting and stopping at the same graduation
mark on the meterdial, and continued until at least 10 or 20 cubic
feet are discharged for one test. The water collected in the tank is
then weighed.
The water passing the meter should always be under pressure
in order that any air in the meter may be discharged through
the vents provided for this purpose. Care should be taken that
there is no air contained in the feedwater. Should the feed
water pump draw from a hotwell, the height of the water in the
hotwell must never be as low as the suctionpipe of the pump.
In case the speed of the feedpump cannot be regulated, as occurs
in some cases where it is driven directly from the engines, a by
pass should be connected with the pipe leading from the pump
to allow some of the water to flow back into the hotwell, if the
STEAMENGINE TESTS. 419
pump lowers the water in the hotwell beyond a given mark,
The meter should be tested both before and after the engine
trial, and several tests of the meter should be made in each case
in order to obtain confirmative results. It is well to make pre
liminary tests to determine whether the meter works satisfactorily
before connecting it up for an engine trial. The results should
agree with each other for two widely different rates of flow.
VI. Leakages of Steam, Water, etc. In all tests except those
of a complete plant made under conditions as they exist, the
boiler and its connections, both steam and feed, as also the steam
piping leading to the engine and its connections, should, so far
as possible, be made tight. If absolute tightness cannot be
obtained (in point of fact it rarely can be), proper allowance should
be made for such leakage in determining the steam actually con
sumed by the engine. This, however, is not required where a
surface condenser is used and the water consumption is determined
by measuring the discharge of the airpump. In such cases it is
necessary to make sure that the condenser is tight, both before
and after the test, against the entrance of circulating water, or
if such occurs to make proper correction for it, determining it
under the working difference of pressure. Should there be exces
sive leakage of the condenser it should be remedied before the test
is made. When the steam consumption is determined by measur
ing the discharge of the airpump, any leakage about the valve
or pistonrods of the engine should be carefully guarded against.
Make sure that there is no leakage at any of the connections
with the apparatus provided for measuring and supplying the feed
water which could affect the results. All connections should, so
far as possible, be visible and be blanked off, and where this cannot
be done, satisfactory assurance should be obtained that there is
no leakage either in or out.
It is not always necessary to blank off a connectingpipe to
make sure that there is no leakage through it. If satisfactory
assurance can be had that there is no chance for leakage, this is
sufficient. For example, where a straightway valve is used for
cutting off a connecting pipe, and this valve has double seats with
a hole in the bottom between them, this being provided with a
plug or petcock, assurance of the tightness of the valve when
420 THE STEAMENGINE AND OTHER HEATMOTORS.
closed can be had by removing the plug or opening the cock.
Likewise, if there is a drainpipe beyond the valve, the fact that no
water escapes there is sufficient evidence of the tightness of the
valve. The main thing is to have positive evidence of the tight
ness of the connections, such as may be obtained by the means
suggested above; but where no positive evidence can be obtained,
or where the leakage that occurs cannot be measured, it is of the
utmost importance that the connections should be broken and
blanked off.
Leakage of reliefvalves which are not tight, drips from traps,
separators, etc., and leakage of tubes in the feedwater heater must
all be guarded against, measured, and allowed for.
It is well, as an additional precaution, to test the tightness of
the feedwater pipes and apparatus concerned in the measurement
of the water by running the pump at a slow speed for, say, fifteen
minutes, having first shut the feedvalves at the boilers. Leakage
will be revealed by the disappearance of water from the supply tank.
In making this test, a gage should be placed on the pump discharge
in order to guard against undue or dangerous pressure.
To determine the leakage of steam and water from a boiler and
steampipes, etc., the watergage glass method may be satisfactorily
employed. This consists in shutting off all the feedvalves (which
must be known to be tight) or the main feedvalve, thereby stop
ping absolutely the entrance or exit of water at the feedpipes to
the boilers  then maintaining the steampressure (by means of a
very slow fire) at a fixed point, which is approximately that of the
working pressure and observing the rate at which the water falls
in the gageglasses. It is well in this test, as in other work of this
character, to make observations every ten minutes, and to con
tinue them for such a length of time that the differences between
successive readings attain a constant rate. Generally the condi
tions will have become constant at the expiration of fifteen minutes
from the time of shutting the valves, and thereafter the fall of
water due to leakage of steam and water becomes approximately
constant. It is usually sufficient after this time to continue the
test for one hour, thereby taking six tenminute readings. When
this test is finished, the amount of leakage is determined by calcu
lating the volume of water which has disappeared, using the area
STEAMENGINE TESTS. 421
of the waterlevel and the depth shown on the glass, making due
allowance for the weight of one cubic foot of water at the observed
temperature. If possible, the gageglass for this test should be
attached close to the boiler.
If there is opportunity for much condensation to occur and
collect in the steampipe during the leakage test, the quantity
should be determined as closely as desirable and properly allowed
for.
In making a test of an engine where the steam consumption is
determined from the amount of water discharged from a surface
condenser, leakage of the pistonrods and valverods should be
guarded against; for if these are excessive, the test is of little use,
as the leakage consists partly of steam that has already done work
in the cylinder and of water condensed from the steam when in
contact with the cylinder. If such leakage cannot be prevented,
some allowance should be made for the quantity thus lost. The
weight of water as shown at the condenser must be increased by
the quantity allowed for this leakage.
VII. Duration of Test. The duration of a test should depend
largely upon its character and the objects in view. The standard
heat test of an engine, and likewise a test for the simple determina
tion of the feedwater consumption, should be continued for at
least five hours, unless the class of service precludes a continuous
run of such duration. It is desirable to prolong the test the
number of hours stated to obtain a number of consecutive hourly
records as a guide in analyzing the reliability of the whole.
Where the water discharged from the surface condenser is
measured for successive short intervals of time, and the rate is
found to be uniform, the test may be of a much shorter duration
than where the feedwater is measured to the boiler. The longer
the test with a given set of conditions, the more accurate the
work, and no test should be so short that it cannot be divided into
several intervals which will give results agreeing substantially with
each other.
The commercial test of a complete plant, embracing boilers as
well as engine, should continue at least one full day of twentyfour
hours, whether the engine is in motion during the entire time or
not. A continuous coal test of a boiler and engine should be of at
422 THE STEAMENGINE AND OTHER HEATMOTORS.
least ten hours' duration or the nearest multiple of the interval
between times of cleaning fires.
VIII. Starting and Stopping a Test. (a) Standard Heat Test
and Feedwater Test of Engine. The engine having been brought
to the normal condition of running, and operated a sufficient
length of time to be thoroughly heated in all its parts, and the
measuringapparatus having been adjusted and set to work, the
height of water in the gageglasses of the boilers is observed,
the depth of water in the reservoir from which the feedwater is
supplied is noted, the exact time of day is observed, and the
test held to commence. Thereafter the measurements determined
upon for the test are begun and carried forward until its close.
If practicable, the test may be commenced at some even hour
or minute, but it is of the first importance to begin at such time
as reliable observations of the water heights are obtained, what
ever the exact time happens to be when these are satisfactorily
determined. When the time for the close of the test arrives,
the water should, if possible, be brought to the same height in
the glasses and to the same depth in the feedwater reservoir
as at the beginning, delaying the conclusion of the test if necessary
to bring about this similarity of conditions. If differences occur
the proper corrections must be made.
Care should be taken in cases where the activity of combustion
in the boiler furnaces affects the height of water in the gageglasses
that the same condition of fire and drafts are operating at one
time as at the other. For this reason it is best to start and stop
a test without interfering with the regularity of the operation of
the feedpump, provided the latter may be regulated to run so as
to supply the feedwater at a uniform rate. In some cases where
the supply of feedwater is irregular, as, for example, where an
injector is used of a larger capacity than is required, the supply
of feedwater should be temporarily shut off.
It is important to use great care in obtaining the average height
of water in the glasses, taking sufficient time to satisfactorily
judge of the full extent of the fluctuation of the waterline and
thereby its mean position. It is important also to refrain from
blowing off the water column or its connecting pipes either during
the progress of the test or for a period of an hour or more prior
STEAMENGINE TESTS. 423
to its beginning. Such blowing off changes the temperature of
the water within and thereby affects its specific gravity and height.
To mark the height, of water in a gageglass in a convenient way,
a paper scale mounted on wood and divided into tenths of inches
may be placed behind it or at its side.
(b) Complete Boiler and Engine Test. For a continuous
running test of combined engine or engines, and boiler or boilers,
the same directions apply for beginning and ending the feedwater
measurements as that just referred to under section, (a). The
time of beginning and ending such a test should be the regular
time of cleaning the fires, and the exact time of beginning and
ending should be the time when the fires are fully cleaned, just
preparatory to putting on fresh coal. In cases where there are
a number of boilers, and it is inconvenient or undesirable to clean
all the fires at once, the time of beginning the test should be
deferred until they are all cleaned and in a satisfactory state,
all the fires being then burned down, to a uniformly thin condition,
the thickness and condition being estimated and the test begun just
before firing the new coal previously weighed. The ending of the
test is likewise deferred until all the fires are satisfactorily cleaned,
being again burned down to the same uniformly thin condition
as before, and the time of closing being taken just before replenish
ing the fires with new coal.
For a commercial test of a combined engine and boiler, whether
the engine runs continuously for the full twenty fourhours of the
day or only a portion of the time, the fires in the boilers being
banked during the time when the engine is not in motion, the begin
ning and ending of the test should occur at the regular time of
cleaning fires, the method followed being that already given. In
cases where the engine is not in continuous motion, as, for example,
in textile mills, where the workingtime is ten or eleven hours out
of the twentyfour, and the fires are cleaned and banked at the
close of the day's work, the best time for starting and stopping a
test is the time just before banking, when the fires are wellburned
down and the thickness and condition can be most satisfactorily
judged. In these, as in all other cases noted, the test should be
begun by observing the exact time, the thickness and condition
of the fires on the grates, the height of water in the gageglasses of
424 THE STEAMENGINE AND OTHER HEATMOTORS.
the boilers, the depth of water in the reservoir from which the
feedwater is supplied, and other conditions relating to the trial,
the same observations being again taken at the end of the test,
and the conditions in all respects being made as nearly as possible
the same as at the beginning.
IX. Measurement of Heatunits Consumed by the Engine. The
measurement of the heat consumption requires the measurement
of each supply of feedwater tp the boiler, that is, the water
supplied by the main feedpump, that supplied by auxiliary
pumps, such as jacketwater, water from separators, drips, etc.,
and water supplied by gravity or other means; also the deter
mination of the temperature of the water supplied from each
source, together with the pressure and quality of the steam.
The temperatures at the various points should be those apply
ing to the working conditions. The temperature of the feed
water should be taken near the boiler. This causes the engine
to suffer a disadvantage from the heat lost by radiation from
the pipes which carry the water to the boiler, but it is, never
theless, advisable on the score of simplicity. Such pipes would
therefore be considered a portion of the engineplant. This con
forms with the rule already recommended for the tests of pumping
engines, where the duty per million heatunits is computed from
the temperature of the feedwater taken near the boiler. It
frequently happens that the measurement of the water requires
a change in the usual temperature of supply. For example,,
where the main supply is ordinarily drawn from a hotwell, in
which the temperature is, say, 100 F., it may be necessary,
owing to the low level of the well, to take the supply from some
source under a pressure or head sufficient to fill the weighing
tanks used, and this supply m.ay have a temperature much below
that of the hotwell, possibly as low as 40 F. The temperature
to be used is not the temperature of the water as weighed in
this case, but that of the working temperature of the hot well.
The working temperature in cases like this must be determined
by a special test and included in the logsheets.
In determining the working temperatures, the preliminary or
subsequent test should be continued a sufficient time to obtain
uniform indications and such as may be judged to be an average
STEAMENGINE TESTS. 425
for tjie working conditions. In this test it is necessary to have
some guide as to the quantity of work being done, and for this
reason the power developed by the engine should be determined
by obtaining a full set of diagrams at suitable intervals during
the progress of the trial. Observations should also be made of
all the gauges connected with the plant and of the water heights
in the boilers, the latter being maintained at a un form point,
so as to be sure that the rate of feeding during the test is not
sensibly different from that of the main test.
The heat to be determined is that used by the entire engine
equipment, embracing the main cylinders and all auxiliary cylin
ders and mechanism concerned in the operation of the engine,
including the airpump, circulatingpump, and feedpumps, also
the jacket and reheater when these are used. No deduction is
to be made for steam used by auxiliaries, unless these are shown
by the test to be unduly wasteful. In this matter an exception
should be made in cases of guarantee tests, where the engine
contractor furnishes all the auxiliaries referred to. He should,
in that case, be responsible for the whole, and no allowance should
be made for inferior economy, if such exists. Should a deduction
be made on account of the auxiliaries being unduly wasteful, the
method of waste and. its extent, as compared with the wastes of
the main engine or other standard of known value, shall be
reported definitely.
The steam pressure and the quality of the steam are to be
taken at some point conveniently near the throttle valve. The
quantity of steam used by the calorimeter must be determined
and properly allowed for.
X. Measurement of Feedwater or Steam Consumption of
Engine. The method of determining the steam consumption
applicable to all plants is to measure all the feedwater supplied
to the boilers and deduct therefrom all the water discharged by
separators and drips, as also the water and steam which escapes
on account of leakage of the boiler and its pipe connections and
leakage of the steam main and branches connecting the boiler
and the engine. In plants where the engine exhausts into a surface
condenser the steam consumption can be measured by determining
the quantity of water discharged by the airpump, corrected for
426 THE STEAMENGINE AND OTHER HEATMOTORS.
any leakage of the condenser, and adding thereto the steam used
by the jackets, reheaters, and auxiliaries as determined inde
pendently. If the leakage of the condenser is too large to satis
factorily allow for it, the condenser should, of course, be repaired
and the leakage again determined before making the test.
In measuring the water it is best to carry it through a tank
or tanks resting on platform weighingscales suitably arranged
for the purpose, the water being afterwards emptied into a reservoir
beneath, from which the pump is supplied.
The simplest apparatus of this kind, having a capacity of, say,
6000 pounds of water per hour, consists of a small hogshead con
nected to the suctionpipe of the pump or injector, and an ordinary
oilbarrel mounted on a platform scale, the latter being supported
by the hogshead on one side and by a suitable staging on the
other. The barrel is filled by a coldwater pipe leading from the
source of supply, and this should be a IJmch pipe for pressures
not less than 25 pounds per square inch. The outlet valve to the
barrel is attached to the side close to the bottom and should be at
least 2J inches in diameter for quick emptying. Where large quan
tities of water are required the barrel can be replaced by a hogs
head, and two additional hogsheads can be coupled together for a
lower reservoir. The capacity reached by this arrangement, when
the weighinghogshead is supplied by a 2Jinch valve under 25
pounds pressure and emptied through a 5inch valve, is 15,000
pounds of water per hour. For still larger capacity it is desirable
to use rectangular tanks made for the purpose and having the
weighingtank arranged so that the ends overhang the scales and
the reservoir below, the outlet valve, consisting of a flapvalve,
covering an opening in the bottom 6 or 8 inches square. With
rectangular tanks this system can be employed for any size of
stationary engine ordinarily met with.
Where extremely large quantities of water must be measured,
or in some places relatively small quantities, the orifice method of
measuring is one that can be applied with satisfactory results. In
this case the average head of water on the orifice must be deter
mined, and, furthermore, it is important that means should be at
hand for calibrating the discharge of the orifice under the condi
tions of use.
STEAMENGINE TESTS. 427
The corrections or deductions to be made for leakage above
referred to should be applied only to the standard heatunit test,
and tests for determining simply the steam or feedwater consump
tion, and not to the coal tests of combined engine and boiler equip
ment. In the latter no correction should be made except for leak
age of valves connecting other engines and boilers, or for steam
used for purposes other than the operation of the plant under test.
Losses of heat due to imperfections of the plant should be charged
to the plant, and only such losses as are concerned in the working
of the engine alone should be charged to the engine.
In measuring jacketwater or any supply under pressure which
has a temperature exceeding 212 F., the water should first be
cooled, as may be done by first discharging it into a tank of cold
water previously weighed, or by passing it through a coil of pipe
submerged in running and colder water, preventing thereby the
loss of evaporation which occurs when such hot water is discharged
into the open air.
XI. Measurement of Steam Used by Auxiliaries. Although
the steam used by auxiliaries embracing the airpump, circulating
pump, feedpump, and any other apparatus of this nature, suppos
ing them to be steamdriven, also the steamjackets, reheaters, etc.,
which consume steam required for the operation of the engine is
all included in the measurement of the steam consumption, as
pointed out in Article X, yet it is highly desirable that the quan
tity of steam used by the auxiliaries, and in many cases that used
by each auxiliary, should be determined exactly, so that the net
consumption of the mainengine cylinders may be ascertained and
a complete analysis made of the entire work of the engine plant.
Where the auxiliary cylinders are noncondensing, the steam con
sumption can often be measured by carrying the exhauststeam
for the purpose into a tank of cold water resting on scales or through
a coil of pipe surrounded by cold running water. Another method
is to run the auxiliaries as a whole, or one by one, from a spare
boiler (preferably a small vertical one) and measure the feed
water supplied to this boiler. The steam used by the air and cir
culating pumpb may be measured by running them under, as near
as possible, the working conditions and speed, the main engine and
other auxiliaries being stopped, and testing the consumption by
428 THE STEAMENGINE AND OTHER HEATMOTORS.
the measuring apparatus used on the main trial. For a short
trial, to obtain approximate results/measurement can be made by
the watergageglass method, the feedsupply being shut off. When
the engine has a surface condenser, the quantity of steam used
by the auxiliaries may be ascertained by allowing the engine
alone to exhaust into the condenser, measuring the feedwater
supplied to the boiler and the water discharged by the airpump
and subtracting one from the other, after allowing for losses by
leakage.
XII. Coal Measurement. (a) Commercial Tests. In com
mercial tests of the combined engine and boiler equipment, or those
made under ordinary conditions of commercial service, the test
should, as pointed out in Article VII, extend over the entire period
of the day; that is, twentyfour hours, or a number of days of
that duration. Consequently the coal consumption should be
determined for the entire time. If the engine runs but a part of
the time, and during the remaining portion the fires are banked,
the measurement of coal should include that used in banking. It
is well, however, in such cases to determine separately the amount
consumed during the time the engine is in operation and that con
sumed in the period while the fires are banked, so as to have com
plete data for purposes of analysis and comparison, using suitable
precautions to obtain reliable measurements. The measure
ment of coal begins with the first firing, after cleaning the furnaces
and burning down at the beginning of the test, as pointed out in
Article VIII, and ends with the last firing at the expiration of the
allotted time.
(6) Continuousrunning Tests. In continuousrunning tests
which, as pointed out in Article VII, cover one or more periods
which elapse between the cleaning of the fires the same principle
applies as that mentioned under the above heading (a), viz., the
coal measurement begins with the first firing after cleaning and
burning down, and the measurement ends with the last firing
before cleaning and burning down at the close of the trial.
(c) Coal Tests in General. When not otherwise specially under
stood, a coal test of a combined engine and boiler plant is held to
refer to the commercial test above noted, and the measurement of
coal should conform thereto.
STEAMENGINE TESTS. 429
In connection with coal measurements, whatever the class
of tests, it is important to ascertain the percentage of moisture
in the coal, the weight of ashes and refuse, and, where possible,
the approximate and ultimate analysis of the coal, following,
all the methods in detail advocated in the latest report of
the Boiler Test Committee of the Society. (See Vol. XXI,
page 34.)
(d) Other Fuels than Coal. For all other solid fuels than coal
the same directions in regard to measurement should be followed
as those given for coal. If the boilers are run with oil or gas, the
measurements relating to starting and stopping are much simplified
because the fuel is burned as fast as supplied, and there is no
body of fuel constantly in the furnace, as in the case of using;
solid fuel. When oil is used it should be weighed, and when
gas is used it should be measured in a calibrated gasmeter or
gasometer.
XIIIXVI. See text.
XVII. Speed. There are several reliable methods of ascer
taining the speed or the number of revolutions of the engine
crankshaft per minute. The simplest is the . familiar method
of counting the number of turns for a period of one minute with
the eye fixed on the secondhand of the timepiece. Another
is the use of a counter held for a minute or a number of minutes;
against the end of the main shaft. Another is the use of a reli
able tachometer held likewise against the end of the shaft. The
most reliable method, and the one we recommend, is the use of a,
continuousrecording engine register or counter, taking the total
reading each time that the general test data are recorded and
computing the revolutions per minute corresponding to the differ
ence in the readings of the instrument. When the speed is above
250 revolutions per minute, it is almost impossible to make a
satisfactory counting of the revolutions without the use of some
form of mechanical counter.
The determination of variation of speed during a single revo
lution, or the effect of the fluctuation due to sudden changes of
the load, is also desirable, especially in engines driving electric
generators used for lighting purposes. There is at present no
recognized standard method of making such determinations j and
430 THE STEAMENGINE AND OTHER HEATMOTORS.
if such are desired, the method employed may be devised by the
person making the test and described in detail in the report.
One method suggested for determining the instantaneous
variation of speed which accompanies the change of load is as
follows :
A screen containing a narrow slot is placed on the end of a
bar and vibrated by means of electricity. A corresponding slot in
a stationary screen is placed parallel and nearly touching the
vibrating screen, and the two screens are placed a short disance
from the flywheel of the engine in such a position that the ob
server can look through the two slots in the direction of the spokes
of the wheel. The vibrations are adjusted so as to conform to
the frequency with which the spokes of the wheel pass the slots.
When this is done the observer viewing the wheel through the
slots sees what appears to be a stationary flywheel. When a
change in the velocity of the flywheel occurs, the wheel appears
to revolve either backward or forward according to the direction
of the change. By careful observations of the amount of this
motion the angular change of velocity during any given time is
revealed.
Experiments that have been made with a device of this kind
show that the instantaneous gain of velocity upon suddenly
removing all the load from an engine amounted to from 1/6 to
1/4 of a revolution of the wheel. 
XVIIIXXV. The greater portion of the matter contained in
these paragraphs will be found in the text.
t Trans. A. S. M. E. Standard Rules.
CHAPTER XV.
SUPERHEATED STEAM AND STEAMTURBINES.
Superheated Steam. Steam in contact with its liquid, all
temperature changes having ceased, is a vapor and obeys the laws
of vapors. The pressure or tension of a vapor can neither be
increased nor decreased by changes of its volume as long as its
temperature is kept constant.
If steam is not in contact with its liquid its temperature may be
raised; in other words, it may be superheated. In a cylinder we
may have superheated, dry, and wet steam at the same instant.
This is due to the fact that dry steam is a very poor conductor
of heat. It will be found, in fact, that the great value of super
heated steam lies in its quality as a poor conductor of heat. The
term contact is to be interpreted as immediate contact.
If the steam in the upper portion of the steamspace of a
vessel containing steam and water is heated, either the pressure
or the volume or both will increase. Steam from a boiler may be
superheated by passing it through a series of highly he: ted tubes
on its way to the engine. The fact that the volume of the super
heater is constant does not prevent the steam from being heated
at constant pressure, since the steam is used in the engine as fast
as it is generated and theoretically the reciprocating piston might
be replaced by one moving in a cylinder of indefinite length.
This process of heating the steam is performed in a superheater.
This consists in a series of castiron or steel tubes or steel tubes
clad in cast iron placed in the back connection or behind the
bridgewall of fire tubular boilers, over the tubes at the mid
third of their length in water tubular boilers, or they may be placed
in a separate setting with a separate grate which is independently
fired. The furnacegases at temperatures between 600 F. and
1500 F. flow around the superheater tubes and the steam passes
through them.
Saturated steam at a high pressure contains more heat than
the same weight of steam at a lower pressure. If therefore steam
at a high pressure is allowed to expand, forming eddies, but (with
out doing external or useful work) to a lower pressure, the excess
431
432 THE STEAMENGINE AND OTHER HEATMOTORS.
of heat mentioned above will be utilized, first in drying the
steam if it be wet, and then in superheating it. This effect is due
to the formation of eddies. This form of superheating takes
place in throttlegoverned engines, in highspeed engines at
short cutoff, and in the Peabody calorimeter. In nozzles,
eddying is prevented and the energy is utilized in giving the
mass of steam additional velocity.
Adheating is a term applied to the superheating of saturated
steam by mixing it with highly superheated steam in such propor
tions that the mixture will possess a prescribed degree of superheat.
Foster Superheater. The Foster superheater is made up of
elements each of which consists of two steel tubes, one inside
of the other and so connected that the steam from the boiler
passes through the annular space between the tubes, the inner
tube being closed at both ends. Castiron discs that taper in a
crosssection from the inner to the outer periphery are shrunk
on the outer tube. These annular gillflanges are placed close
to one another and not only protect the steel tube from cor
rosion but possess a large surface for the absorption of heat,
and also provide a large mass for the retention of heat and so
prevent rapid fluctuations of temperature in the superheat of
the steam.
This superheater is designed with a view to avoid the necessity
for flooding devices or any form of connection between the water
space of the boiler and the superheater. The protection afforded
by the external covering of cast iron is ample to prevent damage
to the surface during the process of steamraising. It is evi
dent that if water is admitted to the interior of a superheater
there is danger of scale forming in the tubes, which must result
in a loss of efficiency or stoppage of the circulation. It is also
evident that care and intelligence must be exercised in drain
ing out a superheater which has been flooded before putting it
into service, and in properly setting the valves in the pipes to
prevent the engine receiving a charge of water." *
The economic advantages of superheated steam have been
known since 1826. After a large number of trials its use was
abandoned on account of troubles arising from improper lubri
cants and improper packing for flangejoints and pistonrod
* Catalog of makers
SUPERHEATED STEAM AND STEAMTURBINES.
433
and valvestem stuffingboxes. The superheaters becoming in
crusted internally were burnt out or were eaten up by the sul
phuric acid formed in damp soot; the cylinders were scored
because the tallow used for lubrication was decomposed at high
temperatures into nonlubricating elements; the joints leaked
from the increased stresses due to increased expansion caused
by higher temperatures. Fortunately the advent of mineral
Detail of Return Header
FIG. 227.
oils, metallic packing, and the general advance in the manufac
ture of structural material used in engineering processes and
increased scientific knowledge now make its use possible and
economical.
Four methods of reducing cylinder waste, due to initial con
densation, are open to us compression, jacketing, compounding,
and superheating. It is pretty well settled that economy lies in
reducing clearance surface to the smallest possible amount and
that heavy compression in many cases causes loss. Jackets are
expensive, are seldom properly operated, and are of value only
434 THE STEAMENGINE AND OTHER HEATMOTORS.
in special cases, arid these cease to exist with a proper degree
of superheating. Superheaters have also reduced the number of
cylinders required in compounding. A test will be given of a
compound engine and superheater that produced results un
rivalled by many tripleexpansion engines. In connection with
steamturbines marked advance in economy is produced by the
use of superheaters.
The greatest percentage increase in economy is obtained
when superheaters are applied to uneconomical engines. Wasteful
little engines with a superheater have nearly the same economy
as large engines of the same type with a superheater. In other
words, the economy of the small one has been increased more
FIG. 227 Foster Superheating Tube.
than that of the large one. If the reheaters placed in the re
ceivers of multipleexpansion engines do not superheat they are
worse than useless. Using highpressure steam to reevaporate
water to lowpressure steam in a receiver is uneconomical. The
water should be taken out by a separator and returned to the
boiler, whilst the dry steam should be superheated to prevent
initial condensation in the next cylinder.
"The purposes of superheating steam, as practised in the
past and as recognized at present, are the following:
"1. Raising the temperature which constitutes the upper
limit in the operation of the heatengine in such manner as to
increase the thermodynamic efficiency of the working fluid.
''2. To so surcharge the steam with heat that it may surrender
as much as may be required to prevent initial condensation at
entrance into the cylinder and still perform the work of expan
sion without condensation or serious cooling of the surrounding
walls of the cylinder.
"3. To make the weight of the steam entering the condenser,
and its final heat charge, a minimum, with a view to the reduc
tion of the volume of the condensing water and the magnitude
and cost of the airpump and condenser system to a minimum.
SUPERHEATED STEAM AND STEAMTURBINES. 435
"4. To reduce the back pressure and thus to increase the
power developed from a given charge of steam and the efficiency
of the engine.
"5. To increase the efficiency of the boilers both by the reduc
tion of the quantity of the steam demanded from the original
heatingsurface and by increasing the area of the heatingsur
face employed to absorb the heat of the furnace and flue gases,
and also by evading the waste consequent upon the production
of wet steam. 7 ' (Thurston.)
If the steam entering a cylinder is only superheated enough
to give dry saturated steam at cutoff the range of temperature
_ m
of the Carnot cycle is unchanged and there is no increase
i
of economy from 1. The other four sources of economy de
pend upon one fundamental fact the poor conductivity of dry
steam. When steamgas passes through the cylinder, the walls
of the latter do not fluctuate so much in temperature. The
hot gas gives up its heat slowly to the walls, and on the exhaust
stroke the latter give up their heat slowly. In other words, the
slightest film of water on the cylinder walls renders possible a
wider fluctuation of metal temperature with its consequent waste
of heat than occurs when superheated steam is used. If one
thermal unit is wasted in superheating steam it prevents the
waste of 2 thermal units caused by initial condensation.
Thermal Laws. From experiments Regnault determined the
specific heat of steam to be .48. The best values, at present, are
those of Knoblauch and Jacobs. Their values show that the
specific heat is a variable ranging from .48 to .6, increasing with
increasing pressure, but decreasing with increasing temperature at
the same pressure. As no authoritative figures have been decided
upon, we shall assume the specific heat at constant pressure to be
constant and to be .48. See Fig. 228 and Table XV,
Hence the total heat required to heat feedwater from ti to T 2 ,
evaporate it at that temperature and then superheat it under a
constant pressure (corresponding to T 2 ) to some temperature T s is
or , = 2
Intensity of Superheating Required. If L = latent heat of steam
entering a cylinder, A = its weight in pounds per stroke, x = the
436 THE STEAMENGINE AND OTHER HEATMOTORS
percentage of initial condensation, then zAL=the amount of heat
lost by the steam in condensing.
0.60
0.55
i
0.50
0.45
0.43
i
\
\
\
j
3}
V
\
^
1

\1
J
8
\
\
\
\
*>"/
s v
\
\
o s
I
fy
N N
s s
^
^
s
$t
""
^,
'&$
N '
^x
V N
^
X,
^
___,
, 
^
^
'5
V
*
.
^
>
x^
*~
^~
^c

/
26
47
Jfe
QB
er>
S
~~
*" *
~
'
,

S"^
^^
;^

/
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I).
A i
s,
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+.
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231bs
._.
.
._
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___


0.
J"
"
482
572 a
212^F 302F 392
Temperature *
FIG. 228. C p of Superheated Steam. (Knoblauch and Jacobs.)
FIG. 229. Separately Fired Superheater.
If superheated steam had to possess that number of thermal
units in excess of those it possesses as saturated steam, it is evident
SUPERHEATED STEAM AND STEAMTURBINES.
437
that the necessary temperature of the superheated steam would
be obtained from the equation
ASA(T s T 2 )=xAL, or
where T s is the temperature of the superheated steam,
T 2 is the temperature of the saturated steam.
If the above were true there would be very little gained by
the use of superheated steam, as we would simply substitute one
FIG. 230. Foster Superheater and Water Tubular Bailer.
waste for another. It is found in practice that a very much lower
and more feasible degree of superheat is necessary. It varies, of
course, with the size and type of engine, ratio of expansion, etc.
In some cases it is only .4 or .5 of the amount indicated by the for
mula above. For example, assume the latent heat of steam to aver
age 875 B.T.U. For each per cent of initial condensation there is a
loss of 8.75 B.T.U. If only .4 of this amount is required when the
steam is superheated, the number of degrees of superheat required
for each per cent of initial condensation would be
degrees approximately. Hence the (approximate) rule.
.4 X8.75
.48
= 7
438
THE STEAMENGINE AND OTHER HEATMOTORS.
To have the steam dry at cutoff, the necessary number of
degrees of superheat of the steam on entrance to the cylinder is
equal to the percentage of initial condensation that would exist
without superheating multiplied by 7. The superheat on leaving
the superheater would depend on the length, character, and cover
ing of the steammain and valvechest.
The following data (Trans. A. S. M. E., Vol. XXV) are instruc
tive in showing loss of pressures and temperatures in the steam
cycle as well as the economy in the use of superheated steam in an
engine that is economical when using saturated steam.*
1 Date of test
May 27
June 19
July 17
July 24
2. Condition of steam: superheated or sat
urated
Sup
Sup
SUP
Sat
3 Net water per hour to boiler.
4633
4018
2684
5630
Pressures.
4c Gagepressure at boiler
147
147.9
148.5
149.3
5. Gagepressure near throttle
141.2
142.4
145.6
145.1
6. Gagepressure receiver
23
17
3
22
7 Vacuum near engine inches
25.11
25.82
26.32
24.47
8 <<! at condenser inches
25.80
26.79
26.81
25.24
8a c Barometer temperatures of steam, de
grees Fahrenheit f
30 16
29 80
30 01
30
9. Leaving the superheater. .
766 4
808
849
10. At the engine throttle
713.7
736 3
756.8
11 Entering the H.P. cyl
634.4
658 6
672
12. Leaving the H.P cyl
346.5
331.5
287.7
262
13. Entering the L.P. cyl
14. Leaving the L.P, cyl
Amount Steam was Superheated,
Degrees Fahrenheit.
15. Leaving the superheater,
16 At the enginethrottle
408
135.1
402
352 5
395.9
128.2
443.4
374 5
353.6
124.1
484.1
393 3
269
17 Entering the H.P. cyl
273.2
296.8
308.5
18 Leaving the H P cyl
84 7
77
52
19 Entering the L P cyl .
146 2
141 4
117.9
7.1
Horsepower and Economy.
20 Revolutions per minute
103 28
102 34
102 49
102.2
21 I H P developed by engine
474 5
420 4
276.8
406.7
22 Water in pounds per I. H.P. .
9 76
9.56
9.7
13.84
23. Maximum temperature to which the feed
water could be heated by the exhaust
of the engine
133.5
125.1
121.7
148.4
24. Coal in pounds per hour (Standard of
Civil Engineers of London) .
1 265
1 257
1.288
1.497
Bore of cylinders, 16.07" and 28.03", measured when hot.
Length of stroke, 42 inches
Revolutions, 103.
* See also Trans. A S M E. ; Vol XXII.
SUPERHEATED STEAM AND STEAMTURBINES. 439
Average data and results of (Schmidt) separate superheater test :
1. Heatingsurface in square feet 642
2. Gratesurface in square feet 4
3. Duration of test in hours 14
4. Pressure of steam furnished superheater (gage) 147.4
Temperatures in Degrees Fah. by Mercury Thermometer:
5. Steam entering the superheater 365 . 6
6. ' ' leaving " 809 . 1
7 Amount steam was superheated 443 . 5
Total Quantities.
8. Steam passing through the superheater in pounds 58,025
9. Heat imparted to the steam in B.T.U 12,352,000
10. Total moist coal fire in pounds 1,473
11. " dry coal consumed in pounds 1,426
12. Coal burnt per square foot of gratesurface per hour in pounds. . 25.5
13. Heat imparted to the steam in the superheater per pound of coal
burned in B.T.U . 8.662
14. Equivalent evaporation from and at 212 F. in pounds per pound
of dry coal. . 8.97
15. Heat of combustion of the dry coal in B.T.U. per pound 14,060
16. Efficiency of the superheater based on the heat of combustion of
the coal in per cent 61.6
Combined Economy of Boiler and Superheater.
17. Actual evaporation of the boiler per pound of dry coal in pounds. . 8 . 586
18. Coal burnt in the superheater in pounds per pound of steam
passing through it . 02458
19. Coal burnt in superheater in pounds per pound of coa burned at
boiler, Item 17Xltem 18 211
20. Actual evaporation of the combined boiler and superheater 7.090
21. Factor of evaporation of the combined boiler and superheater. . 1 .421
22. Equivalent evaporation in pounds per pound of dry coal from
and at 212 F. for the combined boiler and superheater 10.07
23. Efficiency of the combined boiler and superheater based on the
heat of combustion of the coal in per cent 69 . 2
From the above data the student should calculate :
1. The loss of heat in the main steampipe.
2. The probable superheat at cutoff, assuming 20% conden
sation would occur in tests 1 and 2 if dry steam were used.
3. Obtain the paper in the Trans. A. S. M. E., Vol. XXV,
and check one or more percentages of superheating.
4. Assume the mean temperature of fluegases in super
heater at 1500 F., what is the rate of transmission per square
foot per degree difference of temperature per hour?
5. Draw a diagram similar to that on page 197, showing the
thermal losses in the engine cycle.
6. Assume a crosscompound Corliss engine 24" x44" x60";
870 I.H.P.; revs., 72; clearance H.P. cyl., .03%; cutoff, .33
stroke; initial pressure abs., 114; pressure at cutoff, 104.4
abs.; steam accounted for at cutoff, 12.28 pounds; proportion
440 THE STEAMENGINE AXD OTHER HEATMOTORS.
of feedwater accounted for at cutoff, .866; steampipe, 80 feet
long. . .Find the diameter of the steam pipe; assume charac
ter of lagging and bends and find probable heat loss. Design a
Schmidt separate superheater that will supply dry steam at
cutoff, viz., answer the following requirements: Heating
surface; gratesurface; coal; degree of superheat leaving the
superheater, at the throttle, entering cylinder.
The designer calls attention to the following points in the design :
"The doublebeat poppetvalves have seats surrounded by the
inlet steam in such a way that the expansion of the seat is equal
in extent and effect to that of the valve, thus overcoming com
pletely the characteristic defect of ordinary designs of their type of
valve, namely, excessive leakage at any temperature other than
the particular one at which they were originally ground. The
inletvalves are driven by the ordinary tripgear of the builders,
with vacuum dashpots, with the addition of a simple linkage
which controls the closure of the valve independent of the extent
of closing motion imparted by the dashpot, and thus prevents
slamming or partial closing of the valve. The exhaustvalves are
actuated by a system of links devoid of cams, always in connection
with the eccentric, except when handactuated at starting or stop
ping, and which keeps the valve stationary during the forward
stroke, as is necessary when using the poppet type, arid all joints
are adjustable for wear.
"The stuffingboxes are on long necks to take them well away
from the superheat, and the pistonrod stuffingboxes have metallic
packing provided with waterjackets, which, however, have never
been used. The pistonpacking consists of two simple iron spring
rings with joint plates.
"The highpressure cylinder is so designed that the working
portion of its band is a simple cylinder without ribs, all connections
to the cylinder, such as valvecleats, laggingbosses, inlets, and
exhaust gages, etc., being at the ends. . . .
"The only trouble noticed with lubrication was a smoking due
to the carbonization of the animal or vegetable constituents of
the original oil used. On notifying the oilmakers of this trouble
they at once produced an oil which eliminated all complaint.
"The operation of the superheater has proved to be simple;
SUPERHEATED STEAM AND STEAMTURBINES. 441
in fact it is easier to run than a boiler, since the pyrometerdial
is the only thing to be watched. Fire is never built in the super
heater without a flow of steam through the coils, under which
conditions there is no sign of deterioration. The temperature is
readily regulated, even when the engine is shut down for changes.
in the mill, which happens once or twice in twentyfour hours in
regular operation. If the shutdown is for more than a few minutes
a small flow of steam is secured by "cracking" the throttle valve
and allowing a little steam to blow through the engine, but for
short stoppages this is not necessary. The pipes, cylinders, and
receiver are covered with 3 inches of a standard magnesia covering
over pipes and flanges."
Temperatureentropy Diagram for Superheated Steam. In Fig.
231 let erfitzSse^ represent the heatunits expended in heating
one pound of water from ti F. to t 3 F. and converting it into
dry saturated steam at that temperature. To superheat this
steam at constant pressure to some temperature T a requires
Q = .48(T.T 3 ) thermal umts=fdQ=f T8 A8dT.
Hence the entropy
where T s and T 3 are absolute temperatures in degrees Fahrenheit.
This increase of entropy may be laid off from e 4 to some point e t
and erecting a perpendicular = T s the point T 8 is found. By assum
ing a series of values for T 8 a series of points in the curve s 3 T 8 f
may be found. The curve when drawn to the usual scale is
practically a straight line and may be so assumed. That being the
case the value of e
1 s
2 *
If this steam expands adiabatically the line 7 7 /5 2 w 4 indicates
the thermal changes that occur. When the temperature dropped
to ^ the intersecting of the vertical and the saturated steam
Aines show that at that instant the steam is dry saturated steam.
Fuither expansion to ti is followed by the condensation of a part
of the steam equal in amount to  of a pound.
442 THE STEAMENGINE AND OTHER HEATMOTORS.
If the fraction j^ = x , its value may be obtained from the
equation
+e 3 e4+e 4 e 5 ,
AS(T S T 3 )2
or
4
rri i
* o
whence x may be determined.
The efficiency of the added heat is theoretically ' If
5
the practical gain were no greater than this superheaters would
not repay their cost and trouble.
Superheated Steam in Compound Engines. It is practical to
superheat steam to such a temperature that it will be superheated
: !
FIG. 231.
at exhaustopening in the highpressure cylinder, but it would
not be practical, nor is it indeed necessary, to have the initial
temperature so high that the steam is superheated at cutoff in
the lowpressure cylinder. It is better to divide the superheating
into two stages and put superheating coils in the receiver between
the two cylinders. Elsewhere it has been pointed out that any
moisture in the steam from the highpressure cylinder should be
separated out so that the superheating is only applied to dry
saturated steam. It was further pointed out that the receiver
SUPERHEATED STEAM AND STEAMTURBINES. 443
steam should be superheated from 50 to 100 degrees; this would
require 1.5 square feet of pipe surface to the I.H.P.
Durability of Superheaters. Superheaters are best preserved
by keeping a continual supply of steam flowing through them.
The amount of this steam should be proportional to the amount
of coal burning on the grate. In case the engine should slow down
or have a reduced load the amount of steam passing through the
superheater should not be diminished. It is better to bleed
the excess into heaters or into steam used for other purposes.
If this cannot be done the fires in superheating boilers should be
diminished.
In tests of a B. & W. boiler, 5000 sq. ft. heatingsurface, 1000
sq. ft. of superheating surface, a chain gratestoker 75 sq. ft.
surface, the following facts are stated:
1. Superheat varied from 125 to 175 as the boiler horse
power varied from 350 to 750.
2. The horsepower of the superheater varied from 35 to
100 as the boiler horsepower varied from 350 to 700.
3. From 7 to 17% of the b.h.p. was produced in the super
heater as the b.h.p varied from 100 to 900.
When the main boilers were forced there was a greater weight
of gases at a higher temperature passing around the superheating
tubes.*
Steamnozzles. When steam flows through a nozzle it was
shown (page 216) that
V 2
At first sight it would appear that the weight and velocity
of steam delivered by a steamnozzle would continually
increase with a continuous lowering of the back pressure
or the pressure at the exit end of the nozzle. A close
V 2
inspection of the formula for ^~ shows that it includes also the
final volume of expansion, which increases and therefore tends
to diminish the value of the velocity of exit. The demonstra
* Trans. A. S. M. E., Vol. XXVI.
444 THE STEAMENGINE AND OTHER HEATMOTORS
tion below of what is known as Zeuner's formula shows that
the maximum weight of steam that an orifice can deliver is ob
tained when the back pressure, p 2 , is .57 'p^
For steam, if p 2 becomes less than .57pi, the delivered weight
160 150 140 130 120 110 100 90 80 TO 60 50 40 30 20 10 .10
FIG. 232.
remains constant. For perfect gases, if p 2 becomes less than .528pi,
the delivered weight decreases. If p 2 is kept constant and p\
is increased the weight delivered of steam or perfect gases is
increased.
A nozzle must be designed to give definite results under defi
nite conditions. It can be shown that a very slight alteration
SUPERHEATED STEAM AND STEAMTURBINES. 445
of the conditions may produce a very considerable change
in the results. Nozzles may easily be 'too long or too short,
may expand too rapidly or not rapidly enough, and the orifice
at the entrance may be too well rounded or the reverse for exist
ing conditions. If the nozzles are too long the work of friction
is carried off as heat. Short nozzles are desirable with low pres
sures; with high pressures longer nozzles may be used. If
the crosssection of the nozzle increases too rapidly the stream
acquires too many crosseddies.
The maximum weight of steam discharged through a simple
orifice is determined by the maximum velocity in the orifice,
although there may be higher velocities on the discharge
side accompanied by very low gas density. The maximum
velocity in the orifice never exceeds 1500 feet per second no
matter how great the difference between the initial and dis
charge pressures.
Given the ratio , p b and the weight of steam discharged
per second by Zeuner's formula the necessary crosssection at
any part of the nozzle can be found. For a maximum Wi the
value of should be .57. The best results are obtained when
Pi
the steampressure in the nozzle gradually decreases to the back
pressure, otherwise vibratory waves shown in Fig. 232 are set up.
Hence if p 2 is less than .57p l} design the throat or narrowest
part of the nozzle for a p 2 = .57pi and design the exit for a p%
equal to the pressure at the discharge end of the nozzle.
Zeuner's Formula. We have seen that the work of adiabatic
expansion is T^> which becomes * if the expansion is
carried to p 2 = Q. .*. l ^ = E, the intrinsic energy.
T~ 1
V 2 2
The formula ~ = (E 1 + piV 1 )(E 2 +p 2 v 2 ) may be writtea
446 THE STEAMENGINE AND OTHER HEATMOTORS.
It is desirable to get rid of v 2 and obtain results in terms of
or
If the area of the orifice in square feet is A, the volume dis
charged per second will be AV. As the above formulas apply
to one pound weight, it is evident that v 2 is the specific volume
per pound at p 2 , the pressure at the section of area A.
AV
Weight discharged per second = = W.
But V 2 = i>i >". Therefore
Weight discharged per second
 w
To obtain the maximum weight discharged per second let
= r Then the weight W becomes a maximum when
Pi
2. i+ r
(r) r (r) r becomes a maximum.
Differentiating and equating the first differential to zero,
r
i / 2 \L_
Dividing by rr we obtain r= ( Tij r ~ 1 
Substituting the values of ^=77 for steam and air we have:
For air, 7 = 1 .41 ; r = .528 = A
For dry saturated steam, 7 = 1 . 135 ; r = .577 = .
SUPERHEATED STEAM AND STEAMTURBINES. 447
The restriction in the weight discharged is caused by the
actual formation or the tendency to form in the orifice a vend
contractd, or contracted vein, in which the pressure does not drop
below the value of p 2 indicated above, no matter what the
final or exterior pressure may be. From the contracted orifice
the pressures should decrease to the final pressure.
Steamturbines. To understand the action of steam on the
blades of a steamturbine, the student should review the deriva
tion of certain formulas in hydraulics.
We have seen that it requires the expenditure of Wh foot
pounds of energy to raise W pounds through a height of h feet;
that in falling freely through this height the body would acquire a
V 2
velocity of V feet per second; that h = ^ , and hence the energy
V 2
possessed by the body due to its velocity of motion is W~ .
Bodies at rest or moving uniformly, whether in straight or
curved lines, cannot be under the influence of any unbalanced
force. In other words, all forces acting on a body moving uni
formly must be reducible to pairs composed of equal and opposite
forces. A train of cars moving uniformly down a grade has all
resistances exactly equal to the impelling force of gravity; a fly
wheel moving uniformly does no work it is actively useful only
when it is moving nonuniformly.
The force necessary to produce a change of velocity in a body
is proportional to the product of the mass of the body and the
amount of change in the velocity produced in the time that the
force has been acting on the body.
Fdt=MdV,
f
Jo
FT=MV,
y
where m measures the increase in velocity, i.e., acceleration per
unit of time
A small force F, acting for a long time, T, or a large force, F,
acting for a short time, T, will change the velocity of a body of mass
448 THE STEAMENGINE AND OTHER HEATMOTORS.
M from to V feet per second, or add V feet per second to any
previously acquired velocity. If a body has any velocity, V feet
per second, we may suppose that such velocity was acquired from
zero velocity in one second; therefore
F=MV.
If a body took T seconds to acquire a velocity of V feet per
V
second (initial velocity = 0), the mean velocity would be ~ and
V
the space passed over would be T. If, however, a body has a
velocity of V feet per second, we may suppose that velocity was
V
acquired in one second, hence the space passed over would be ^
under the action of a force F=AIV.
As energy is the product of a force and the distance through
which that force was exerted, the energy exerted on the body will
F MV 2 WV 2
be the product of M F and ^ or 5 or ^ . In other words, the
z z zg
energy put into the body is equal to the energy it possesses in
virtue of its acquired velocity.
As g is always expressed in feet per second, it is wise to express
all other quantities, in the same equation, in terms of units homo
geneous with it. Hence, in dealing with a continuous stream, it is
convenient to express M, the mass of the fluid stream passing per
second, by  , where w is the weight of the fluid per cubic foot,
i/
A is its crosssectional area in square feet, and F is its velocity in
feet per second. The force in pounds that could be exerted by
such a stream, if its line of action were diverted through 90, would
wAV 2
be FQQ=MV or , since the velocity in the original direction
\J
is reduced to zero. Hence the force exerted is proportional to the
velocity squared. Analyzed, the expression is (wAV) pounds mul
tiplied by feet per second divided by feet per second. The pro
duction of this force causes no loss of energy so long as no portion
of the force is exerted through a distance. In fact, if the stream is
bent through 180 by means of a frictiomess bend, the force that
SUPERHEATED STEAM AND STEAMTURBINES. 449
the stream exerts on the bend in the direction of the original
stream is twice the above amount, or
wAV*
V 180 ^
Friction, of course, causes a reduction of energy, since the frictional
resistance has its line of action parallel but opposite to the line of
motion of the stream.
A derivation of a general formula for the force exerted when
the line of action of a stream is bent through any angle a will now
be given.
Impulse Due to a Jet Moving on a Curved Blade. Let a
stream, crosssection A square feet, weight w pounds per cubic
foot, velocity V feet per second, measured where crosssection of
stream is A square feet, strike a frictionless vane, BC, of such
curvature that the stream is deflected through a degrees, as shown
in Fig. 170. Each ds of the vane will react radially an amount
exactly equal to the radial force exerted by the stream through
having its line of action diverted. The amount of this radial force
on any elementary ds is equal to the centrifugal force of the
weight of the fluid that is on that area at that instant.
wAdsV 2
dr r = .
9r
The horizontal component of this force, dF x , = dF r sin 0.
The vertical component of this force, dF y , = dF r cos 6.
The total force exerted on the whole vane along the X and Y
axes will be equal to the integral of the above quantities between
the limits, and a, for the angle 6.
/* a /* 
^0:= / dF x = / <iFrsin# = /  1 sin#
^t/O t/O t/0 $r
/" /* a /* a t^7lc?sF 2
^= / ^7,= / dFr cos 6= I  cos 6
t/o t/o t/o </r
Keeping in mind that 6 and dd measure the lengths of arcs at unit
radius, we may get rid of the variable, r, by substituting ds = rdd.
450 THE STEAMENGINE AND OTHER HEATMOTORS.
Hence Fx== f Q
But
wAV 2
sin Odd = (1  cos a) ,
i7 t7
s*
*A* WAV2 '
cos dad = sin a.
V2(lcosa).
FIG. 233.
But the weight of fluid flowing per second, W, =wAV. Hence
WV WV WV / _
F x =  (1 cos a), F y =  sin a, F r =  v 2(1 cos a).
O \J u
Knowing the totals, F x and F v , the direction of the resultant
impulse F r is given by
F x 1cosa
r y sin a
(/? being the angle between the totals F y and F r .)
NOTE. The above formulas may be gotten more simply thus: If
the stream is turned through 90 and the velocity in the original
WV
direction becomes zero the force is  . Hence for any other angle,
WV WV
= and 2F = ; we have F x =  (1 cos a) and F v =  sin a.
y y
SUPERHEATED STEAM AND STEAMTURBINES.
451
The values of F given for the angles 90 and 180 may be ob
tained from these general equations by making a = 90 or 180.
The value of cos a is additive if the angle through which the
stream is turned is greater than 90 and subtractive if it be less
than 90.
In the derivation of the formula a indicated the angle through
which the stream is turned. Frequently, however, the supple
mentary angle or the angle beween the entering and departing
streams is used. Hence the preceding formulas often appear as
WV
F x =  (1+cosa),
y
WV .
F y =  sin a,
y
F r =  \2(l + cosa).
A modification of the preceding lines of motion is seen in
Fig. 171, where the entering and leaving streams are inclined at
FIG. 234.
angles a and /? with F, the line of action of the required force.
For a stationary and frictionless vane the entering and departing
velocities must be equal since there can be no loss of energy. The
452 THE STEAMENGINE AND OTHER HEATMOTORS.
WV t
impulse due to V f in its line of action is  . The reaction due to
V 2 in its line of action is  . Resolving these forces along the
y
line of action of F and we have
WV e
PI = F e cos a =  cos a,
cos/9.
WV
As V . = V 2 , ^ =  '(cos a + cos /?) .
c/
The action or the impulse of the stream against the bucket when
stationary, as in the preceding examples, or when moving, as in
the examples that follow, and whether friction is regarded or dis
regarded, may be found by the application of the following rule.
Draw the line of motion of the vane or bucket. Find the
velocities of entrance and departure of the stream relative to the
bucket section. Resolve these velocities along the line of motion
of the bucket. To obtain the impulse multiply the algebraic sum
W wAV
of these components by =  . Hence
u \J
iv AV
F =  (T t cosaf F/cos/?),
t7
where A is the crosssection in square feet at the section where V
is measured, Vi is the relative velocity of entrance and V f is the
relative velocity of exit from the wheel.
The same result will be obtained if F t  is the absolute velocity
at entrance and V f the absolute velocity at exit from the wheel,
since the sum of the components of these velocities is the same
as the sum of the components of the relative velocities.
The work done per second will evidently be the above force
multiplied by the velocity per second of the vane. If v is that
velocity then the work = Fv.
In Fig. 235 let the bucket move in the direction of F with the
velocity v. The velocity of entrance relative to the bucket sec
tion is V v. The velocity of departure is necessarily the
SUPERHEATED STEAM AND STEAMTURBINES.
453
same. Resolving the velocity of entrance along F and we obtain
(V v) cos = V v. Resolving the velocity of departure relative
to the bucket section along F and we obtain (F v) cos a. As
FIG. 235.
the stream has been turned through more than 90 these quan
tities are to be added.
Hence
F= V
cosa).
In Fig. 236 let the bucket move in the direction F with the velocity
v. If the absolute velocity of entrance of the stream be V e , its
velocity relative to the bucket section on entrance is F; in the
direction shown and, on departure, the relative velocity is V f =Vj,
neglecting frictional and other resistances. Resolve the relative
velocities along the direction of F and obtain
W
F= V f (cos a + cos ft)
y
Vf equals V+ since there is no friction, v is the velocity of
the bucket and F 2 is the absolute final velocity of the stream.
From the velocity diagrams, other equivalents may be obtained
for F
W
F = (V t cos AD + F/cos/?),
o
W
F = (F e cosAF 2 cos).
454 THE STEAMENGINE AND OTHER HEATMOTORS.
Blade Angles. If the entering stream struck the back of a
revolving blade the motion of the latter would be impeded and
the efficiency would be lowered. The angle a of the back
of the blade on the entering side in Fig. 236 is determined by
FIG. 236.
the relations that exist between V e , v and A. Hence a can be
determined from the relation found as follows :
sin (a A) sin a cos A cos a sin A
V t sin a
whence
sin a
cot a= cot A
= cos A cot a sin A,
F e sin A*
Shock is avoided, then, by having the entering angle of the
back of the blade parallel to the relative motion of the
entering stream. On the other hand, the angle of leaving is
one of the principal factors in determining the efficiency of the
mechanism. The difference in the energy of a stream on entering
and on leaving a blade must appear either as friction or as useful
work. Efficiency is increased by making the energy rejected as
small as possible.
If a stream has an absolute velocity, V, before it meets a
resistance and an absolute velocity of V 2 afterwards the loss of
SUPERHEATED STEAM AND STEAMTURBINES.
455
energy of the stream is
W(V? V 2 2 ) wA.V t (V 2  7 2 2 )
This
2g 2g
loss of energy may appear as the work of friction, useful work in
moving the vane against a resistance or both combined.
Disregarding friction, let us determine the conditions of maxi
mum efficiency. It will evidently depend upon making V% or bd,
Figs. 236 and 237, a minimum.
bd 2 = ed 2 +eb 2 2(ebxef).
Disregarding friction,
ab = bc = ed,
bd 2 = ab 2 +eb 2 2(ebxef),
ae 2 =ab 2 +eb 2 +2(eb xbg),
bd 2 = ae 2 ~2(eb xbg) 2(eb xef),
bd 2 = V 2 2 = V 2 2v(Vi cos a +Vi cos /?),
V 2 2 = V? 2vVi(cos a +cos /?) .
Maximum Efficiency under Various Conditions. 1. If the
stream is turned through 180 both a and y9 will be zero, hence
cos # = cos/? = l.
F 2 = and v = Vt=^.
For the highest theoretical efficiency the stream should be
turned through 180 and the velocity of the vane should be one
half the velocity of the entering stream.
Fig. 237.
2. As a rule, it is not feasible to have a = ^ = 0. When V s ,
a, and /? are fixed, V 2 has a minimum value when (vV;) is a maxi
mum. If V s and a are fixed in amount, a circular arc can be
456 THE STEAMENGINE AND OTHER HEATMOTORS.
passed through a, b, and e, since we have given a chord and the angle
subtended by the chord and as Vi must be less than V . Let abe
., XT lJ Vi sm a
be the circular arc and b the varying point on it. JNow   
is the area of the triangle abe and so is ae multiplied by the
altitude. Since sin a is a constant, anything that increases the
area of the triangle increases the value of vVi. The altitude
perpendicular to ae is a maximum when b is the middle point of
the arc abe. Hence vV is a maximum when v = Vi or ^ = 9'
Therefore, when F, a, and /5 are fixed, the best economy occurs
when the speed of the blade, v, is such that vcos^=^.
3. If V f is fixed in direction, and we know that /?=a, but
we do not know the value of either. (Fig. 237.)
As F is fixed in direction, A and F e cos A are constant.
Fs cos /? = Fi cos a. F2 2 is made a minimum by making vVi cos /?
= (eb xbg) a maximum. As egr is a constant, the maximum rectangle
or product of its parts, when divided into two parts, occurs when
eo
the parts are equal, viz., form a square of which ^r is a side.
Hence v = JF cos A is the condition of maximum efficiency.
De Laval Steamturbines. In the De Laval steamturbine,
Fig. 238, steamjets issuing from suitably designed nozzles im
pinge against the vanes or buckets of a single turbine wheel
designed and constructed to revolve at revolutions varying from
30,000 per minute in the 10H.P. size to 11,000 per minute
in the 300H.P. size. The steam enters the passageway be
tween buckets at one side of the wheel, passes through at
constant pressure, but with rapidly diminishing velocity, and
is discharged on the other side into the atmosphere or con
denser. The diagrammatic sketch, Fig. 239, shows how the
pressure in the nozzle decreases from that of the boiler to
that of the atmosphere or condenser. The turbinewheel re
volving in this low pressure has, therefore, low frictional resist
ance on the sides and the thrust in the direction of the axis
SUPERHEATED STEAM AND STEAMTURBINES. 457
is practically very small. It further shows that the maximum
velocity of the steam is generated in one nozzle in one stage and
the total absorption of this velocity takes place in one running
wheel. The simplicity of this arrangement is as remarkable
as are the velocities that it necessitates.
The centrifugal stresses generated in the turbinewheels of
this design requires not only the use of special metal but special
FIG. 238. The De Laval Turbine Wheel and Nozzles.
forms and special care in balancing. The wheels are made of
forged nickel steel, flaring (in a crosssection) from the periphery
to the hub, solid in the larger sizes to avoid loss of strength due
to perforation even for the axle, and mounted on a flexible shaft
to avoid the vibration stresses that are inevitable when an imper
fectly balanced mass is rotating with a rigidly fastened shaft.
Even if the wneel were perfectly symmetrical in shape, at the
high speeds at which these wheels rotate the slightest difference
in mass density would set up vibration waves which would pro
458 THE STEAMENGINE AND OTHER HEATMOTORS.
duce enormous stresses. The velocity of rotation of the tur
bineshaft is reduced by one or more pairs of spiral gears, ratio
of ten to one, meshing in opposite directions to transfer all axial
thrust to the slowermoving shaft.
Theoretical Design. The expansion in the Laval nozzle is
practically adiabatic. From the entropy diagram we may easily
Condenser or
exhaust pressure
Condenser or
'exfiaust pressure
FIG. 239. Diagrammatic Sketch of De Laval Turbine.
calculate the loss of heat as heat when steam expands adiabatic
ally from any given pressure to that of the atmosphere or to a
given pressure in a condenser. The heat so lost is the value of
V t 2
(HiH 2 ) in the equation ^ = (Hi~H 2 )778. Hence we may
Z 9
obtain the value of V t (theoretical velocity). In the De Laval
nozzles this velocity may reach 2500 or 3000 feet per second
or more. The practical value of F = .
SUPERHEATED STEAM AND STEAMTURBINES. 459
It was shown on page 456 that when V t is given in direction
and amount and that a=/? the maximum efficiency of the tur
bine is obtained when the lineal velocity of the vanes, v, = 7, cos A.
This makes bd at right angles to the direction of v and gives a
y e 2 _ 7 2 2
maximum value to ~ ^ ^ ' ls 20 degrees, JF cosA = the
required lineal velocity of the buckets = v = .477*. Hence if V e
has a value of 25003000 feet per second, the velocity of the buckets
will have to be 1175 to 1410 feet per second. The actual velocity
of the periphery of the wheel in the 10H.P. size is 525 feet per
second and 1100 in the 300H. P. size. The makers claim that
these reductions are made not so much for the difficulties arising
in the turbine construction as for economic reasons.
In the discussion of efficiencies, for the sake of simplicity all
references to the quantitative effect of friction were omitted. In
practice this feature merits close attention. In the chapter on
entropy, it was shown that when one mass moved over another
friction was created. This friction increases in turbines with the
density of the steam and velocity of the moving vanes. In adia
batic expansion, considerable quantities of water are formed and
the presence of this water materially increases the friction. Hence
we see the economic reason of reducing the velocity of the vanes.
Whilst other forms of turbines have much lower velocities, the
amount of surface that the steam passes over is also materially
increased and it is doubtful if the friction is any less in them.
In practice A = 1720, a=/? = 30, 7 3 = .707 Z  to .857* The
, V? .057,2 Vt* 7 2 2
indicated work per pound of steam = ~ .3rr TT
2g 2g 2g 2g
With the large machines the .3 may decrease to .10 or .15.*
Curtis Turbine. In this turbine the total expansion of the
steam is divided between two to four sets of nozzles in place of
being confined to one set. Further, instead of one rotating wheel
absorbing the kinetic energy of the steam from each of these sets
two or more such wheels are used. The latter are separated from
each other by stationary discs carrying fixed vanes which alter the
direction of the steam as it leaves the rotating wheels in such
manner that its velocity may be partially utilized in the next
* Stodola.
460
THE STEAMENGINE AND OTHER HEATMOTORS.
rotating wheel. The diagrammatic sketch, Fig. 240, shows the loss
of pressure and the gain in velocity of the steam in two sets of
nozzles. In its flow through each set of stationary and rotating
wheels the static pressure is practically constant whilst the velocity
head is absorbed in the work of the rotating wheels. The cross
hatched area shows the division of the actual work among the
Loss from ^x ^
Eddies, Nozzles,
Bemaining Velocity
FIG. 240 Diagrammatic Sketch ol Curtis Turbine.
moving wheels, the dotted line showing the limits of the theoretical
work.
In the De Laval turbine it is necessary to make V 2 as small as
possible, as it represents waste velocity. We have seen that the
velocity of steam leaving a frictionless and stationary vane is the
same as the entering velocity. If the energy in the steam leaving
SUPERHEATED STEAM AND STEAMTURBINES. 461
a rotating wheel is not wasted, but can be utilized in a succeeding
rotating wheel, there is no necessity to reduce V 2 . This permits
a reduction of v, the lineal velocity of the turbine vanes. In fact,
if there are six rotating wheels, their velocity may be theoretically
onesixth that which is required when there is only one rotating
wheel.
This reduction in the required velocity of the rotating vanes
without too great loss in efficiency is extremely desirable for
many mechanical reasons. In the first place the problems of
construction in the turbine itself are rendered less difficult, and,
in the next place, direct connection with generators becomes pos
sible. The high speed of the De Laval turbine has to be reduced
by gearing, which is not practical in large sizes; for instance, the
largest De Laval turbine is a 300kw. unit, whilst that of the Curtis
type is 6000 kw.
In the De Laval turbine a defect was found in the friction
that resulted from wet steam moving at high velocity past the
vanes. In the Curtis turbine the velocity is lowered and the
steam is drier, but there is a considerable increase in the surface
over which the steam must pass. Rateau * claims that the Curtis
design is an inefficient one and will disappear. On the other hand,,
Jacobus t asserts that "if we take the figures given for the water
consumption of the De Laval, Rateau, and Curtis wheels and
compare them with the results obtained for corresponding powers
and pressures of the WestinghouseParsons turbine we will
find that they are practically the same." In making comparisons
care must be taken to compare turbines of similar dimensions
operating at equal power. In turbines, only the delivered or
brake horsepower is measured. As the friction is practically the
same at all powers, it is evident that at low powers the water
consumption will be excessive when compared to that at high ones
of the same machine.
Fig. 241. The turbineblade may be sketched in if we have the
velocity of entrance AB, the peripheral velocity CB, and the bL de
angle J. For A C will be the angle of the back of the blade at entrance,
and if there is no friction CD = AC will be the relative and CE the
* Trans. A. S. M. E., Vol. XXV, p. 788
f Ibid., p 774.
462 THE STEAMENGINE AND OTHER HEATMOTORS.
A
FIGS. 241 and 242. (From Thomas' Steamturbines.)
SUPERHEATED STEAM AND STEAMTURBINES.
463
absolute velocity of departure, as DE = CB. For a series of buckets,
as in the Curtis turbine, where AB represents the initial velocity
and NP the final velocity a diagram similar to Fig. 179 may be
drawn. In this theoretical diagram AC = CD, EK=KL, etc. If
the friction is to be considered then CD = (1  f)AC, KL = (1  /') EK,
etc., where /, /' are the coefficients of friction.
Stodola has the following (Fig. 243) :
FIG. 243.
The friction in a nozzle has the effect of decreasing the exit
velocity to the value
where c denotes the theoretical value
C
= \ / 2g(H l  # 2 )778.
The coefficient <j> can be taken in long nozzles with condensation
at .95 to .90; in short nozzles with free exhaust at .95 to .975.
Combinir.g GI with u again gives (relative velocity) w 1} but this
is decreased by friction and eddy currents during exhaust to the
smaller value
464 THE STEAMENGINE AND OTHER HEATMOTORS.
in which depends upon the velocity Wi, on the form of the
blades and other factors. It appears that the smallest value of
</> is .7; with smaller values of w 1} <f> would increase, and wi h
Wi = 820 feet might approximately be estimated at from .85 to .9.
Finally w 2 and +u give the velocity of exit c 2 .
These losses by friction expressed as loss of work are, in the
nozzle,
in the bladechannel,
The "indicated work " per pound of steam is
__ p __
Ll ~
c 2 2
__ __ __
2g 2g 2g 2g'
The indicated efficiency,
LI
" = r 
The indicated power in H.P.,
TTT T
Ni = ~, where (W = weight of steam per second).
Deducting from NI the wheel and bearing friction we get the
effective power at the turbineshaft, >? e = Tp.
In any case, if the absolute velocities at entrance to, and exit
from, any wheel be resolved in the direction of motion of the
buckets, or, in other words,
Let c e and c a = the peripheral components of the initial and
final absolute velocities,
P = total peripheral force,
M = mass of steam flowing per second,
u = peripheral velocity of the wheel,
then work per second, Pu, =M(c a c e )u. (See page 452.)
SUPERHEATED STEAM AND STEAMTURBINES 465
The following data and Fig. 244 are taken from Thomas on
Steam Turbines:
T corresponding to 160 pounds abs. = 824 F. abs.
T " " 14 " " =670F. "
Steam initially dry. Velocity of turbine blades = u =400 feet
per second. Angle of nozzles = 20.
In the second stage the quality has been increased from the
heat arising from friction from .868 to .912. In this stage, steam at
14 pounds, quality .912, is to expand to a ; vacuum of 29" or a
temperature of 540 absolute.
Fig. 247 illustrates the general arrangement of the Curtis
turbine. The flyball governor at the top regulates in a positive
manner the opening of one or more small pistons, shown at the
right of the cut. These control the admission of steam and there
fore the power of the governor.
Parsons Turbine (Fig. 248). An examination of the dia
grammatic sketch of the Parsons turbine will disclose the following
peculiarities :
1. The buckets or vanes of the rotating discs of the Parsons
type are carried on revolving drums.
2. The stationary vanes are carried from the casing and
have no diaphragm reaching to the axle or shaft.
3. There are no nozzles as in the Curtis type. In their
place are stationary vanes uniformly spaced over the entire
periphery. As a result all the vanes of the turbine are in con
tinuous use.
4. If we call a circle of stationary and a circle of revolving
vanes a stage, that the number of stages is very great, ranging
from 50 to 100. They are not shown in this sketch because of
the scale required for clearness.
5. That the velocity of the steam increases in the stationary
circle of vanes. In the revolving vanes it first decreases and
then increases.
6. That the fall of pressure is practically uniform and occurs
in both the stationary and revolving circles of vanes.
7. That the entering angle of the rotating vanes is almost a
right angle and the leaving angle is quite acute, the shape differ
466 THE STEAMENGINE AND OTHER HEATMOTORS.
DIAGRAM FOR IDEAL
FIRST STAGE,
FIG. 244.
SUPERHEATED STEAM AND STEAMTURBINES. 467
DIAGRAM AS MODIFIED BY FRICTION LOSSES.
FIRST STAGE.
Y'
TWO STAGE IMPULSE TURBINE,
FIG. 245.
468 THE STEAMENGINE AND OTHER HEATMOTORS.
DIAGRAM AS .MODIFIED BY FRICTION LOSSES,
SECOND STAGE.
The entrance and exit angles of the buckets,
whether moving or stationary, are not neces
sarily made equal to each other, but are
modified to suit the energy distribution aimed
at in any given case.
FIG. 246.
SUPERHEATED STEAM AND STEAMTURBINES. 469
FIG. 247.
470 THE STEAMENGINE AND OTHER HEATMOTORS.
, Stationary
Condenser or
Exhaust Pressure
Boiler
Pressure
cc 5j
M
4
\
\
\
CfL
CO
Lost
Steam Velocity
X~
Condenser or
Ekhaust Pressure
FIG. 248. Diagrammatic Sketch of Parson's Turbine.
SUPERHEATED STEAM AND STEAMTURBINES. 473
ing materially from the lunes of the Curtis type, and hence is
easily recognized.
The outletopening between two buckets of a rotating vane
being smaller than the inlet opening, compels the steam to expand
and accelerate its motion, since a constant mass must pass between
the vanes. Force is required to produce this acceleration, and
this force produces a reaction which acts in the direction of the
rotating vane. Therefore the steam acts by impulse on the enter
ing face of the vane and by reaction on the leaving face.
In the De Laval turbine we noted that the wheel revolved in
lowpressure steam, and that the pressure was nearly the same on
both sides of the wheel. The Parsons turbinevanes revolve in
highpressure steam, and the pressures are unequal and must be
balanced either by balancing pistons or by an opposing turbine.
The general construction of the Parsons turbine is shown in the
crosssection, Fig. 249.
Clearance is objectionable, but often unavoidable. The sta
tionary blades in the Parsons turbine are carried by the casing, and
they must come as close as possible to the revolving drum to compel
the steam to pass between the blades. This clearance area is annu
lar in shape in the Curtis and in the Parsons turbine, the inner
diameter of the ring in the one being the diameter of the shaft
and in the other that of the steamdrum. Any vibration of the
axis, due to whipping, causes a considerable motion at a radius as
large as that of a drum, hence the clearance in the Parsons turbine
must be greater than that in the Curtis type.
Analysis of the Parsons Turbine. In discussing this turbine we
shall consider a stationary and a revolving row of blades as mak
ing a set or stage. The kinetic energy generated by the fall of
pressure in the stationary row is absorbed through its impulse
on the blades of the revolving row. The reaction caused by the
increase in the relative velocity from Vi to v 2 (Figs. 250 and 250# is
absorbed in the revolving row. The work done is then made up
of three parts.
1. The total kinetic energy created by fall of pressure
in the first row.
2. The reaction due to the increase of relative velocity
in the second row.
474 THE STEAMENGINE AND OTHER HEATMOTORS.
3. The kinetic energy in the steam due to its absolute
velocity at exit from .the revolving row.
Since the velocity at entrance to the first row of stationary
Stationary M M & JS M
FIG. 250a.
blades is negligible, the total kinetic energy generated there is
per pound of steam per second
SUPERHEATED STEAM AND STEAMTURBINES.
475
The reaction work due to the increase of relative velocity
from Vi to V2 is
The kinetic energy due to the absolute velocity of the steam
at exit from the first row of revolving blades is ^ . Hence
The net work done in the first stage is K=K 8 +K m ^ .
The total work done in the moving blades is K t =K a +K m .
The fraction called the "degree of reaction " is^.
In the second stage, if Vi is the absolute velocity of entrance
to the stationary row of blades and F 2 the absolute velocity at
exit from the revolving row, and if the relative velocity in the
Stag? A
Stage B <
Stage C <t
FIG. 251.
second row is increased from Vi to v% as before, the net work done
will be (Fig. 251)
Fi 2 F 2 2 v 2 2 v l 2
476 THE STEAMENGINE AND OTHER HEATMOTORS.
Condenser or
Exhaust Pressure
Fia. 252. Diagrammatic Sketch of HamiltonHolzwarth Turbines.
SUPERHEATED STEAM AND STEAMTURBINES. 477
If there are (n 1) similar stages the total work for n stages,
including the first, will be
2g 2g
+ (n
The HamiltonHolzwarth turbine is, like the Parsons tur
bine, a fullstroke turbine; that is, the steam flows in one con
tinuous belt or veil in screw line through the turbine.
The steam works only by impact, not by reaction, thus avoid
ing the balancing pistons of Parsons.
In the stationary blades, which reach up to the shaft in order
to restrict the dangerous clearance to a minimum, the steam
has a chance to expand and reach a certain velocity and a cer
tain direction in which it impinges the next running wheel.
The absolute velocities of the steam in this turbine are higher
than in the Parsons turbine, but they are lower than in the Curtis
and much lower than in the De Laval. In this turbine the steam
is expanded in every stationary blade down to a certain pressure
and accelerated up to a certain velocity, which is nearly exhausted
in the following runningwheel.
SteamEngine versus the SteamTurbine. The steamengine
and the steamturbine are often compared and it is desirable
to point out the advantages of each. The steamengine finds
its most efficient territory in the high ranges of pressure whilst
the turbine is best adapted to low ranges.* To deal with low
pressures the steamengine cylinders become enormous in size
hence difficult to construct, operate, and repair the mechanical
friction losses are excessive and the same is true of thermal losses
due to varying temperature of the cylinder walls due to thermal
cyclic changes. At low pressures the steamturbine is free of
these excessive mechanical and thermal losses.
A combination of the steamengine and steamturbine is
rapidly coming into favor. A good Corliss engine with cylinder
* At high ranges of pressure the steam turbine is handicapped by the
small specific volume of steam and the consequent high leakage and rotation
losses which increase directly with the pressure. In reciprocating engines
these losses are about constant no matter what the pressure.
478 THE STEAMENGINE AND OTHER HEATMOTORS
ratios of 1 to 2.5 or 1 to 3.5, exhausting at 15 or 20 pounds abso
lute, will have at normal load an efficiency of 72% of that of
the RankineClausius cycle. The steamturbine working from
15 or 20 pounds absolute down to a moderate vacuum will give
73% efficiency and 70% is guaranteed in the market. The com
bined efficiency (65 to 75% of the ideal cycle) is considerably
higher than that given by either engine or turbine alone.
In many cases the steamturbine can be profitably added to
existing plants. The lowpressure turbine may be used in rolling
mills or in certain cases where it is desirable to: (1) Increase
the capacity of an efficient engine plant. (2) Increase the effi
ciency of an inefficient engine plant. (3) Replace an inefficient
condensing plant.
That these effects may be accomplished is easily seen when
we remember that a plant of noncondensing engines with a
water rate of 30 or 35 pounds of water per kilowatt hour may
be converted into a turbineengine plant with a consumption
of 15 or 18 pounds of water per kilowatt hour even in compara
tively small sizes. In other words, for the same consumption
of coal and water an increase of 80 to 100% of capacity has been
obtained.
Turbine Auxiliaries. Ideally, the efficiency of the turbine
increases with each increase in the vacuum, but practically the
increase is not in proportion. In other words, the efficiency, as
measured at the coal pile, must consider the costs of producing
excessively high vaccua. If the injection water is warm the
condenser becomes inefficient owing to its inability to work with
small temperature differences between the discharge water and
the steam. As a result of the improvement in jet condensers
there has been an interchange in the efficiency position of the sur
face and jet condensers.
A good surface condenser should operate within 15 difference
of temperature between steam and discharge water and a good
barometric condenser should operate within 10. In practice,
twice these differences are often tolerated. There are on the
market condensers of the jet type that are able to operate within
2 to 5 of the steam temperature without bulky or wasteful
auxiliaries. For example, assuming a cooling tower capable of
SUPERHEATED STEAM AND STEAMTURBINES. 479
cooling the water down to the temperature of the air, 75 F.,
what vacuum will it be possible to maintain?
(1) A perfect condenser (no temperature difference between
steam and discharge water) would require 220 volumes of water
for 29 inches of vacuum. For 28 inches it would require 35
volumes.
(2) An efficient condenser of the jet type, working within 5
difference of temperature, can maintain 28 inches with 43 volumes.
(3) An ordinary jet condenser, working on 10 difference will
require 57 volumes to maintain 28 inches.
(4) The ordinary surface condenser, working with 20 differ
ence, cannot maintain 28 inches of vacuum without using the
impracticable amount of 140 volumes of water.
The more efficient jet type is responsible for reducing the
water consumption to onethird of that possible with the surface
condensing type.*
Among the recent improvements may be mentioned the Le
blanc rotary airpump attached to ejector condensers, illustrated
and described in Engineering, May 7, 1909. With this type of
plant it is stated that the vacuum obtained is never less than
98.5% of that theoretically possible and that 99% is often ex
ceeded, provided the joints are maintained reasonably airtight.
Steamturbines. In a turbineengine station suppose that
onehalf of the 500 horsepower of auxiliaries circulating air, feed,
and oilpumps, fans for furnaces, coal, and ashconveyors, coal
crushers, mechanical stokers, and lowpressure water service
are in continuous use, using 100 Ibs. of steam per I.H.P. and
exhausting into a feedwater heater. Assuming 13,000 horse
power for the turbine and an efficiency of 14 Ibs. of water per
horsepower, what would be the gain in economy by driving the
auxiliaries electrically and heating the feedwater by steam from
an opening in the turbine casing where the normal steampressure
is 15 Ibs. per sq. in. absolute? (Engineering, MayApril, 1906.)
*See papers in Power, by J. R. Bibbins, 19051909, and Rateau and
Hood, 1907.
CHAPTER XVI.
GASENGINES AND GASPRODUCERS.
Gasengines.
The Lenoir Cycle. This, the earliest gasengine cycle, natu
rally followed the characteristics of the steamengine cycle. It
has been practically abandoned from its lack of economy In
the Lenoir cycle (Fig. 253)
FIG. 253.
1. Gas and air are sucked in for less than halfstroke.
2. The charge is fired and there is an immediate rise in
pressure at practically constant volume at this point in the
stroke.
3. Expansion follows during the remainder of the stroke.
4. The piston returns, sweeping out the gases for the full
stroke.
The Beau de Rochas or Otto Cycle. We shall see from the
entropy diagrams that it is economical to compress the gases
in a cylinder before igniting them. The Lenoir engine was double
acting and gave trouble from overheating. To avoid these diffi
culties, the Otto engine is singleacting, so that the cylinderbore
and the piston, on one end, are exposed to atmospheric tem
perature. The following is the Otto cycle (Fig. 254).
1. The gas to be burnt and the air to support combustion
are drawn past some form of governor into the cylinder during
the whole of one stroke, AB.
480
GASENGINES AND GASPRODUCERS.
481
2. On the returnstroke, BC, this gas mixture is com
pressed into the clearance space of the engine.
3. The gas is exploded, the piston being practically on
the deadcenter, and expansion during the entire stroke fol
lows, CD and DE f '.
4. The burnt gases must be swept out during the return
stroke, E'E and BA.
It is evident that there can only be one explosion and one
effective stroke in four strokes or two revolutions.
In one form of the twocycle singleacting engine, a closed
vessel is obtained by encasing the engine. We must examine
the cycle first on the crank side of the piston and then on the
other side. On the compression stroke, or the stroke towards
the head, air is drawn into the case. On the next or explosion
stroke this air is slightly compressed. We must now examine
into the. events that occurred on the other side of the. piston
during these two strokes. After the explosion of the charge and
before the expansion is completed, ports are uncovered to allow
the air in the case to sweep through the cylinder and displace
the burnt gases. This action is called scavenging. A further
movement of the piston closes the airports and opens gasports
and the gas charge is admitted. The piston now being at the
end of its stroke, the returnstroke is made, compressing the mix
ture of gas and air.
482 THE STEAMENGINE AND OTHER HEATMOTORS.
Gasengines, then, are divided into fourcycle, twocycle, single
acting, doubleacting, scavenging, and nonsea vengi ig types.
The more regular action of the twocycle type is offset by its
necessary air and gaspumps (in large engines). The short
time for suction may prevent proper scavenging. Improper
scavenging produces premature ignition which is unsafe in
large engines. Where the burnt gases are thoroughly swept
out, or where water is injected on the suctionstroke, high com
pression up to 400 Ibs. per sq. in. may be used even with gases
containing large amounts of hydrogen. The water about a
pint to the horsepower although heated to 3500 F. will not
dissociate on account of the high pressure. It, therefore, acts
as a thermal flywheel. Combustible liquids like alcohol or kero
sene could be similarly used. One great advantage of the four
cycle engine is that the time required to make the double stroke
tends to secure a charge that is more thoroughly mixed and
at a higher temperature than is possible in other types.
In governingengines of any considerable size the cutting out
of an entire charge is a method that is no longer used. If the gas
alone is throttled, below half load the mixture is too weak and may
not explode. By throttling both air and gas the mixture will
ignite properly at all loads, but with heavy throttling the internal
pressure may be 6 or 7 pounds below the atmosphere, and this
becomes a load on the engine. With this system, unless the com
pression is heavy initially under light loads, the compression will
be too light and lean mixtures will not explode. In large engines
the compression ranges from 170200 pounds per square inch.
Igniters furnish much vexatious trouble. The hottube is no
longer used except with small sizes. Lowtension magnetos are
now much used, but they will give place to hightension systems
with the introduction of reliable insulation. Mica tubes and
washers furnish the best insulation at present.
To keep the metal of the engine cool, much attention must be
paid to the water circulation. The water must not leave deposits
of any kind, the circulation must be positive in all parts, the
cylinderheads and valvechambers meriting much attention. Pis
tons are cooled through hollow pistonrods.
GASENGINES AND GASPRODUCERS. 483
Cooling water required per B.H.P.hour for engines of 200 to
1000 H.P. (quoted from the "Gasengine ") :
Gallons.
''Cylinders, cylinderheads, and stuffingboxes 4 to 5J
Pistons, pistonrods If " 2f
Valve boxes and seats and exhaustvalves " 1}
" These figures imply water entering at 53.659 F. and leaving
the cylinderjackets at 7795 F., the pistons at 95104 F., and
the valve seats and boxes at 113 F."
The following are approximate heat balances :
c
Heat converted into work
asoline
motors.
16
51
31
2
Gasengines.
22
33
44
1
19.4
33
43
4.6
6.3
87
21
35
40
4
15.47
85
25
27
38
10
11.15
85
22
43
36
1
17.12
86
Heat lost to jacketwater
Heat carried off by exhaustgase 3. .
Radiation etc
Brake horsepower. . .
Mechanical efficiency, per cent. . . .
. .
Cost per B.H.P. Cost 20 H.P.
Relative Costs. per Hour, for 300 Days
Cents. of 10 Hours.
''Electricity, 5 c. per Kw 5.00 $.$,000
Gasoline. 20 c. per gal 2.95 1,770
Steam, coal $3.50 2.49 1,494
Gasoline, 15 c. per gal 2.33 1,398
City gas, $1 per M 2.25 1,350
Crude oil, 5 c. per gal 2.10 1,260
Gasoline, 10 c. per gal * 1 .70 1,020
Suctionproducer, coal $4.25 1 . 23 738
" Depreciation, interest, and repairs were figured at 15 per cent of
the first cost; oil, fuel, attendance, etc., were all added in the costs."
(Quoted from " Gasengines.") Changes in the cost of electricity
and in the cost of coal, where anthracite must be used for the pro
ducer, may change these figures materially. Allow 20 cu. ft. of
gas and oneeighth gallon of gasoline per B.H.P.
Alcohol may be made from substances containing either starch
or sugar. In the former class we find potatoes, corn, rice, barley,
and wheat; in the other class are sugarbeets and molasses from
cane or beetsugar. Alcohol can be made from otherwise waste
material, as from diseased potatoes, bitter molasses, sawdust, corn
pith, etc. By denaturizing the alcohol it may be made unfit for
human consumption. This is accomplished by adding substances
484 THE STEAMENGINE AND OTHER HEATMOTORS.
that vary with the subsequent use of the alcohol. Such substances
are pyradin, picolin, benzene, wood alcohol, gasoline, acetone oil
derived from the grease of sheepwool. Wood alcohol is CH 4 0.
Ethyl alcohol (spirits of wine), C 2 H 6 0, is from the fermentation
of grapejuice or glucose.
The use of small motors is growing enormously. The produc
tion of gasoline is limited, being about 2% of the petroleum ob
tained. The price is therefore limited by the demand. The fol
lowing sums up the advantages of alcohol when compared to
gasoline :
1. It can be produced as cheaply as gasoline.
2. The raw materials are illimitable, hence no fear of
scarcity.
3. It is far safer. Fires can be extinguished with water.
4. It is clean and sanitary and leaves no deposits in the
cylinder.
5. It can stand far more compression than gasoline in small
nonscavenging engines.
6. In boats the leakage from a defective pipe will be mixed
with the bilge water and unexpected explosions prevented.
7. With high compression more power can be obtained from
alcohol in small motors than from gasoline, since it is dangerous
to compress the latter to an equal extent. The consumption is
1.1 pints to the B.H.P. in a 10H.P. motor.
Calorific Power of Gases. The calorific power of a compound
gas, w^hich can be burnt or oxidized, should not be computed from
the calorific power of its component elements, as heat may have
been given out or may have been absorbed when its elements
united in its formation. For example, the calorific power of 16
pounds of marshgas, CH 4 , computed from its elements would be
= 12x14,500 = 174,000,
H= 4x63,000 = 252,000,
or 25,600 per Ib.
By actual experiment the calorific power is 23,600, or a differ
ence of 3000 B.T.U. On the other hand, acetylene gives out
GASENGINES AND GASPRODUCERS. 485
more heat than that derived from a theoretical computation. In
one pound of acetylene there is .923 pound of C and .077 pound
of H. Therefore
C = 14,500 X. 923 = 13,383
H = 63,000 x. 077= 4,851
18,234
From experiment the actual heatequivalent is 21,500, or an excess
of 3266 B.T.U.
We shall need the following calorific powers :
Marsh gas (methane), CH 4 21,000 B.T.U.
defiant gas, or ethylene, C 2 H 4 18,900 "
Acetylene 20,750 "
From the above the heatequivalent of any mixture of these
gases may be obtained, as in the following example :
Pounds.
Marshgas 2 . 34 X 21,000 = 49,140
Ethylene (olefiant gas) 13 X 18,900 = 2,457
Hydrogen .. .60X63,000= 37,800
Carbon monoxide 20.32X 4,500= 91,440
Nitrogen 60. 17
Carbon dioxide and oxygen 16.44
100.00 180,837
Thermal units per pound = 1808
If the weight of the gas per cubic foot is known, then the thermal
value per 1000 cubic feet may easily be calculated.
Rise in Temperature in Gas Combustion. The theoretical rise
in temperature due to the heat liberated in combustion may be
calculated if we make certain assumptions :
1. That the gases are burnt in a nonheatabsorbing cham
ber, so that all the heat is spent in raising the temperature of
the gases.
2. That we know the weights of the gases composing the
mixture and their specific heat either at constant volume or at
constant pressure, depending upon the corresponding conditions
of combustion.
Hence, if W i} W 2 , Wa, TF 4 , W 5 represent the weight of the gases
486 THE STEAMENGINE AND OTHER HEATMOTORS
present, and Ci, C 2 , CB, C*, C 5 represent the proper specific heats,
then H = WC
where H = total heat of combustion,
T = nse in temperature.
It is evident if W and W 5 represent gases that were not
or could not be burned that the resulting rise in temperature
would be very much less than it would have been had they been
absent. Thus, when gases are burned in air the necessity of
raising the temperature of the noncombustible nitrogen decreases
very materially the possible rise in temperature of the whole
mixture.
Producergas (Figs. 255, 256, and 257). In the gasproducer
air passes in and burrs part of the fuel coal or coke into C0 2 .
FIG. 255.
The nitrogen of the air and the C0 2 rise, and the latter, if the
temperature is high enough, may break up into 2 (CO). Very
little use could be made of this CO on account of the large amount
of inert nitrogen that accompanies it.
Suppose, however, we blow steam on the redhot coals also,
the steam will be decomposed, thus: C+H 2 = CO+2H.
The CO obtained in this way is unaccompanied by inert nitro
gen, but, on the contrary, carries with it a large percentage of H
which has high calorific power. Evidently the more steam that
is decomposed the better, but it requires heat to decompose the
steam and this heat must be supplied by the heat evolved when
the air unites with carbon to form carbon monoxide. The rela
tion that exists between the amount of CO formed by the "air
GASENGINES AND GASPRODUCERS.
487
burned carbon" and that formed by the " steamburned carbon"
is, theoretically, that of equality as indicated below.
In the formula C+H 2 = CO+2H we may say that 2 pounds
of H and 16 pounds of united with 12 pounds of C to form
28 pounds of CO and 2 pounds of H.
FIG. 256.
Heat absorbed (per pound of H) in the separation of H
and when combined in the form of steam
= 63,0009[966 + (21232)] 52,500
Heat given out in burning 6 pounds of C to CO = 6 X4500 +27,000
Heat absorbed for each pound of carbon burned by the
steam = 25500/6.
25,500
4,250
As 4500 thermal units are liberated by the "airburned
carbon" per pound, and this must provide for all heat radiated
and otherwise wasted, it is evident that the percentage of car
488
THE STEAMENGINE AND OTHER HEATMOTORS.
bon that may be steamburned must be very much less than
that which is airburned. It is feasible to burn 3 pounds of
carbon with air to 1 pound of steamburned carbon.
If air is a mixture of
Ibs. CO @ 12.8 cu. ft. per lb.= 89.6
" N 12.77 " " " =178.78
3 Ibs. C+4lbs. O = 7
Nitrogen with 4 Ibs. O =14
1 Ib. C burned to CO by
steam = 2.33 " CO 12.8 " " "
To furnish 1J Ibs. of O
requires fi 8 = .17 " H @ 178.93 " " "
Cubic feet per pound of
29.82
29.82
FIG. 257.
Expressed in percentage the gas has the following volume and
weight.
Volume. Weight.
Carbon monoxide, CO ........... 36 . 4% 39 . 7%
Hydrogen, H ............ 9.1 .7
Nitrogen, N ............ 54 . 5 59 . 6
In finding the heat liberated when one pound of CO is burned
to C02 it is necessary to find the amount of C burned. Further,
we must remember that if one pound of C burned to CO gives
4500 B.T.U. and 14,500 if burned to C0 2 it will follow that
for each pound of C in carbon monoxide only 10,000 B.T.U.
will be liberated when that gas is converted into C0 2 .
The heatequivalent of the above gas will be:
.397 x
= 1707,
.007X53000=2^ B.T.U.
or
2078
14
148 B.T.U. per cu. ft.
GASENGINES AND GASPRODUCERS. 489
We have seen that the adiabatic compression of air is accom
panied by a great waste of power if the air is to be conveyed
through long pipes, as the air will lose all heat due to tempera
ture above its surrounding envelope from conduction, radiation,
etc. In a similar way producergas often loses all its heat above
that due to atmospheric temperature. To purify the gas it
is led through scrubbers and it comes into intimate contact with
streams of water. Producergas is, in general, an agent to pro
duce heat at some place other than at the place where the gas
was generated. It is desirable, then, to convert all heat gen
erated in the producer into some form of latent energy similar
to the molecular separation in the case of steam.
Gas from Soft Coal. Anthracite and coke are alone used as
fuel in gasproducers in combination with gasengines in small
plants. The high cost of anthracite prevents competition with
steamengines in many cases. By the use of soft coal a much
richer and cheaper gas may be made. The difficulties to be over
come lie in the presence of tar, ammonia, dust, and other
residual matter. Caking coals cannot be used, as they melt
and stop the passage of the gases. In large plants, scrubbers
of various kinds are used as well as dustcollectors.
The tarry deposits have always given trouble. In recent
producers, however, by the use of underfeeding, these deposits are
brought into contact with hot fuel and are decomposed, giving free
H and marsh gas. Professor Fernald, at a meeting of the
A. S. M. E., read a paper on "Results of the Preliminary Pro
ducergas Tests by the U. S. Geological Survey Coaltesting
Plant at St. Louis." A brief summary of this paper in the
shape of tables of twentyfour of the principal tests is given
in Power, .January, 1906. "The experience gained during these
tests showed that neither a purifier nor an economizer is required
in order to use bituminous coal." These tables give the average
composition of the gas from coals from various parts of the coun
try by volume, the number of cubic feet per pound of coal, and
the heatunits per cubic foot of gas. The third table gives eco
nomic results of the use of the gas. In general, a cubic foot of
gas gave 140150 B.T.U., but the number of cubic feet of gas
per pound of coal varied from 25 to 82.
490 THE STEAMENGINE AND OTHER HEATMOTORS
Calculation of Pressure in the Gasengine. Theory and prac
tice always agree when the theory has been derived from a con
sideration of all the facts. If a definite weight of gas of known
composition mixed with a definite weight of air is fired, af ier hav
ing been drawn into a gasengine and compressed into a definite
clearance space, the resulting pressure will ordinarily be less than
half the expected pressure. As a definite amount of heat is liber
ated which should result in a definite rise in temperature and pres
sure, there must be a source of heat loss. This is found in the heat
absorbed by the cylinder walls. This one fact compels us to resort
finally to experiment under actual conditions to obtain accurate
results.
For example, the mixture that gives the highest pressure will
not develop the most power hi a given engine. Suppose a mixture
of one part gas and four parts air gave a very high theoretical tem
perature and pressure, the heat loss to the walls would be high,
due to the high temperature of the gas. Suppose that to the same
weight of gas double the volume of air were used, the temperature
of the gas would be lower, the heat loss less, and the heat remaining
in the gas greater. We may or may not get more work out of the
new mixture. Whilst there is more heat in it, this heat is at a
lower temperature.
Brannt records experiments made with mixtures of oilgas
specific gravity .68:
Oilgas, Volumes. Air, Volumes. Explosive Effect.
1 4.9 None
5. 6 to 5. 8 Slight
6 to 6 . 5 Heavy
7 to 9 Very heavy
10 to 13 Heavy
14 to 16 Slight
17 to 17.7 Very slight
18 to 22 None
Even if the best mixture of gas and air is used, threefourths to
fourfifths of the heat is wasted either in the jackets, exhausts, or
radiation.
Indicator and Entropycards. The theoretical cards from
4cycle and 2cycle engines using any explosive mixture are iden
tical. The card from the Diesel oilengine, however, differs in
GASENGINES AND GASPRODUCERS.
491
a few particulars. The practical card, Fig. 1896, differs very
materially from the theoretical one, taking some such form as
ABCD'FBA, or, when the engine is not properly adjusted, some
such form as that indicated by ABCD"E"BA.
The entropy analysis given below is based on an article by
Professor Reeve, Trans. A. S. M. E., Vol. XXIV.
The line AB of the indicatorcard (Fig. 254) is represented by
the point B in the entropy diagram (Fig. 258), since the position
FIG. 258.
of B is sufficient to indicate the thermal characteristics of the fujl
gas charge. If the compression is truly adiabatic, BC is the
course of our tracingpoint. If the walls absorb heat there will be
a loss of entropy, and the tracingpoint will wander to the left.
The charge is fired and the gas is heated at constant volume, so
that the piston is practically stationary during the formation of
lines CD or C'D'. To prevent overheating the cylinder walls, a
waterjacket which abstracts heat and wastes it must be applied
for mechanical reasons. Its effect in decreasing economy is seen
in the difference of the positions of D and D'. If the expan
sion were truly adiabatic the straight line DE would be followed.
A careful plotting of the entropy changes would give some such
492 THE STEAMENGINE AND OTHER HEATMOTORS.
line as D'ZE' '. The initial decrease in entropy of the line D'Z
indicates a very rapid loss of heat, but the swerving of the curve
ZK to the right indicates the reception of heat by the gas from the
cylinder walls. This action is similar to the reevaporation of
condensed steam toward the end of the stroke in a steamengine.
The line EB indicates expansion at constant volume.
To draw the entropy diagram of the Otto cycle the following
artifice and form will be found useful.
On the indicatorcard (Fig. 254) and the entropy diagram
(Fig. 258) let us suppose the suctionstroke line AB has been
made. Let us ideally compress the gas from B at constant pres
sure (abstracting heat) along the line BA till some point y is
reached. Then let the gas be heated at constant volume, thus
tracing the line yXZ perpendicular to AB in the indicator card.
At the points X and Z the temperature and entropy of the gas
would be identical with that required by those points on the indi
cator diagram. The point y is an auxiliary that will disappear.
At the points B and y we are dealing with the same mass of a
perfect gas, hence
T B T v
Cooling constant mass at constant pressure,
T " V '
1 y v y
Heating at constant volume,
TV PV TJL = PV
rp p * rp r>
J x 1 x 1 z * z
At the points X and B we are dealing with the same mass of a per
fect gas, hence we may write
GASENGINES AND GASPRODUCERS. 493
The ratio of .one pressure to another, or of one volume to another,
is easily found if both are measured on a fine decimal scale. Divide
the indicatorcard into a series of two points, such as (X, Z),
(X', Z'), etc., and tabulate the ratio
^ ?L ?*L *JL * V** Yj I*
PB'PB'PB' ?B ' ' V x > V f > V x ,> V,,' '
The value of T B must be assumed. It lies between 600 F.
and 670 F. (absolute). The absolute values of all derived quan
tities are affected by the uncertainty in the absolute value of T Bf
but the relative values are absolutely unaffected. Making this
assumption the values of the temperatures at all points are obtained
from the equation
. T P x V B
From the ideal method of obtaining the points y and X we may
write our entropy equation
T T
<t>x<l>y = C v \Qge~ and <t>B<f>y = C P logt^~,
1 y 1 y
Cy and Cp being the thermal specific heats at constant volume and
constant pressure.
By subtraction
m m
<t>x~ 4>B = C V log, ~ C P loge TiT
C F (log.J 2 1.404 log. J?
= 2.3026 C F (log 10 Jpl.404 lo glo ~
= 2.3026 C v (log  1.404 log
As a rule only relative values of entropy are required, hence the
coefficient 2.3026 C v may be omitted.
494 THE STEAMENGINE AND OTHER HEATMOTORS.
y
In the following form the term 1.404 log pF is placed first,
to bring together the two quantities whose difference is desired.
Suppose TT = 1.49, its log = . 1732 . . (1)
T r.
A x " " =.06928
.004 x " " =.00069
.2432
jr = 1.778, " " =.2499 (2)
B
^ = 3.602, its log = .5565 (3)
* JC
P 2
as (j> x </>B +log TT = </>z <t>B .5632
LX
T x P x V B
Subtracting (1) from (2), since log  =log p log y,
* B * B ' x
log  .0767.
B
Assume T B = 600 F. A., log 600 = 2.7781
log T x = 2.8548 ... (4)
7^ = 715.8 F. A.
F.
p
Adding log ^ to log T x , (3) + (4) = log T z = 3.41 13
t x
r z =2578F.A.
Therefore, noting the use of ratios:
1. With the sliderule set to the initial absolute pressure,
take each point on the card in turn, divide the pressure at
GASENGINES AND GASPRODUCERS. 495
that point by the initial pressure, and note the logarithm of
the result.
2. With the sliderule set to the total length of the indi
catorcard (including clearance) divide it by the total volume
at each point of the card in turn, and obtain the logarithm of
the quotient.
404
3. Add to (2) TTTTT: of itself by sliderule or by arithmetic.
4. The difference found by subtracting (3) from (1) is
the entropy of the desired point.
5. The difference found by subtracting (2) from (1) is the
logarithm of the temperature ratio; this logarithm should be
set down at one side.
6. With the slide rule set to the initial absolute tempera
ture enter the table of logarithms with (5), and multiply
its number by the initial absolute temperature; the result
is the absolute temperature of the desired point. Thus, let
!T 5 600 F. A.:
(1) log  =0.2499
(2) log JS =0.1732
4
^ of ditto =0.06928
(4) Entropy =0.0067
(5) log ~ =0.0767
(6) T absolute = 715.8
of ditto =0 . 00069 460 . 9
(3) = . 2432 T Fahrenheit =255 F.
In this way some twenty points, or sufficient for an entire
analysis, can be calculated and plotted inside of an hour.
A natural gas has the following composition :
Carbon dioxide (and H 2 S) . * ........ 1 . 80 per cent
Oxygen ........................... 70 " "
Hydrocarbon ...................... 50 " "
Carbon monoxide .................. 55 tl "
Hydrogen ......................... 60 " "
Methane ......................... 92.05 " "
Nitrogen ......................... 3.80 " "
496 THE STEAMENGINE AND OTHER HEATMOTORS.
What is the thermal value of this gas per cubic foot? Assum
ing its value at 1000 B.T.U per cubic foot, what would be the
efficiency of a gasengine using 12.7 cubic feet per B.H.P. With a
thermal efficiency of 27.6%, how many cubic feet of gas will a
13" Xl4" engine use making 257 revolutions per minute? Assume
a clearance of 20% and a mixture of gas and air in the proportion
of 1 to 11, what will be the theoretical temperature and pressure
after an explosion, the piston being on the deadcenter?
Diesel Cycle. In this remarkable cycle
1. The air alone and not the explosive mixture is compressed.
2. The degree of compression exceeds that of all other types.
3. This compression is adiabatic and nothing is done to
make it isothermal.
4. The degree of compression is so great that the tempera
ture causes spontaneous combustion, as the charge or com
bustible is forced in at a higher pressure.
5. Just as powder for cannon is made in grains as large as
an inkstand to delay combustion and produce a uniform rather
than a rapidly diminishing pressure, so in this motor the charge
is supplied gradually for the same purpose.
BA
PIG. 259.
FIG. 260.
The indicatorcard and entropy diagram are represented in
Figs. 193 and 194, but not to scale. The diagrams are lettered to
FIG. 261. Valves of Diesel Engine.
497
GASENGINES AND GASPRODUCERS.
499
indicate the same events. AB is the suction ; BC is the compres
sion; CD is the preliminary and DB the after or isothermal heat
lines due to the gradual combustion of the injected oil; EF is the
adiabatic expansion line; and FB is the expansion line at constant
volume. Operating between 500 and 35 pounds per square inch,
this motor has an efficiency ranging between 36 and 45%. The
following data are from the Journal of the A. S. N. E., November,
1905:
Date
Trial
Feb 13
Trial
Feb. 14
Trial
Feb 14
Trial
Feb 14
Time
f 3.55P.M.
! to
9.17A.M.
to
il.21 15
to
2.01 30
to
Duration minutes..
I 5.55
120
11. 12 15
115 25
1.30 15
129
2.59 3
58
Diam. of cylinders, inches
Stroke of pistons feet
22.05
2 4605
Revs, per min
150.16
152.8
150.3
150.2
Jacketwater per min
166 8
169 85
157 85
140
Initial temp, of jacketwater, F
Final temp, of jacketwater, F
Temp, of outside air, F
46.3
125
48
46.3
127.4
48
46.3
104.6
48
46.3
82
48
Temp, of exhaustgases, F
783
806
496
275
Analysis of exhaustgases: CO 2
5.6
6.8
3.2
N
" " " Air
42.9
51 5
51.3
41 9
21.5
75 3
Oil used pounds
390 3
398
221 1
44 23
Oil used per hour pounds
195 1
207 2
102 8
45 76
Blast pressure, atmospheres
Max. pres. shown by indicator dia j
grams in pounds per sq. in 1
61.5
510
515
66.3
515
525
50.9
490
480
35
485
480
M.E.P., pounds per square inch:
On first piston
525
82 9
500
80 7
505
51 6
500
23 2
On second piston
92 3
93 9
52 6
20.1
On third piston
110
115 6
64 8
33.9
Average in the three cylinders. .
Indicated horsepower
95.05
609.3
96.7
634 8
56.33
363.6
25.4
163.3
Oil per I.H.P. per hourpounds
.3202
3264
.2828
.28
Output of dynamo kw
333
352
168 2
22.24
Brake HP of engine
475 5
502 5
245
546
H P absorbed in friction
133 8
132 8
118 6
10 87
B H P /I H P
78
805
675
334
Power absorbed by motor, kw
H P given out by motor
38
44 8
41
48 3
31.6
36 8
23.6
26 2
I.H.P. in compressor cylinders
Power absorbed in belt and compres
sors HP.
36
8
40
8
28.8
8
18.2
8
Estimated B H P of engine
435 1
458 7
213 8
32.4
Estimate of mech. effic. if pump had
been driven by engine
Oil per brake H.P., pounds
.715
.444
.723
.451
.588
.481
.198
1.415
500
THE STEAMENGINE AND OTHER HEATMOTORS.
Tri
ill.
Tria
1 II.
B.T.U.
Per Cent.
B.T.U.
Per Cent.
To calorific value of one pound of oil
20050
100
20,050
100
By heatequivalent to work done
7 944
39 6
7,794
38.9
By heat carried off in jacketwater
4 070
20 3
4,110
20.5
By heat carried off in exhaustgases
By radiation and error
7,030
1 006
35.1
5
6,056
2,090
30.2
10.4
To calorific value of oil used per H. P. per min.
By heatequivalent to work done
107
42.4
100
39 6
109
42.4
100
38.9
By heat carried off in jacketwater
21.7
20 3
22.3
20.5
By heat carried off in exhaust gases
37 5
35.1
32.9
30.2
By radiation and error
5.4
5
11.4
10.4
Trial
III.
Tria
IV.
B.T.U.
Per Cent.
B.T.U.
Per Cent.
To calorific value of one pound of oil
20,050
100
20,050
100
By heatequivalent to work done
8998
44 9
9078
45.3
By heat carried off in jacketwater
By heat carried off in exhaustgases
By radiation and error. ...
5,300
7,200
1 438
26.4
35.9
7 2
6,570
} 4,402
32.8
21.9
To calorific value of oil used per H.P. per min
By heatequivalent to work done
By heat carried off in jacketwater
By heat carried off in exhaustgases
By radiation and error
94.5
42.4
25
33.9
6.8
100
44.9
26.4
35.9
7.2
93.6
42.4
30.6
J20.6
100
45.3
32.8
21.9
"The air for pulverizing the oil and spraying it into the cylinders
was compressed in an independent pair of threestage vertical air
compressors, worked by a twothrow crankshaft, beltdriven by a
motor receiving current from the dynamo upon the engine crank
shaft. This wasteful arrangement as compared to driving the
compressors direct was adopted to meet special conditions."
A study of the tables will furnish problems, and will give a
more definite conception of the engine than can be obtained from
a description.
GASENGINES AND GASPRODUCERS. 501
RULES FOR CONDUCTING TESTS OF GAS AND OILENGINES.
CODE OF 1901.*
I. Objects of the Tests. At the outset the specific object of
the test should be ascertained, whether it be to determine the ful
filment of a contract guarantee, to ascertain the highest economy
obtainable, to find the working economy and the defects as they
exist, to ascertain the performance under special conditions, or to
determine the effect of changes in the conditions, and the test
should be arranged accordingly.
Much depends upon the local conditions as to what prepara
tions should be made for a test, and this must be determined
largely by the good sense, tact, judgment, and ingenuity of the
expert undertaking it, keeping in mind the main issue, which is
to obtain accurate and reliable data. In deciding questions of
contract, a clear understanding in regard to the methods of test
should be agreed upon beforehand with all parties, unless these are
distinctly provided for in the contract.
II. General Condition of the Engine. Examine the engine and
make notes of its general condition and any points of design, con
struction, or operation which bear on the objects in view. Make
a special examination of all the valves by inspecting the seats an 1
bearing surfaces, note their condition, and see if the pistonrings
are gastight.
If the trial is made to determine the highest efficiency, and the
examination shows evidence of leakage, the valves, pistonrings,
etc., should be made tight and all parts of the engine put in the
best possible working condition before starting on the test.
III. Dimensions, etc. Take the dimensions of the cylinder or
cylinders whether already known or not ; this should be done
when they are hot and in working order. If they are slightly worn,
the average diameter should be determined. Measure also the
compression space or clearance volume, which should be done,
if practicable, by filling the spaces with water previously meas
ured, the proper correction being made for the temperature. (See
Section III, Steamengine Code.)
* Trans. A. S. M. E.
502 THE STEAMENGINE AND OTHER HEATMOTORS.
IV. Fuel. Decide upon the gas or oil to be used, and if the
trial is to be made for maximum efficiency, the fuel should be the
best of its class that can readily be obtained, or one that shows
the highest calorific power. (See Section IV, Steamengine Code.)
V. Calibration of Instruments Used in the Tests. All instru
ments and apparatus should be calibrated and their reliability
and accuracy verified by comparison with recognized standards.
Apparatus liable to change or to become broken during the tests,
such as gages, indicatorsprings, and thermometers, should be
calibrated both before and after the experiments. The accuracy
of all scales should be verified by standard weights. In the case of
gas or watermeters, special attention should be given to their
calibration, both before and after the trial, and at the same rate
of flow and pressure as exists during the trial.
(a) Gages. (See Section V, Steamengine Code.)
(b) Thermometers. (See Section V, Steamengine Code.)
(c) Indicatorsprings. The indicatorsprings should be cali
brated with the indicator in as nearly as possible the same condi
tion as to temperature as exists during the trial. This temperature
can usually be estimated in any particular case. A simple way of
heating the indicator is to subject it to a steampressure just before
calibration. Compressed air or compressed carbonicacid gas are
suitable for the actual work of calibration. These gases should be
used in preference to steam, so as to bring the conditions as near
as possible to those w r hich obtain when the indicators are in actual
use. When compressed carbonicacid gas is used, and trouble
arises from the clogging of the escapevalves with ice, the pipe
between the valve and gastank should be heated. With both air
and carbonic acid the pipes leading to the indicator should also be
heated if it is found that they are below the required temperature.
The springs may be calibrated for this class of engines under a
constant pressure if desired, and the most satisfactory method is
to cover the whole range of pressure through which the indi:ator
acts : first, by gradually increasing it from the lowest to the highest
point, and then gradually reducing it from the highest to the lowest
point, in the manner which has heretofore been widely followed
by indicatormakers; a mean of the results should be taken. The
calibration should be made for at least five points, two of these
GASENGINES AND GASPRODUCERS. 503
being for the pressures corresponding to the maximum and mini
mum pressures, and three for intermediate points equally distant.
The standard of comparison recommended is the deadweight
testing apparatus, a mercury column or a steamgage, which has
been proved correct by reference to either of these standards.
The correct scale of spring to be used for working out the mean
effective pressure of the diagrams is the average based on this cali
bration, ascertained in the manner pointed out in Section XIV,
Steamengine Code.
(d) Gasmeters. A meter used for measuring gas for a gas
engine should be calibrated by referring its readings to the dis
placement of a gasometer of known volume, by comparing it with
a standard gasmeter of known error, or by passing air through the
meter from a tank in which air under pressure is stored. If the
latter method is adopted, it is necessary to observe the pressure of
the air in the tank and its temperature, both at the tank and at
the meter, and this should be done at uniform intervals during the
progress of the calibration. The amount of air passing through
the meter is computed from the volume of the tank and the ob
served temperatures and pressures.
The volume of the gas thus ascertained should be reduced to
the equivalent at a given temperature and atmospheric pressure,
corrected for the effect of moisture in the gas, which is ordina ily
at the saturationpoint or nearly so. We recommend that a
standard be adopted for gasengine work, the same as that used
in photometry, namely, the equivalent volume of the gas when
saturated with moisture at the normal atmospheric pressure at a
temperature of 60 F. In order to reduce the reading of the volume
containing moist gas at any other temperature to this standard,
multiply by the factor
459.4+60 6 (29.92 s)
459.4+ t ' 29.4
in which b is the height of the barometer in inches at 32 F., t the
temperature of the gas at the meter in degrees F., and s the vacuum
in inches of mercury corresponding to the temperature of t obtained
from steamtables.
504 THE STEAMENGINE AND OTHER HEATMOTORS.
For calibrating watermeters refer to Section V, Steamengine
Code.
VI. Duration of Test. The duration of a test should depend
largely upon its character and the objects in view, and in any case
the test should be continued until the successive readings of the
rates at which oil or gas is consumed taken at, say, half hourly
intervals become uniform and thus verify each other. If the
object is to determine the working economy, and the period of
time during which the engine is usually in motion is some part of
twentyfour hours, the duration of the test should be fixed for this
number of hours. If the engine is one using coal for generating
gas, the test should cover a long enough period to determine with
accuracy the coal used in the gasproducer; such a test should be
of at least twentyfour hours' duration, and in most cases it should
extend over several days,
VIIc Starting and Stopping a Test. In a test for determining
the maximum economy of an engine, it should first be run a suffi
cient time to bring all the conditions to a normal and constant
state. Then the regular observations of the test should begin and
continue for the allotted time.
If a test is made to determine the performance under working
conditions, the test should begin as soon as the regular prepara
tions have been made for starting the engine in practical work,
and the measurements should then commence and be continued
until the close of the period covered by the day's work.
VIII o Measurement of Fuel. If the fuel used is coal furnished
to a gasproducer, the same methods apply for determining the
consumption as are used in steamboiler tests. (See Vol. XXI,
p. 34.)
If the fuel used be gas, the only practical method of measure
ment is the use of a meter through which the gas is passed. Gas
bags should be placed between the meter and the engine to diminish
the variation of pressure; and these should be of a size proportion
ate to the quantity used. Where a meter is employed to measure
the air used by an engine, a receiver with a flexible diaphragm
should be placed between the engine and the meter. The tem
perature and pressure of the gas should be measured, as also the
barometric pressure and temperature of the atmosphere, and the
GASENGINES AND GASPRODUCERS. 505
quantity of gas should be determined by reference to the calibration
of the meter, taking into account the temperature and pressure of
the gas.
If the fuel is oil, this can be drawn from a tank which is filled
to the original level at the end of the test and the amount of oil
required for so doing being weighed; or, for a small engine, the oil
may be drawn from a calibrated vessel such as a vertical pipe.
In an engine using an igniting flame the gas or oil required for
it should be included in that of the main supply, but the amount
so used should be stated separately if possible.
IX. Measurement of Heatunits Consumed by the Engine.
The number of heatunits used is found by multiplying the number
of pounds of coal or oil or the cubic feet of gas consumed by the
total heat of combustion of the fuel as determined by a calorimeter
test. In determining the total heat of combustion no deduction
is made for the latent heat of the water vapor in the products of
combustion. There is a difference of opinion on the propriety of
using this higher heating value, and for purposes of comparison
care must be taken to note whether this or the lower value has
been used. The calorimeter recommended for determining the
heat of combustion is the Mahler for solid fuels or oil, or the
Junker for gases, or some form of calorimeter known to be equally
reliable. (See Poole on "The Calorific Power of Fuels.")
It is sometimes desirable, also, to have a complete chemical
analysis of the oil or gas. The total heat of combustion may be
computed if desired from the results of the analysis, and should
agree well with the calorimeter values. (See Section XVII,
Boilertest Code.)
In using the gas calorimeter, which involves the determination
of the volume instead of the weight of the gas, it is important that
the results should be reduced to the same temperature as that
corresponding to the conditions of the engine trial. The formula
to be used for making the reduction is that already given in Section
T,d.
For the purpose of making the calorimeter test, if the fuel used
is coal for generating gas in a producer, or oil, samples should be
taken at the time of the engine trial and carefully preserved for
subsequent determination. If gas is used, it is better to have a
506 THE STEAMENGINE AND OTHER HEATMOTORS.
gascalorimeter on the spot, samples taken, and the calorimeter
test made while the trial is going on.
X. Measurement of Jacketwater to Cylinder or Cylinders.
The jacket water may be measured by passing it through a water
meter, or allowing it to flow from a measuringtank before entering
the jacket, or by collecting it in tanks on its discharge. If measur
ingtanks are used, the same system of arrangement is recommended
as that employed for feedwater measurements in boiler and
steamengine tests. (See Section XI, Steamengine Code.)
XI. Indicated Horsepower. The directions given for deter
mining the indicated horsepower for steamengines apply in
all respects to internalcombustion engines. (See Section XIII,
Steamengine Code.)
The pipe connections for indicating gas and oilengines should
be removed as far as possible from the ports and ignition devices
and made preferably in the cylinderhead. The pipes should be
as short and direct as possible. Avoid the use of long pipes, other
wise explosions of the gas in these connections may occur.
Ordinary indicators suitable for indicating steamengines are
much too lightly constructed for gas and oilengines. The pencil
mechanism, especially the pencil arm, needs to be very strong to
prevent injury by the sudden impact at the instant of explosion;
a special gasengine indicator is required for satisfactory work,
with a small piston and a strong spring.
XII. Brake Horsepower. The determination of the brake
horsepower, which is very desirable, is the same for internal com
bustion as for steamengines.
XIII. Speed. The same directions apply to internalcombus
tion engines as to steamengines for the determination of speed,
and reference is made to Section XVII, Steamengine Code, for
suggestions on this subject.
In an engine which is governed by varying the number of
explosions or working cycles, a record should be kept of the num
ber of explosions per minute, or, if the engine is running at nearly
maximum load, by counting the number of times the governor
causes a miss in the explosions.
One way of mechanically recording the explosions is to attach
to the exhaustpipe a cylinder and piston arranged so that the
GASENGINES AND GASPRODUCERS. 507
pressure caused by the exhaustgases operates against a light
spring and moves a register, which is provided for automatically
counting the number.
XIV. Recording the Data. The time of taking weights and
every observation should be recorded and note made of every
event however unimportant it may seem to be. The pressures,
temperatures, meterreadings, speeds, and other measurements
should be observed every twenty or thirty minutes when the con
ditions are practically uniform, and at more frequent intervals if
they are variable. Observations of the gas or oil measurements
should be taken with special care at the expiration of each hour,
so as to divide the test into hourly periods, and reveal the uni
formity or otherwise of the conditions and results as the test goes
forward.
All data and observations should be kept on suitably prepared
blank sheets or in notebooks.
XV. Uniformity of Conditions. When the object of the test is
to determine the maximum economy, all the conditions relating
to the operation of the engine should be maintained as constant
as possible during the trial.
XVI. Indicator Diagrams and their Analysis. (a) Sample
Diagrams. Sample diagrams nearest to the mean should be
selected from those taken during the trial and appended to the
tables of the results. If there are separate compression or feed
cylinders, the indicator diagrams from these should be taken and
the power deducted from that of the main cylinder.
XVII. Standards of Economy and Efficiency. The hourly
consumption of heat, determined as pointed out in Article IX,
divided by the indicated or the brake horsepower, is the standard
expression of engine economy recommended.
In making comparisons between the standard for internal
combustion engines and that for steamengines it must be borne
in mind that the former relates to energy concerned in the genera
tion of the force employed, whereas in the steamengine it does not
relate to the entire energy expended during the process of com
bustion in the steamboiler. The steamengine standard does not
cover the losses due to combustion, while the internalcombustion
engine standard, in cases where crude fuel, such as oil, is burned
508 THE STEAMENGINE AND OTHER HEATMOTORS.
in the cylinder, does cover these losses. To make a direct com
parison between the two classes of engines considered as complete
plants for the production of power, the losses in generating the
workingagent must be taken into account in both cases, and the
comparison must be on the basis of the fuel used; and not only
this, but on the basis of the same or equivalent fuel used in each
case. In such a comparison, where producergas is used and the
producer is included in the plant, the fuel consumption, which will
be the weight of coal in both cases, may be directly compared.
The thermal efficiency ratio per indicated horsepower or per
brake horsepower for internalcombustion engines is obtained in
the same manner as for steamengines, referred to in Section XXI,
Steamengine Code, and is expressed by the fraction
2545
2545
B.T.U. per H.P. per hour*
XVIII. Heatbalance. For purposes of scientific research a
heatbalance should be drawn which shows the manner in which
the total heat of combustion is expended in the various processes
concerned in the working of the engine. It may be divided into
three parts: First, the heat which is converted into the indicated
or brake work; second, the heat rejected in the coolingwater of
the jackets; and third, the heat rejected in the exhaustgases,
together with that lost through incomplete combustion and radia
tion.
To determine the first item, the number of footpounds of
work performed by, say, one pound or one cubic foot of the fuel
is determined; and this quantity divided by 778, which is the
mechanical equivalent of one British thermal unit, gives the num
ber of heatunits desired. The second item is determined by
measuring the amount of coolingwater passed through the jackets,
equivalent to one pound or one cubic foot of fuel consumed, and
calculating the amount of heat rejected, by multiplying this quan
tity by the difference in the sensible heat of the water leaving the
jacket and that entering. The third item is obtained by the
method of differences; that is, by subtracting the sum of the first
two items from the total heat supplied. The third item can be
subdivided by computing the heat rejected in the exhaustgases as
GASENGINES AND GASPRODUCERS. 509
a separate quantity. The data for this computation are found by
analyzing the fuel and the exhaustgases, or by measuring the
quantity of air admitted to the cylinder in addition to that of the
gas or oil.
XIX. Report of Tests. The data and results of a test should
be reported in the manner outlined in one of the following tables,
the first of which gives a complete summary when all the data are
determined, and the second is a shorter form of report in which
some of the minor items are omitted. (The complete form only
is given, pp. 510513.)
XX. Temperatures Computed at Various Points of the Indi
cator Diagram. The computation of temperatures corresponding
to various points in the indicator diagram is, at best, approximate.
It is possible only where the temperature of one point is known
or assumed, or where the amount of air entering the cylinder along
with the charge of gas or oil, and the temperature of the exhaust
gases, is determined.
If the amount of air is determined for a gasengine, together
with the necessary temperatures, so that the volume and tempera
ture of the air entering the cylinder per stroke, and that of the gas,
are known, we may, by combining this with other data, compute
the temperature for a point in the compressioncurve. In this
computation we must allow for the volume of the exhaustgases
remaining in the cylinder at the end of the stroke. The tempera
ture at the point in the compressioncurve where it meets or
crosses the atmospheric line will be given by the formula
459.4, (A)
V" + V'"+V
where V is the total volume corresponding to the point where the
compressioncurve meets or crosses the atmospheric line; V ff
the volume of the air at atmospheric pressure entering the cylinder
during each working cycle, reduced to the equivalent volume at
32 degrees Fahr.; V" the volume of the gas consumed per cycle
reduced to the equivalent at atmospheric pressure and 32 degrees
Fahr.; and V"" the volume of the exhaustgases retained in the
cylinder reduced to the same basis. To reduce the actual vol
umes to those at 32 degrees Fahr. multiply by the ratios of
510 THE STEAMENGINE AXD OTHER HEATMOTORS.
491.4r (T f +459.4), where T' is the observed temperature of the
air and of the gas used as fuel. For the exhaustgases retained
in the cylinder at the end of the stroke T' may be taken as the
temperature of the exhaustgases leaving the engine, provided
the engine is not of the scavenging type.
Having determined the temperature of a point in the com
pressioncurve, the temperature of any point in the diagram may
be found by the equation
T^(T +459.4)^5^459.4 (B)
Here T\ is the desired temperature of any point in the diagram
where the absolute pressure is PI and the total volume V\; and
P and V are the corresponding quantities for the point in the
compressionline having the temperature T computed from the
formula (A).
Formula (B) holds only where the w r eight of the gases contained
in the cylinder is constant. It is also assumed in this formula
that the density of the gas compared to air at the same temperature
and pressure is the same before and after explosion.
A second method may be employed, provided the air which
enters the cylinder is measured. This will allow for any difference
in the density of the gas before and after explosion, and more
exact values for temperatures on the expansioncurve may be
obtained than by the first method.
In this method the density of the exhaustgases compared to
air at the same temperature and pressure is computed, assuming
perfect combustion, and including the effect of the water vapor
present, and from this density the volume of the gases exhausted
per cycle is determined. If the volume exhausted per cycle,
added to the volume of the gas retained in the clearancespace at
the end of the stroke, be called V in equation (B) and T be the
observed temperature of the exhaustgases, this equation may be
used for determining the temperature of any point in the diagram
in the way already described. This method is more complicated
than the first, as it involves the determination of the theoretical
density after explosion, but it possesses the advantage that it
may be applied to an oil as well as to a gasengine.
GASENGINES AND GASPRODUCERS. 511
A third method of computing the temperature of various
points in the diagram may be employed where analyses of the
exhaustgases as well as of the fuel have to be made. This method
is more complicated than the first, but, in common with the sec
ond, it possesses the advantage that it may be applied to an oil
as well as to a gasengine.
In applying the third method the volume of the exhaustgases
discharged per working cycle would be given by the formula
(C)
where D is the density of the exhaustgases at their observed tem
perature, computed from the analysis, assuming the vapor of
water produced through burning the hydrogen in the fuel to be in
a gaseous state, R the weight of the air which enters the cylinder
per pound of fuel, and w the weight of the fuel consumed per work
ing cycle. The value of R, providing there are no unconsumed
hydrocarbons, may be computed by employing the formula
NC
where N, C0 2 , and CO represent the proportions, by volume, of
the several constituents of the exhaustgases, and C the weight of
carbon consumed and converted into C0 2 or CO per pound of
fuel burned, computed from the analysis of the fuel and of the
exhaustgases. t
Having determined the volume V 2 of the exhaustgases, formula
(B) may be used in computing the temperature, in which case T
will represent the temperature of the exhaustgases as in the second
method, P the pressure of the exhaust, and V the volume of the
exhaustgases V 2 discharged per stroke, added to the volume of
the gases retained in the cylinder at the end of the stroke.
The value of R given in equation (D) is approximate, on account
of the fact that the percentage of N should be that due to the air
alone, and not that due to the air in addition to that contained
in the fuel gas. Where extreme accuracy is desired, the value
found for R may be used to determine the percentage of N which
in the analysis of the exhaustgases is due to the N in the fuel
gas, and this value may be subtracted from the total N showa
512 THE STEAMENGINE AND OTHER HEATMOTORS.
by the analysis of the fuel gases in order to obtain the correct
value of N to be used in equation (D).
DATA AND RESULTS OF TEST OF GAS OR OILENGINE.
ARRANGED ACCORDING TO THE COMPLETE FORM ADVISED BY THE ENGINE
TEST COMMITTEE, AMERICAN SOCIETY OF MECHANICAL ENGINEERS,
CODE OF 1902.
1 . Made by of
on engine located at
to determine
2. Date of trial
3. Type of engine, whether oil or gas
4. Class of engine (mill, marine, motor for vehicle, pumping, or other) ....
5. Number of revolutions for one cycle, and class of cycle
6. Method of ignition
7. Name of builders
8. Gas or oil used
(a) Specific gravity deg. Fahr.
(6) Burningpoint ' ' "
(c) Flashingpoint " "
9. Dimensions of engine:
IstCyl. 2dCyL
(a) Class of cylinder (working or for compressing the
charge)
(Vertical or horizontal)
(c) Single or doubleacting
(d) Cylinder dimensions
Bore in.
Stroke ft.
Diameter of pistonrod in.
Diameter of tailrod "
(e) Compression space or clearance in per cent of vol
ume displaced by piston per stroke:
Head end
Crank end
Average
(/) Surface in square feet (average)
Barrel of cylinders
Cylinderheads
Clearance and ports
Ends of piston
Pistonrod
(g) Jacket surfaces or internal surfaces of cylinder
heated by jackets, in square feet
Barrel of cylinder
Cylinderheads
Clearance and ports
(h) Horsepower constant for one Ib. M.E.P., and
one revolution per minute
GASENGINES AND GASPRODUCERS. 513
10. Give description of main features of engine and plant, and illustrate
with drawings of same given on an appended sheet. Describe the
method of governing. State whether the conditions were constant
during the test.
TOTAL QUANTITIES.
11. Duration of test hours
12. Gas or oil consumed cu. ft. or Ibs.
13. Air supplied in cubic feet cu. ft.
14. Coolingwater supplied to jackets "
15. Calorific value of gas or oil by calorimeter test, determined
by calorimeter B.T.U.
HOURLY QUANTITIES.
16. Gas or oil consumed per hour cu. ft. or Ibs.
17. Coolingwater supplied per hour Ibs.
PRESSURES AND TEMPERATURES.
18. Pressure at meter (for gasengine) in inches of water ins.
19. Barometric pressure of atmosphere:
(a) Reading of height of barometer ins.
(6) Reading of temperature of barometer deg. Fahr.
(c) Reading of barometer corrected to 32 F ins.
20. Temperature of cooling water:
(a) Inlet deg. Fahr.
(6) Outlet "
21. Temperature of gas at meter (for gasengine) " "
22. Temperature of atmosphere:
(a) Drybulb thermometer " "
(6) Wetbulb thermometer " "
(c) Degree of humidity per cent.
23. Temperature of exhaustgases deg. Fahr.
How determined
DATA RELATING TO HEAT MEASUREMENT.
24. Heatunits consumed per hour (Ibs. of oil or cu. ft. of gas per
hour multiplied by the total heat of combustion) . . . .B.T.U.
25. Heat rejected in cooling water:
(a) Total per hour "
(6) In per cent of heat of combustion of the gas or oil
consumed per cent
26. Sensible heat rejected in exhaustgases above temperature
of inlet air:
(a) Total per hour B.T.U.
(6) In per cent of heat of combustion of the gas or oil
consumed per cent.
27. Heat lost through incomplete combustion and radiation per
hour:
(a) Total per hour B.T.U.
(6) In per cent of heat of combustion of the gas or oil
consumed per cent.
514 THE STEAMENGINE AXD OTHER HEATMOTORS.
SPEED, ETC.
28. Revolutions per minute rev.
29. Average number of explosions per minute
How determined
30. Variation of speed between no load and full load rev.
31. Fluctuation of speed on changing from no load to full load, measured
by the increase in the revolutions due to the change
INDICATORDIAGRAMS.
32. Pressure in Ibs. per sq. in. above atmosphere:
1st Cyl. 2d Cyl.
(a) Maximum pressure
(6) Pressure just before igni.ion
(c) Pressure at end of expansion
(d) Exhaust pressure
33. Temperature in deg. Fahr. computed from diagram:
(a) Maximum temperature (not necessarily at maximum pressure). . . .
(6) Just before igniton
(c) At end of expansion
(d) During exhaust
34. Mean effective pressure in Ibs. per sq. in
POWER.
35. Power as rated by builders:
(a) Indicated horsepower H.P.
(6) Brake "
36. Indicated horsepower actually developed:
First cylinder H.P.
Second cylinder "
Total "
37. Brake H. P., electric H.P., or pump H.P. according to the
class of engine
38. Friction indicated H.P. from diagrams,, with no load on
engine and computed for average load '. . "
39. Percentage of indicated H.P. lost in friction per cent
STANDARD EFFICIENCY RESULTS.
40. Heatunits consumed by the engine per hour:
(a) Per indicated horsepower B.T.U.
(6) Per brake horsepower
41. Heatunits consumed by the engine per minute:
(a) Per indicated horsepower "
(6) Per brake horsepower
42. Thermal efficiency ratio:
(a) Per indicated horsepower per cent
(6) Per brake horsepower ' ' "
MISCELLANEOUS EFFICIENCY RESULTS.
43. Cubic feet of gas or Ibs. of oil consumed per H.P. per hour:
(a) Per indicated horsepower
(6) Per brake horsepower
GASENGINES AtfD GASPRODUCERS. 515
HEAT BALANCE.
44. Quantities given in per cents of the total heat of combustion of the fuel:
(a) Heat equivalent of the indicated horsepower. .... .per cent
(6) Heat rejected in coolingwater " lt
(c) Heat rejected in exhaustgases and lost through radia
tion and incomplete combustion " "
Sum = 100 " "
Subdivision of Item (c):
(cl) Heat rejected in exhaustgases
(c2) Lost through incomplete combustion
(c3) Lost through radiation, and unaccounted for
Sum = Item (c).
ADDITIONAL DATA.
Add any additional data bearing on the particular objects of the test
or relating to the special class of service for which the engine is to be used.
Also give copies of the indicatordiagrams nearest the mean and the corre
sponding scales. Where analyses are made of the gas or oil used as fuel,
or of the exhaustgases, the results may be given in a separate table.
CHAPTER XVII.
BOILING IN A VACUUM.
Multiple Effects, Vacuumpans, and Freshwater Distillers.
Many substances can only be evaporated properly at tempera
tures below 212 F., as, for instance, sugar solutions, milk, and
many substances used in chemical preparations. The pressure
at which these substances are boiled must be reduced below
atmospheric pressure by condensing their vapors and removing
air or noncondensible gases by means of an airpump, as in the
case of condensingengines.
Omitting radiation losses from consideration, all the heat
applied to the liquid that is being boiled is contained in the
vapor that is sent to the condenser. If this heat is wasted, the
economy of the operation is very low. This method is called
boiling in a single effect. It is the method employed in boiling in
the vacuumpans of cane and beetsugar houses.
The steam arising from the boiling liquid in an effect can
be used to evaporate more of the same liquid in a second effect
if the temperature of boiling in the second one is thirty or more
degrees lower than that in the first one. This necessary difference
of temperature to make the heat flow is obtained by making
the pressure in the second effect lower than that in the first. The
amount of this pressure is easily obtained from a table of boiling
points and the corresponding pressures of the substance boiled.
In a similar manner the vapor arising from the second effect
may be used to evaporate a further quantity from the given
liquid in a third effect in which the temperature and absolute
pressure is less than in the second effect.
At first sight it would seem that this process could be carried
on indefinitely. It has its limits, however. The vapor from the
516
BOILING IN A VACUUM.
517
last effect must be condensed and its temperature must be thirty
or more degrees above the temperature of the dischargewater
cf the condenser. Hence the lowest pressure or the pressure
in the last effect is that maintained in the condenser. The upper
limit is determined by other conditions. Having the upper and
lower limits or total range of temperature and an assumed range
in each effect, the number of effects is easily found by dividing
the total range by the range of temperature in each effect.
In cane and beetsugar houses, the exhauststeam from the
main and auxiliary engines is the source of supply of steam to
FIG. 262.
Section on AB.
the first effect. As a rule, its pressure is from 7 to 10 pounds
above the atmosphere, hence its temperature is from 230 F. to
240 F. If a vacuum of 27 inches is maintained in the last effect
corresponding temperature is 115 F. there is a difference of
240115 = 125 F. If a triple effect is used there will be a
difference of some 40 between the two sides of the heating
surface in each effect.
In Fig. 262 the first, second, and third effects are marked
1, 2, 3, respectively; the steampipe bringing steam to the first
effect is marked $; the vapor arising from the first effect is brought
518 THE STEAMENGINE AND OTHER HEATMOTORS,
down and delivered to the second effect at a point corresponding
to that in No. 1 ; the vaporpipes of the second and third effects
differ in diameter, as the volume of the vapor delivered in
creases greatly as the pressure is decreased. The vapor from the
third effect is condensed by coming into contact with the injection
water flowing through the pipe /. The air is drawn off through
the pipe A, protected by a shelf, by the dryair pump. The dis
chargewater flows away by gravity,,
Examining No. 1 more in detail we find that it is made of
four belts called the dome, the calander, the tubebelt, and the
bottom. The effect is supported by the tubebelt in order that
the bottom may be readily dropped for repairs.
In none of the effects is the steam admitted directly among the
tubes. The steam passes around the effect in an annular belt
and is admitted to the tubespace through narrow slots, shown
much enlarged in the No. 2 effect. This distributes the steam
and prevents the foaming that would otherwise occur near the
steampipe opening. The circulation of the juice is up through
the small tubes 2 inches in diameter and 30 to 40 inches long
and down through the downcomer 24 inches or more in diameter
marked D.
The action then is as follows: Steam, pressure 25 pounds
absolute, temperature 240 F., enters the steamspace of No. 1
effect. The temperature of the juice on the other side is 40 de
grees lower, or 200 F. ; therefore the gage G\ should show 7 inches
mercury vacuum = 11 pounds absolute. The steam at 200 F.
passes into the steambelt of No. 2. The juice on the other
side of its tubes must be ai 200 40 = 160 F. Hence gage G 2
should show 20 inches of mercury vacuum. The steam at
160 passes into No. 3, and the gage G% should show 26.5 inches
of mercury vacuum. It is the custom to show the vacuum in the
effects rather than the absolute pressure. The efficiency of
the heatingsurfaces would be greatly increased by increasing
the vacuum to 28 inches.
As the condensed steam in No. 1 belt is at a pressure higher
than that of the atmosphere it is easily drained off. As the pres
sure in the other two belts is less than that of the atmosphere an
airpump, called a sweetwater pump, is necessary to draw off
BOILING IN A VACUUM. 519
the condensed steam and produce the necessary vacuum that
exists over the juice surface in Nos. 1 and 2; that in No. 3 is pro
duced by the airpump connected to the condenser at A. If the
multiple effect is more than 34 feet from the ground the con
densed steam in the tubebelts of the second and third effects
will drain off automatically through drippipes terminating in
barrels of water on the ground. It is wise to connect by a half
inch pipe the steamspace to the vaporspace over the top tube
sheet in each effect, as shown in No. 1 at V. This permits the
easy withdrawal of air and (in beetsugar factories) ammonia that
accumulate in the upper part of the steamspace and interfere
with the efficiency of the tubes.
The raw, clarified juice enters No. 1 at / and the syrup of
proper density 2830 Beaume is drawn off by a pump at
Sy 3 , a uniform level being kept in all three effects by regulating
valves Sy% and /. The juice therefore passes through the three
effects, becoming denser as it loses water that has been evaporated.
Theory of the Multiple Effect.
Let = temperature of the juice entering the apparatus;
TI = temperature of the boiling juice;
T 2 = temperature of the steam for heating this juice;
C=rate of transmission in thermal units per unit area per
degree difference of temperature between the steam
and juice side, =22 calories per square meter per 1
Cent., diff. = 4.5 B.T.U. per square foot per 1 Fahr.
diff. of temperature between the two sides per minute;
A =area of the heatingsurface;
Q = amount of heat transmitted per minute =AC(T 2 TI) ;
;,i = total heat of steam, above 32 F., at T! = 1091. 7 +
.305 (T 7 ! 32);
1/2 = latent heat of steam given off in condensing = 1091. 7 f
.305(r 2  32) (T 2  32);
S c = weight of steam condensed in the intertubular space;
W v = weight of water evaporated from the juice.
If the substance evaporated from any liquid is any other than water,
the proper changes must be made in the specific heat and heat of
vaporization. Then the fundamental equations are:
520 THE STEAMENGINE AND OTHER HEATMOTORS.
Q = S C L 2 , .. S c =j.
J^>2
Q
Taking the normal back pressure of the exhauststeam from
all engines at 10 pounds, gage, the corresponding temperature is
240 F. Assume that the temperature of the thin beetjuice from
the filters or the thin canejuice from the clarifiers at 170 F. This y
of course, varies, but a few degrees either more or less will not be
important. Assume that the highest vacuum is 26.5 inches of
mercury, so that the temperature of the thick juice is 120 F. The
difference of temperature between the highest steam and the coolest
juice is 240 120 = 120 F.
With the above data we shall derive the theoretical equations
for single, double, and triple effects. It will then be seen that the
capacity of a double or triple effect is no greater than that of a
single effect working between the same range of temperature
120 in this case but that the economy of a double effect is
twice, and that of a triple effect is three times, that of a single
effect (theoretically). In practice the economy of the double
effect is one and a half, and that of a triple effect twice that of a
single effect.
The theory given applies to the distillation of fresh water
by multiple effects. By the use of live steam instead of exhaust
steam the number of effects (and hence the economy of opera
tion) may be increased due to the increased total range of tem
perature.
SINGLE EFFECT.
TI = 120 F. juice entering the effect is hotter than boiling juice
inside;
T 2 = 240 F.;
T 2 T 1 = 240  120 = 120 F. ;
C = 4.5 B.T.U. per minute;
BOILING IN A VACUUM. 521
A = one square foot, therefore Q = l x4.5x!20 = 540 B.T.U.
per square foot;
S c = Y~ = steam condensed per square foot of heatingsurface
L 2
540
~ 1091.7 +.305(240 32) (240 32) ~* 57p
W v = water evaporated per square foot cf heating surf ace
540
"1091.7 +.305(120 32) (17032)"
Therefore a single effect will evaporate, under these conditions,
.55 pound of water per minute per square foot of heatingsur
face and will require .57 pound of steam, or, in other words,
one pound of steam in condensing evaporates .96 pound of water.
DOUBLE EFFECT.
In a double effect the range of temperature in each effect will
2C
2
First Effect.
120
be onehalf that in a single effect, or with our data ^ = 60.
T 2 ' = 240 F. as before;
120
T 1 f = T 2 ^ = 240 60= 180 F. = temperature of boiling
juice in the first effect;
o = 170 F. temperature of juice entering (he first effect;
Q =A'C(T 2 f T l '} = l x4.5 X60 = 270 B.T.U. ;
Jli (t 32) = 1091.7 +.305(180 32) (17032) =998 B.T.U.;
Z, 2 ' = 1091. 7 +.305(24032)  (24032) =946 B.T.U.;
. 285 pound;
pound.
Second Effect.
The steam entering the second effect will have the temperature
of the boiling juice in the first effect, and as the juice is run from
the first to the second effect the temperature of the juice entering
522 THE STEAMENGINE AND OTHER HEATMOTORS.
the second effect will be the same as that of the boiling juice
in the first effect.
S c " = steam condensed in the second effect;
Wi" = water evaporated in the second effect;
7Y' = 180 F. = temperature of steam entering second effect;
t ' = 180 F. = temperature of juice entering second effect;
TI" = 120 F. = temperature of boiling juice in the second effect;
L 2 " = 1091. 7 +.305(180 32) (180 32)= 988 B.T.U.;
V (to 32) = 1091.7 +.305(12032) (18032) =970 B.T.U.
In the first effect we assumed one square foot of heating surface.
We cannot assume one square foot of heatingsurface in the Second
effect, for we must have such an area in the second effect as will
transmit (under the assumed conditions) the heat that is sent
from the first effect.
The heat that is transmitted through the heatingsurface of the
second effect is Se'Lz". But S C " = W V ', the water evaporated
from the first effect. Therefore
Q = . 272x988 = 268.7 B.T.U. =^"x4.5(180120);
.A = .99 square foot;
< ~ 970
In the two effects we have 1.99 square feet of heatingsurface
required for the evaporation of .272 +.277 = .55 pound of water,
or the evaporation for two square feet in the double effect is the
same as that for one square foot in the single effect. But the
amount of steam condensed from the source of supply is only
.285, or onehalf that required from the outside by the single
effect.
TRIPLE EFFECT.
In the triple effect between the same temperature limits 240
to 120 the range in each effect is 40 F. The area of heating
surface in the second and third effects must be found as it was
found in the case of the second effect of the double effect. In
general it will be found theoretically that three square feet are
required to do the work of one square foot in the single effect,
BOILING IN A VACUUM.
523
Density o
Co co id id
id O 00 05
f Thin Juice ir
id id id hk
tf> id O 00
i Degrees Bea
_ _ _ _
05 ^. id
time.
CD 00 a 05
o
to os
*0
i 1 tO CO rfi.
O H* fcO h
^

to CO 4^ Cn
en o
00 Cn CO O
o
1
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s
o
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to en os q
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Cn Cn OS <I
CO CO Cn O
Cn OS OS <!
OS OS <! <J
CO 00 tO OS
00
id
id
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o
CONCE1
AGE OF VOLUME
APPROXIM^
Density of Cc
H* tO tO
O O CO
CO 4^ Cn OS
CD <! Cn CO
5 2 3 o
id
% % o 3
S 3
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1
524 THE STEAMENGINE AND OTHER HE AT MOTORS.
but there will only be required onethird the quantity of steam
from the source of supply.
Actual Design of Multiple Effects. The actual design of
economical multiple effects is considerably more complicated
than would be indicated by the preceding theory. As a matter
of fact the coefficient of heat transfer is not the same in each of
the effects. This is easily seen from Professor Perry's theory.
In the last effect the molecules of steam are far apart, their rate
of vibration is low, they have far less power of brushing away
the water on the heating surface than in the first effect. As a
result of numerous experiments Claassen gives the following
values for C, the calories per square meter per degree Cent., differ
ence of temperature between the heating and boiling fluids per
minute; for the first body, 40; for the second body, 30; for
the third body, 20; and for the fourth body, 10, when the sur
faces are clean.
While it is possible to attain the rates indicated above when
the surfaces are clean it is not possible when the surfaces become
foul. It is better then to assume the following rates for C. For
the first body, 32; for the second body, 25; for the third body,
17; for the fourth body, 9. Instead of having equal fall of tem
perature in each effect, it is better to make the product of the
fall of temperature in any effect and the heat transfer coefficient
in that effect a constant. Thus, if the fall in temperature in the
first effect is 10 and 32 is the coefficient in that effect then the
fall in the last effect should be 35.5, viz., the product 10X32 =
constant.
The specific heat of the boiling liquid is not constant in the
different effects and it should therefore be considered. Further,
a very considerable economy arises if steam coming from the
different effects is diverted from entering the following effect
and is used to raise the temperature of the raw juice gradually
to the temperature needed in the clarifiers. The heat coming
from the condensed steam in each effect may also be so utilized.
If steam is diverted, however, from its regular course a change
must be made in the heating surface of the effects for it is
essential that each effect should only be able to condense the
steam from the preceding effect.
BOILING IN A VACUUM. 525
For example, the juice from the mill at 20 C. might be raised
by steam passing into the condenser from 20 to 48 C. By
vapor from the second effect it might be heated to 88 C. It
could be heated from 88 to 94 by vapor from the first effect.
In case the raw juice is sent through the filters and cooled it may
be heated a second time to 94 C. As a result of this method
the heating surfaces in a quadruple effect for a house grinding
1000 tons of cane per day would be :
453 square meters for the first effect; 325 for the second;
264 for the third, and 280 for the fourth. This multiple
effect would operate on exhaust steam alone and no coal or
wood boilers would be necessary. The bagasse would furnish
sufficient heat. The solution of this problem is interesting,
but too long for this treatise.
Measurements of Density of Liquids. The density of liquids is
taken by means of hydrometers whose indications are called
degrees. The hydrometer is generally made of glass. It con
sists of a graduated stem with two bulbs. When floating in a
liquid it is maintained in an upright position by its low center of
gravity, due to the presence of shot in the bottom bulb. The
upper bulb containing only air gives the necessary buoyancy.
The zero reading is at the top of the scale for liquids heavier
than water and at the bottom for liquids lighter than water.
With sugar solutions either the Beaume or the Brix hydrometer
may be used. To convert Beaume (or Baume) readings into
specificgravity readings see Kent's Handbook, page 165.
To find the amount of water evaporated from a sugar solution
when its density is increased from one hydrometer reading to
another :
Let <r = the specific gravity of liquid driven off;
GI = the specific gravity corresponding to the lower reading;
G 2 = the specific gravity corresponding to the higher reading;
Vi = original volume of liquid ;
x = percentage of original volume that is evaporated;
Vi(lx) = final volume ;
GxVi= weight of the vapor driven off;
If the part evaporated is water, G 1;
526 THE STEAMENGINE AND OTHER HEATMOTORS.
Tabulating the results obtained for the evaporation from one
Beaume reading to a higher one, we obtain the preceding table.
If a mill grinds 500 tons of sugarcane per day, with an extrac
tion of 80%, what will be the heatingsurface required theoretically
in a triple effect working between 240 and 120 F., and reducing
the juice from 6 to 26 Beaume?
Weight of juice in pounds,
WOX20MX80_
1UU
Volume of juice in cubic feet,
sp.gr.). /
From table, volume of juice evaporated
800,000. X .80
" 62.5xl.041
Weight of water evaporated in 24 hours
800,000 x. 80x62.5
62.5X1.041 = 615 > 00 '
Weight of water evaporated per minute
615,000
2460
The required heatingsurface would be
427
7^= 2250 square feet.
BOILING IN A VACUUM
527
This quantity must be multiplied by a factor of safety to cover
(1) the maintenance of a less range of temperature; (2) the direction
of the tubes whether horizontal or vertical; (3) amount of scale
on the tubes; (4) the drawing off of air in the intertubular space;
FIG. 263.
(5) improper care, not keeping the pressures in each effect at the
proper point ; (6) inequality in the daily tonnage of cane.
The factor of safety is sometimes as high as 2.
Fig. 263 represents a diagrammatic sketch of a vacuumpan,
as used in sugarhouses and refineries. In theory it is a single
effect, as the steam arising from the sugar solution, boiling under
20 to 26 inches of vacuum, goes immediately to a condenser.
528 THE STEAMENGINE AND OTHER HEATMOTORS.
The economy of the process is low in reality only a small
amount of evaporation is performed in the pan. An approximate
idea may be obtained from the following terse summary of results.
Start with 10 cubic feet of juice as it comes from the sugarcane,
boil it down in the multiple effect to 2 cubic feet by evaporating
8 cubic feet of water away. The resulting liquid has the consist
ency of table syrup. Evaporate the 2 cubic feet of syrup to
1 cubic foot in the vacuumpan The residue is a mixture of 50 to
60% of molasses and 50 to 40% of crystallized sugar. This mass
flows slowly, and when cold hardly flows at all. Hence the
peculiar construction of the pan. It must be built so that the
massecuite will flow out
The boiling is done by a series of coils, each one with its own
steamvalve, drain, and trap. Coils are from 4 to 6 inches in di
ameter and 40 to 60 feet long. Most of the boiling is done by the
lower coils, as the upper ones are used only at the end of the process.
In a pan containing seven rows of coils an expert sugarmaker,
who knows the kind of syrup he is getting, will draw in syrup till
three or more coils are covered. He will boil it down, shutting off
coils that will soon become uncovered, until he has the syrup at the
proper density. He will then cause crystallization or " form grain "
by a sudden chilling of the mass as he has a saturated hot solution,
which when chilled becomes supersaturated and will form grain.
To do this he increases the vacuum (thus lowering the boiling
point) or gives a strong feed of .cold syrup. The remainder of
the process consists in building up the grain.
The transfer of heat per square foot of surface per degree
difference of temperature is low not over 1.4 B.T.U. because of
the density and stiffness of the mass during a large part of the
process and also because of the small amount of time that the
upper coils are in use.
The principal broad point of interest is the relative length of
a coil and its diameter. Only a definite weight of steam can pass
the crosssection of any tube, and it is useless and in fact detri
mental to have more surface than is required to transfer the heat
to the liquid that is being boiled. To be efficient the tubes must
be kept clear of water. The circulation of the boiling mass is of
great importance, and the width of the central channel is at least
BOILING IN A VACUUM. 529
onequarter the diameter of the pan. Vibration stresses are high,
and the tubes must be strongly secured to prevent rubbing. A
pinhole in a tube necessitates shutting it off.
Problem. What should be the maximum length of a 6inch
tube using steam at 80 pounds gage; vacuum 22 inches; rate of
heat transfer 2.1 B.T.U.?
CHAPTER XVIII.
REFRIGERATION.
Refrigerating Machinery. When a gas is compressed, heat
equal to the work done on it is added to the gas and its tempera
ture rises high above the normal. If this compression is performed
in a tubular vessel, the gas may be cooled by passing water at
ORDINARY temperature through the tubes. The third step is to
allow the gas to expand, either freely or doing work. As a result
of this expansion the temperature of the gas may be lowered far
below 32 Fahr. If the heat had not been abstracted by the
water, as shown above, the final temperature of the expanded
gas would have been the original temperature. Having the cold
gas, there are many obvious ways of using it (fourth stage) in
cooling a room or freezing water in cans. The third and fourth
stages may bs combined in practice.
The refrigeration cycle has, then, four stages and is the in
verse of the heat cycle, and the theoretical heat equations apply
equally well to both cycles. There are many systems of refrigera
tion. The absorption system is more economical than the com
pression system, but the latter is the more practical and is used
more extensively. The use of a compressor may be avoided by
absorbing the ammonia in water and then driving it off under
high pressure by heat. We shall give short descriptions of a Com
pressed Air System as used on board ships and of the Ammonia
Compression System as commonly found ashore.
First Stage. From formulas, page 118, we find if w pounds
of dry air are compressed from P , Vo, T Q to PI, F 1; 7\, and are
expelled at PI, with a constant pressure, P , on the other side of
the piston.
AI= jy(Pi7iPoFo)=net work in footpounds required per
stroke,
530
REFRIGERATION. 531
w r K v (T l TQ} footpounds, or wK p (T l T Q ).
The final temperature of compression is
or
Second Stage. Let the air be cooled at constant pressure
(Pi = P 2 ), its temperature falling to T 2 ( = T theoretically) and
its volume to V 2 . The amount of heat abstracted =
Q 2 = wK p (Ti T 2 ) footpounds;
The amount of coolingwater in gallons =
c = Q 2
778x8.3(^1^)'
ti = temperature of dischargewater from the condenser,
" " injection " to " "
Third Stage. The air is now allowed to expand in an expansion
cylinder doing net work =
A 2 = wK p (T 2 T 3 ),
/P 3 \ rl
when T 3 = final temperature of expansion = 7 7 2 ( p ) * ,
as Pi = P 2 .
Fourth Stage. The cold air at T 3 is allowed to absorb the
heat equal to C footpounds from the substance to be chilled.
.The amount of heat gained by the air equals the refrigeration
effect on the substance to be chilled,
where T 4 = final temperature of the cold air.
Theoretically, to produce a cycle, 7 7 4 should equal T .
In other words, the initial temperature of the substance to be
chilled the final temperature of the cold air that caused the chill
532 THE STEAMEXGINE AND OTHER HEATMOTORS.
ing and the initial temperature of the air entering the compressor
The power required per stroke = A i  A 2 ;
rp _ rp
rp _ rp
~
or
T T
Theoretically, ^ = TJT
1 2 i \
Ammonia Compression System. Fig. 264 is a diagrammatic
sketch illustrating the fundamental elements of an ammonia com
pression system. In a reservoir, R, is a supply of liquid and
gaseous ammonia under a pressure of 150200 pounds per square
inch. By opening a valve, a, capable of very fine adjustment
I,''!''' 1 .;. 1 !! 1 ! 1 ,!'!! 1 '!!''!! 1 ilV''!!."!' 1 '.'''! '' 'I'Vi'ViiKll'ltlil,.,! '''''
li! 1 !!!! 1 '!'!"!!!!! 11 !::!!;!!' 1 !! 1 '^
FIG. 264.
generally a needlevalve the liquid ammonia is admitted into
the tubes, B, enclosed in . brine. The pressure and temperature
in these tubes are quite low, some 30 pounds absolute and F.,
for instance, as they are on the suction side of the compressor
cylinder. On the delivery stroke of the piston of this cylinder
REFRIGERA TION. 533
the ammonia that had become completely gasefied and finally
superheated by its free expansion at the low pressure in the
tubes, B, is compressed up to a pressure as high or a trifle higher
than that in the reservoir. The high superheat arising from this
compression is removed by the action of the coolingwater on
the tubes of the condenser, C, through which the gas flows on
its way to the reservoir R. Under practically constant pressure the
gas gives up first its superheat and then its latent heat, and
trickles back into the reservoir as liquid ammonia.
The conversion of the liquid into gaseous ammonia in the
tubes, B, requires heat. This is supplied by the brine which is
thereby cooled to some temperature between and 32 F. The
brine is forced through pipes in the room to be chilled or around
the cans containing the water distilled so as to be free of air
bubbles to be frozen. The brine is used :
1. To prevent sudden changes of temperature in the cooling
room, its effects being similar to those of a flywheel on the rota
tion of an engine.
2. To prevent the damage that would occur with an ammonia
leak.
As ammonia disintegrates brass, none of that metal should
be exposed to that alkali. All the tubes and fittings should be
of extrastrong metal, and all screwed joints must be soldered to
insure tightness. For efficient compression the compressor clear
ance must be very small and preferably filled with heavy oil at
the end of the stroke; the valves must be perfectly true, as the
slightest wear reduces the economy. The compressor is exposed
to heavy pressure and high temperature, hence great strength is
necessary. The piston and valvestems must have very deep
packingboxes, as ammonia leakage is extremely difficult to
prevent.
In Fig. 265 let A represent the state of the liquid ammonia to
the immediate left of the valve, a, Fig ; 264. The expansion that
takes place when the liquid passes through the valve, a, is expan
sion at constant heat (Fig. 122, page 224), consequently AB is not
a straight line. The heat of the vapor and liquid at B is the
same as the heat of the liquid alone at A in excess of that at g
assumed as an origin. Heat from the brine is absorbed in pro
534
THE STEAMENGINE AND OTHER HEATMOTORS.
ducing the evaporation represented by the line BC. In passing
through pipes in the air and into the warm compressor the gas is
superheated, as shown by CD. DE represents the rise in tempera
ture due to adiabatic compression in the compressor cylinder. If
the mean pressure existing in the condensertubes be taken, it will
be found that the gas entering the condenser, C, from the com
595
555
515
475
582
FIG. 265.
pressor has a temperature far in excess of that corresponding
to that pressure as shown in Table X of Peabody's tables, or as
shown in Kent, page 993. The coolingwater absorbs the super
heat and then the latent heat of the ammonia gas, and finally
some of the heat of the liquid ammonia, as shown by the lines
EF, GF, and GA.
The data for the entropy diagram were taken from Kent,
page 998, where other data may be found.
Average high ammonia pressure above atmosphere 151 Ibs.
Average back ammonia pressure above atmosphere 28 "
REFRIGERATION. 535
Pounds ammonia circulated per minute 28. 17
Probable temperature of liquid ammonia, entrance to
brinetank 71.3 F.
Temperature of ammonia corresponding to average back
pressure +14 F.
Average temperature of gas leaving brinetanks 34.2
Temperature of gas entering compressor 39
Average temperature of gas leaving compressor 213
Average temperature of gas entering condenser 200
Temperature due to condensing pressure 84.5
Heat given ammonia :
By brine, B.T.U. per minute 14,776
By compressor, B.T.U. per minute. 2,786
By atmosphere, B.T.U. per minute 140
Heat taken from mmaonia :
By condenser, B.T.U. per minute 17,242
By jackets, B.T.U. per minute 608
By atmosphere, B.T.U. per minute 182
The heat given and received per pound of ammonia may be
found by dividing those quantities per minute by 28.17. Assume
the specific heat at constant pressure of ammonia vapor = 1.1 and
that of the liquid = .52. The minimum entropy is that of liquid
ammonia at 14 F. = 475 F. Abs. Let it be the starting
point for entropy measurements. Assume one pound of ammonia
passing through the cycle. The heat required to raise the tempera
ture of the liquid to 71.3 F. =532.3 F. Ab3. will be .52(532475),
and dividing by  2  will give the entropy of A. More
532 3
accurately the difference of entropies of g and A = .52 log '.
4/O
The difference between the heat in the liquid at B and at A
is available in evaporating liquid between B and A. The entropy
at
.52 '532 475)
475
At C all the liquid has been evaporated. The temperature at
D is 39 +461 =500 F. Abs. The heat required to superheat from
536 THE STEAMENGINE AND OTHER HEATMOTORS.
475 to 500 is 1.1(500475), and hence the increase of entropy
from 475 to 500 is readily found.
The compression is assumed to be adiabatic and the point E
is laid off. The excess of the entropy of F over that of G is readily
found.
The data show variations from this theoretical cycle. The
heat areas are given and may be plotted approximately, and
compared with those of the theoretical diagram. The area
beneath BC or the heat abstracted from the brine is the effective
area.
Refrigeration Units. The unit adopted to measure the cooling
effect, or the refrigeration, is the heat required to melt one pound
of ice, which is 144 British thermal units. Dividing the refrig
eration, measured in British thermal units, by 144, the icemelting
capacity in pounds is obtained. The unit for a ton (2000 Ibs.) of
icemelting capacity is therefore 288,000 British thermal units.
The commercial tonnage capacity is the refrigerating effect,
expressed in tons of icemelting capacity, produced by a machine
in 24 hours, when running continuously under the standard set of
conditions.
Considering the matter from the standpoint of cost of plant
and of steam and water economy, the best set of conditions to
adopt seems to be those which often exists in icemaking, namely,
that the temperature of the saturated vapor at the point of lique
faction in the condenser be 90 F., and the temperature of evap
oration of the liquid in the refrigerator be F.
The icemaking capacity is not the icemelting capacity of a
machine, but is less, being usually about onehalf the latter, be
cause in making a pound of ice more refrigeration than 144 British
thermal units is required, owing to cooling the water to 32 F.
and certain unavoidable losses incident to the process.
The commercial tonnage capacity of any refrigerating machine
using liquefiable vapor is based upon the actual weight of the
refrigerating fluid that is circulated between the condenser and
the refrigerator, and that is actually evaporated in the refriger
ator. Under the conditions specified above twentyfive pounds of
anhydrous ammonia per hour must be evaporated in the refrig
erator for one ton of commercial tonnage capacity. For other
REFRIGERATION. 537
refrigerating fluids we do not at present make any recommenda
tions as to the weight of the fluid that must be circulated.
The actual refrigerating capacity (in tons) of a machine may
be determined from the quantity and range of temperature of brine,
water, or other secondary fluid circulated as a refrigerant. The
actual refrigerating capacity under the standard set of conditions
should correspond closely to the commercial tonnage capacity.
DATA AND RESULTS OF STEAMENGINE TEST. 1
ARRANGED ACCORDING TO THE COMPLETE FORM ADVISED BY THE ENGINE
TEST COMMITTEE OF THE AMERICAN SOCIETY OF MECHANICAL ENGI
NEERS. CODE OF 1902.
1. Made by of.
on engine located at
to determine. ..
2. Date of trial
3. Type of engine (simple, compound, or other multiple expansion; con
densing or noncondensing) :
4. Class of engine (mill, marine, locomotive, pumping, electric, or other)
5. Rated power of engine.
6. Name of builders
7. Number and arrangement of cylinders of engine; how lagged; type of
condenser
8. Type of valves
9. Type of boiler
10. Kind and type of auxiliaries (air, circulating, main, and feedpumps;
jackets, heaters, etc.)
IstCyl. 2dCyl. 3d Cyl.
11. Dimeadons of engine
(a) Single or doubleacting
(6) Cylinder dimensions:
Bore in.
Stroke ft.
Diameter of pistonrod in.
Diameter of tailrod in.
(c) Clearance in per cent of volume displaced by piston per stroke:
Head end
Crank end
Average
* Quoted from Vol. XXIV, A. S. M. E.
538 THE STEAMENGINE AND OTHER HEATMOTORS.
(d) Surface in square feet (average):
Barrel of cylinder
Cylinderheads
Clearance and ports
Ends of piston
(e) Jacket surfaces or internal surfaces of cylinder heated by jackets, in
square feet:
Barrel of cylinder
Cylinderheads
Clearance and ports
Receiver jackets
(/) Ratio of volume of each cylinder to volume of highpressure cyl
inder
(gr) Horsepower constant for one pound mean effective pressure and
one revolution per minute
12. Dimensions of boilers:
(a) Number
(6) Total grate surface sq. ft.
(c) Total waterheating surface (external) sq. ft.
(d) Total steamheating surface (external) sq. ft.
13. Dimensions of auxiliaries:
(a) Airpump.
(6) Circulating pump
(c) Feedpumps
(d) Heaters
14. Dimensions of condenser
15. Size, length, and number of turns in main steampipe leading from the
boiler to the engine
16. Give description of main features of plant and illustrate with drawings
to be given on an appended sheet
TOTAL QUANTITIES, TIME, ETC.
17. Duration of test hours.
18. Length of time engine was in motion with throttle open hours.
19. Length of time engine was running at normal speed "
20. Water fed to boilers from main source of supply Ibs.
21. Water fed from auxiliary supplies:
(a) Ibs.
(6) "
(0 "
22. Total water fed to boiler from all sources Ibs.
23. Moisture in steam or superheating near throttle per cent or deg.
24. Factor of correction for quality of steam, dry steam being unity ,
REFRIGERATION. 539
25. Total dry steam consumed for all purposes .......... Ibs.
(In case of superheated steamengines determine, if practicable, the tem
perature of the steam in each cylinder.)
26. Total coal as fired .......... Ibs.
(Where an independent superheater is used this includes coal burned in,
the superheater.)
27. Moisture in coal .......... per cent.
28. Total dry coal consumed .......... Ibs.
29. Ash and refuse .................. "
30. Percentage of ash and refuse to dry coal .......... per cent.
31. Calorific value of coal by calorimeter test, per pound of dry coal, de
termined by ........................ calorimeter ............ B.T.U.
32. Cost of coal per ton of 2240 Ibs .................. $
HOURLY QUANTITIES.
33. Water fed from main source of supply .......... Ibs.
34. Water fed from auxiliary supplies:
(a) .......... Ibs.
35. Total water fed to boilers per hour .............. Ibs.
36. Total dry steam consumed per hour .............. "
37. Loss of steam and water per hour due to drips from mains, steampipes^
and to leakage of plant .......... Ibs.
38. Net dry steam consumed per hour by engine and auxiliaries .......... Ibs.
39. Dry steam consumed per hour:
(a) Main cylinders ................ , ., Ibs.
(6) Jackets and reheaters. . , ........... "
(c) Airpump. , . ...................... "
(d) Circulating pump .................. "
(e) Feedwater pump. ................. ' '
(/) Other auxiliaries ................. "
40. Dry coal consumed per hour:
(a) During running period.. . , .......... Ibs.
(6) During banking period . ., .......... "
(c) Total ............................. '
41. Injection or circulating water supplied condenser per hour .......... cu. ft
PRESSURES AND TEMPERATURES (CORRECTED).
42. Steampressure at boiler by gage ................... Ibs. per sq. in.
43. Steampipe pressure near throttle by gage ........... " "
44. Barometric pressure of atmosphere in inches of mercury .......... ins.
45. Pressure in first receiver by gage ................... Ibs. per sq. in.
46. Pressure in second receiver by gage ................ " lt
47. Vacuum in condenser:
(a) In inches of mercury .......... ins.
(6) Corresponding total pressure ................. Ibs. per sq. in.
48 Pressure in steamjacket by gage .................. " "
49. Pressure in reheater by gage ...................... " "
50. Moisture in steam or superheating at boilers ...... per cent or deg. Fahr*
540 THE STEAMENGINE AND OTHER HEATMOTORS.
51. Superheating of steam at first receiver ................... deg. Fahr.
52. Superheating of steam in second receiver ................. " "
53. Temperature of main supply of feedwater to boilers ...... " "
54. Temperature of auxiliary supplies of feedwater:
(a) .......... deg. Fahr.
(b) .......... " "
(c) .......... " "
55. Ideal feedwater temperature corresponding to the pressure of the steam
in the exhaustpipe, allowance being made for heat derived from jacket
or reheater drips ............ deg. JFahr.
56. Temperature of injection or circulating water entering condenser ..........
.......... deg. Fahr.
57. Temperature of injection or circulating water leaving condenser .....
deg. Fahr.
58. Temperature of chimney gases entering economizer .......... deg. Fahr.
59. Temperature of chimney gases leaving economizer ........... " "
60. Temperature of water entering economizer .................. " "
61. Temperature of water leaving economizer .................. " "
62. Temperature of air in boilerroom ......................... " "
63. Temperature of air in engineroom ......................... ll tf
DATA RELATING TO HEAT MEASUREMENTS.
64. Heatunits per pound of feedwater, main supply ........... B.T.U.
65. Heatunits per pound of feedwater, auxiliary supply ....... ''
(a) ............. B.T.U.
(c) .............. "
66. Heatunits consumed per hour, main supply ............. B.T.U.
07. Heafcunits consumed per hour, auxiliary supplies:
(a) .......... ..B.T.U.
(6) ............ "
(c) ............ "
68. Total heatunits consumed per hour for all purposes .......... B.T.U.
69. Loss of heat per hour due to leakage of plant, drips, etc ...... "*
70. Heatunits consumed per hour
(a) By engine alone ............ B.T.U.
(6) By auxiliaries ..............
71. Heatunits consumed per hour by the engine alone, reckoned from tem
perature given in line 55 .......... B.T.U.
INDICATOR DIAGRAMS.
1st CyU 2u Cyi. 3d Cyl.
72. Commercial cutoff in per cenc of stroke ........
73. Initial pressure in Ibs. per sq in. above atmos
phere ..................................
74. Back pressure at midstroke above or below
atmosphere in Ibs. per sq. in, .............
75. Mean effective pressure in Ibs, per sq, in, ..........
76. Equivalent mean effective pressure in Ibs, per sq. in:
(a) Referred to first cylinder.  ............
REFRIGERA TION. 54 1
(&) Referred to second cylinder
(c) Referred to third cylinder
77. Pressures and percentages used in computing the steam accounted for by
the indicator diagrams, measured to points on the expansion and
compression curves
Pressure above zero in Ibs. per sq. in.:
(a) Near cutoff
(6) Near release
(c) Near beginning of compression
Percentage of stroke at points where pressures are measured:
(a) Near cutoff
(6) Near release
(c) Near beginning of compression
Percentages of stroke at points where pressures are measured:
(a) Near cutoff
(6) Near release
(c) Near beginning of compression
78. Aggregate M E.P. in Ibs. per sq. in. referred to each cylinder given in head
ing
79. Mean back pressure above zero Ibs. per sq. in.
80. Steam accounted for in Ibs. per indicated horsepower per hour:
(a) Near cutoff
(6) Near release
81. Ratio of expansion
82. Mean effective pressure of ideal diagram Ibs. per sq. in.
83. Diagram factor per cent.
SPEED.
84. Revolutions per minute rev.
85. Piston speed per minute ft.
86. Variation of speed between no load and full load rev.
87. Fluctuation of speed on suddenly changing from full load to no load, measured
by the increase in revolutions due to the change rev.
POWER.
88. Indicated horsepower developed by mainengine cylinders:
First cylinder H.P.
Second cylinder "
Third cylinder "
Total "
89. Brake H.P., electric H.P., pump H.P., or dynamo H.P., according to the
class of engine H.P.
90. Friction I. H.P. by diagrams, no load on engine, computed for average
speed... H.P.
91. Difference between indicated and brake H.P H.P.
92. Percentage of indicated H.P. of main engine lost in friction per cent.
93. Power developed by auxiliaries:
(a) H.P.
(5) "
(c) '
542 THE STEAMENGINE AND OTHER HEATMOTORS.
STANDARD EFFICIENCY RESULTS.
94. Heatunits consumed by engine and auxiliaries per hour:
(a) Per indicated horsepower B.T.U.
(fe) Per brake horsepower ' '
95. Equivalent standard coal consumed by engine and auxiliaries per hour,
assuming calorific value such that 10,000 B.T.U. are imparted to the
boiler per lb.:
(a) Per indicated horsepower Ibs.
(6) Per brake horsepower ' '
96. Heatunits consumed per minute :
(a) Per indicated horsepower B.T.U.
(5) Per brake horsepower "
97. Heatunits consumed by engine per hour corresponding to ideal maximum
temperature of feedwater given in line 55, British standard:
(a) Per indicated horsepower B.T.U.
(6) Per brake horsepower "
EFFICIENCY RATIOS.
98. Thermal efficiency ratio :
(a) Per indicated horsepower per cent
(6) Per brake horsepower ' '
(c) Ratio of efficiency of engine to that of an ideal engine working
with the Rankine cycle per cent
MISCELLANEOUS EFFICIENCY RESULTS.
(The horsepower on which the above efficiency results (94 to 103) are based
is that of the main engine exclusive of the auxiliaries.)
99. Dry steam consumed per I.H.P. per hour:
(a) Main cylinder including jackets Ibs.
(6) Auxiliary cylinders, etc "
(c) Engine auxiliaries "
100. Dry steam consumed per brake H.P. per hour:
(a) Main cylinders, including jackets Ibs.
(6) Auxiliary cylinders, etc "
(c) Engine and auxiliaries "
101. Percentage of steam used by mainengine cylinders accounted for by
indicator diagrams;
1st Cyl. 2d Cyl. 3d Cyl,
(a) Near cutoff
(6) Near release
102. Dry coal consumed by combined engine and boiler plant per I.H.P. per
hour:
(a) During running period Ibs.
(6) During banking period . '
(c) Total "
103. Dry coal consumed by combined engine and boiler plant per brake H.P.
per hour:
(a) During running period Ibs.
(6) During banking period "
(c) Total "
REFRIGERATION. 543
104. Water evaporated under actual conditions per Ib. of dry coal Ibs.
105. Equivalent evaporation from and at 212 F. per pound of dry coal
Ibs.
106. Efficiency of boilers based on dry coal per cent.
107. Combined efficiency of boiler and engine plant "
ADDITIONAL CALCULATIONS RECOMMENDED FOR SPECIAL
CLASSES OF STEAMENGINES.
WATERPUMPING ENGINES.
108. Duty per 1,000,000 heatunits imparted to the boiler ft.lbs.
109. Duty per 1000 pounds of dry steam "
110. Duty per 100 pounds of actual coal consumed by plant "
111. Number of gallons of water pumped in twentyfour hours gals.
LOCOMOTIVES.
112. Dynamometric horsepower H.P.
113. ' 'Standard Coal" of 10,000 B.T.U. value consumed, per dynamometric
horsepower per hour Ibs.
ELECTRICLIGHT ENGINES AND THOSE DRIVING GENERATORS FOR ELECTRIC
RAILWAYS.
114. Current amperes
115. Electromotive force volts
116. Electrical power generated in watts watts
117. Electrical horsepower generated H.P.
118. Efficiency of generator per cent
119. Heatunits consumed per electrical horsepower per hour B.T.U.
120. Dry steam consumed per electrical horsepower per hour Ibs.
121. Dry coal consumed per electrical horsepower per hour:
(a) During running period Ibs.
(6) During banking period * ;
(c) Total "
Additional Data. Add any additional data bearing on the particular objects
of the test or relating to the special class of service for which the engine is used.
Also give copies of indicator diagrams nearest the mean and the corresponding
scales.
CHAPTER XIX.
CONSTANTS FOR LOWSPEED STEAMENGINE DESIGN.*
THE purpose of the investigation here described was to derive
from reliable data constants to be used in the design of the
steamengine. The work is confined to the general class known
as " slowspeed " engines, principally of the Corliss type. Printed
forms, enumerating all the most important particulars to be
considered, were sent to nearly all the builders of this class of
engine, with the request that they insert the data desired.
Seventy engines by a dozen different makers, ranging from 60
to 800 horsepower in size, are represented in the work.
The method of obtaining the constants is a graphical one,
and may be most clearly explained by means of an example.
The diameter of the pistonrod is calculated in order to insure
sufficient stiffness, the rod being treated as a long compression
member. Using Euler's formula, and assuming the length of
the rod to be the same as that of the stroke, it can be readily
shown that
d = C'VSD 2 L 2 , . , ..... (1)
where d is the diameter of the rod, S the steam pressure, D the
diameter of the piston, L the length of stroke, and C' a constant.
Assuming a constant value for S and combining it with C',
(2)
Values of d and VDL taken from the data were plotted upon
coordinate paper, the series of points for each make of engine
* Sibley Journal and Trans. A. S. M. E., Vol. XVIII, and Bulletin of the
University of Wisconsin.
544
CONSTANTS FOR LOWSPEED STEAMENGINE DESIGN. 545
being connected in order by straight lines. A double circle
indicated two coincident points. A straight line representing
in position and direction the mean of the different series was
then drawn as a heavy full line, and two others marking the
extremes were drawn as heavy broken lines. The location of
these mean and extreme lines was determined simply by inspec
tion; they were drawn through the origin of coordinates when
possible. The slope of these lines determine the mean and
extreme values of the constant C in equation (2).
The same general method was employed in the case of each of
the other parts treated, a rational formula being used when
practicable. In all work involving the power of the engine,
the rating has been taken at 100 pounds per square inch gauge
pressure, cutoff at quarter stroke, noncondensing. Where the
steam pressure is a factor in the constant, values of the constant
at other pressures than 100 pounds have been computed and
tabulated. Factors of safety and stresses are calculated on
the assumption that the unbalanced pressure on the piston is
100 pounds per square inch.
The notation used is as follows:
D = diameter of piston ;
L = length of stroke;
A = area of piston;
S = steam pressure (gage) ;
H. P. = rated horsepower;
N = re volutions per minute;
C and B = constants.
All dimensions are in inches unless otherwise stated.
Pistonrod. The formula is d = C\ / DL and
d = .112V7)Z for the mean,
= .136V / DL for the maximum,
= .098V5L for the minimifm.
If LI, the free length of the pistonrod is taken at 1.1L we
have, on substitution in Euler's formula,
546 THE STEAMENGINE AND OTHER HEATMOTORS.
4 : 4X1.21L2X64'
The factors of safety in the above cases are ("gg ) , ("AQ") '
/gg\4
and ( gg ) , since the strength varies as the fourth power of the
diameter of the rod.
* PISTONROD, d = CVDL.
Steam
Pressure.
Mean
Constant.
Maximum
Constant.
Minimum
Constant.
80
.106
.129
.093
100
.112
.136
.098
120
.117
.142
.102
150
.124
.150
.108
Connectingrod. Only rods of circular midsection are con
sidered. The formula is similar to the preceding, so that
d = C'^SIPLf = CV5ZT, where LI is the length of the rod
from center to center and d is the diameter in the middle. The
constants obtained give
.0935\ / DL 1 for the mean,
= .105 v DLi for the maximum,
for the minimum.
The factors of safety are (1.94) 4 , (2.18) 4 , and (1.69) 4 . The
values of L vary from 2.75L to 3L, or from 5} to 6 " cranks."
* CONNECTINGROD, d =
Steam
Pressure
80
Mean
Constant.
.0885
Maximum
Constant.
.0994
Minimum
Constant.
.0763
100
.0935
.1050
.0816
120
.0978
.1100
.0854
150
.1030
.1160
.0893
* Barr and Trooien give practically the same values.
CONSTANTS FOR LOWSPEED STEAMENGINE DESIGN. 547
Main Journal. The wellknown formula for torsion is used,
/TT T)
<j=(7\ ' ' and the constants obtained give
' for the mean,
ITT T>
= 7.8 \Tf" f r the maximum,
ITT p
= 5.66 \ rp for the minimum.
The stresses in the outer fiber corresponding to these constants
are respectively 1250, 678, and 1775 pounds per square inch.
The corresponding constants by Barr are 6.8, 8.0, and 6.0
respectively for one journal only, sidecrank engines.
Trooien gives the following values for the constants in the
formula
,7 C ' R
c ~~
= .30;
0=7.2 mean value;
= 8.0 maximum value;
= 6.4 minimum value.
The length of the bearing necessary for cool running is given
TT T)
by the formula l=C ^ ' ,
TT T)
I = 1 .56 7 + 7 for the mean,
LJ
TT T)
= 2.27 7* + 7 for the maximum,
LJ
TT T)
= 0.86 f^ + 7 for the minimum.
Li
Using the empirical formula l = Cd the constants obtained
by Barr and Trooien give
Z = 1.9d for the mean,
=2.1d for the maximum,
=*= I. Id for the minimum.
548 THE STEAMENGINE AND OTHER HEATMOTORS.
To prevent " seizing/' the bearing area must be made pro
portional to the total pressure. The formula used is dl = C'SA
= CD 2 and the constants obtained give
* dl = AID 2 for the mean,
= .503Z) 2 for the maximum,
= .36Z) 2 for the minimum.
Neglecting the weight of the flywheel and the pull of the belt,
the bearing pressures corresponding to the constants are respec
tively 178.5, 156, and 218 pounds per square inch of projected
area.
MAIN JOURNAL, dl = CD*.
Steam Mean Maximum Minimum
Pressure.
Constant.
Constant.
Constant.
80
.352
.402
.288
100
.440
.503
.360
120
.528
.604
.432
150
.660
.755
.540
*125
.60
.66
.50
Crankpin. Only " overhung " cranks are considered. The
constants obtained give for the length
TT p
Z = .515 j L + 2" for the mean,
TT T)
= .655 j^ + 2" for the maximum,
TT TJ
= .345 V~ + 2" for the minimum.
L
Barr uses the same formula with constants 20% greater,
namely, .6, .8, and .4 respectively.
TT TJ
The base formula =(7^ is derived from the fact that
the projected area of the pin should be proportional to the heat
(arising from lost work of friction) which must be dissipated.
* Barr and Trooien give practically the same values.
CONSTANTS FOR LOWSPEED STEAMENGINE DESIGN. 549
The empirical formula d = CD gives
d= .278D for the mean,
= .339D for the maximum,
= .221D for the minimum.
Trooien gives .27, .32, and .21 as the constants from over
hung crankpins of Corliss type, using I = l.l4d as the mean
relation of length to diameter of pin. The constants in the
formula l = Cd are
C=1.14 mean value,
= 1.30 maximum value,
= 1.0 minimum value.
The formula for the diameter of the pin is d = C'VSD 2 l =
C^D 2 l and the constants given
d = . 384f / D 2 T for the mean,
= .5QQf D 2 l for the maximum,
= .320^^" for the minimum.
Assuming the whole load to be concentrated at the outer end
of the pin, the stresses corresponding to these constants are re
spectively 14,150, 6,400, and 25,000 pounds per square inch.
CRANKPIN, d =
Steam
Pressure.
Mean
Constant.
Maximum
Constant.
Minimum
Constant.
80
.356
.464
.297
100
.384
.500
.320
120
.408
.531
.340
150
.440
.572
.366
The projected area is given by
= .07D 2 for the mean,
= .09D 2 for the maximum,
= .05D 2 for the minimum.
* Barr gives the same constants.
550 THE STEAMENGINE AND OTHER HEATMOTORS.
The corresponding pressures are respectively 1120, 865, and
1640 pounds per square inch.
CRANKPIN, dl = CD\
Steam
Pressure.
Mean
Constant.
Maximum
Constant.
Minimum
Constant.
80
.056
.073
.041
100
.070
.090
.050
120
.084
.109
.061
150
.105
.136
.077
Crosshead Pin. The length is usually the same as that of
the crankpin. In the formula I = Cd, Trooien gives
C = 1.43, Barr gives C = 1.3 mean value,
= 1.9 =1.5 maximum value,
= 1.0, =1.0 minimum value.
For cross bending if l = l.25d Trooien gives for C in formula
d=CD,
C = .25 mean value,
= .28 maximum value,
= .17 minimum value
The bearing area is given by
* d/ = .058Z) 2 for the mean,
= .083Z) 2 for the maximum,
= .042D 2 for the minimum.
CROSSHEAD PIN, dl = CD*.
Steam
Pressure.
Mean
Constant.
Maximum
Constant.
Minimum
Constant.
80
.046
.066
.034
100
.058
.083
.042
120
.070
.100
.050
150
.087
.125
.063
* Barr gives the same values.
CONSTANTS FOR LOWSPEED STEAMENGINE DESIGN. 551
Crosshead Shoes. The area of the shoe. or shoes on which the
pressure comes is given by the formula
* Area = .37 D 2 for the mean,
= .52Z) 2 for the maximum,
= .23D 2 for the minimum.
The greatest pressures on the guide corresponding to these
constants is 36.1, 58, and 25.6 pounds per square inch respectively.
CROSSHEAD SHOE, Area = CD 2 .
Steam Mean Maximum Minimum
Pressure Constant. Constant. Constant.
80 .296 .416 .184
100 .370 .520 .230
120 .444 .624 .276
150 .555 .781 .345
Steam Ports and Pipes. The areas of the ports are given by
the formula, area port = CA X piston speed and the constants
obtained give
Area steam port = .000152A X piston speed for the mean,
= .000208Ax piston speed for the maximum,
= .000 108 Ax piston speed for the minimum,
and
Area exhaust port = .000181 Ax piston speed for the mean,
= . 0002564. X piston speed for the maximum,
= .000239^4. X piston speed for the minimum.
As the piston speed is generally 600 feet per minute (with
800 for a maximum and 400 for a minimum) we have more simply,
Area steam port = .09 A for the mean,
= .10A for the maximum,
= .08A for the minimum,
and Area exhaust port = .11^1 for the mean,
= .125A for the maximum,
= .10 A for the minimum.
* Ban* and Trooien use the same values.
552 THE STEAMENGINE AND OTHER HEATMOTORS.
The velocity of steam in
Steam ports is 6.800 for the mean,
9.000 for the maximum,
5.000 for the minimum.
Exhaust ports is 5500 for the mean,
7000 for the maximum,
4000 for the minimum.
Steam pipes is 6000 for the mean,
8000 for the maximum,
5000 for the minimum.
Exhaust pipes is 3800 for the mean,
4700 for the maximum,
2800 for the minimum.
The diameter of the steampipe is given by
d = .324L> for the mean,
= .373D for the maximum,
= .253D for the minimum.
The diameter of the exhaustpipe is given by
d = AOOD for the mean,
= .463Z) for the maximum,
= .3577) for the minimum.
Belting. The mean belt speed is 3900 feet per minute, vary
ing from 2600 to 5600 feet per minute. The following constants
were also observed :
Square feet belt per minute = 27.4 H.P.f 1250 for the mean,
= 29.0 H.P. + 3000 for the maximum,
= 23.2 H.P.  for the minimum.
Barr gives
Square feet belt per minute = 35 H.P. for the mean,
= 42 H.P. for the maximum,
= 30 H.P. for the minimum.
CONSTANTS FOR LOWSPEED STEAMENGINE DESIGN. 553
Trooien gives
Square feet belt per minute = 21 H.P. + 1000 mean value,
= 35 H.P. + 1000 maximum value,
= 18.2 H.P. + 1000 minimum value.
The Weight of the Engine, including the flywheel, is given by
Total weight = 148 H.P. for the mean,
= 195 H.P. for the maximum,
= 112 H.P. for the minimum.
Trooien gives
= 132 H.P. for the mean,
= 164 H.P. for the maximum,
= 102 H.P. for the minimum.
The Steam Cylinder. The mean thickness of the cylinder is
given by the formula = .024Z) + .66 inch.
Barr gives t = .05Z) f .3 inch,
= .054D + .28 inch mean value,
Trooien, = .072D + .28 maximum value,
= .035D + .28 minimum value.
for both high and slow speed engines.
Flanges. The mean thickness of the flanges and heads is
1.25, with extremes of l.Ot and l.7t.
Bolts. The number of cylinderhead bolts is expressed by
N = CD, where C = .7 and N = number of bolts.
The sizes of bolts vary from f " to If", generally being from
f" to 1". The least number used is eight. Neglecting the
load due to screwing up, the total crosssection of the bolts at
the root of the thread is given by a = C'SD 2 = CD*. The con
stants obtained give
a = .0199D 2 for the mean,
= .0405D 2 for the maximum,
= .0138D 2 for the minimum.
554 THE STEAMENGINE AND OTHER HEATMOTORS.
The stresses on the bolts corresponding to these constants are
respectively 3950, 1940, and 5960 pounds per square inch.
CYLINDERHEAD BOLTS, A = CD 2 .
Steam Mean Maximum Minimum
Pressure. Constant. Constant. Constant.
80 .0159 .0324 .0110
100 .0199 .0405 .0138
120 .0239 .0486 .0166
150 .0298 .0607 .0207
Barr gives d =777+7^ inch, where d is the nominal diameter
4U Zi
of the stud. Trooien gives d = .04D + f inch.
Piston. The face or length of the piston is given by
Face = .330D for the mean,
= .4457) for the maximum,
= .257D for the minimum.
Barr and Trooien give the same values.
The thickness of piston shell is .6 to .7 of the thickness of
the cylinder walls.
There are generally two piston rings turned to a diameter
} inch larger than the diameter of the cylinder.
Clearance volume varies from 2 to 5 per cent in Corliss engines.
Ratio of length of stroke to cylinder diameter in engines having
a speed less than 110 revolutions per minute.
5 = 8 in.,
C=1.63 mean value,
= 2.40 maximum value,
= 1.15 minimum value.
For engines having a speed between 110 and 200 revolutions
per minute,
L=CD,
C = 1.36 mean value,
= 1.88 maximum value,
= 1.03 minimum value.
CONSTANTS FOR LOWSPEED STEAMENGINE DESIGN. 555
Flywheels. Some makers consider only the effect of the rim,
others take various proportions of the weight of the hub and arms
into consideration. For standard Corliss engines Trooien gives
=
B = . 000,000,004,5,
C= 890,000,000,000 mean value,
= 1,330,000,000,000 maximum value,
= 625,000,000,000 minimum value
The corresponding values of K are
K = 4000 mean value,
= 6000 maximum value,
= 2800 minimum value.
The diameter of the flywheel in inches is CL.
C = 4.4 mean value,
= 5.25 maximum value,
= 3.25 minimum value.
The width of the face is
W = C(D l B),
or W
5 = 50;
C = .22 mean value,
= .30 maximum value,
= .18 minimum value.
K = 13 mean value,
= 15 maximum value,
= 9 minimum value.
Velocity of the rim is
68 feet per seconu mean velocity,
82 feet per second maximum velocity,
40 feet per second minimum velocity.
556 THE STEAMENGINE AND OTHER HEATMOTORS.
A note with respect to the materials used may be of interest.
Pistonrods usually are made of mild steel, indifferently specified
as " openhearth " or " machinery " steel, but one maker using
crucible steel. Connectingrods are made of both wroughtiron
and steel, with no marked preponderance in favor of either. For
crankshafts, most builders use wrought iron, but openhearth
and crucible steel are also employed. Crankpins and crosshead
pins are usually the same as the pistonrod; a few crossheads
are cast solid with the pin, both steel and iron being used.
CONSTANTS FOR HIGHSPEED ENGINE DESIGN.*
In designing the modern highspeed automatic engine, it has
been found that the constants used for the slower type of engine
do not give satisfactory results. It was for the purpose of
obtaining these constants that the present thesis was under
taken.
Printed blanks were sent to all the manufacturers of high
speed automatic engines, with the request to fill in the dimen
sions and weights asked for. Ten responded in time to permit
the use of their data. About six or eight sizes of center crank
engines of each maker were selected, ranging from 35 to 250 horse
power.
Rational formulae were selected for all the important parts of
the engine. To illustrate the method of deriving the constants,
we will take a particular case. The formula for the diameter of
the pistonrod is
d = VsC'D 2 L*, (1)
where d is the diameter of rod, S the steam pressure (100 pounds
gage), C" a constant, D the diameter of the piston, and L the
length of stroke. Combining S and C ; into one constant, C, we
have
d = CV5T, (2)
* See Sibley Journal, Trans. A. S. M. E., Vol. XVIII, and Bulletin of Uni
versity of Wisconsin.
CONSTANTS FOR HIGHSPEED ENGINE DESIGN. 55?
We substituted in (2) the values of d, D, and L, taken from
the data, and then plotted d as one coordinate and VDL as the
other. The points were marked by a small circle, and where
two points coincided, by a double circle. All the points of each
engine were connected by a certain broken line. A mean line,
and two extreme lines were drawn, and from their equations,
the constants were obtained, x = diameter of pistonrod, y = \/DL;
x
therefore, since d = CvDL, c = ,  =  = cotangent of the angle
with the horizontal. In some cases, as in equation (1), the con
stant varies as some power of the steam pressure. For these
cases tables have been constructed giving the constant for each
increase of 10 pounds, from 50 to 200. These tables have been
abbreviated for the purposes of this abstract. For simplicity all
dimensions are in inches unless otherwise specified, and whenever
the steam pressure is a factor, it has been taken at 100 pounds
gage. In the case of engines not so rated, that pressure has
been stated as safe. The complete derivation of the formulas
here given may be found by reference to the original thesis.
In this work the following conventions have been used:
A = area of piston;
D = diameter of piston;
L = length of stroke;
H. P. = horsepower;
S = steam pressure per square inch;
N = revolutions per minute;
d = diameter of part under discussion,
1 = length of part under discussion;
h = height of part under discussion ;
b = breadth of part under discussion.
Pistonrods. The formula is d = C\ / DL, and
d = .145 VDL for the mean,
= .1775v / DL for the maximum,
= .119 VDL for the minimum.
Barr gives the same values.
558 THE STEAMENGINE AND OTHER HEATMOTORS.
TABLE I.
PISTONROD, d = CVDL.
Steam Mean Maximum Minimum
Pressure. Constant. Constant. Constant.
50 .1220 .1490 .1000
80 .1372 .1675 .1125
110 .1487 .1815 .1219
140 .1579 .1928 .1294
170 .1659 .2023 .1359
200 .1726 .2109 .1415
For steam pressures other than 100 pounds, Table I gives
the constants for the various pressures.
Connectingrods. The usual formula is,
T the breadth,
and the constants obtained give
6 = .0545v / 5ZTfor the mean,
= . 0693 v'DL" for the maximum,
= .0443 v Z)L for the minimum.
The steam pressure is the same function of the constant as in
the connectingrod formula.
TABLE II.
CONNECTINGROD, 6 = C\ // )L.
Steam
Pressure.
Mean
Constant.
Maximum
Constant.
Minimum
Constant.
50
.0459
.0583
.0376
80
.0515
.0655
.0419
*110
.0558
.0710
.0454
140
.0593
.0754
.0483
170
.0623
.0792
.0507
200
.0648
.0825
.0526
f!25
.073
.094
.05
* Barr gives these values approximately,
t Trooien.
CONSTANTS FOR HIGHSPEED ENGINE DESIGN. 559
Table II gives values of the constants for rectangular section
only.
The height of the rod is generally considered to be twice the
breadth, plus a certain percentage to compensate for the inertia
of the rod itself. The following values of the height were
obtained :
h = 2.73b for the mean,
= 4.006 for the maximum,
= 2.186 for the minimum.
Trooien gives 2.28, 3.0, and 1.85 for the value of these constants.
The mean factor of safety of the connectingrod with Barr's
constants is 27; with Trooien's constants it is 60.
Also for the length of the rod we found,
/ = 3.00L " cranks " for the mean,
= 3.32L for the maximum,
= 2.46L for the minimum.
Main Journal. For the prevention of heating, the length
should be
(TT T> \
^ + 5.23 j for the mean,
(TT p \
Y + 9.04 ) for the maximum,
(TT "P \
'j 1  + 3 ) f or the minimum.
The ratio of length to the diameter was found to be
Z = 2.03(d + .49) for the mean,
= 2.05(d + .17) for the maximum,
= 1.63d, for the minimum.
Barr gives 2.2, 3.0, and 2.0; Trooien gives 2.1, 2.9, and 1.6.
For the prevention of expulsion of lubricant, the bearing area
should be sufficiently large, and proportional to the area of
piston, or
dl=C'SA = CA.
560 THE STEAMENGINE AND OTHER HEATMOTORS.
The values found for the constant give
dl = .489 A for the mean,
= .739 A for the maximum,
= .3675A for the minimum.
Barr gives .46, .70, and .37; Trooien gives .48, .78, and .32.
TABLE III.
MAIN JOURNAL, dl = CA.
Steam
Pressure.
Mean
Constant.
Maximum
Constant.
Minimum
Constant.
50
.2445
.3695
.1838
80
.3912
.5912
.2940
110
.5379
.8129
.4043
140
.6846
1.0346
.5145
170
.8313
1.2563
.6248
200
.9780
1.4780
.7350
The constant in this case varies directly as the steam pressure,
and Table III gives values for the constant for the different
pressures.
In all these engines, the main shaft has the same diameter
throughout its length, and for strength the formula is
N '
The constants found give
ITT p
d = 7.56\ r^ for the mean,
ITT p
= 8.76 \ n. 7 ' for the maximum,
/TT p
= 5.98 \^ for the minimum.
Barr gives 7.3, 8.5, and 6.5; Trooien gives 6.6, 8.2, and 5.4.
Crankpin. For value of the constant, in the formula,
~H.P.
L
which gives the length necessary to avoid heating, we found,
CONSTANTS FOR HIGHSPEED ENGINE DESIGN. 561
HP
/ = .333^ + 2.2 for the mean,
H.P.
= .417 T + 3.92 for the maximum,
TT T>
= .192 ' + .88 for the minimum.
LJ
Barr gives .30, .46, and .13 as values of C and 2.5" as the value
of B.
For bearing area, we found, from dl = CS'A = CA,
dl = .22 A for the mean,
= A4A for the maximum,
= .0693 A for the minimum.
Barr gives .24, .44, and .17 as the values of the constant (7 k
TABLE IV.
CRANKPIN, dl = CA.
Steam
Pressure.
Mean
Constant.
Maximum
Constant.
Minimum
Constant.
50
.110
.220
.0347
80
.176
.352
.0554
110
.242
.484
.0762
140
.308
.616
.0970
170
.374
.748
.1178
200
.440
.880
.1386
As a check the ratio of length to diameter was found and is
l = d for the mean,
l = l.22d for the maximum,
/= .9<i for the minimum.
Trooien gives .87, 1.25, and .66 as the constants.
In centercrank engines, assuming that the distance from
center to center of main bearings is 4.2d, Trooien finds, in calcu
lating d for strength, the following constants in the formula,
d = CD,
C=.40 mean value,
= .526 maximum value,
= .28 minimum value,
562 THE STEAMENGINE AND OTHER HEATMOTORS.
Crosshead Pin. For the bearing area the formula is
and the values of the constant found give
d = .1045A for the mean,
= .346A for the maximum,
= .0664 A for the minimum.
TABLE V.
CROSSHEAD PIN, dl=CA.
Steam
Pressure.
Mean
Constant.
Maximum
Constant.
Minimum
Constant.
50
.0523
.1730
.0332
80
.0836
.2768
.0531
110
.1150
.3806
.0730
140
.1463
.4844
.0930
170
.1777
.5882
.1129
200
.2090
.6920
.1328
Barr
100
.08
.11
.06
Trooien
125
.10
.15
.037
The ratio of length to diameter was found to be
/ = 1.335d for the mean,
= 2d for the maximum,
= 1.07d for the minimum.
Trooien gives 1.25, 1.5, and 1.0.
Barr gives 1.25, 2.0, and 1.0.
Crosshead Shoes. For the bearing area of the crosshead
shoes, the constants found give, in the equation,
Area = .61 1 ( A + 25) for the mean,
= .69801 + 123) for the maximum,
= .46 (A 2) for the minimum.
CONSTANTS FOR HIGHSPEED ENGINE DESIGN. 563
TABLE VI.
CROSSHEAD SHOES, Area = CA.
Steam Mean Maximum Minimum
Pressure. Constant. Constant. Constant.
50 .3055 .3490 .230
80 .4888 .5584 .368
110 .6721 .7678 .506
140 .8554 .9772 .644
170 1.0387 1.1866 .782
200 1.2220 1.3960 .920
Barr
100 .63 1.60 .45
Trooien
125 .53 .72 .37
For the maximum pressure per square inch of shoe, Barr gives
27 for the mean,
38 for the maximum,
10.5 for the minimum,
Trooien gives 39.5 for the mean,
57 for the maximum,
28 for the minimum.
Cylinder Dimensions. The ratio of length of stroke to diam
eter of cylinder in engines having a speed greater than 200 revo
lutions per minute,
L = CD.
C=1.07 mean,
= 1.55 maximum,
= .82 minimum.
Clearance volume varies from 5 to 11 per cent.
The thickness of the cylinder cover at the center varies con
siderably, but may be taken at 2.75 times the thickness of cylin
der walls. The thickness of the flanges for holding cylinder
covers may be taken at 1.12 times the thickness of the cylinder
walls. For number and size of bolts, see Slowspeed Engine Design.
Piston and Piston Speed. For obtaining the dimensions of
the face of piston there is no rational formula applicable, but
564 THE STEAMENGINE AND OTHER HEATMOTORS.
an empirical formula was constructed; the ratio of face to
diameter being found thus for horizontal engines,
Face = .4375D for the mean,
= .65D for the maximum,
= .299D for the minimum.
Trooien gives .40, .47, and .30 as the constants.
For ascertaining the piston speed a curve was plotted with
revolutions per minute as one coordinate, and length of stroke
as the other. The resulting mean curve is an equilateral hyper
bola showing that for this class of engines the piston speed is
constant, and is 600 feet per minute.
Trooien gives
600 = mean speed,
900 = maximum speed,
320 = minimum speed.
Steam Ports and Pipes. In designing ports it is customary to
consider the velocity of steam through the passage as equal to
the ratio of the area of the piston to the area of the passage,
multiplied by the piston speed. Since the piston speed is quite
constant, about 600 feet per minute, the area of these passages
is proportional to the area of the piston. For the steam ports
the relation is
Area of steam ports = .0936 A for the mean,
= .136A for the maximum,
= .0544A for the minimum.
Barr gives for the velocity of steam through steam ports,
5500 mean,
6500 maximum,
4500 minimum.
Area steam ports = .11 A mean,
= .13 A maximum,
= .09A minimum.
For the steampipes,
Diam. of pipe = .452D 1.42 for the mean,
= .54D 1.02 for the maximum,
= .382D1.07 for the minimum.
CONSTANTS FOR HIGHSPEED ENGINE DESIGN. 565
Barr gives for the velocity of steam through pipes,
6500 mean,
7000 maximum.
5800 minimum.
Diam. of pipe = .30Z) mean,
= .32D maximum
= .29Z) minimum.
For the exhaustpipe,
Diam. of pipe = .503Z) 1.4 for the mean,
== .5D for the maximum,
= .57) 2.24 for the minimum.
Barr gives for the velocity of steam through exhaust pipes,
4400 mean,
5500 maximum,
2500 minimum.
Diam. of exhaust pipe = .37Z) mean r
= .50D maximum,
= .33D minimum.
Belting. The relation between the square feet of belting per
hour and horsepower transmitted was found to be
Square feet belting per hour = 2000 (H. P. + 50) for the mean,
= 2000(H.P.+95) for the maximum,
= 2000(H.P.50) for the minimum.
Barr gives
Square feet belting per minute = 55 H.P. mean,
= 70 H.P. maximum,
= 40 H.P. minimum,
Flywheel. For governing, Professor Thurston in his " Manual
of the Steam Engine," shows that the weight of the rim of flywheel
TT T>
is proportional to Trifp. where DI is the diameter of wheel in
inches. The constants found give
566 THE STEAMENGINE AND OTHER HEAT MOTORS.
TT T)
Weight of rim = 833,000,000,000^ 2 ^ 3 for the mean,
TT T)
= 2,780,000,000,000 ^ ' ' for the maximum,
TT T)
= 341,000,000,000^^ for the minimum,
Barr gives 1200, 2000 and 650 billions for the constants.
Trooien gives 1300, 2800, and 660 billions for the constants
for engines up to 175 H.P. For large engines, however, the
TT T)
formula W = Cx + B seems better.
= 1000,
C= 720,000,000,000 mean,
= 1,140,000,000,000 maximum,
= 330,000,000,000 minimum.
The relation between the length of stroke and the diameter of
the flywheel is given by Di = CL.
C = 4.4 mean,
= 5.0 maximum,
= 3.4 minimum.
For the linear velocity of the periphery, we averaged the
velocities of each maker, and then took a total average. This
average gave 4232 feet per minute, and varies from 5730 to
3060 feet per minute.
Reciprocating Parts. The weight of reciprocating parts is
D 2
proportional to = and the constants give
Z> 2
Weight of parts = l,850,000^p,
the mean curve being an equilateral hyperbola.
Trooien gives
2,000,000 mean,
3,400,000 maximum,
1,370,000 minimum.
CONSTANTS FOR HIGHSPEED ENGINE DESIGN. 587
In cases, where obtainable, the balance weight opposite the
crankpin was about 75 per cent of the weight of the reciprocating
parts.
Weight of Engine. It being of possible interest, the relation
between the total weight of engine and rated horsepower was
found, and is
Weight of engine = 117(H.P. 7).
For beltconnected highspeed engines Trooien gives for in
formula TF = CxH.P.,
C= 82 mean,
= 120 maximum
= 52 minimum.
For directconnected engines the weight of the engine without
the generator was 10 to 25 per cent greater than the weight of
beltconnected engines of the same capacity.
APPENDIX.
I.
IMPORTANT PROPERTIES OF FAMILIAR SUBSTANCES.
Specific
Gravity.
Water, 1.
Specific
Heat,
Water, 1.
Meltingpoints,
Degrees Fahr.
Weight in
Pounds.
Metals from 32 to 212
Aluminum
Antimony
2.63
6.712
9.823
8.1
8.788
7.5
7.744
19.258
11.352
13.598
8.800
16.000
10.474
7.834
7.291
7.191
0.9
0.88
0.0006
0.87
1.000
0.922
0.212
0.0508
0.0308
0.0939
0.092
0.1298
0.1138
0.0324
0.0314
0.0333
0.1086
0.0324
0.056
0.1165
0.0562
0.0953
0.6588
0.31
0.487
0.416
1.000
0.504
'si6
476
1692
1996
2250
2900
2590
608
39
2640
3700
2000
4000
446
680
Per cu. ft.
0.1100
0.2428
0.3533
0.2930
0.3179
0.2707
0.2801
0.6965
0.4106
0.4918
0.3183
0.5787
0.3788
0.2916
0.2637
0.26
Bismuth
Brass
Copper . .
Iron, cast
" wrought . . .
Gold
.Lead
Mercury at 32 . .
Nickel
Platinum
Silver
Steel
Tin
Zinc
Liquids:
Alcohol (mean). . .
Oil, petroleum . .
Steam at 212 .
Turpentine
Water 62
Solid:
Ice at 32
Gases.
Air
Specific
Gravity,
Air*],
Temp.
32 F.
Atmos.
Pressure.
1.0000
1.589
0.8982
0.9764
1.5290
0.9847
0.0695
0.5560
0.9714
1.1051
2.2130
Specific
<
0.1689
0.398
0.245
0.173
0.171
0.332
2.406
0.467
0.173
0.155
Heat.
C P.
0.2375
0.438
Specific Heat
*Z. &P
131.40 184.77
Weight
per Cu.
Ft. at
32 F.
Atm.
Pres.
0.0807
Alcohol
Acetylene gas
0.0730
0.0781
0.1234
0.0794
0.0056
0.0449
0.0784
0.0892
0.1786
Carbon monoxide, C<
Carbon dioxide CO 2 .
3. . .
0.245
0.216
0.404
3.409
0.593
0.244
0.2175
0.154
134.59
133.04
259.3
1871.87
363.33
134.59
120.59
190.61
168.05
314.31
2652.2
461.35
189.83
169.21
Ethylene, C 2 H 4 . . . .
Hydrogen. . .
Methane CH 4
Nitrogen. ...
Oxygen
Sulphur dioxide, SO 2
Gases.
Weight
per
Cu. Ft.
at 62 F
Volumf
POUE
. 32 F.
$ of One
(1, at
62 F.
Specific Heat per Cubic Foot
at Co
Pres
32 F.
nstant
sure.
62 F.
at Con
Vol
32 F.
stant
ume.
62 F.
Air. .
0.7612
0.0736
0.1156
0.0735
0.0052!
0.0421
0.0789
0.0841
12.39
12.82
8.15
12.82
3 178.2
22.39
12.73
11.20
13.14
13.61
8.65
13.60
189.4
23.75
13.53
11.90
0.0192
0.0195
0.0266
0.0343
0.0191
0.0265
0.0191
0.0194
0.0181
0.0182
0.0251
0.0297
0.0180
0.0250
0.0180
0.0183
0.0136
0.0135
0.0210
0.0259
0.0135
0.0209
0.0136
0.0138
0.0127
0.0127
0.0198
0.0244
0.0127
0.0197
0.0128
0.0130
Carbon monoxide. . .
Carbon dioxide. . .
Ethylene.
Hydrogen
Methane
Nitrogen
Oxygen
571
572
APPENDIX.
II.
HYPERBOLIC OR NAPERIAN LOGARITHMS.
N.
Log.
N.
Log.
N.
Log.
N.
Log.
N.
Log.
1.00
0.0000
2.30
0.8329
3.60
.2809
4.90
1.5892
6.40
1.8563
.05
0.0488
2.35
0.8544
3.65
.2947
4.95
1.5994
6. .50
1.8718
.10
0.0953
2.40
0.8755
3.70
.3083
5.00
.6094
6.60
1.8871
.15
0.1398
2.45
0.8961
3.75
.3218
5.05
.6194
6.70
1.9021
.20
0.1823
2.50
0.9163
3.80
.3350
5.10
.6292
6.80
1.9169
.25
0.2231
2.55
0.9361
3.85
.3481
5.15
.6390
6.90
1.9315
.30
0.2624
2.60
0.9555
3.90
.3610
5.20
.6487
7.00
1.9459
.35
0.3001
2.65
0.9746
3.95
.3737
5.25
.6582
7.20
1.9741
.40
0.3365
2.70
0.9933
4.00
.3863
5.30
.6677
7.40
2.0015
.45
0.3716
2.75
1.0116
4.05
.3987
5.35
1.6771
7.60
2.0281
.50
0.4055
2.80
1.0296
4.10
.4110
5.40
1.6864
7.80
2.0541
.55
0.4383
2.85
1.0473
4.15
.4231
5.45
1.6956
8.00
2.0794
.60
0.4700
2.90
1.0647
4.20
1.4351
5.50
1.7047
8.25
2.1102
.65
0.5008
2.95
1.0818
4.25
1.4469
5.55
1.7138
8.50
2.1401
.70
0.5306
3.00
1.0986
4.30
1.4586
5.60
1.7228
8.75
2.1691
.75
0.5596
3.05
1.1154
4.35
1.4701
5.65
1.7317
9.00
2.1972
.80
0.5878
3.10
1.1314
4.40
1.4816
5.70
.7405
9.25
2.2246
1.85
0.6152
3.15
1 . 1474
4.45
1.4929
5.75
.7492
9.50
2.2513
1.90
0.6419
3.20
1.1632
4.50
1.5041
5.80
1.7579
9.75
2.2773
1.95
0.6678
3.25
1.1787
4.55
1.5151
5.85
.7664
10.00
2.3026
2.00
0.6931
3.30
1.1939
4.60
1.5261
5.90
.7750
11.00
2.3979
2.05
0.7178
3.35
1.2090
4.65
1.5369
5.95
.7834
12.00
2.4849
2.10
0.7419
3.40
1.2238
4.70
1.5476
6.00
.7918
13.00
2.5649
2.15
0.7655
3.45
1.2384
4.75
1 . 5581
6.10
.8083
14.00
2.6391
2.20
0.7885
3.50
1.2528
4.80
1 . 5686
6.20
.8245
15.00
2 7081
2.25
0.8109
3.55
1.2669
4.85
1 . 5790
6.30
.8405
16.00
2.7726
III.
HEATING VALUES OF VARIOUS SUBSTANCES.
The following table gives the heating values of different pure fuels as deter
mined by burning them in oxygen in a calorimeter.
Heatunits.
AJthoity.
Cent.
Fahr.
Acetylene, C.H 2 to CO 2 and H 2 O . .
Alcohol, methyl or wood, CH 4 O. . . .
'' ethyl or sugar C H 6 O. . ..
10,109
5,307
7,183
\ 10,102
\ 9,915
9,977
/ 8,080
1 8,137
2473
/ 2',403
\ 2,385
5,607
fl 1,858
\ 11,957
5,400
/ 34,462
\ 34,342
/ 13,120
\ 13,063
9,700
2,250
18,196
9,558
12,933
18,184
17,847
17,862
14,544
14,647
4451
4,323
4,293
10,093
21,344
21,523
9,720
62,032
61,816
23,616
23,513
17,460
4,050
Thomsen
Favre and Silberman
< . < i t (
Thomsen
Favre and Silberman
St ohman
Favre and Silberman
Berthelot
Favre and Silberman
1 1 ft < i
Thomsen
Favre and Silberman
< <
Thomsen
Various
Favre and Silberman
Thomsen
t i
Favre and Silberman
Various
N. W. Lord
Benzole gas, C 6 H to CO 2 and H 2 O. .
Benzene
Carbon (wood charcoal) to CO 2 . . .
Carbon to CO
CO to CO per unit of CO
CO to CO 2 per unit of C
Ethylene (Olefiant gas), C 2 H 4 to
Gas illuminating .
Hydrogen gas to H^O . . .
Methane (Marsh gas), CH 4 to CO 2
and H 2 O
Sulphur to SO*
APPENDIX.
573
IV.
OXYGEN AND AIR REQUIRED, THEORETICALLY, FOR THE COM
BUSTION OF VARIOUS SUBSTANCES
Pure dry air is a mixture made up of 20.91 parts of O and 79.09 parts of N
by volume (viz., in the ratio of one part of O to 3.782 parts of N), or 23.15 parts
of O and 76.85 parts of N by weight (viz., in the ratio of 1 part of O to 3.32
parts of N).
Lbs. of
O per Ib.
Fuel.
Lbs. of N
3.32XO.
Air per Ib.
= 4.32X0
Gaseous
Product
per Ib.
Carbon to CO 2 C+20 = CO"
2*
8.85
11.52
12 52
Carbon to CO . C + O=CO
il
4.43
5.76
6 76
Carbon monoxide to CO 2 . .CO + O = CO 2
Alcohol . . CH 6 O + 60 = 2CO 2 + 3HoO
2A
1.90
6.93
2.47
8.94
3.47
9 94
Acetylene C 2 H 2 +50 = 2CO 2 +H 2 O
Ethylene C 2 H 4 + 6O = 2CO 2 +2H 2 O
Hydrogen' 2H + O = H O
3A
3
8
9.99
10.1
26.56
13.00
13.14
34 56
14.00
14.14
35 56
Methane . . .CH 4 +4O = CO 2 +H 2 O
4
13.28
17 28
18 28
Sulphur S+ 2O = SO 2
1
3.32
4.32
5 32
V.
RELATIVE HUMIDITY, PER CENT.
Difference between the Dry and Wet Thermometers, Degrees F.
fi
1
2
3
4
5
6
7
8
9
1C
11
12
13
14
15
16
17
18
19
20
21
22
23
24
26
28
30
Relative Humidity, Saturation being 100. (Barometer = 30 ins.)
32
89
79
69
59
49
39
30
20
11
2
40
92
S3
75
68
00
52
45
37
29
23
15
7
50
93
87
80
74
07
01
55
49
43
38
32
27
21
10
11
5
60
94
89
83
78
73
08
03
58
53
48
43
39
34
30
20
21
17
13
9
5
1
70
95
:)0
86
81
77
72
08
04
59
55
51
48
44
40
30
33
29
25
22
19
15
12
9
6
80
96
91
87
83
79
75
72
68
04
01
57
54
50
47
44
41
3S
35
32
29
20
23
20
18
12
7
90
96
92
89
85
81
78
74
71
08
05
01
58
55
52
49
47
44
41
39
36
34
31
29
20
22
17
13
100
96
93
89
80
83
80
77
73
70
08
05
02
59
56
54
51
49
46
44
41
39
37
35
33
28
24
21
110
97
93
90
87
84
81
78
75
73
70
07
05
02
00
57
55
52
50
48
46
44
42
40
38
34
30
20
120
97
94
91
88
85
82
80
77
74
72
09
07
05
02
60
58
55
53
51
49
47
45
43
41
38
34
31
140
97
95
92
89
87
84
82
79
77
75
73
70
08
00
64
62
00
58
56
54
53
51
49
47
44
41
38
574
APPENDIX.
VI.
WEIGHTS OF AIR, VAPOR OF WATER, AND SATURATED MIXTURES
OF AIR AND VAPOR AT DIFFERENT TEMPERATURES, UNDER
THE ORDINARY ATMOSPHERIC PRESSURE OF 29.921 INCHES OF
MERCURY
el
1.
Mixtures of Air Saturated with Vapor.
oT
ofc.2
is;
03 P
>
o2
ID
Elastic
Force of
Weight of Cnbic Foot of the
Mixture of Air and Vapor.
Weight
5~
2i
S
the Air in
of
Temperat
Fahrenhe:
Weight of i
of Dry Ail
Temperat
Elastic Foi
Inches of
1
Mixture
of Air and
Vapor,
Inches of
Mercury.
Weight
of the Air,
Ibs.
Weight
of the
Vapor,
pounds.
Total
Weight of
Mixture,
pounds.
Vapor
mixed
with 1 Ib.
of Air,
pounds.
.0864
.044
29877
.0863
.000079
.086379
.00092
12
.0842
.074
29.849
.0840
.000130
.084130
.00155
22
.0824
.118
29.803
.0821
.000202
.082302
.00245
32
.0807
.181
29.740
.0802
.000304
.080504
.00379
42
.0791
.267
29.654
.0784
.000440
.078840
.00561
52
.0776
.388
29 583
.0766
.000627
.077227
.00819
62
.0761
.556
29.965
.0747
.000881
.075581
.01179
72
.0747
.785
29.136
.0727
.001221
.073921
.01680
82
.0733
1.092
28.829
.0706
.001667
.072267
.02361
92
.0720
1.501
28.420
.0684
.002250
.070717
.03289
102
.0707
2.036
27.885
.0659
.002997
.068897
.04547
112
.0694
2.731
27.190
.0631
.003946
.067046
.06253
122
.0682
3.621
26.300
.0599
.005142
.065042
.08584
132
.0671
4.752
25.169
.0564
.006639
.063039
.11771
142
.0660
6.165
23.756
.0524
.008473
.060873
.16170
152
.0649
7.930
21.991
.0477
.010716
.058416
.22465
162
.0638
10.099
19.822
.0423
.013415
.055715
.31713
172
.0628
12.758
17.163
.0360
.016682
.052682
.46338
182
.0618
15.960
13.961
.0288
.020536
.049336
.71300
192
.0609
19.828
10.093
.0205
.025142
.045642
1.22643
202
.0600
24.450
5.471
.0109
.030545
.041445
2.80230
212
.0591
29.921
0.000
.0000
.036820
.036820
lufinite.
The weight in Ibs. of the vapor mixed with 100 Ibs. of pure air at any given
temperature and pressure is given by the formula
62.3 X E 29.92
29.92  E X ~y '
where E = elastic force of the vapor at the given temperature, in inches of mer
cury; p absolute pressure in inches of mercury, = 29.92 for ordinary atmos
pheric pressure.
APPENDIX.
575
VII.
ENTROPY OF WATER AND STEAM.
Id
c"!
'" .
iss
*<
1
&
r
Specific Heat
of Water.
^fe
"egg,
.^00
^1
w
Entropy of 1
Ib. of Steam
L
T'
~k
l<3
fil
w
J.s
si 1 .
9*3
1 &<
fl
fj
1
f*
Specific Heat
of Water.
1*
9?fc
1*1
H
1
i^ifc
w
Entropy of 1
Ib. of Steam
from 32 F.
P
T
C
6
4>
+ <]>
p
Ta
C
e
<f>
o+t
1
2
3
562.8
587.1
602.4
1.0009
1.0069
0.134
0.175
0.201
1.853
.749
.686
.987
.924
887
115
120
125
798.7
801.9
805 6
1.0436
0.490
0.494
498
1.096
1.089
1.082
.586
.583
.580
4
614
220
641
861
130
807 9
501
1 076
577
5
6
623.0
631
0.235
247
.603
578
.841
825
135
140
810.8
813 6
0.505
508
1.069
1 063
.574
571
7
637.7
0.257
.557
814
145
816 4
512
1.057
.569
8
643.7
268
1 532
800
150
819
515
1 051
566
9
10
15
20
25
30
649.2
654.1
673.9
688.8
700.8
711.1
V.0076
0.277
0.285
0.315
0.338
0.356
370
1.513
1.496
1.432
1.384
1.348
319
.790
.781
.747
.722
.704
689
155
160
165
170
175
180
821.5
824.1
826.6
829.0
831.4
833 7
'.'.'.'.'.'.'.
0.518
0.521
0.524
0.527
0.530
533
1.045
1.040
1.035
1.030
1.025
1 019
.563
.561
.559
.557
.555
.552
35
40
720.0
728.0
0.384
0.395
.293
271
.677
666
185
]90
835.9
838 2
0.536
539
1.014
1.009
.550
..548
45
50
55
60
735.1
741.7
747.7
753.4
0.405
0.415
0.423
0.431
.252
.234
1.218
1.203
.657
.649
.641
.634
195
200
205
210
840.3
842.4
844 . 5
846.5
'.'.'..'.'.'.
0.542
0.544
0.547
0.549
1.004
1.001
0.996
0.992
.546
.545
.543
1.541
65
70
75
80
85
90
95
100
105
110
758.6
763.5
768.2
772.7
776.9
780.9
784.7
788.4
792.0
795.4
.0070
.0079
.0107
.0245
.0341
.0412
.0436
0.438
0.444
0.450
0.455
0.461
0.466
0.472
0.477
0.481
0.485
1.190
1.179
1.167
1.157
1.147
1.138
1.128
1.119
1.112
1.105
.628
.623
.617
.612
.608
.604
.600
.596
1.593
1.590
215
220
230
240
250
260
270
280
290
300
848.5
850.5
854.4
858.1
861.7
865.2
868.6
871.8
875.0
878.2
1.0436
1.0439
1.0446
1.0454
1.0461
1.0470
1.0478
1.0486
1.0495
0.551
0.554
0.557
0.563
0.567
0.571
0.575
0.579
0.583
0.587
0.989
0.984
0.976
0.969
0.962
0.955
0.948
0.941
0.935
0.928
1.540
1.538
1.535
1.532
1.529
1.526
1.523
1.520
1.518
1.515
576
APPENDIX.
PROPERTIES OF SATURATED STEAM.
IToTB. The following table gives the data required by the engineer in this connection as based upon the expr?toents of Regnault. The temper*
fores, pressures, and heatiaeasures are all from Regnault s experiments. The other quantities were calculated by Mr. R. H. Huel.* adopting the for
mulas of kankine already given to obtain quantities not ascertained by direct experiment. The two parts of thf latent heat of vaporization are separately
determined, and the internal thus distinguished from the external work of expansion. British measures are adopted. The nomenclature is sufficiently
well explamed by the tableheadings.
tpai ajnbs jad
spanod m 'ain^oBA v 3Aoqn aanrsajj
%
M M m + in<0 txCO ONg
= sr?
*
4
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578
APPENDIX
PROPERTIES OF SATURATED STEAM (Continue*).
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APPENDIX.
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APPENDIX
581
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APPENDIX.
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APPENDIX.
583
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584
APPENDIX.
X.
MEAN PRESSURES FOR VARIOUS METHODS OF EXPANSION.
Values of . Adiabatic Expansion of Steam
Ratio of
Expansion.
Cutoff, .
r
Percentage of Steam and Value of n.
100
1.135
90
1.125
80
1.115
76
1.111
70
1.105
60
1.095
50
1.085
100
1.333
2
i
.829
.831
.833
.834
.835
.836
.837
.810
21
*
.785
.787
.788
.789
.790
.791
.793
.754
2*
f
.744
.746
.747
.748
.749
.750
.751
.714
21
T 4 T
.707
.708
.710
.711
.712
.713
.714
.675
3
$
.675
.676
.677
.678
.679
.681
.683
.639
31
T 4 3
.644
.645
.647
.468
.649
.650
.652
.606
3$
TS
.633
.635
.636
.637
.639
.641
.643
.600
3*
f
.616
.618
.619
.620
.622
.624
.626
.576
3
A
.591
.592
.593
.594
.595
.596
.598
.552
4
1
.567
.568
.570
.572
.573
.574
.576
.523
4i
f
.525
.527
.528
.530
.531
.533
.534
.486
5
i
.488
.491
.493
.494
.496
.498
.500
.447
5i
T 2 T
.458
.460
.462
.463
.465
.467
.470
.417
6
*
.432
.434
.435
.437
.439
.441
.443
.390
6$
TJ
.409
.410
.411
.413
.415
.417
.420
.369
7
I
.387
.390
.392
.394
.400
.403
.405
.345
8
1
.355
.356
.357
.358
.360
.361
.363
.312
10
rV
.298
.300
.302
.303
.304
.305
.308
.263
20
fa
.170
.173
.175
.177
.178
.180
.182
.144
50
A
.080
.082
.083
.084
.084
.085
.086
.063
100
*
.044
.045
.045
.046
.046
.047
.048
.034
APPENDIX.
585
XL
MEAN PRESSURES FOR VARIOUS METHODS OF EXPANSION.
Values of for Steam, Air Gas. and Mixtures.
Pi
I
4
8
Steam and Leakage,
Actual Engines.
c
Gases.
3"

Irf
l
.S 
w .
x'" u ' =
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n, 0.50.
n, 0.75.
if?
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go "
1.00.
n, 141.
S
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OQ
O
2
i
.841
.825
.914
.875
.783
.846
.801
21
1
.793
.787
.888
.844
.733
.804
.753
2J
I
.760
.745
.866
.800
.683
.766
.707
2
T 4 T
.717
.700
.846
.785
.638
.731
.668
3
1
.695
.665
.824
.752
.598
.699
.638
31
T 4 3
.665
.635
.802
.732
.578
.670
.596
3*
TV
.652
.625
.796
.716
.568
.661
.588
31
2
.632
.605
.782
.704
.548
.642
.568
31
T 4 F
.608
.580
.775
.684
.515
.616
.538
4
1
.587
.550
.750
.664
.486
.566
.518
4
I
.540
.510
.720
.624
.441
.555
.473
5
1
.510
.482
.695
.600
.406
.522
.428
5i
T 2 T
.478
.455
.674
.560
.371
.492
.406
6
.1
.454
.420
.650
.530
.349
.465
.378
6
T a j
.430
.390
.632
.515
.326
.441
.358
7
}
.409
.375
.612
.500
.303
.421
.337
8
t
.372
.340
.697
.468
.276
.385
.302
10
TV
.326
.284
.532
.412
.225
.330
.253
20
?v
.192
.165
.396
.272
.103
.200
.138
50
B v
.091
.074
.245
.193
.050
.098
.060
100
Ik
.053
.040
.180
.134
.025
.056
.032
586
APPENDIX.
XII.
MEAN PRESSURE RATIOS.
r
.0
A
B
C
r
A
ll
.503 .488
r
9.6
A
B
C
r
17.8
A
B
C
1. 0001. 000 1.000
5.3
.478
.312
.340
.324
.194 ! .218 .204
.1
.996
.996
.996
5.4
.472
.497
.482
9.7
.310 .338
.322
18.0
.192 .216 .202
.2
.983
.983
.983
5.5
.467
.492
477
9.8
.307
.335
.319
18.2
.190 .215 .200
.3
.966
.968
.967
5.6
.461
.486
.471
9.9
.305
.333
.317
18.4
.189 .214 .199
.4
.947
.952
.950
5.7
.456
.481
.466
10.0
.303
.330
.314
18.6.
.187 .212 .197
.5
.928 .934
.931
5.8
.450
.475
.460
10.2
.299
.325
.310
18.8
.185 .210 .195
.6
.910
.919
.914
5.9
.445
.470
.455
10.4
.295
.321
.306
19.0
.183 .208 .193
.7
.890
.900
.895
6.0
.440
.465
.450
10.6
.291
.317
.302
19.2
.182 .207 .192
.8
.870
.880
.875
6.1
.434
.460
.445
10.8
.287
.313
.298
19.4
.180 .205:. 190
.9
.850
.862
.856
6.2
.429
.455
.440 11.0
.283
.309
.294
19.6
.179 .204 .189
2.0
.833
.846
.840
6.3
.424
.450
.435 11.2
.279
.305
.290
19.8
.178
.202 .187
2.1
.8171 .830
.824
6.4
.419
.445
.430
11.4
.275'. 301
.286
20.0
.177 .2001.186
2.2
.798
.812
.805
6.5
.414
.441
.426
11.6 .272i.298
.283
20.2
.175
.1981.184
2.3
.780 .795
.787
6.6
.409
.436 .4211 11.8
.2681.294
.279
20.4
.174
.196 .183
2.4
.763
.780
.771
6.7
.405
.432 .417 I 12.0
.264 .290
.275
20.6
.173
.194
.182
2.5
.748
.766
.756
6.8
.401
.428!. 4131: 12.2
.261
.287
.272
20.8
.171
.193
.180
2.6
.732
.750
.740
6.9
.396
.424
.408 12.4
.257
.283
.268
21.0
.169
.192
.178
2.7
.718
.736
.726
7.0
.393
.421
.405
12.6
.254
.280
.265
21.2
.168
.191
.177
2.8
.705 .723
.713
7.1
.389
.417
.401
12.8
.251
.277
.262
21.4
.167
.190
.176
2.9
.692
.710
.700
7.2
.385
.413
.397
13.0
.248
.274
.259
21.6
.165
.188
.174
3.0
.680
.699
.688
7.3
.381
.410
.393
13.2
.245
.271
.256
21.8
.164
.187
.173
3.1
.668
.687
.676
7.4
.377
.406!. 3901
13.4
.242
.268
.253
22.0
.1631.186
.172
3.2
.656
.675
.664
7.5
.373
.402 .386
13.6
.239 .265
.250
22.2
.162 .185!. 171
3.3
.645
.664
.653
7.6
.370
.399.383
13.8
.236 .262
.247
22.4
.161
.1841.170
3.4
.634
.653
.642
7.7
.367
.396 .380
14.0
.234 .260
.245
22.6
.160
.183 .169
3.5
.622
.642
.631
7.8
.363
.392 .376
14.2
.231
.257
.242
22.8
.1591.182 .168
3.6
.612
.632
.621
7.9
.360
.389:. 373
14.4
.228
.254
.239
23.0
.158
.180;. 167
3.7
.602
.622
.611
8.0
.356
.385 .370
14.6
.225
.251
.236
23.2
.156
.179'. 165
3.8
.593
.613
.602
8.1
.353
.382
.367
14.8
.223
.249
.234
23.4
.155
.178 .164
3.9
.584
.604
.593
8.2
.350
.379
.364
15.0
.221 . 247 1. 232
23.6
.164
.177
.163
4.0
.572
.596
.583
8.3
.347
.376
.361
15.2
.219
.245
.230
23.8
.153
.176
.162
4.1
.565
.587
.575
8.4
.344
.373
.358
15.4
.217 .242
.227
24.0
.151
.174
.160
4.2
.556
.578
.566
8.5
.341
.371
.355
15.6
.215 .240
.225
24.2
.150
.173
.159
4.3
.548
.570
.558
8.6
.338
.368
.352
15.8
.213 .238
.223
24.4
.149
.172
.158
4.4
.540
.563
.550
8.7
.335
.364
.349
16.0
.2111.236
.221
24.6
.148
.171
.157
4.5
.532
.555
.542
8.8
.332
.361
.346
16.2
.209 .234
.219
24.8
.147
.170
.156
4.6
.525
.548
.535
8.9
.330
.358
.343
16.4
.207
.232
.217
25.0
.146
.169
.155
4.7
.518
.542
.528
9.0
.327
.355
.340
16.6
.205
.230
.215
4.8
.511
.535
.521
9.1
.324
.353
.337
16.8
.203
.228
.213
4.9
.504
.528
.514
9.2
.322
.351
.335
17.0
.201
.226
.211
5.0
.496
.522
.506
9.3
.320
.348
.332
17.2
.199
.224
.209
5.1
.490
, .515
.500
9.4
.317
.345
.329
17.4
.197 .222
.207
5.2
.484
.509
.494
9.5
.315
.343
.327
17.6
.195 .220
.205
Column r, the ratio of expansion =
iQ_Q r s f For dry steam, expanded with
" A, ratio of mean to initial pressure, = \ out gain or loss of heat, in
Pi r { a nonconducting cylinder.
B,
Pm = 1+hyp. log, r t For damp steam, ex
pj r t panded receiving heat.
i7_ifi r ^ fFor dry steam, expanded
ii iHI I receiving heat sufficien*
Pi r [ to prevent liquefaction.
' \Jl VilJT .IftlJll, CAJJHH*C;VJ.
C, " " " * ^ = { receiving heat sufficient
Pi r [ to prevent liquefaction.
RULE. To find the mean pressure exerted throughout the stroke, multiply the initial
pressure by the number opposite the ratio of expansion, in the column corresponding with the
conditions of expansion. (From Northcott.)
APPENDIX
587
XIII.
TERMINAL PRESSURE RATIOS,
Pz
r
A
B
C
r
A
B
C
r
A
B
C
r
A
B
C
1.0
0.00
0.0
0.00
4.7
5.58
4.7
5.18
8.3
10.5
8.3
9.47
13.8
18.5
13.8
16.2
.1
1.11
1.1
.11
4.8
5.70
4.8
5.29
8.4
10.6
8.4
9.59
14.0
18.8
14.0
16.5
.2
1.22
1.2
.21
4.9
5.84
4.9
5.41
8.5
10.7
8,5
9.64
14.2
19.1
14.2
16.8
.3
1.31
1.3
.32
5.0
5.98
5.0
5.52
8.6
10.9
8.6
9.76
14.4
19.4
14.4
17.0
.4
1.45
1.4
.43
5.1
6.11
5.1
5.64
8.7
11.0
8.7
9.88
14.6
19.7
14.6
17.2
.5
1.57
1.5
.54
5.2
6.24
5.2
5.76
8.8
11.2
8.8
10.0
14.8
20.0
14.8
17.5
.6
1.69
1.6
.65
5.3
6.38
5.3
5.88
8.9
11.3
8.9
10.2
15.0
20.3
15.0
17.8
1.7
1.80
1.7
.75
5.4
6.51
5.4
6.00
9.0
11.5
9.0
10.3
15.2
20.6115.2
18.0
1.8
1.92
1.8
.87
5.5
6.64
5.5
6.12
9.1
11.6
9.1
10.4
15.4
20.9115.4
18.2
1.9
2.04
1.9
1.98
5.6
6.78
5.6
6.23
9.2
11.8
9.2
10.6
15.6
21.2
15.6
18.5
2.0
2.16
2.0
2.08
5.7
6.91
5.7
6.35
9.3
11.9
9.3
10.7
15.8
21.5
15.8
18.7
2.1
2.28
2.1
2.20
5.8
7.05
5.8
6.47
9.4
12.0
9.4
10.8
16.0
21.8
16.0
19.0
2.2
2.40
2.2
2.31
5.9
7.18
5.9
6.59
9.5
12.2
9.5
10.9
16.2
22.1
16.2
19.3
2.3
2.52
2.3
2.42
6.0
7.32
6.0
6.71
9.6
12.3
9.6
11.0
16.4
22.4
16.4
19.5
2.4
2.64
2.4
2.53
6.1
7.45
6.1
6.83
9.7
12.5
9.7
11.1
16.6
22.7
16.6
19.8
2.5
2.76
2.5
2.64
6.2
7.59
6.2
6.95
9.8
12.6
9.8
11.3
16.8
23.0114.8
20.0
2.6
2.89
2.6
2.76
6.3
7.73
6.3
7.07
9.9
12.8
9.9
11.4
17.0
23.3 17.0
20.3
2.7
3.01
2.7
2.87
6.4
7.86
6.4
7.18
10.0
12.9
10.0
11.5
17.2
23.6
17.2
20.5
2.8
3.14
2.8
2.99
6.5
8.00
6.5
7.30
10.2
13.2
10.2
11.7
17.4
23.9
17.4 20.8
2.9
3.26
2.9
3.10
6.6
8.14
6.6
7.42
10.4
13.5
10.4
12.0
17.6
24.2
17.6
21.
3.0
3.39
3.0
3.21
6.7
8.27
6.7
7.54
10.6
13.8
10.6
12.3
17.8
24.5
17.8
21.3
3.1
3.51
3.1
3.32
6.8
8.41
6.8
7.66
10.8
14.1
10.8
12 5
18.0
24.8
18.0
21.6
3.2
3.64
3.2
3.43
6.9
8.55
6.9
7.78
11.0
14.3
11.0
12.8
18.2
25.1
18.2
21.8
3.3
3.77
3.3
3.55
7.0
8.69
7.0
7.90
11.2
14.6
11.2
13.0
18.4
25.4 18.4
22.0
3.4
3.89
3.4
3.67
7.1
8.83
7.1
8.02
11.4
14.9
11.4
13.3
18.6
25.7 18.6
22.3
3.5
4.02
3.5
3.79
7.2
8.96
7.2
8.14
11.6
15.2
11.6
13.5
18.8
26.018.8
22.5
3.6
4.15
3.6
3.90
7.3
9.10
7.3
8.27
11.8
15.5
11.8
13.7
19.0
26.3 19.0
22.8
3.7
4.28
3.7
4.01
7.4
9.24
7.4
8.38
12.0
15.8
12.0
14.0
19.2
26.6J19.2
23.1
3.8
4.41
3.8
4.13
7.5
9.38
7.5
8.49
12.2
16.1
12.2
14.2
19.4
26.919.4
23.3
3.9
4.54
3.9
4.25
7.6
9.52
7.6
8.62
12.4
16.4
12.4
14.5
19.6
27.219.6
23.6
k 4.0
4.66
4.0
4.36
7.7
9.66
7.7
8.74
12.6
16.7
12.6
14.8
19.8
27.519.8
23.9
4.1
4.79
4.1
4.47
7.8
9.80
7.8
8.87
12.8
17.0 12.8
15.0
20.0
27.9:20.024.1
4.2
4.91
4.2
4.60
7.9
9.94
7.9
8.99
13.0
17.3
13.0
15.2
21.0
29.521.025.4
4.3
5.05
4.3
4.71
8.0
10.1
8.0
9.11
13.2
17.6
13.2
15.5
22.0
31.022.226.7
4.4
5 18
4.4
4.82
8.1
10.2
8.1
9.23
13.4
17.9
13.4
15.7
23.0
32. 6 23. 028. O
4.5
5.32
4.5
4.95
8.2
10.3
8.2
9.35
13.6
18.2
13.6
16.0
24.0
34.1 24.029.3
4.6
5.45
4.6
5.06
Column r, ratio of expansion =
" A, ratio of initial to final pressure p 2 =
P2
C.
For dry steam, expanded without
gain or loss of heat in a noncon
ducting cylinder.
For damp steam, expanded receiv
ing heat.
For dry steam, expanded receiving
sufficient heat to prevent liquefac
tion.
RULE. To find the final pressure obtaining with any ratio of expansion, divide the initial
pressure by the number opposite the ratio of expansion, in the column corresponding with the
conditions of expansion.
588
APPENDIX.
W S
C 
O
Cd ffi
K *
* %
g O
< K
K 3
H E
^ g
s 1
fa
II
W
II?
Ill
g.l g
!!
Q X
CO 1C 1C "t CO fC CM CM CM H < i H fH t i O
. . v s_
.
O 2;
S *i .
5
CMCMCMrlrl^^^^^^^r^OOOCO
CM
CM
co p CM x *** co CM t rc 01 io i i r> ?o
c "^ cMHOOiXXt^r^t^cocoic>C'*Tficcrcc ?
i
3
3 3
S3
S
fe.tf v CCHr^fTHO>XCOiCCOCMOO5t^COTfCM^H
a^ o T f r f^^ : 5t l ^r'
a
CU CM CO ' O X CO >C Tf Tf CO CM ^H O O5 O5 X t> CO O
I
S a
5 Q
APPENDIX.
589
TABLE XV.
SPECIFIC HEAT (C p ) OF SUPERHEATED STEAM AT CONSTANT
PRESSURE.
(According to the experiments of Knoblauch and Jacobs.)
Average
Pressure,
Lbs. per Sq.
In. Absolute.
Average
Temperature,
Degrees
Fahrenheit.
Specific
Heat,
Cp.
Average
Pressure,
Lbs. per Sq.
In. Absolute.
Average
Temperature
Degrees
Fahrenheit.
Specific
Heat,
Cp.
28.466
300
0.478
85.4
366
0.531
370
0.470
424
0.500
465
0.474
500
0.476
475
0.474
584
0.472
566
0.476
661
0.490
655
0.486
113.86
370
0.554
661
0.494
464
0.483
56 93
339
0.502
563
0.490
411
0.472
563
0.480
501
0.479
564
0.491
580
0.470
653
0.488
582
0.414
662
0.492
578
0.550
673
0.499
662
0.492
INDEX.
Absolute zero, 7
pressure, correct, 267
Absorption, refrigeration by, 531
Accelerated motion, 347, 448
Action of clearance steam, 189
Adheating, 432
Adiabatic compression, 141
curve, 143
expansion, 141, ratio of tempera
tures in, 143
Advance, angle of, 92
Air, and vapor, weights of, Table VI
composition of, Table IV
cooling in condensers, 282
leaks in condensers, 234
specific heat of, Table I
thermometer, 6
Airpump, 23, 269
action of, 276
design, 218, 224, 225
dry, 282
Edward's, 272
efficiency, 270
for surface condenser, 273, 278
wet, 281
Alcohol, 53
Alden brake, 34
Allen denseair machine, 531
Ammonia icemachines, 531
Angles, blade, 454
Angular acceleration, 348
advance, 92
displacement, phase degrees, 405
Areas representing heat, 147153, 208
Astatic, 336
Atmosphere, Table VI
Auxiliaries, measurement of steam used
by, 427
Balance wheel, design, 387
Balancing engines, 400403
Barometric condenser, 236
Barrel calorimeter, 171
Barrus calorimeter, 173
Baume hydrometer, 524
degrees converted into specific grav
ity, 524
Bearing, details of, 17
Belting, 552, 564
Belt wheel, design, 386
Bilgram valvediagram, 103; geomet
rical relations of, 107
Blade angles, steamturbines, 455
Boiler efficiency, 35
feedpump, 13, 285, 287, 289
horsepower, 36
Boiling and evaporation, 128
in vacuo, 534
Boilingpoints of water, Table VIII
Bolts, number and size, 553
Boulvin's temperatureentropy dia
gram, 221
Boyle's law, 137
Brake horsepower, definition of, 32
Brakes, friction, 32
Bridge, thickness of, 113
British thermal unit, definition of, 5
Buckeye valvegear, 364
C P , C v , for perfect gases, Table I
Calibration of gages, 386, 427
indicatorsprings, 7476, 502
thermometers, 8, 419
Calorific power of gases, 476
Calorimeter:
Barrus continuous water, 173
Carpenter, 172
Junker, 506
Mahler, 506
normal reading of, 175, 178
Peabody, 173
separator, 173
throttling, 173
water equivalent of, 176
Carbon, airburnt, 488
steamburnt, 488
Carnot cycle, 154, 228
Centrifugal force, 329; derivation of
formula for, 330
Charles' law, 137
Circulating pump, 25, 288, 290
Circulation of water in the boiler, 181
Clearance, definition, 72
line, 72
steam, elimination of, 84
surface, 186
surface, effect of, 188
volume, 72, 416
591
592
INDEX.
Coal, heating value of, 35
in gasproducers, use of, 490
measurement of, 429
per horsepowerhour, measurement
of, 35
standard, thermo value of, 36, 417
Coalgas, analysis of, 486
heating value of, 489, 490
Column, mercury, 28
Coefficient, heat transmission, 256, 257,
258
Combining indicatorcards, 318
Combustion, heat of, 36, 485
of coal, rate of, 137
temperature arising from, 486
Compound engines:
combining cards of, 317
diagram factor of, 322
distribution of work in, 308, 311, 316
method of laying out the cards for,
304, 311
ratio of expansion in, 306, 320
records made by, 304
size of, to find, 315
theory of, 307
Compound quantities 2, 4
Compressedair formulas, theoretical
and practical, 142
Compression, and expansion of air,
142
of steam, 188
work done during, 142
Concentration of canejuice, 527
Condensation in steamengines, 158
pipes, 182, 186
Condensation at constant volume, 219
initial, 326
Condensers :
barometric, 236
condensing surface in, 241
correct pressure in, 267
design of, 235
dimensions of, 234
ejector, 238
increasing surface efficiency of, 262
jet, 238
pressure in, 28
surface, 23, 239
syphon, 238
transmission of heat in, 243
tubes, of 241
Condensing, gain by, 267
water, 235
Condensing water, coolers for, 265
use of, 233
Connectingrod: design, 546, 558;
division of mass for turning mo
ment, 401 ; division of mass for
shaking forces, 401 ; effects caused
by the obliquity of, 88
Constant heat curve, 224
temperature curve, 213
Constant volume, condensation at, 186
curve, 219, 220
Constants (R) for perfect gases, Table I
Contraflo condenser, 260
Coolingtower, 265
effect of change of season on opera
tion of, 267
Cork insulation, 183
Corliss engines, 18, 366, 368
Counterbalancing engines, 400, 402
Coverings for steampipe, 183
Crankpin, design, 548, 560
Crankshaft, turning effort in, 382, 406
Cranks, combination of, 405
throw of, 85
twisting moment in, 382
Critical temperature, 152
Cross compound engines, 311314
Crosshead pin, design, 550, 562
shoes, 565
Crossed rods, definition, 358
Crosssection paper, logarithmic, use
of, 144
Curves:
adiabatic, 141
constant heat, 219
constant volume, 221
general expansion, 139, 143
hyperbolic, 83, 139
isothermal, 78
saturated steam, 78, 213
superheated steam, 441
waterline, 210
Cutoff, actual, 65
commercial, 65
real or actual, 65
Cycle, Beau de Rochas, 481
Carnot, 154, 228
Diesel, 497
Lenoir, 481
Rankine, 228
Cylinders, details of, 201
dimensions, 562
Cylinder walls, thermal action of, 188,
189
thickness of, 112, 553
Cylinder waste, reducing, 435
Degree of reaction, 476
De Laval turbine, 457
Denseair machine, 531
Design of, see part required
Diagram, Bilgram, 103
compound engine, 308
crankpin pressure, 382, 406
of effective driving pressure, 382, 406
of shaking forces, 404
of turning moment, 382
Zeuner valve, 93, 94
Diagram factor, compound engi es,
266
simple engines, 81
INDEX.
Dimensions of steam ports and pipes,
110, 434, 502, 551, 564
Distillation, 517
Division of mass of connectingrod for
pin pressures, 401 ; shakingforces,
401 ; turningmoment, 401
Double poppetvalves, 371, 451
Dryness of steam, methods of deter
mining, 171
Drysteam fraction, 193
Eccentric, throw of, 85, 89
equivalent, 360
rod, 87, 357
Eccentricity, 85
Economizer, 13
Economy of vacuum production, 264
ratio of, of an engine to ideal engine,
229
Effects, multiple and single, 517
Efficiencies, combining, 40
definition of, 35
gasengine, 508
maximum, of jets, 456
mechanical, 35
Efficiency, of injectors, 297
of steamengines, 267
thermal, 42, 263
Ejector condenser, 322
Electrical units, 32
Elementary quantities, 1, 2, 131
Ellipse, valve, 114
Energy, definition of, 3
forms of, 4
kinetic, 3, 331
potential, 126
sources of, 14
transformation of, 4, 126, 378, 456
ratio of economy of, to an ideal
engine, 229
Engines, see kind of
average steam consumption of, 37
details of, 1721
Entropy, chart, 590
definition of, 207
derived from indicatorcard, 225, 491
diagram of a real engine, 229
tables, 575, 582
Equivalent, eccentric, 360
evaporation, 170
factors of evaporation, 170
weight at crankpin center, 402
Evaporation, factor of, 37
rate of, in boilers, 36
Evaporation and drying, 129
Evaporation by the multiple system,
latent heat of, 164
table of, Table VIII
total heat of, 164
Evaporators, 517
Exhaustports, width of, 113
Expansion, adiabatic, 141
at constant volume, 219, 220
following the law PF" = C, 139
hyperbolic, 77
of water, 163
of water when heated, 163
proper ratio of, 325
real ratio of, 72
valve, Meyer, 370
External work in adiabatic expansion,
142, 215
in isothermal expansion, 79, 213
Factors of evaporation, 170
Feedpump, 73, 285, 287, 289
Feedwater heaters, 248
choice of, 250
closed, 251
heating surface of, 256, 257
open, 251
percentage of gain in, 253
versus economizers, 254
measuring, 427
Flanges, 553
Flow of air, in pipes, 117
through orifices, 447
Flow of steam through pipes, 117
Flywheels :
accurate weight of, 407, 555, 565
approximate weight of, 384
Foaming, cause and prevention, 181
definition of, 180
Force, centrifugal, 330
exerted by a deflected stream, 449
moment of, 2
required to produce acceleration, 347
Form, steamengine tests, 537
Formula for:
adiabatic expansion, 141
Barrus calorimeter, 173
calorimeter correction, 175, 178
Carpenter calorimeter, 172
centrifugal force, 330
energy of reciprocating parts, 379
381
flywheels, 385, 407
heat to produce wet steam, 169
I. H. P. of an engine, 31
impulse trom jets, 449, 453, 456
Peabody calorimeter, 177
perfect gases, 135, 142, 148, 153
revolving pendulum governor, 332
Rites governor, 349, 386
shaft governors, 341
steam velocity in nozzles, 216
superheated steam, 437
the total heat of evaporation, 165
turning force and moment, 2
weight of steam accounted for by
the indicator, 193
Friction brakes, 32, 34
Friction of elbows, valves, pipes, 118
594
INDEX.
Friction of a governor, 339
of air in pipes, 118
of steam in pipes, 118
Fuel economizers, 13
gas, 485, 495
heat of, 486
measurement of, 505
Fundamental equations of thermo
dynamics, 152
Gage, Bourdon, 27
vacuum, 28
Gages, see Calibration
Gallons, displacement of a pump in, 329
Gas, alcohol, 482
ammonia, Table I
calorific equivalent of, 486
combustion, rise in temperature, 486
Gasengines:
efficiency of, 484
test, form of, 538
test, rules for, 502
Gas, flow of, in pipes, 117
illuminating, fuel valve of, 486
meters (see Calibrating), 504
producers, 487
Gases, Charles' law of, 137
Joules' law of, 137
specific heats of, 571
weight and specific gravity of, 571
Gasolineengines, 484
Governors :
details of, 19
flyball, 332
friction, 338
Hartnell, power of, 339
practical forms of, 334
Proell, 335
Rites inertia, 348, 386
sensitiveness of, 334
shaft, 343
throttling, 328
weighted, 332
Xjrate area, to find, 37
Green's fuel economizer, 13
HamiltonHolzwarth turbine, 480
Heat balance of gasengines, 484, 508
consumption in a gasengine, 505
consumption in a steamengine
plant, 36, 41
curve of constant, 224
effect on solids, liquids, gases, 130
expansion by, 131
graphical illustration of expenditure
of, 43
interchanges, 196
internal work, 132
latent, of evaporation, 132
mechanical equivalent of, 9
of combustion, 35, 486, 490
of the liquid, 162
Heat represented by areas, 148153
required at meltingpoints, Table I
required to produce steam, 165
specific, 132, 134
storing, 127
total, in steam, 132, 164
transmission of, in boilers, 242, 245
in condensers, 242 ; in cylinders, 303 ;
in feedwater heaters, 298 ; in mul
tiple effects, 520 ; in vacuumpans,
522
Heaters, feedwater, 248, 256, 298
Heating surface of boilers, definition
of, 11
values of various substances, 572
Heatunits, 132
Helical springs, 348
Hirn's analysis, 194
Horsepower, boiler, 36
to supply electric lamps, 39
Horsepower, definition, 31
brake, 32
equivalents of, 32
hour, 35
indicated, 31, 42
of steamengines, 31, 42
Hot water, transmission of heat
through pipes carrying, 184
Hotwell, definition of, 23
Houghtaling reducing motion, 54
Humidity, relative, Table V
Hyperbola, equation of, 68, 69
construction of, 68, 69
Hyperbolic logarithms, Table II
Ice, specific heat of, 160
latent heat of, 160
making machines, 510
making, units of, 484
Ideal engines, ratio of economy to,
229
Impact of bodies, 295
Indicated horsepower, 31, 42, 73
Indicatordiagrams :
analysis of, 192
area of, 79
converting, into entropy diagram,
225, 491
correction of, for clearance, 82; for
energy of reciprocating parts, 381
of gasengines, 492; converted into
entropy diagrams, 225
pendulum rig for taking, 59
reducing motions for, 59
water consumption shown by, 191
Indicators, see Calibration, 46
Crosby, 46
Tabor, 52
Indicatorsprings, testing, 7476
Inertia governors, theory of, 349, 000
Inertia of indicator pistons, 65
Initial condensation, 186, 302, 326
INDEX.
595
Initial amount of superheat required
to prevent, 437
Injection water, 235, 241
Injectors, theory of, 292
method of using, 296
Interchange of heat in cylinders, 196,
198, 303
Internal energy, 164
Isochronous, 337
Isothermal expansion, 68, 69, 77
work done during, 79
Jacket steam, 198, 303
water, 426
Jet condenser, 26, 233
impulse due to, 450
Joules' equivalent, 9
Journal, main, design, 547, 559
Kinetic energy, 3, 131, 164, 330
Lap and lead of valves, 89, 111
Latent heat:
of evaporation, 1G3, Table VIII
of fusion, 120, Table I
Leakage of air, 234 ; gas and oil, tests
for, 502
of steam, tests for, 414, 421
of water, tests for, 421, 427
Lenoir cycle, 481
Link arc, 353, 360
Links, 352
Liquids, expansion of, 131, 132
heat of, 162
molecular movement in, 127
vaporizing, 130
weight and specific gravity of,
Table I
Locomotives, 568
Logarithms, converting hyperbolic to
common, 494
hyperbolic, Table II
Marine engines:
airpump for, 274
circulating pump for, 290
diagram factors for, 325
link for, 354
ratio of expansion in, 325
Mass of connectingrod, division of, to
find effective and shaking forces,
377, 401
Maximum efficiency of jet action, 426
Measuring clearance, 417
engines, 416
revolutions, 430
Mechanical equivalent of heat, 9
Meltingpoint of solids, 290
Metals, specific gravity, of Table I
Meyer valvegear, 370
Midposition of valve, 92
Moisture in steam, 169
Molecular motion, 128
Moment of a force, 294
of inertia, 400
Momentum, 294
Multiple distillation, 517
Multiple effects, 517
expansion engines, proper ratio of
expansion, 325
Naperian logarithms, Table II
Napier's formula, 172, 178
Normal reading of a calorimeter, 175,
178
Nozzles, flow in, 444, 446
in calorimeters, 170
in steamturbines, 457, 464 
velocity of steam in, 216
Open rods, definition, 358
Orifices, flow of steam from, 172, 178
flow of water from, 416
thermal effects on steam flowing
through, 216, 224, 446
Oxygen required for combustion,
Table IV
Parabolic governor, 338
Parsons' steamturbine, 466
Peabody calorimeter, 173
Pendulum, or conoidal governor, 332
Perfect gases, definition of, 127
primary laws of, 135, 142, 145
Phase degrees, 373, 406
Pin, pressure on crank, 382
Pipes, equivalent, 119
exhaust, 552, 564
flow of air in, 115
flow of gas in, 116
flow of steam in, 116
loss of head in, 118
steam, covering for, 183
steam, sizes of, for engines, 110, 118,
551, 563
Piston, design, 562
details of, 20, 554
Piston movement, 86
Pistonrod, design, 545, 557
Pole degrees, 374
Poppetvalves, 371
Port, width of, 90, 111, 551, 563
Portopening, 90
Potential energy, 3
Pounding of engines, 380
Power of a governor, 339
of an electric circuit, 32
rate of work, 31
Pressure, bearing, 548
Pressure from producergas, 491
net steam, 375
volume and temperature, relations
in perfect gases, 147
Priming, 181
Producergas, 487
596
INDEX.
Producergas, pressure from, 491
Proell governor, 335
Properties of substances, 477
Pumps :
air, 23, 277284
average steam consumption of, 37
boilerfeed, 13, 285
capacity of, 289
cards from, 283, 286
centrifugal, 290
circulating, 25, 288
displacement of in gallons, 289
efficiency of, 285
piston speed of, 289
sizes of, 289
speed of water through, 288
Purifiers, 254
Pyrometer, see Calibration, 419
Quality of steam, 166, 177, 180
R, for perfect gases, Table I
Radiation in steamcalorimeters, 175
Rankine cycle, 228, 229
Rankine's formula for flow of steam
178
Rates, 30
Ratio of expansion, 72, 321
proper, in multipleexpansion en
gines, 325
Reaction, degree of, 476
Receivers, definition of, 16
design of, 298, 325
effect of, 325, 326
reheating in, 298
size of, 326
Reciprocating parts, 375
concentrated at crankpin, 377
Recompression, 189
Reducing motion, 59
Reducing wheels, 54
Reevaporation, 187
Refrige rat ingmachines, 530
Allen denseair, 530
ammonia absorption, 530
ammonia compression, 532
entropy diagram of, 535
icemelting capacity, 537
Regnault's formula, 166
Reheaters, 297
Revolutions, measuring, 420
Saddlepin, position of, 358
Saturated steam, dry, definition of, 166
expansion curve of, 213
line, 213
pressures, Tables VIII to XIII
wet, definition of, 166
Scavenging, 482
Sensitiveness of a governor, 334
Separator calorimeter, 173
Separators, 13, 297
Shaftgovernor, 3'41
Shaking forces, 404
Simple engine, diagram factor, 81
Slidevalve :
balanced, 351
diagrams, 93, 101
lap and lead of, 88
Solids, meltingpoint of, 160
properties of, Table I
Specific gravity:
of gases, Table I
of liquids, Table I
of solids, Table I
Specific heat, definition of, 132
of gases, 132, 134, 571
of liquids, 132
of solids, 132
of superheated steam, 589
Speed, measuring, 430
Springs, calibration of, 76
for governors, 348
Standard boiler, 41
efficiency, 41
Standard coal, 41
Standard form for testing gasengines,
512, see Tests
rules for testing gasengines, see
Tests; for testing steamengines,
see Tests; for testing rules, see
Tests
steamboiler, 41
Standards of efficiency and ecnoomv.
508
Starting and stopping tests, 424
Steam, accounted for by indicator, 191
actual consumption of, 37, 201
condensation of, due to expansion,
200
condensation of, initial, 186, 302, 326
dry saturated, 169
expansion curves, 213
expansive working of, 301
flow, 110, 588
in nozzles, 216, 445
in orifices, 172, 178
in pipes, 115
jacket, 198, 303, 305
lead, 111
line at constant pressure, 212
loss of pressure of, 321
moisture in, 169
nozzles, 447
pipe covering, 183
pipes, 116
plant, 425
ports, 90, 110
quality, see Calorimeter
separator, 13
superheated, see Superheater
table, Table VIII, IX
velocity of, in nozzles, 216
INDEX.
597
Steam, weight of, accounted for by
indicator, 191
Steamboiler, economy of, 13, 35
heatingsurface of, 1 1
Steamcalorimeters, 171
Steamengines :
compound, 305
Corliss, 366, 368
counterbalancing, 400403
expansion work in, 68, 69, 77
leakage of steam in, 185, 414, 421
mean effective pressure in, 77, 79
measurement of steam in, 438
measure of duty in, 36
most economical point of cutoff,
325
proportions of cylinders of, 304,
305
ratio of expansion in, 70, 321
steam consumption in, 186
tests of, rules for conducting, see
Tests
using superheated steam, 441
Steampipes, 551, 563
Steamports, 551, 563
Steamturbines, economy at various
loads, 462
economy at various speeds, 462
economy of various sizes, 462
effect of water in, 462
Superheated steam, data of test, 436
efficiency of, 363, 437
engines using, 438
entropy diagram of, 441
in compound engines, 442
lubrication when using, 440
regulation of, 440
specific heat of, 170, 436
total heat of, 435
turbines, 434
Superheater, Foster, 432
data of, 438
durability, 443
Superheating, intensity required, 435
Surface section, ratio, 265
Streams, measurement of force due to
449
turning the path of, 449
Sugar, manufacture of, 517
Surface condenser, 23
Tandem compound engine, 307
Tangential pressure on crankpin, 382
Temperature, absolute, 7
definition of, 5
mean, to find, 245
volume and pressure, relations be
tween, 147, 510
Temperatureentropy diagram, 225 ;
from indicatorcard, 225, 491
Test of Diesel engine, 500
Testing, indicator springs, 505
Tests, standard form for gasengine,
513537 ; standard for steam
engine, 537
standard method of making gas
engine, 502 ; complete engine and
boiler, 425; steamengine, 32, 36,
54, 57, 62, 63, 70, 72, 73, 7478,
193, 229, 318, 321, 325, 41130
Thermal action of cylinder walls, 187
Thermal efficiency, definition, 42, 263
Thermal unit, definition of, 5
Thermodynamics, definition of, 14
first law of, 8
fundamental equations of, 152
second law of, 9
Thermometers, definition of, 5
calibration of, 8, 419
Thickness of cylinder walls, 112
of bridge, 113
Throttlingcalorimeter, 173
Torque, 2
Total heat, in steam, 165
required to produce saturated steam,
165 ; superheated steam, 437
Turbines :
Curtis, 460
De Laval, 454
HamiltonHoltzwarth, 480
Parsons, 466
steam, 445
Turning forces, analysis of, 386, 406
Twisting moment, 2
Unit of heat, 5 ; of temperature, 5 ; of
work, 2
Vacuum gage, true meaning of reading,
267
pan, 517, 528
production, economy in, 264
pumps, 268
Valve, Corliss, drop or detachable, 356
Valvediagrams, 93, 94, 100
geometrical relations, 97
Valve ellipse, 114
lap or travel, 88, 89
seats, area through, 110
slide, 88
Vaporizing water, 163
Vapors, definition of, 127, Table VI
Velocity and acceleration of pistons,
86
Velocity of steam in nozzles, 216 .
in passages and ports, 107
Volume, temperature and pressure, re
lations of, in perfect gases, 147
one pound of steam, 576, 582
Water, boilingpoint of, equation of,
161
boilingpoint of, Table VIII
598
INDEX.
Water, equivalent of a calorimeter, 175
expansion of, 163
friction brake, 34
gas, 488
line, 210
meters, see Calibration, 429
per horsepowerhour, definition of,
35
pumping engines, tests, 542
specific heat of, Table VII
Weight of engine, 553, 567
Weight of gases, Table I
of liquids, Table I
of one pound of steam, 576, 582
of solids, Table I
of steam accounted for by the indi
cator, 191
of steam discharged from a nozzle,
447
Weights of air, vapor of water, and
saturated mixtures of air and
vapor at various temperatures
and constant pressures, 574
Wet steam, 169
saturated steam, 167
Woolf type of compound engine, 322
Work, definition of, 2
of acceleration, 448
done in accelerating a steamjet, 476
during expansion, 142, 215
Working steam and clearance steam,
82, 227
Zero, absolute, 7
Zeuner valvediagram, 94, 100
Zeuner's formula for the flow of per
fect gases from a nozzle, 446
Zinc in condenser tubes, 24.1
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MATERIALS OF ENGINEERING.
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Black's United States Public Works Oblong 4to, 5 00
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Byrne's Highway Construction 8vo, 5 00
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Church's Mechanics of Engineering 8vo, 6 00
Du Bois's Mechanics of Engineering.
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* Eckel's Cements, Limes, and Plasters 8vo, 6 00
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Fowler's Ordinary Foundations 8vo, 3 50
* Greene's Structural Mechanics 8vo, 2 50
* Holley's Lead and Zinc Pigments Large 12mo, 3 00
Holley and Ladd's Analysis of Mixed Paints, Color Pigments and Varnishes.
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Johnson's (C. M.) Rapid Methods for the Chemical Analysis of Special Steels,
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Johnson's (J. B.) Materials of Construction Large 8vo, 6 00
Keep's Cast Iron 8vo, 2 50
Lanza's Applied Mechanics 8vo, 7 50
Lowe's Paint for Steel Structures 12mo, 1 00
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Maire's Modern Pigments and their Vehicles 12mo, $2 00
Martens's Handbook on Testing Materials. (Henning.) 2 vols 8vo, 7 50
Maurer's Technical Mechanics 8vo, 4 00
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Metcalf 's Steel. A Manual for Steelusers 12mo, 2 00
Morrison's Highway Engineering 8vo, 2 50
Patton's Practical Treatise on Foundations 8vo, 5 00
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Sabin's Industrial and Artistic Technology of Paint and Varnish 8vo, 3 00
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Snow's Principal Species of Wood 8vo, 3 50
Spalding's Hydraulic Cement 12mo, 2 00
Textbook on Roads and Pavements 12mo, 2 00
Taylor and Thompson's Treatise on Concrete, Plain and Reinforced 8vo, 5 00
Thurston's Materials of Engineering. In Three Parts 8vo, 8 00
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Tillson's Street Pavements and Paving Materials 8vo, 4 00
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Waterbury's Cement Laboratory Manual 12mo, 1 00
Wood's (De V.) Treatise on the Resistance of Materials, and an Appendix on
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Wood's (M. P.) Rustless Coatings: Corrosion and Electrolysis of Iron and
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RAILWAY ENGINEERING.
Andrews's Handbook for Street Railway Engineers 3X5 inches, mor. 1 25
Berg's Buildings and Structures of American Railroads 4to, 5 00
Brooks's Handbook of Street Railroad Location 16mo, mor. 1 50
Butts's Civil Engineer's Fieldbook 16mo, mor. 2 50
Crandall's Railway and Other Earthwork Tables 8vo, 1 50
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* Crockett's Methods for Earthwork Computations 8vo, J 50
Dredge's History of the Pennsylvania Railroad. (1879) Papet 5 00
Fisher's Table of Cubic Yards Cardboard, 25
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Hudson's Tables for Calculating the Cubic Contents of Excavations and Em
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Ives and Hilts's Problems in Surveying, Railroad Surveying and Geodesy
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Molitor and Beard's Manual for Resident Engineers ..... 16mo, 1 00
Nagle's Field Manual for Railroad Engineers 16mo, mor. 3 00
* Orrock's Railroad Structures and Estimates 8vo, 3 00
Philbrick's Field Manual for Engineers 16mo, mor. 3 00
Raymond's Railroad Engineering. 3 volumes.
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Searles's Field Engineering 16mo, mor. $3 00
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Webb's Economics of Railroad Construction Large 12mo, 2 50
Railroad Construction 16mo, mor. 5 00
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DRAWING.
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Abridged Ed 8vo, 1 50
Coolidge's Manual of Drawing 8vo, paper, 1 00
Coolidge and Freeman's Elements of General Drafting for Mechanical Engi
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Durley's Kinematics of Machines 8vo, 4 00
Emch's Introduction to Protective Geometry and its Application 8vo, 2 50
French and I ves' Stereotomy 8vo, 2 50
Hill's Textbook on Shades and Shadows, and Perspective 8vo, 2 00
Jamison's Advanced Mechanical Drawing 8vo, 2 00
Elements of Mechanical Drawing 8vo, 2 50
Jones's Machine Design:
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Kimball and Barr's Machine Design 8vo, 3 00
MacCord's Elements of Descritpive Geometry 8vo, 3 00
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McLeod's Descriptive Geometry Large 12mo, 1 50
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Industrial Drawing. (Thompson.) 8vo, 3 50
Moyer's Descriptive Geometry 8vo, 2 00
Reed's Topographical Drawing and Sketching 4to, 5 00
Reid's Course in Mechanical Drawing 8vo, 2 00
Textbook of Mechanical Drawing and Elementary Machine Design.. 8vo, 3 00
Robinson's Principles of Mechanism 8vo, 3 OO
Schwamb and Merrill's Elements of Mechanism 8vo, 3 00
Smith (A. W.) and Marx's Machine Design 8vo, 3 00
Smith's (R. S.) Manual of Topographical Drawing. (McMillan.) 8vo, 2 50
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Warren's Drafting Instruments and Operations 12mo, 1 25
Elements of Descriptive Geometry, Shadows, and Perspective 8vo, 3 50
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Elements of Plane and Solid Freehand Geometrical Drawing. . . . 12mo, 1 00
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Weisbach's Kinematics and Power of Transmission. (Hermann and
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Wilson's (H. M.) Topographic Surveying 8vo, 3 50
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Woolf's Elementary Course in Descriptive