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Full text of "Sewer design"

WORKS OF 
PROFESSOR H. N. OGDEN 

PUBLISHED BY 

JOHN WILEY & SONS, Inc. 



Sewer Construction. 

8vo, xii+335 pages, 
$3.00. 



figures. Cloth, 



Sewer Design 

Second Edition, Rewritten. 8vo,xiii + 
248 pages, 71 figures, 5 plates. Cloth, 
$2.00 net. 

BY OGDEN AND CLEVELAND. 
Practical Methods of Sewage Disposal. 

For Residences, Hotels and Institutions. 
8vo, vi+132 pages, 52 figures. Cloth, 
$1.50 net. 



SEWER DESIGN 



BY 

H. N. OGDEN, C.E. 

MEM. AM. SOC. C. E. 

Professor of Sanitary Engineering, Cornell University 



SECOND EDITION 

TOTAL ISSUE, FIVE THOUSAND 



NEW YORK 

JOHN WILEY & SONS, INC. 

LONDON: CHAPMAN & HALL, LIMITED 
1913 





<-' s V K 

V.r 



O 



Copyright, 1899, 1913, 

BY 

H. N. OGDEN 



THE SCIENTIFIC PRESS 

ROBERT DRUMMOND AND COMPANY 

BROOKLYN, N. Y. 



PREFACE TO FIRST EDITION 



THE following pages represent, except for some necessary 
minor changes, a course of lectures given in the College of Civil 
Engineering, Cornell University. 

The course is an elective one, intended for those students 
whose intention to enter the field of Sanitary Engineering 
calls for more special and detailed work than is required of all 
Civil Engineering students. Supplementing as it does the 
regular course in Sanitary Engineering, it must preserve with- 
out duplication a continuity in the two courses which is obtained 
through the direct supervision of the Dean of the College, 
Professor E. A. Fuertes, who also gives the general course. 
These conditions may serve to explain some recognized peculiar- 
ities and omissions in the subject-matter of the following pages, 
tolerated only on account of the general work already done by 
students here specially studying that in which they wish to 
excel. 

Another cause, leading to the omission of certain discus- * 
sions which might properly be brought up under the title 
chosen, lies in the fact that the lectures here given represent 
but one-third of the year's work, the subjects of Sewage Dis- 
posal and Sewer Construction being taken up in the other two 
terms of the year. 

Thus, merely to serve the divisions of the college year, all 
questions of constructive design and field construction are 
remanded to another course of lectures not conveniently included 
here. 

It is believed that due acknowledgment has been made 
to the various books and periodicals and to the reports of the 

prominent engineers from which this monograph has been 

iii 



293075 



iv PREFACE TO FIRST EDITION 

prepared, and it is hoped that the collection and unification of 
this scattered material may not only aid the students examining 
the question of Sewer Design for the first time, but may also be 
a convenient reference for older engineers who have hitherto 
been obliged to put together the data from many publications. 
Special acknowledgment is made to the published papers 
of Emil Kuichling, C.E., of Rochester, N. Y., for the chapters 
on Storm-water Discharge and Mathematical Formulae; to the 
report of Dexter Brackett, C.E., on the Future Water-supply of 
Boston, Mass. ; to the thesis of Elon H. Hooker on Suspension of 
Solids in Flowing Water; to the Hering & Trau twine Transla- 
tion of Kutter for the chapter on Kutter's Formula, and for that 
on the Development of the other and earlier Hydraulic Equa- 
tions; to Hering's Report to the National Board of Health 
for the chapter on Lateral Location; and to Baumeister for the 
general arrangement of sewer systems. 



PREFACE TO SECOND EDITION 



AFTER fifteen years of use in his classes, the author has been 
enabled to prepare a second edition of this little book, partly 
for the purpose of correcting certain minor errors and partly 
that certain additional material might be inserted. 

In recent years a great deal of attention has been given to 
the careful analysis of the problem of rainfall and run-off; notably 
by Messrs. Grunsky, Gregory and Nordell, and only after much 
hesitation was it decided to omit any extended review of their 
thorough, detailed discussion. The relation between rainfall 
and run-off is dependent upon many very uncertain factors, and 
any close mathematical analysis of the way in which water, 
delivered to any area as rain, is collected into one channel 
at a single point of the area must include so many assumptions 
that the result may be far from the truth, although correct 
according to the theory followed. It was decided, therefore, to 
again follow the method of Kuichling, adopted in the first edition, 
as being reasonably safe in principle and at the same time 
holding clearly before the student the chief factor that enters 
into the relation, viz., the impervious character of the surface 
on which the rain falls. Reference is made, however, to the more 
mathematical treatment, and anyone interested may consult 
the original papers if he so desires. 

The use of better jointing material for vitrified pipe has 
made it possible to eliminate leakage entirely, if sufficient care 
be taken in construction. Various asphaltic preparations and 
other patented articles are on the market and if properly used 
will ensure a perfectly water-tight pipe line. This fact modifies 



vi PREFACE TO SECOND EDITION 

somewhat the earlier statements about the necessary amount 
of leakage to be considered. 

The problems that have been added have been found very 
useful in affording an insight into some of the broader questions 
that enter into the design of sewers, as well as in giving the stu- 
dent a chance to apply his theory to a concrete example. 

The book as a whole is not materially changed, and continued 
experience in large classes has confirmed the author in his belief 
that for the general course student in Civil Engineering it con- 
tains the essentials of sewer design so arranged as to be readily 
intelligible to the average mind. 

H. N. 0. 



CONTENTS 



PAGE 

PREFACE iii 

LIST OF ILLUSTRATIONS viii 

LIST OF DIAGRAMS ix 

LIST OF TABLES xi 

CHAPTER I 
GENERAL CONSIDERATIONS 

Development of Sewerage Systems; Col. Waring's Advocacy of the " Separate 
System." Arguments for this System as against the " Combined Sys- 
tem." Conclusions i 

CHAPTER II 

PREPARATORY MAPS AND DATA 

Maps Required; their Scale, Accuracy, and Extent; Information Needed for 
Maps; Surveys, Methods and Cost; Soundings, Borings; Levels; Speci- 
fications for Maps submitted to the N. Y. State Dept. of Health .... 13 

CHAPTER III 

EXCESSIVE RAINS 

Brooklyn and Providence Studies; U. S. Weather Bureau Records; Maximum 
Intensities; Kuichling's Studies; Relation between Intensity and Dura- 
tion; Talbot's Diagrams; Rochester Diagrams; Other Diagrams 31 

CHAPTER IV 

PROPORTION REACHING THE SEWERS 

Conditions Affecting this Proportion; Early London Gagings; Rochester 
Gagings; Sudbury River Gagings; European Experience; Kuichling's 
Conclusions 54 

CHAPTER V 

RELATION OF DENSITY TO PERCENTAGE 

Variety in Impervious Surfaces; Percentage of Rain Discharged from Each; 
Amount of Impervious Surface Compared with Density of Population; 
Density and Percentage of Rain Discharged Compared 70 



viii CONTENTS 

CHAPTER VI 

MATHEMATICAL FORMULA 

PAGE 

Hawksley; Biirkli-Ziegler; Adams, McMath; Analysis of Factors Com- 
pared with those' of N. Y. Diagrams; New Orleans Diagram; Crane's 
Slide-rule; Dow's Diagram 78 

CHAPTER VII 

ESTIMATING FUTURE POPULATION 

Census Reports; Chicago and Baltimore Curves; Comparison of Different 
Cities; Boston and Brockton Methods; Laws of Rafter-Baker; Kuich- 
ling's Law; Future Population of Ithaca 93 

CHAPTER VIII 

AMOUNT OF SEWAGE PER CAPITA 

Relation between Amount of Sewage and Water-supply; Consumption in 
American Cities; Analysis for Boston's Future Supply; Analysis at New- 
ton, Mass.; Examples of Variation of Water-consumption and of Sewage- 
flow in American Cities; Methods of Stating the Amount of Maximum 
flow 105 

CHAPTER IX 

GROUND-WATER REACHING SEWERS 

Variation in Height of Ground-water; Statistics of Amount of Infiltration; 
Coffin's Experiments on Tightness of Pipe-joints; Senior's Experiments; 
Conclusions 142 



CHAPTER X 
GRADES AND SELF-CLEANSING VELOCITIES 

Hooker's Thesis on Suspension of Solids in Flowing Water; Relation by 
Experiment between Velocity and Suspension; Effect of Shape and 
Specific Gravity of Pieces Moved; Velocities Required by Engineers; 
Grades Required to Secure these Velocities 153 

CHAPTER XI 

DEVELOPMENT OF FORMULA FOR FLOW 

Chezy formula; de Prony's Formula; Eytelwein's Formula; Weisbach's 
Coefficients; Latham's Tables; Darcy's Experiments; Bazin's Formula; 
Humphreys & Abbot; English Formulae 165 



CONTENTS ix 

CHAPTER XII 

KUTTER'S FORMULA 

PAGE 

Origin and Method of Construction; Diagram for Value of c; Diagram for 

Finding v; Flynn's Tables, with Examples of Use; Colby's Slide-rule 175 

CHAPTER XIII 

SEWER DIAGRAMS 

Olive's, Staley & Pierson's, and FitzGerald's Based on Latham's Tables; 
Hering's, Moore's, Talbot's, Bailey's, Adams & G3mmell's, and Hill's, 
based on Kutter's Formula; Author's Diagrams 184 

CHAPTER XIV 

USE OF DIAGRAMS 

Example in Determining the Size of a Storm- water Drain for Ithaca; Example 

in Finding the Size of an Outfall for Separate System 190 

CHAPTER XV 

SEWER PLANS 

Location of Outfall; Perpendicular System; Intercepting System; Zone 
System; Fan System; Radial System; Lateral Disposition; Location of 
Flush-tanks; Grade of Sewer-crown; Curve-resistance in Manholes; 
Elevation of Flow-lines in Confluent Streams 195 

CHAPTER XVI 

SEWER CROSS-SECTIONS 

Egg-shaped Sections; Advantage in Velocity Compared with Circular Pipes; 

Velocity at Different Depths 207 

CHAPTER XVII 

FLUSHING 

General Methods; Gates and Hand-flushing; Van Vranken Tank; Field- 
Waring Tank; Rhoads- Williams Tank; Miller Tanks 213 

CHAPTER XVIII 

USE OF TANKS 

Cost of Flush-tanks in First Cost and in Maintenance; Engineering Evidence 
as to Value of Tanks; Theoretical Need for Tanks; Experimental 
Studies in Ithaca; Conclusions 22 S 



LIST OF ILLUSTRATIONS 





FIG. 


PAGE 


Pile-driver 


i 


21 


Test Boring-machine 


2 


21 


Test-rod-driver 


3 


22 


Crane's Slide-rule for McMath's Formula 


16 


9 1 


Defective Sewer Section 


45 


153 


Colby's Sewer Computer 


46 


182 


Perpendicular System of Laying Out 


48 


196 


Intercepting " 


49 


197 


Zone " " " 


50 


198 


Fan " " " 


5 1 


199 


Radial " " " 


52 


200 


Location of Laterals 


53 


2O2 





54 


202 


' ' ' ' 


55 


203 





56 


204 


Egg-shaped Sewer, "Old Form " 


57 


208 


"New Form" 


58 


20 9 


Circular and Egg-shaped Compared 


59 


209 


Van Vranken Flush-tank 


61 


215 


Field- Waring 


62 


216 


Rhoads- Williams Flush-tank 


63 


218 


Miller " " 


64 


22O 


" " Special Form 


65 


221 


Merritt Automatic Siphon 


66 


223 




X 





LIST OF DIAGRAMS 



FIG. PAGE 

Sketch of Sewer Plan, Showing Lettering, etc 4 27 

Rainfall Intensity in New England States 5 40 

" Rochester 6 42 

" " Boston, etc 7 43 

" " Baltimore, etc 8 44 

" ' * Washington, etc 9 45 

' < " Philadelphia 10 46 

" " Savannah n 47 

Various Rainfall Curves 12 49 

' ' Run-off Curves 13 68 

Relation between Density of Population and Percentage of Rainfall 

Reaching Sewers k 14 75 

Run-off at New Orleans 15 89 

Population Curve for Chicago 17 94 

" " " Baltimore 18 94 

" ' ' " Boston 19 95 

1 ' " " Brockton 20 97 

Variation of Rate of Growth with Size of City 21 99 

". 22 101 

Population Curve for Ithaca 23 103 

Water-consumption and Sewage-flow at Atlantic City 24 106 

" Des Moines 25 108 

Records of Water-meters in Manhattan 26 114 

Water-consumption and Water Waste, in New York 27 120 

Water-consumption Curves for New York and Fall River 28 121 

Increase of per Cap. Consumption with Growth of City 29 122 

Effect of Meters on Water-consumption 30 124 

Reduction in Fall River through Use of Meters 31 125 

" " Cleveland through Use of Meters 32 125 

Water-consumption in Binghamton 33 127 

' ' from Hemlock Lake 34 1 28 

in Chicago and Fall River 35 129 

" in Atlantic City 36 131 

Sewage-flow, Canton, O 37 132 

Schenectady, N. Y 38 133 

Weston Hospital, W. Va 39 133 

' ' Omaha, Neb 40 134 

xi 



xii LIST OF DIAGRAMS 

FIG. PAGE 

Sewage-flow, Chatauqua, N. Y 41 134 

Cadillac, Mich 42 135 

Gloversville 43 136 

Hourly Variation at Gloversville . 44 138 

Available Length of 6-inch Laterals 47 188 

Proportional Velocities and Discharges at Different Depths of a Circular 

Pipe 60 211 

Comparison of Grade and Velocity in 6-inch Pipe 67 228 

Flush-waves, Green St. (30 Cu. Ft. Flush) 68 234 

' ' Green St. (40 Cu. Ft. Flush) 69 234 

Cayuga St 70 234 

' ' Aurora St 71 235 



LIST OF TABLES 



TABLE PAGE 

Cost of Survey near Chicago I. 19 

Maximum Rate of Rainfall at Washington, D. C II. 35 

" Intensity for 5-, 10-, and 6o-minute Intervals III. 35 

" Rates of Rainfall in Eastern United States IV. 36 

Equations of Rainfall Curves, Savannah, Ga V. 48 

Rainfall Discharged by Sewers, Rochester, N. Y VI. 58 

Rainfall and Stream-flow, Sudbury River, Mass VII. 62 

Percentage of Roof, Street, and Yard Surface per Acre VIII. 72 

Classification of Street Surfaces IX. 74 

Relation between Population and Impervious Surface X. 74 

Different Kinds of Surface, Ithaca, N. Y XI. 75 

Rates of Increase of Population, 1840-1880 XII. 98 

1910 XIII. 100 

Consumption of Water in Small Cities of United States XIV. no 

Large Cities of United States XV. in 

" " " Boston, etc., by Meter XVI. 112 

" ' ' " Manhattan by Meter XVII. 113 

Metered Water for Trade and Mechanical Purposes XVIII. 116 

Water Not Accounted for by Reasonable Use XIX. 118 

Consumption of Water in terms of First Faucet XX. 126 

Sewer-gagings at Des Moines and Elsewhere XXI. 130 

Velocities at which Dragging Begins XXII. 156 

Specific Gravity of Pieces Moved by Flowing Water XXIII. 158 

Weisbach's Values f or c XXIV. 167 

Comparative Valeus of "c" by Formulae of Weisbach and Kutter XXV. 186 

Rhoads- Williams Automatic Siphons XXVI. 219 

Relation between Velocity and Grade 6-inch Lateral XXVII. 228 

Flush-waves, Green St. Sewer. XXVIII. 236 

Cayuga St. Sewer XXIX. 236 

" Aurora St. Sewer XXX. 237 

" First St. Sewer XXXI. 237 

Distances and Slopes between Manholes, Ithaca XXXII. 238 

xiii 



SEWER DESIGN 



CHAPTER I 
GENERAL CONSIDERATIONS 

IN preparing the design and making the plans for a system 
of sewers for any given city, there are some preliminary ques- 
tions to be settled before the location of the mains and the 
sizes of the pipes can be determined. Perhaps the first of these 
questions is whether the system shall be designed to carry house- 
sewage alone, or rain-water from the streets, roofs, and yards 
as well. Arguments for the one arrangement or the other have 
been carried on in the abstract for many years, chiefly from 
the sanitary standpoint, but the question is properly settled by 
the local conditions of the place under consideration. 

The combined system, as the system intended for rain-water 
and sewage is called, is the result of growth and development and 
so has the prestige that comes from age. Not very long ago, 
the function of sewers was to carry off the storm-water falling on 
the streets and to keep the yards and basements dry; while 
the privies, which were then generally used, were cleaned and 
cared for without reference to the sewers. When water- 
closets came into use they were, after a time, for it was at 
first forbidden by law, allowed to discharge into the storm- 
sewers. In this way the channels, which may have been in the 
beginning brooks, afterwards walled in and arched over as the 
city grew, came to be the receptacles for the house-refuse and 
water-closet wastes. Naturally, the channels thus developed 
were not of the best section or design for this, their final use, 



2 SEWER DESIGN 

and in England and in the older cities of this country, where 
examples of the process are yet to be seen, accumulations of 
filth and deposits of rubbish are the evidences of rough interiors, 
flat gradients, and shallow depths. 

Small sewers for house-sewage were used in the United 
States before 1880, and sanitary engineers now prominent in 
this country prepared plans for sewerage systems, using small 
pipes and keeping out practically all the storm-water. But it 
is due to Col. Geo. E. Waring that the old prejudices have 
been so entirely removed and the manifest advantages of small 
pipe-sewers so strongly emphasized. It was in 1880, in a public 
address, that he said that the conditions of drainage had been 
changed, and that engineers must recognize that the number 
of water-closets now used made the construction of sewers 
for their exclusive care a necessity. 

This use of small pipe-sewers with its accompanying details 
of construction was patented under the name '" Waring 's 
Separate System," and under this patent Col. Waring was 
paid large royalties by some of the cities for which he acted as 
consulting engineer.* The principal features of the " Waring 
System " as described under U. S. patents 236,740 and 278,339 
are: first, absolute exclusion of the rain-water; second, ventila- 
tion of street-sewers through house-pipes not trapped against 
the sewer; third, automatic flush-tanks at the head of every 
lateral; and fourth, soil-drainage by pipes laid in the sewer- 
trenches. 

Waring's prejudice against combined sewers was very strong, 
as indicated by the following quotation from a public address 
delivered in 1880: " In closing permit me to formulate my 

* In a letter to the author dated January 30, 1899, the executor of Col. Waring 
wrote as follows in reference to these patents: 

"The patents to which you refer (which are the property of the Drainage 
Construction Company of Boston) are still in force. The patents have been 
disputed, and suits are now in progress, with a view' to establishing their validity. 
Pending decision, the owners are granting licenses upon a cash payment of half 
royalties five cents per lineal foot of sewer or an agreement to pay full royalties 
if the patents are sustained by the courts." 

Both patents have now (1912) expired. 



GENERAL CONSIDERATIONS 3 

opinion on this subject by saying that the present manner of 
disposing of storm-water in sewered towns by removing it from 
the surface where it is needed to the sewer where it creates 
a nuisance is a relic of barbarism, and that its continuance 
indicates an overriding of reason by tradition." This he later 
qualified by saying: " I think that the necessary sanitary 
requirements may be met by the combined system if due atten- 
tion is given to the details, and if enough money is spent." He 
aroused much controversy among engineers, and the sanitary 
advantages of both methods were discussed at length. 

In the second annual report of the Massachusetts State 
Board of Health, 1881, p. 25, is a paper by E. C. Clarke, 
then engineer in charge of the Boston sewers, giving briefly 
all the arguments in favor of the combined system; and a paper 
by Benezette Williams, in the Journal of the Ass'n of Eng. 
Soc., Vol. IV, page 175,* gives additional discussion from the 
same point of view. In his book on Sewerage, Col. Waring 
devotes a chapter to the question, discussing the papers here 
referred to, and, while disavowing himself a hard-and-fast 
advocate of the separate system, practically says that storm- 
water sewers are incidental, and that for them only main 
outlets are in any case needed, while the sewers of his system 
are everywhere essential. 

The arguments for the combined system are as follows: 

i. Sewage from houses forms only an inconsiderable part 
of the noxious materials that constitute the wastes of a town; 
chemical analysis fails to detect any great difference between 
the sewage of a water-closet town and that of a town where 
earth privies and the pail system are used; that is, the waste 
water from sinks, baths, laundries, and the wash of paved 
streets contains enough organic matter to be nearly as foul, 
chemically, as the discharge of water-closets. This other mate- 
rial therefore requires as careful treatment as the water-closet 
matter. 

To this it is answered that while this may be true so far as 

* See also Jour. Ass'n. Eng. Soc., Vol. Ill, pp. 37, 67, 158, 183. 



4 SEWER DESIGN 

chemical examination goes, the real danger in sewage comes 
from definite disease-germs which are only found in sewage 
proper, and therefore the latter is the dangerous material. It 
is further said that the sewers should not in any case be 
made to take the place of street-sweeping carts, and that if 
the streets are kept clean, as they should be, the wash- 
water from them will not be foul, and will require no special 
care. 

State Boards of Health have gradually acquired the right to 
regulate the disposal of sewage, and it is their usual practice 
to insist upon small pipe-sewers for house-wastes only and to 
disregard storm-sewage altogether. This indicates that the 
current scientific belief is that the real danger to health does 
not come from street wash, even if it does decompose and 
appear offensive. 

2. In the matter of keeping the sewers clean, the large 
sewer, it is said, has the advantage over the small, both in that 
it can accumulate a larger amount of sewage for flushing pur- 
poses, which from the greater hydraulic radius will have a greater 
velocity and scouring power for the same grade, and in that, 
while ordinary obstructions will be cared for by flushing, there 
will be times when excessive deposits will occur which must be 
removed by hand, and then a sewer large enough for a man to 
enter can be cleaned at a much less expense than the small 
pipe which must be opened from the surface or cleaned by rods 
worked from the manholes. 

To this it is answered that experience shows that flushing 
by automatic flush-tanks is sufficient to keep the smallest sewer 
constantly clean, and that stoppages in the pipes are of rare 
occurrence and easily removed. On the other hand, a large 
sewer, in which there is a variable flow, allows floating matter 
carried along in large volumes to be deposited later on the walls 
of the sewer, clinging in a slimy layer to the uneven brick sur- 
faces; when the amount of sewage becomes less, this matter, 
in the warmth and darkness, generates noxious gases and fosters 
the development of bacteria. These micro-organisms when 



GENERAL CONSIDERATIONS 5 

dried may float off in the air to escape through the traps into 
houses or through manholes into the streets. 

3. On account of the larger air-space over the flowing liquid 
in the combined sewer, the gases of decomposition given off 
by the sewage are largely diluted, and there is nothing to fear 
from them ; whereas, with the small sewers, the degree of con- 
centration is greater, and there is consequently more danger 
of forced traps and greater annoyance from ventilating manholes. 

The reply is that, owing to the greater amount of air to be 
moved, the ventilation is really less perfect in the large sewer, 
and that, from the slime which accumulates on the walls after 
flooding, there is more matter to decompose. The deposits 
which, it is admitted, occur in the mains of the combined s 
tern add considerably to the offensive gases during deco 
position. 

4. The combined system is the more economical; for if 
the use of the sewer is restricted to house-sewage, then there 
will be required for the rain-water another system of pipes 
of equal extent, and the cost of the two systems will be greater 
than that of one. This follows from the fact that the cost of 
engineering, superintendence, pumping, sheeting, etc., are 
practically the same for a large sewer as for a small one, and 
that the cost of excavation does not increase in a direct ratio 
with the size of the pipe used; and further, since the flow of 
sewage is insignificant compared with that of the storm-water,, 
a sewer large enough for the latter will serve for the former pur- 
pose without additional expense. 

The answer to this is that the system for rain-water need 
never be co-extensive with that for house-sewage, since the 
street-gutters will serve for the former purpose so long as the 
flow in them does not become a nuisance; consequently the 
length of the large main may be reduced nearly one-half. Fur- 
ther, that the rain-water drains when built seldom need be 
laid to the same depth or to the same outfall, as they may be 
discharged into any convenient watercourse at the nearest 
point. Also, if rain-water flowing on the streets does accumulate 



JJ. VO 

* 




6 SEWER DESIGN 

in excessive amounts, the result is nothing more serious than 
a temporary inconvenience, and no damage is done, as 
might be the case were sewers to be gorged with an excess of 
rain. 

5. Finally, it is said that if the rain-water is kept out of the 
sewers, periodic flushing, which is of great value, will be lost, 
and in the case of the street serving as a storm-sewer there 
will be yards and alleys too low to be drained into it, whereas 
they could be drained into a storm-water sewer. 

To this answer is made that for the irregular flushing by 
rain the regular use of flush-tanks can be substituted; and in 
case the sewage has to be pumped or treated, instead of being 
arged directly into a river, the presence of the rain-water 
not only undesirable but absolutely forbidden. 

To sum up the reasons for selecting, for a city, sewers to 
carry storm-water and sewage, or sewage only, the arguments 
just cited may be reduced as follows: It is improbable that 
any house-refuse that would go into a combined system would 
be kept out of a separate system, so that the only contribution 
to the former not allowed in the latter is the rain-water from the 
roofs, yards, and streets and any large amount of manufactur- 
ing refuse which might be rejected from a separate system on 
account -of the large proportion not requiring purification. If 
the streets are decently cleaned, there is no reason for expecting 
the rain to act as a scavenger, and it is better to dispose of the 
street-sweepings by means of sweeping-machines than to allow 
the rain to wash these accumulations into the sewer, to be cleaned 
out by hand or discharged into a river or harbor, there to be 
dredged out. There is, therefore, no sanitary reason why 
rain-water should not be separately disposed of. 

As to the dangers from slime deposited on the walls of large 
sewers the case is suppositionary, and the evil effects entirely 
unproved. Notwithstanding numerous examinations of sewer- 
air, no pathogenic germs have ever been found a negative argu- 
ment, to be sure, but of some weight. Judged by chemical 
standards, the air in sewers is generally better than that in schools, 



GENERAL CONSIDERATIONS 7 

halls, etc. General statistics of the health of sewer-laborers 
show no ill effects from their employment. 

It is hard to see why it should not be possible to keep both 
systems clean, since the inverts of both may be made to the same 
radius, and so the velocity with the same grade kept equal. 
If the water for flushing has to be bought, the same quantity 
used in frequent flushes of small pipes will probably keep the 
sewer cleaner than single flushes, larger in amount but applied 
at such infrequent intervals to a large sewer that the deposits 
become hard and fast between times. However, modern practice 
seems to have the tendency to do away with flush-tanks and to 
keep the sewers clean by hand-flushing in such amounts and at 
such times and places as may be found necessary. 

The alleged advantage of having the sewer large enough 
to enter is nothing, since with proper grades and velocities the 
cost of removing the few stoppages that occur is much less than 
the interest on the money required to build the larger sewer. 

Only a few years ago, the author heard of a city engineer 
who still believed that large sewers only should be built and 
therefore, even for laterals of short blocks, constructed only 
brick sewers 24 inches in diameter. The excessive cost thus 
incurred was a heavy burden on the small village (near Pitts- 
burgh) and no better sewer was provided than if a 6-inch pipe 
had been used. Indeed, on a low grade the large sewer would 
be distinctly inferior. 

The question of ventilation is based on conditions which 
do not, or should not, occur. Both sewers are designed to 
carry all material to the outfall before decomposition has begun, 
so that, unless by some accident deposits take place, there is 
no decomposition in the sewer, and therefore no gases to be dis- 
pelled. Should deposits occur and gases arise, the ventilation 
through the manholes for the same sewage-flow should be as 
complete in the one case as in the other; any slime left on the 
sides of the large sewer after a rain would in decay be so diluted by 
the greater amount of air that the offence would probably not 
be any greater. The sewers which are cited to show the bad 



8 SEWER DESIGN 

quality of the air contained are those of fifty years ago, when 
the laws governing the flow of sewage were not so carefully 
heeded, and when the street- washings were hurried into the 
sewer to form deposits. With equal care in the design there 
seems to be no reason why the small or the larger sewer should 
be the better ventilated. 

While it is true that two systems, one for sewage and one for 
storm-water, over the same area, will cost about two-fifths 
more than a single combined one, yet the assumption that their 
lengths will be the same is not true. The need for storm- 
sewers and their necessary length to reach a watercourse are 
matters to be based on a study of the local conditions, but it 
is safe to say that in any city there are many blocks which would 
carry all the storm-water from the centre of the block to the 
cross street at the end without any nuisance or damage, and 
that therefore the construction of storm-water sewers in those 
blocks would be a municipal waste. In a printed discussion 
of some years ago,* Mr. Robert Moore of St. Louis, stated that 
on the steep streets of Kansas City, Mo., the storm- water wash 
in the gutters becomes a serious matter after it has run 500 to 
600 feet, and that 1000 feet is the limit of endurance. Mr. 
Chanute, in replying, said that from actual experience in 
Kansas City he has yet to find the water at 1500 feet the unen- 
durable nuisance mentioned. From his own experience the 
author believes that in small cities water from 2000 feet of paved 
street does not unduly gorge the gutter or cause any annoyance. 
Mr. Horner of the St. Louis Sewer Dept., says t that while 
there are in St. Louis sewer inlets which drain 1200 feet of 
street satisfactorily, he believes that this is a greater length 
than is generally warranted, since at the lower end the flow of 
water in the gutters is inconveniently deep. 

On the other hand, it is more than likely that in a large part 
of the city there are streets where the two sewers would have to 
be carried at the same depth and in the same direction, and 

* Jour. Ass'n. Eng. Soc., Vol. III. p. 69. 
t Engineering News, Vol. LXIV, p. 326. 



GENERAL CONSIDERATIONS 9 

that therefore it would be economy to combine the two and 
build one sewer for the two purposes. In what streets this 
should be done, and how far it is economy to do it, must be 
determined by careful study and comparative computations. It 
is as grave a fault to design a separate sewer for a street that 
needs a storm-water sewer discharging into the same outfall as 
to build a storm-water sewer where none is needed. 

It is often possible, in reconstruction or improvements, to 
use an old sewer for storm-water alone with entire success, 
building new sewers for the house-sewage. It is therefore 
necessary to know with accuracy the sizes and grades of all old 
sewers in order that if possible they may be incorporated into 
the design in hand. 

The regulations of the different State Boards of Health are 
in many cases the real cause of determining whether a separate 
system or a combined system shall be built. In New York 
State, for example, no system of sewers in any community may 
be built unless, according to the laws, the places have received 
the approval of the State Department of Health. This approval 
is withheld as a matter of established policy for plans showing 
combined sewers discharging without the action of a disposal 
plant into inland waters. Since the cost of purifying or 
even treating storm-water is financially as impossible as it is 
unreasonable, it follows that in New York State all sewer 
systems are now built on the separate plan and the necessary 
storm drains are built according to a separate design. 

Where combined sewers are already in operation and it is 
proposed to make extensions for the sake of house connections, 
the attitude of the Department of Health is made to agree with 
local conditions. If the extension is long compared with that 
part of the combined system affected, they may require new 
separate sewers laid to replace the old pipes. If short, they 
may require the entire sewer system to be replaced 'by pipes for 
domestic sewage, the system discharging into a disposal plant. 
The construction of this last, or at least its design and a promise 
to construct, is often made a condition precedent to grant- 



10 SEWER DESIGN 

ing the approval for the construction of the extensions asked 
for. 

Sometimes extensions to combined systems are approved 
provided the dry-weather flow shall be treated in a disposal 
plant and that there shall also be treated dilutions of from 
3- to 5 -fold, depending on the ordinary concentration of the 
domestic sewage, the excess being discharged untreated into 
watercourses where it is assumed, because of its greater dilu- 
tion, it will not be dangerous nor cause offence. 

The desirability of the sewer acting as a ground-water 
drain has been strongly urged. Waring says that the primary 
object of sewerage is the removal of fouled waste water and of 
subsoil water. Therefore he makes a line of drain-tile laid in 
the sewer- trench an essential part of his system. The sanitary 
advantages of a dry subsoil are sufficiently evident and are 
not a question for discussion here. Whether the sewer-pipes 
shall serve for the purpose or not is of some interest. The 
disadvantages apparent are the uncertainty introduced in 
determining the proper size of the pipe-lines, since the amount 
of ground-water flow can only be determined when it is encoun- 
tered, and then for that time only, the ground-water flow being 
quite as variable as any other stream flow. Again, since the 
height of ground-water seldom remains permanent, it is possible 
that openings left to admit ground-water may at times allow 
sewage to escape, thus polluting the soil and reducing the 
carrying power of the sewage. It seems better therefore either 
to provide a separate line of pipes for ground-water, discharg- 
ing at near and convenient points, or else to arrange for the 
ground-water to enter without the opportunity for the sewage 
to escape. This may be done by providing special openings, 
as in a pipe with siphon attachment patented by S. E. Babcock 
of Little Falls, N. Y., and described in Engineering News, Vol. 
XXVII, p. 66 1, or by a special pipe, laid where the amount 
of ground-water makes it necessary and discharged into the 
sewer at a convenient manhole. It is the general practice 
to-day, however, to omit any such connection, and if drain- 



GENERAL CONSIDERATIONS 11 

tile are laid, to carry them separately to one or more out- 
falls. 

The question of drainage of cellars and low yards through 
the storm-water sewers is a serious one best settled by expediency. 
Like exceptionally low basement fixtures, they require for their 
individual accommodation a general lowering of the sewer-line 
or some special pipe or arrangement. The question resolves 
itself into one of the general versus the individual good : whether 
it is just to add to the general cost of the whole work for the 
peculiar benefit of one or two. When the whole section is low 
and relief can be given only by special means, then, as citizens, 
the householders are entitled to it, but it is probable that the 
individual case is more fairly neglected. 

The combined system is not adapted to any case where 
the sewage has to be pumped, treated by chemicals, or dis- 
posed of on land; the rain-water must be kept out of the* sewers, 
and no ground- water or other unpolluted water allowed to 
enter in all such cases. 

PROBLEMS 

1. Given the formula of hydraulics Q=AC\/RS, define carefully each 
of the factors used, and notice particularly the units employed. 

' 2. Given the formula of hydraulics V = CVRS, show algebraically 
that on the same grade a 6-inch pipe flowing half full has a less velocity 
than a 1 2-inch pipe half full. Express numerically if C = ioo and S = i 
foot in 100 feet. 

3. Compute the velocities in a pipe if, in one case the pipe flows full, 
in another, half full, and in another one-quarter full. Assume a 1 2-inch 
pipe on a grade of 26 feet to the mile, and that C = 100. 

4. Assume an area of one square mile on which there are 12,000 persons. 
If the rainfall is assumed to be at the rate of 2 inches per hour, how much 
water falls on the area in cubic feet per second? If the domestic sewage 
flow is at the rate of 100 gallons per head per day, what is the sewage 
flow? If one-third the rainfall reaches the sewer, what is the ratio of 
storm-water flow to house-sewage flow? 

5. If a 1 2-inch pipe-sewer laid, costs 90 c. per running foot and brick- 
work for a 4-foot circular sewer costs $20 per thousand, and excavation 
in trench costs 60 c. per cubic yard, compare the cost of the 1 2-inch domestic 



12 SEWER DESIGN 

sewer with the 4-foot storm-sewer, each 3000 feet long. Brick sewer re- 
quires 200 brick per lin. ft. 

6. A pipe lateral system contains 18,000 feet of 8-inch pipe, 2000 
feet of lo-inch pipe and 600 feet of 1 2-inch pipe. A small section con- 
taining 100 people is too low to drain into the system, and it is found that 
to serve this section the system must be lowered an average depth of 
5 feet, the soil being a hard clay, in which excavation costs 75 cents per 
cubic yard. Compute the interest at 5 per cent on this additional amount 
and compare with the cost of pumping the sewage of 100 persons (80 
gallons per head per day) 5 feet high, if the installation costs $650, and 
the running expenses are at the rate of 20 cents per million gallons lifted 
one foot. 



CHAPTER II 
PREPARATORY MAPS AND DATA 

A PROPER treatment of the subject-matter of the last chap- 
ter, as well as of many other points to come up in the study of 
sewer design, will depend upon a thorough knowledge of the 
physical and topographical conditions affecting the work. 
It is therefore necessary to obtain certain information before 
a real consideration can be given to the design proper. The 
first requisite is a map on which to lay down the desired lines 
of sewers, locate the mains, and determine the possible posi- 
tion of the outfall or outfalls. This may be an old city map, pro- 
vided it covers the ground required and is reasonably accurate, 
more inaccuracy in the map being tolerated if the grades are 
all good and the location of the outfall practically determined 
within a short distance. On the other hand, if the ground is 
generally level and the location of the outfall undetermined, 
the need for accuracy in the preliminary study of grades is 
correspondingly increased. This map should be drawn on a 
scale of from 200 to 400 feet to an inch; and the area covered 
should be that of the existing town or city, of the region where 
the outfall may be located, and of all territory which may 
ultimately be drained into the system; it should also include 
any high land which may furnish storm-water to drain into a 
system of storm-water sewers, should they be contemplated.* 
It is often easiest to collect these data by taking an old map 
which covers, perhaps, only a part of the territory desired and 
extending it where necessary by means of new surveys. The 

* In the regulations of the New York State Department of Health, it is 
specified that the maps and the designs made, shall include all the territory within 
the boundary lines of the city, whether the proposed construction covers the 
entire area or not. 

13 



14 SEWER DESIGN 

old map must always be regarded with suspicion, however, 
and its accuracy questioned until proved. Since it will in no 
case be possible to scale horizontal distances from such a map 
with sufficient exactness for the statement of the lengths of 
pipe required for the proposal of the bidders, it is better to 
chain the lengths of all the streets, and for the preliminary 
study of grades use the true distances. These distances can be 
recorded at the street intersections, as stations starting from the 
centre of some street assumed as zero, and then the ^profiles 
which are made will require no correction, and the first state- 
ment of quantities made will be true until the pipe is laid in 
the ground. This map will show (see Plate I) the location of 
the lines of pipe, their sizes and grades, and the location and 
character of the outfall. The sizes and grades are generally 

marked by figures, thus: , indicating a 1 2-inch pipe on a 

.6 per cent grade, or a grade of .6 feet in a hundred feet. It 
has been suggested that the size of the pipes might be expressed 
by the thickness of broken lines, making the width of the lines 
in inches equal the diameter of the pipe in feet, and the length 
of the dash five times the diameter of the pipe, the spaces between 
the dashes being the length of the dash, all being drawn to the 
scale of the map. The advantage claimed is that on a map 
reduced by photography, or otherwise, the sizes can be read 
in this way when figures would be illegible. (Proc. Phila. 
Engrs., Vol. XII, p. 105). 

If no plans are available, a survey must be made on which 
the preliminary studies can be based. A most economical 
and satisfactory method of collecting approximate data is 
described by ]. H. Fuertes in the Transactions of the American 
Society of Civil Engineers * as practised by him in connec- 
tion with investigations made of the New York water supplies 
and in a survey for a report on an improved sewerage system 
for Harrisburg, Pa. The method involves the use of two 
aneroid barometers with vertical scales in feet and adjusted 

* Summarized in Engineering Record, Vol. XLIII, p. 349. 



PKEPARATORY MAPS AND DATA 15 

to read alike at the office at the beginning of each half day. 
One barometer remains in the office, where it is read at three- 
minute intervals with the times noted. The other is taken 
through the city by horse and buggy and readings taken at 
every street intersection, at intermediate points where the 
surface grade changes, at water levels, etc. The times of read- 
ing are also noted, while the distances are estimated from the 
number of revolutions of the buggy wheel. The office readings, 
when plotted, show graphically the variations due to changes 
in barometric pressure alone and give the corrections from the 
initial reading to be applied to the field readings. About 
20 miles of street can be covered in a day and the elevations 
should check to within a few feet of the true elevations, the 
difference being too small to invalidate any preliminary plans 
or conclusions. Mr. Fuertes, referring to some topographical 
work done in this way outside of a certain city, gives the cost as 
$457 for field work and $136 for office mapping, a total of $593. 
The area covered was 9500 acres, so that the cost of the fielp 
work was at the rate of 4.8 cents per acre and the mapping 1.5 
cents per acre, a total cost of 6.3 cents per acre. This served 
to provide a topographical map with contours at 2o-foot inter- 
vals and on the scale used (one mile to the inch) made maps 
very similar to those of the United States Geological Survey. 

It will be necessary to have another set of maps to show 
details of location not possible on the small-scale maps 
details which are not needed until actual construction begins. 
This work is therefore usually carried along with the construc- 
tion. These latter maps (see Plate II*), made on a scale of 
40 to 60 feet to an inch, are plotted on separate sheets about 
20X30 inches, as nearly as the size of paper at hand makes 
convenient. The paper should be of parchment or a similar 
thin paper from which blue-prints can be made; if this is not 
procurable, a medium weight of bond paper will serve the pur- 
pose. These large-scale sheets are of great use to the field- 
party, who, when engaged in staking out the line on the ground, 

* Copied from Engineering News, Vol. XXXV. p. 2. 



16 SEWER DESIGN 

take from the office either blue-prints made from the parchment 
paper, or the bond maps or notes made from them. On these 
sheets, usually mapping two blocks, are plotted the street, 
curb, and gutter lines, trees, lamp-posts, hydrants, and catch- 
basins, the front and side lines of the houses and barns, the 
existing water- and gas-mains, and all old sewers. The profiles 
of the streets plotted just below on the same sheet show the 
street surface, with lines of intersecting streets, depth of rock, 
and position of all pipes and drains. Cellar-bottoms which 
might govern the depth of the sewer are plotted. These last 
are easily obtained by reading the level-rod on the house-sill 
outside and then adding the inside measurements of the cellar 
height. 

The reasons for these requirements are self-evident. It 
is for the city's interest to have the sewer laid in another part 
of the street from the water or gas, first because thereby dangers 
of breakage during construction are lessened, and second 
because future repairs to any of the lines will be more easily 
accomplished in separate trenches. If the sewer has to be laid 
in a trench along the middle of which a water-main must be 
slung up, the work on the sewer is done at an additional cost 
to the contractor, who is likely to claim an " extra " for it, and 
with the chance of damage to both pipes. If the sewers are 
laid out regardless of the position of other pipe-lines, it still 
remains possible to move either line when they are found to lie 
in the same trench, but the cost of this re-trenching, once or 
twice repeated, more than covers the cost of a preliminary 
investigation. 

Information concerning the location of the water- and gas- 
pipes can often be obtained from the companies' offices, but 
it is rarely accurate and is often only to be had through the 
good will of a foreman who has grown old on the works. The 
position of gas-drips and water-gates should always be located 
in the field and plotted as a check. The profiles showing the 
depth of the cross-pipes are of value in determining the depth 
of the sewer-pipes, and it is desirable to dig enough test-pits 



PREPARATORY MAPS AND DATA 17 

to make sure of critical points and of the main crossings. It 
rarely happens that the system of sewer-pipes will lie above 
the other pipes, and it is necessary, therefore, that they be 
designed to come enough below to allow at least 6 inches of 
dirt between the top of the sewer-pipe and the bottom of the 
water- or gas-pipe. It is awkward to find, just before joining 
in a lateral that is already laid, that the sewer-grade is of the 
same elevation as a 1 5-inch water-main, and that the sewer 
must go over or under and get back to the old grade within 
50 feet. The old sewers and drains should be incorporated in 
the survey and mapped with care, since they may be made a 
part of the new system. They should be thoroughly examined 
and their condition, grade, and position personally noted and 
recorded. It may be that a small house-sewe r can be laid 
inside of an old storm-sewer, saving the cost of re-excavation. 

The data for these maps are generally only to be obtained by 
a survey, which in open and unimproved land may be made 
at the time of staking out, but under ordinary conditions should 
be done before, since the information is needed for the staking 
out. A convenient field-party for this survey is a transit man, 
two chainmen, and the chief of party, who acts as note-keeper. 
In one day such a party will, from actual experience, survey 
from 2000 to 6000 feet of street on both sides, taking plus 
distances of fence-lines and side lines of houses* (prolonging 
them by eye across the transit-line), measuring from the transit- 
line to curb- and street-lines, and pacing to the front lines of 
houses. The average distance run by such a party in the small 
city of Ithaca in the summer of 1895 was 4400 feet per day. 
This work was plotted by one man in six days, making cost of 
the work, mapped and plotted, about $18.50 per day, or $22.25 
per mile. 

Additional data as to the cost of surveys such as might be 
needed for work of this character are given as follows: 

At St. Louis, where the entire cost of a careful survey of 

* For detailed directions of approved surveying methods for locating buildings 
along a street, see Engineering News, Vol. LIV, pp. 173, 310, 380. 



18 SEWER DESIGN 

the city was $16,900, the different parts of the survey were 
divided up into triangulation, n per cent; precise levelling, 
1 6 per cent; topography, 36 per cent; and office work, 37 per 
cent. The average cost in toto is given as $724.50 per square 
mile, or $1.13 per acre.* 

In the Trans. Am. Soc. C.E., Vol. XXX, p. 611, are given 
a number of instances of the cost of topographical surveys in 
different parts of the world, most of them, however, covering 
larger areas and using other methods than those required for 
the survey of towns. A letter is quoted from Mr. J. C. Olmstead 
to the effect that for the purposes of landscape architecture 
the ordinary cost of suitable survey will range from $2.50 to 
$20 per acre, being generally about $5 per acre. 

The following summary, Table I, is taken from an article t on 
the cost of survey of a 4ooo-acre tract near Chicago, and is as 
complete in all details as would be needed for any sewer-survey. 
The article gives an admirable description of the various ele- 
ments entering the cost and their effect upon the accuracy and 
total cost of the survey. 

In connection with the New York State Canals, extensive 
surveys were made in 1899, under the direction of the U. S. 
Deep Waterways Commission. Along the Mohawk Valley 
from Albany to Herkimer about 47,000 acres were surveyed 
and mapped to a scale of 200 feet to an inch, with 2-foot con- 
tours. The average cost was 86 cents per acre. A large amount 
of detail was included, especially at the cities and villages along 
the route. 

Borings were made by driving a casing and washing out the 
material inside by forcing water down through a smaller 
interior pipe. The average cost of 55,521 lineal feet of penetra- 
tion, about 2 per cent being in river bottom, and the average 
depth of hole being 29.5 feet, was 54 cents per vertical foot.{ 

* Jour. Ass'n Eng. Soc., Vol. XII, p. i. 
t Trans. Ass'n Civ. Engrs. of Cornell University, 1898, p. 68. 
J For detailed descriptions and costs of surveys in Croton Drainage Area, 
see Engineering News, Vol. LXII, p. 428. 



PREPARATORY MAPS AND DATA 



19 



In 1909, the New York State Water Supply Commission * 
made stadia surveys of three small areas of ground, the char- 
acter of the work being similar to that required for preliminary 
design of sewers in outlying territory of large cities. The work 
included detailed topography, the location of all railroads, 
highways, buildings, fences, etc. The three separate areas 
were of 18.2, 56.1, and 21.8 square miles in extent, and the 

TABLE I 

SHOWING COSTS OF SURVEY NEAR CHICAGO 







Cost. 






Total. 


Per Acre. 


Per Cent. 


Superintendence 
Bases . . 


$200.24 
2.8^ 02 


0.051 
OO7 


8.2 


Bench-marks 
Transit-lines for locating contours 


62.52 
8so 08 


.Ol6 

216 


^o / 

2.6 

34 8 


Levels for contours 
Topography 


594.65 

1 3O 31 


151 


24-3 


True meridian 


6 oo 


u oo 

OO2 


/ 


Soundings, etc 


66 02 


OI 7 


U 'O 

2 7 


Indexing notes 


jO OO 






Perpetuating survey 


I 2T OO 


Q2 2 


u.q. 

5-3 








o 


Mapping 8 section maps 


2446 . 73 
674. 1 1 


O.62O 
O 171 


IOO.O 

60 -z 


' ' i general map 


1 80 07 




T Q j- 


Incidental 


118 86 


O3.O 


10.5 












937-04 


0.247 


IOO.O 


Total 


-24.10 77 


o 867 













Or 87 cents per acre. 

field work in each case cost almost exactly 75 per cent of the 
total cost. The work was done by stadia and was plotted in 
the field to a scale of 100 feet to the inch and then reduced in 
the office to the smaller scale of 400 feet to the inch. 

The depth of rock and the character of the soil must be 

* Engineering-Contracting, Vol. xxxiii, p. 419. 



20 SEWER DESIGN 

determined by borings or test-pits, the latter being preferable. 
Enough soundings should be taken to explore thoroughly the 
ground through which the sewer is to pass, since the location 
of the mains may depend on the character of the ground. If 
there are two possible locations for a deep main, one through 
rock and one through soil, the cheaper design will of course 
locate it in the soil as determined by the borings, and even a 
longer line may be cheaper to build on account of the character 
of the trenching. Contracts are now rarely let at a lump sum 
for the system, but rather at unit prices for the different kinds 
of work, so that rock found in unexpected places has to be 
paid for, and goes to make the work cost more than the engineer's 
estimate. Where water and quicksand are encountered, there 
has as yet been found no just way of paying for the extra work 
involved, and it must be covered by the percentage added by the 
contractor to cover such contingencies. It may be noted here 
that a cheaper and fairer method would be to pay the contractor 
directly, and just in. proportion to the amount of this extra 
work. In laying out the best lines, the designing engineer should 
have the location of rock, quicksand, water-pockets, and soft 
clay in mind, to avoid them if possible, and get the maximum 
efficiency at the minimum cost. The proper attitude towards 
the contractor, also, is to give him all the information possible 
as to the nature of the work, in order to reduce the percentage 
added for unknown difficulties and to secure closer bids. 

The examination for rock is most easily made by driving 
a bar or pipe, i to i| inches in diameter, to refusal, although 
the method is open to the objection that a large boulder may be 
mistaken for the solid rock. Such a rod, driven by mauls and 
twisted by a wrench as it goes down, will easily penetrate 30 
to 40 feet of soil or clay, and by the use of an open pipe a core 
may be brought up. A f-inch pipe will drive better (in 8-foot 
lengths the driving protected by a cap), but a 2-inch pipe will 
bring up the better core. If it is decided to thoroughly explore 
the ground, it is a simple and effective plan to rig up a small 
hand pile-driver, using a block of wood for the weight. 



PREPARATORY MAPS AND DATA 



21 



Fig. i (from Engineering News, Vol. XXIX, p. 242) shows 
a portable and economical pile-driver for such a purpose. The 
verticals are made of 2 X 4-inch stuff, and the hammer of a 
section of an oak or other hard- wood tree which may be growing 




FIG. i 




Lievation 



conveniently at hand. It may be run on wheels or slid on 
runners. To hold the uprights steady, snub-lines are pro- 
vided. The hammer is worked by hand power, three or more 
men raising and lowering the weight. 

Fig. 2 illustrates a test boring-machine described in Engineer- 



22 



SEWER DESIGN 



ing News, Vol. XXI, p. 423. The cost is given as not more 
than $25, and it is said to bore through earth of any kind to a 
depth of 28 to 30 feet. The drill-rod should be square, and the 
flare of the chisel-point about 3^ inch on each side. The iron 
cross-bar is made of bar iron, ij inches square and about 4 
feet long, with an eye for the drill-rod forged in. The cross- 



9 Sheave 



Triangular Piece Pivoted 

in Pipe Cap, 
with rings for guys. 



Hammer 



Hammer 




FlG. 3. 



bar is held to the drill-rod by a set-screw f inch diameter, and 
holes in the drill-rod allow the placing of a f-inch pin for the 
lifting-chain to bear against. 

Fig. 3 shows in detail another form of driver (Engineering 
News. Vol. XXI, p. 484), the construction and arrangement 
being sufficiently well shown in the drawing. 

With a common wood-auger i| inches diameter, with exten- 
sion-rods keyed on, and with levers 3 feet long, borings 50 to 



PREPARATORY MAPS AND DATA 23 

100 feet deep can be very expeditiously made in common soil 
or clay. In addition, the auger will bring up samples of the 
material passed through in sufficient quantity to determine 
the nature of the soil. (Baker.) A post-hole auger in dry soils 
will reach depths of 10 to 12 feet and bring up the soil. A more 
satisfactory method in some respects is to follow the work of 
the engineers for the Rapid Transit Commission in New York 
City in sounding for rock on Broadway, which was as fol- 
lows: 

" Here two or three lengths of 2 -inch pipe were driven 
first to serve as a casing. In order to drive this pipe a small 
portable pile-driver was used, the top of the pipe being covered 
with a protecting cap. The hammer, weighing 150 pounds, 
was directed between four light metal guides, and had a fall of 
about 6 feet, the whole arrangement being supported on a cast- 
iron stand. The hammer was raised by hand-power. After 
the casing had been put down, the protecting cap was removed 
and a tee screwed on in its place, and down the pipe was inserted 
a f-inch wash-pipe with a chisel-point, in the corners of which 
were two small holes. Water was forced into this wash-pipe 
while two men worked the pipe down by hand. The water 
thus discharged, washing the sand away from the foot of the 
wash-pipe, flowed upward between the wash-pipe and the 
casing, carrying the sand with it. This water and sand flowed 
out of the side opening on the tee at the top and was caught 
in a bucket and sampled by the inspector in charge."* 

These borings were made at an average rate of 6 feet per 
hour, three laborers and an inspector being employed on each 
machine. The soil was sand and gravel, and about f of each 
boring was cased. 

Patton, in his treatise on Foundations, gives the following 
method as satisfactory: A 3- to 8-inch pipe of terra cotta or 
iron is pressed into the ground as far as possible; then a long 
narrow bucket with cutting-edge and a flap-valve a little dis- 
tance above the cutting-edge, opening inwards, is lowered into 

* Am. Soc. C. E., Vol. XXVIII, p. 13. 



24 SEWER DESIGN 

the pipe and is alternately raised and dropped. The material 
is collected in the bucket, and at intervals the bucket is lifted 
entirely out and emptied. This is repeated; the pipe gradually 
sinks, a man standing on the top if necessary. Other sections 
of the pipe are added from time to time. It becomes necessary 
sometimes to pour water into the pipe to aid in the cutting and 
flow of the material into the bucket. The bucket should be 
connected by a rope passing over a sheave connected with a 
frame or shears above. Great depths can be reached by this 
method with reasonable rapidity and at no great cost. 

Levels should be run and frequent benches established and 
checked along all the streets. For the preliminary study on 
the large map the levels are best expressed as contours show- 
ing on flat ground differences of i foot. The profiles on the 
separate sheets will require a vertical scale different from the 
horizontal, depending on the grade of the street, and it is better 
to hold to one vertical scale through all, rather than change 
it for each sheet. Ten feet to the inch will generally serve, 
though 4 feet to the inch is not too large for flat country. Levels 
should be read at the bottom, and at the surfaces of all creeks 
or brooks crossed by the sewer. Such points may serve for 
outfalls or for flushing-gates, so that the high- and low-water 
elevations should be found if possible. 

Of late years, particularly through the experience of the 
U. S. Geological Survey, much data has been collected on the 
value of various methods of running levels, particularly as 
those methods affect accuracy and cost. On the long aqueduct 
lines now under construction, as for Los Angeles and for New 
York City, similar valuable data has been acquired.* 

The most common practice is to use two rodmen and to 
read more than one wire on the level rod. On the Los Angeles 
work the average number of miles run per day was 5.2 and the 
cost including that involved in establishing frequent bench- 
marks was $13.20 per mile. On the Catskill Aqueduct work, 
with the same force, but with the addition of a note-keeper, 

* See Engineering News, Vol. LX, p. 311, and Vol. LIX, p. 186. 



PREPARATORY MAPS AND DATA 25 

the rate was from two to four miles per day, with bench-marks 
established every quarter mile. 

These sheet-maps may be indexed on the large map, num- 
bering the sheets to correspond with the numbers on the map; 
or a separate index-map may be drawn on one of the sheets 
and bound up with the others, in sections if need be. 

It is interesting to note that the directions offered above, 
which have been developed from the general practice of this 
country, agree in scales, etc., with the instructions for similar 
work issued by the Local Government Board of England (see 
Rawlinson's Suggestions, 1878).* 

PROBLEMS 

7. If 5-foot contours on a certain map drawn to a scale of 300 feet 
to the inch are | inch apart, what is the surface slope in feet per mile? 
In per cent? 

8. With two barometers, make a survey of an area of about 25 acres, 
plotting 2-foot contours. Select a part of the city that has marked 
differences in elevation and for which the street plan is available. 

10. With chain or tape only, make a survey of a portion of some 
assigned street (about 600 lineal feet). Record the position of all street- 
lines, trees, posts, fences, including back lines of lots, houses and barns, 
with all surfaces indications of underground pipes. Plot to a scale of 40 
feet to the inch. Compute the cost of the survey in units of acres per 
day. 

11. Compare the cost of making a survey of the city of , using 

the data of this chapter and checking by the results of Prob. 10. 

12. Compare the cost of digging (no sheeting) test-pits, 3 feet wide 
by 4 feet long to average depths of 12 feet, with the cost of wash-borings 
as given in this chapter. 

13. With a given city map, estimate the cost of running levels and 
establishing bench-marks for future work, assuming necessary salaries 
for different members of the party. 

* See also Municipal Engineering, Vol. XXI p, i6i 



26 SEWER DESIGN 



RULES AND REGULATIONS FOR THE PREPARATION AND 
SUBMISSION OF PLANS FOR SEWERAGE SYSTEMS 
AND SEWAGE-DISPOSAL WORKS 

As Enacted by the State Dept. of Health of New York State, 1912 

1. General Plans. General plans on a scale of not less than 300 
feet to one inch, and preferably not greater than 100 feet to one inch, 
covering the entire area of the municipality, must accompany every 
application in the case of a new sewer system, or any extension or modi- 
fication of any existing sewer system, unless such a general plan of the 
entire area of the municipality has already been submitted. These plans 
must have shown upon them all existing and proposed streets, the surface 
elevation at all street intersections and at all points where changes of 
grade occur, and contour lines for intervals of not less than 5 nor more 
than 10 feet. The plans must also show sewers upon all streets in the munic- 
ipality or the sewerage district, even if the construction of some of the 
sewers may be deferred. Should there be areas, which on account of 
the topography, or for other reasons, cannot drain into the proposed 
system, a definite statement to this effect must be made in the engineer's 
report and the probable future drainage of this disregarded territory 
discussed. The plans must also show clearly the location of all existing 
"sanitary" and "combined" sewers, but not of drains used exclusively 
for sub-soils or for surface-water; the location and general arrangement 
of existing and proposed sewage-disposal works, and the location of all 
existing and proposed outlets. The magnetic meridian, title and date, 
and the direction of flow and mean-water elevation of the principal streams 
must also be clearly shown. 

2. Lettering, Figures and Symbols. The lettering and figures must 
be of appropriate size, and of distinct outline. Surface elevations should 
preferably be placed just outside street lines opposite their respective 
positions, and at street corners, preferably in the angle outside street 
line, in the upper right angle if but one, and in the other angles if mote 
than one. The elevations of all sewer inverts must be shown at street 
intersections, at the ends of all lines, and at all points where changes in 
alignment and grade occur. These elevations must be clearly and dis- 
tinctly written close to the manhole or flush-tank, parallel with sewer- 
line, and expressed at least to the nearest irV foot. All manholes, flush- 
tanks, catch-basins, lampholes and other appurtenances must be shown 



PREPARATORY MAPS AND DATA 



27 



upon the plans in suitable symbols appropriately "referenced" in the 
title. The sizes and gradients of all proposed sewers, and of existing 
sewers, must be marked appropriately along sewer-lines between all 
consecutive manholes or flush-tanks, with arrows showing the direction 




FIG. 4. 



of flow. All sewers and other appurtenances must be shown by black 
lines and conventional signs, and not by colors. As an example of 
the lettering to be used at a street intersection, the following sketch is 
offered.* 

3. Profiles. Profiles upon separate sheets, showing all sewers 12 
inches or more in diameter, and all main intercepting and outfall sewers 

* Plate loaned by Theodore Horton, Chief Engineer, N. Y. State Dept. of 
Health. 



28 SEWER DESIGN 

when less than 12 inches in diameter, and all other available profiles, 
must be submitted with the plans. Upon these profiles must be shown 
all manholes, flush-tanks, inverted siphons and other appurtenances. 
The horizontal scale of these profiles must be at least as great as the scale 
of the corresponding plans, and the vertical scales not less than 10 feet 
to i inch. Both scales must be clearly shown upon the profiles. Figures 
showing the sizes and gradients of sewers, the surface elevations and sewer 
inverts, must be shown upon the profiles with the same frequency, or at 
the same points, as shown upon the plans. All stream crossings and sewer 
outlets must be shown upon profiles with elevations of stream-bed, and 
the normal, high, and low water levels if these data are available. 

4. Detail Plans. (a) Detailed plans of sewer sections and of all 
ordinary sewer appurtenances, such as manholes, flush-tanks, inspection- 
chambers, inverted siphons, as well as of any special appurtenance or struc- 
ture, must accompany general sewer plans. These detail plans must be 
drawn to such a scale as to show suitably and clearly the nature of the 
design and all details, such as manhole-frames and covers, iron pipes and 
valves, flushing-gates, siphons, etc. They should have marked upon them 
all dimensions, grades and explanatory notes necessary to make them 
readily intelligible and a complete guide for construction. 

(6) Complete detailed plans for sewage-disposal works must be sub- 
mitted in all cases where it is proposed to construct works for complete 
purification at the time of the construction of the sewarage system. If, 
however, it is proposed to construct only a portion of the complete works, 
at this time, detailed plans of such portions only need by submitted. In 
the latter case future provision must always be made for complete puri- 
fication works, and a reserve area must be shown upon the general plans 
for these works, and, if possible, a statement of the general type or method 
which it is proposed to adopt when complete purification works may be 
required. 

5. Specifications, Estimates of Cost. Specifications for the con- 
struction of the system of sewers and sewage-disposal works, including 
estimates of cost of the same, where these have been made, must accompany 
all plans for original or new systems. With plans for extensions of existing 
systems, specifications may be omitted, provided these extensions are to 
be constructed in accordance with specifications filed previously with 
original plans. 

6. Engineer's Report. A report, which would usually be written 
by the designing engineer, must be presented with all plans for original 
systems, giving full information upon which the design is based. This 
report must include a description of the extent of area which it is proposed 
to include within the system at the present time and in the future; the 
estimated present and future population to be served; the estimated per 



PREPARATORY MAPS AND DATA 29 

capita rates or volume of sewage to be provided for; the allowance, if any, 
for storm- or roof-water, and the full reasons for the inclusion of such 
water in the system. The report should include a description of all con- 
ditions peculiar to the locality, affecting in any way the design of the 
system; a description of all special devices used in the design and of any 
special points to be observed in the maintenance and operation of the 
system. The report must contain a full description of the general arrange- 
ment and all special features of the proposed sewage-disposal works, the 
reasons for the choice of the method or type proposed and a full description 
of the proposed operation of the plant. A full statement must be given 
of the capacities of the various parts of the works, the population which 
works are designed to serve and the reasons for any unusual capacities 
adopted. 

7. General Requirements. (a) All plans, specifications and reports 
must be submitted in duplicate, and the application for approval must 
be submitted on blanks issued by the Department for the purpose and 
signed by the proper municipal authorities or their properly authorized 
agent (in the latter case a letter of authorization must accompany the 
application). If approved, the original set will in general be returned 
and the duplicate set, if clear and distinct prints, on suitable paper or 
cloth, will be filed with the Department according to law. 

(6) In general, and except in certain restricted districts and for very 
cogent reasons, the Department will approve of plans for new systems 
only when designed upon the "separate" plan, in which all rain-water 
from roofs, streets and other areas, and all ground-water other than 
unavoidable leakage and a very restricted allowance for cellar drainage, 
shall be excluded. When plans for the extension of "combined" sewers, 
already built and in operation in full accordance with the provisions of 
the Health Law, are submitted, approval will in general be given only in 
cases where the district tributary to the sewer extension is of limited 
area and cannot be included in a new and distinct sewer district con- 
struction upon the" separate" plan. 

(c) The Department will in general approve only of plans which include 
disposal works for such complete purification as will produce a clear and 
"stable" effluent. If it is proposed to omit certain portions of these 
works for the complete purification of the sewage, there must be shown 
upon the plan a reserve area and the general arrangement of the type, 
methods and devices which it is proposed to instal in the future when 
such complete works are required; and included in the engineer's report 
the full reasons why any of such portions of the complete works are tem- 
temporarily omitted. 

(d) The approval of the Department is not required by law for drains 
designed and used exclusively for storm-water, subsoil-water and for other 



30 SEWER DESIGN 

purposes of drainage where no sewage or wastes are allowed to enter them. 
If any sewage or other waste matter or products are discharged into such 
drains, they come under the definition and classification of sewers, for 
which the approval of the Department, and a permit therefrom, must 
be secured in accordance with the Public Health Law and the above 
regulations. 



CHAPTER III 
EXCESSIVE RAINS 

IF storm- water drains are to be constructed, it becomes 
necessary to determine, as closely as possible, the amount 
of storm-water likely to enter the sewer. Evidently it will 
be due to two influencing conditions: the actual amount of 
rain falling in a given time, and the proportion of that amount 
reaching and carried off by the sewer. Only recently has 
careful observation been brought to bear on these points, 
and even now only an approximate estimate is possible, as 
the conditions are continually changing. 

It should here be pointed out that the run-off for sewers differs 
in this respect from the run-off for storage and for power pur- 
poses. As long-time stream-gagings become more available-, 
there is a growing tendency to disregard altogether studies of 
the rainfall over the watershed, as being valueless if not 
misleading. Thus Clemens Herschel has declared * that in 
forming a judgment as to the discharge of a river, a knowledge 
of rainfall is of no importance and that therefore rainfall 
records should cease to have the attention given them as in the 
illogical reports on stream flow of the past. 

Mr. J. C. Hoyt, of the U. S. Geological Survey, also says f 
that it is difficult to understand how engineers can continue 
to estimate run-off from rainfall data. 

For maximum rates of run-off, however, a knowledge of 
maximum rates of rainfall is essential and the local conditions 
known before any indication of the probable run-off is obtained. 

It may also be asserted that, while the annual rainfall 
is an interesting meteorological study and while engineers 

* Trans. Am. Soc. C. E., Vol. LVIII, p. 30. 
t Trans. Am. Soc. C. E., Vol. LVIII, p. 34. 

31 



32 SEWER DESIGN 

interested in water-power and water-storage will continue to 
refer to the amount of water falling per year as a basis for 
their studies, such facts have no bearing on the needed capacity 
of sewers. The fact that in New England the annual rainfall 
is about 40 vertical inches and in Kansas only 20, does not 
mean that the sewers in the former area must all be twice 
the capacity of those in the latter. Nor is it necessary, because 
the rainfall in Washington is 1 20 inches per year to build sewers 
there three times as large as in New England. There is then 
a difference between the amount of rain falling per year and 
some other characteristic that determines the necessary size of 
a sewer. 

In this country the first extended study of the subject was 
made by Col. J. W. Adams in designing the early sewers for 
Brooklyn. He noted the fact, since emphasized by A. J. 
Henry in a special report of the Weather Bureau, that excessive 
rains, or those that do damage, are naturally divided into two 
broad classes: (a) rains of great intensity and short duration, 
and (b) rains of light intensity and long duration; and that of 
the two classes, the first are far more damaging and destructive. 
Col. Adams, after consulting all the meagre rainfall records 
available, chiefly those of 1849 to J 856, and noting that there 
were but 19 days in .which the rainfall in 4 hours was an inch 
or over, and but 15 days in which the rainfall for the entire 
24 hours was as much as 2 inches, that the heaviest storms 
reported were two of i\ inches in 4 hours, and that there was 
no reported occurrence of as much as i inch within the hour, 
concluded that if he made provision in his Brooklyn sewers 
to carry off a rainfall of i inch per hour it would be sufficient. 

The two reports on the sewerage of Providence, one by 
J. H. Shedd, published in 1874, and one by S. M. Gray, pub- 
lished in 1884, represent the next advance in the study of the 
question of rainfall. Mr. Shedd noted that of 185 storms 
recorded for the 26 years before 1860 only 20 were at a rate 
of over \ inch per hour, while 165 were of less, and that of 
139 storms recorded in the 14 years, 1861-1875, 20 were over 



EXCESSIVE RAINS 33 

\ inch, and 119 were less. Mr. Gray pointed out that great 
care must be taken to determine the exact duration of the 
storm, and also of the heavy showers that may fall during a 
long rain, and that meteorological records are to be used only 
with great caution. He explained that the records, as generally 
made, can seldom be depended on for the rates of fall, since 
as a rule they give only the total amount of rain falling at 
certain times, paying little heed to the exact time when the 
storms begin or end; that is, the records fail to distinguish 
between a fall of i inch within the hour, however short the 
actual duration of the storm, and another which continues 
at a constant rate for the whole hour. Mr. Gray, however, 
gave no precise data as to the proper amount to be considered 
in the case of the Providence sewers. 

With the demand for more knowledge, aroused in great 
part by the work of a few engineers, came more data from 
different parts of the country to which the engineers of the 
Boston Water Board contributed largely. It was soon found 
that the early records were not entirely trustworthy, that the 
location of the gage had not been well considered, and that 
the rate of fall could not be derived with any exactness from 
published records either public or private. 

In 1888 the U. S. Weather Bureau began reporting excessive 
rains, i.e., rains of 2.50 inches or more in twenty-four hours 
and of i inch or more in one hour, but from the nature of the 
observations it is rarely known, in the case of rains of an inch 
or more in an hour, whether the rain was of an even intensity 
for the whole period, or whether most of it fell in a small 
fraction of the time. These records, with such value as they 
possess, are now available, as noted at the Weather Bureau 
stations through the United States (see Monthly Weather 
Review) . 

By a study of these figures it is seen that rainfalls of the 
rate of an inch per hour, assumed by Col. Adams and Mr. 
Shedd to be rare, are by no means infrequent. It is now 
proved that such storms occur several times a year, instead of 



34 SEWER DESIGN 

once in several years as was thought to be the case; also, that 
rains of a much heavier rate occur, lasting from ten to forty 
minutes. For example, in 1890 there were reported in New 
York State eleven storms contributing over an inch in an hour, 
and in Massachusetts six.* 

In the spring of 1889 five self-registering rain-gages were 
stationed throughout the country. This number has since 
been increased to over two hundred, and there are now published 
in the Monthly Weather Review tables of maximum rainfall in 
five-, ten-, and sixty-minute intervals, giving valuable data 
for all parts of the country. 

The special bulletin " D " of the Weather Bureau for 1897 
deals largely with this question of excessive rains. This bulletin, 
issued in direct response to the request of a number of civil and 
municipal engineers, gives the maximum intensities at Weather 
Bureau stations equipped with self-registering rain-gages. 
Its accompanying text is, in part, as follows: 

" Excessive rains of high intensity are not prevalent on the 
Western coast, although there the total annual rainfall is greater 
than in any other portion of the United States. In the Western 
States are found the most violent rains of this class, that is, 
the cloudbursts of the mountainous and arid regions. The 
rain seems to pour down rather than to fall in drops. The 
amount of water falling has never been ascertained. In August, 
1890, a storm passed over Palmetto, Nev., and contributed to 
a rain-gage, not exposed to the full intensity of the storm, 
8.8 inches in an hour. In August, 1891, two storms passed 
Campo, Col., within a few moments of each other, and the 
gage, before being carried away by the storm, showed a fall 
of 11.5 inches during the hour. But these downpours are 
found only between the Sierras and the foothills of the Rockies; 
while the common heavy rainfalls are found east of the io5th 
meridian, and principally during the summer months. They 
are most frequent in connection with summer-afternoon thunder- 
storms, but occasionally occur in the track of the West Indian 

* Weather Review for 1890. 



EXCESSIVE RAINS 



35 



TABLE II 

HIGHEST RATE PER HOUR OF RAINSTORMS OCCURRING AT 
WASHINGTON, D. C., DURING THE PAST 16 YEARS 



For any 



Inches. 



Date. 



5 consecutive minutes . 

10 " . 
15 

20 " . 
25 

30 " . 

40 " . 

50 " " - 

60 " " . 

120 



7-50 



4 50 
3-90 
3.6o 
3-15 
2-75 
2.30 
1.98 
1.23 



Sept. 
Sept. 
June 
June 
June 
June 
June 
June 
June 
July 



3, 1882 
16, 1888 
27, 1881 
27, 1881 
27, 1881 
27, 1881 
10, 1876 
10, 1876 
10, 1876 

26, 1886 



TABLE III 

MAXIMUM INTENSITY OF RAINFALL FOR PERIODS OF 5, 10, AND 
60 MINUTES AT WEATHER BUREAU STATIONS EQUIPPED WITH 
SELF-REGISTERING GAGES, COMPILED FROM ALL AVAILABLE 
RECORDS. 



5 Minutes 



10 Minutes. 



60 Minutes. 



Bismarck 9 . oo 

St. Paul 8.40 

New Orleans 8.16 

Milwaukee . . 7 . 80 

Kansas City 7 . 80 

Washington 7 . 50 

Jacksonville 7 . 44 

Detroit 7 . 20 

New York City 7 . 20 

Boston 6.72 

Savannah 6 . 60 

Indianapolis 6 . 60 

Memphis 6 . 60 

Chicago 6 . 60 

Galveston 6 . 48 

Omaha 6 . oo 

Dodge City 6 . oo 

Norfolk 5-76 

Cleveland 5 . 64 

Atlanta 5 . 46 

Key West 5 . 40 

Philadelphia 5 . 40 

St. Louis 4 . 80 

Cincinnati 4.56 

Denver 3 60 

Duluth 3.60 



6.00 
6.00 
4.86 
4. 20 
6.60 



.08 
.00 
.92 



2 .OO 
1.30 
2.18 

1-25 
2.4O 
1.78 
2 . 2O 
2.15 



4.98 
6.00 

3-9 
4.80 

5-92 
5.58 
4.80 
4.20 
5.46 
3.66 
5.46 
4.80 
4.02 
3-84 

4. 20 

3-30 
2.4O 



I. 60 

1.68 

2. 21 



I. 60 

1.86 
i. 60 
2-55 
i-55 
i-34 
i-55 

I . 12 

1-50 
2.25 

1-50 
2.2 S 
1.70 

1.18 
i-35 



36 



SEWER DESIGN 



hurricanes. They are more abundant on the Gulf and South 
Atlantic coasts than at inland points." 

This report shows for Washington, D. C., 73 storms rain- 
ing at the rate of i inch per hour or over in fifteen years before 
January i, 1897. For Savannah, 62 in eight years; for St. 
Louis, 36 in the same time. To show that the intensity becomes 
a maximum as the time of the storm becomes less, the table 
opposite is given. 

Table III from the same Bulletin shows, in another form, 
the same thing. It gives the maximum intensity of rainfall 
for periods of five, ten, and sixty minutes at Weather Bureau 
stations equipped with self-registering gages, and is compiled 
from all available sources. 

Table IV, abridged from a paper by C. W. Sherman * on 
" Maximum Rates of Rainfall at Boston," shows again the 
relation between the intensity and length of the storm. 

TABLE IV 

MAXIMUM RATES OF RAINFALL, AUTHENTICALLY REPORTED 
FOR THE EASTERN UNITED STATES 



Duration 
in minutes 


Rate, inches 
per hour 


Place 


' Date 


Reported by 


4 


8.40 


Philadelphia. . . . 


Aug. 3, 1898 


Webster 


5 


8.16 


1 1 


Aug. 3, 1898 


Webster 


5 


8.50 


" 


Sept. 14, 1904 


Webster 


5 


8.40 


Boston 


July 18, 1884 


Sherman 


15 


9. 20 


Embarrass, Wis . 


May , 1881 


Allen 


15 


Q.OO 


Sandusky, O . . . . 


July, , 1879 


Allen 


20 


6.78 


Brattleboro, Vt. . 


July 7, 1897 


Allen 


25 


6.00 


Kansas City, Mo. 


May 12, 1886 


Allen 


25 


5.76 


Indianapolis, Ind. 


July, 1876 


Allen 


3O 


< 6O 






Hoxie 


O 

27 


ww 
q 80 






Talbot 


O 1 

60 


o uw 
4ro 






Talbot 


70 


o 
3-78 






Talbot 


75 


4.02 






Nipher 


no 


2-95 


Philadelphia. . . . 


Aug. 3, 1898 


Henry 


I 20 


7 OO 






Hoxie 




O '-"-' 









Heavy rains at the Chestnut Hill Reservoir in Boston 

* Trans. Am. Soc. C. E., Vol. LIV, p. 212. 



EXCESSIVE RAINS 



37 



have been reported as follows, the figures given showing the 
intensity in inches per hour:* 







Duration. 






20 Min. 


30 Min. 


60 Min. 


August, 1899 . . 


4.80 


3.40 


2 . IO 


August, 1892 


2.55 


2.54 


I. 60 


July, 1880 


3.06 


2 . 34 


I ?"? 


July, 1894 


3 24 


2. 2O 


I . 13 











From St. Louis, Mo., the following data f are reported by 
W. W. Horner, Asst. Engr., St. Louis Sewer Department, the 
figures again expressing intensity in inches per hour: 



Duration. 



Date. 


10 Min. 


30 Min. 


60 Min. 


1897 


5-58 






1898 


6.00 






1900 


5-40 




2.8 5 


1900 


5-22 


2. 5 6 


1-49 






2 8l 




I on 2 




2 .02 


1 .40 


1907 


5-4 


2.80 


i-59 


1908 




2.18 




IQOQ 






i .37 











A. J. Mitchell, of the U. S. Weather Bureau Station at 
Jacksonville, Fla., reports J the following high rates in the 
several cities mentioned, in addition to those already quoted 
by Mr. Sherman in Table IV: 











Intensity 


Location. 


Date. 


Amt. of Rain. 


Duration. 


in Inches 










per Hour. 


Washington, D. C 


June, 1 88 1 


2 . 34 inches 


37 min. 


3.78 


Biscayne Bay, Fla 


March, 1874 


4.1 " 


30 " 


8.2 


Newton Pa 


Aug., 1843 


55 " 


40 " 


8.25 


Galveston, Tex 


June, 1871 


3-95 " 


14 " 


16.8 


Concordia, Pa 


Aug., 1843 


16.0 " 


3 " 


32.0 



* Engineering Record, Vol. XL II, p. 29. 

f Engineering News, Vol. 64, p. 329. 

J Engineering Record, Vol. XL VII, p. 539. 



38 SEWER DESIGN 

Mr. Mitchell very properly points out that while the 
occurrence of very heavy rains lasting a few moments only is 
interesting, such rains have but little practical significance, both 
because they occur at such infrequent intervals and because they 
affect so limited an area. He also recalls that such extraordinary 
occurrences are considered by the courts before whom suits 
for damage have come * as beyond the need for considera- 
tion in engineering work, being thus classed with earth- 
quakes, fires, strikes and other calamities impossible to 
foresee. 

Mr. J. N. Hazlehurst, in studying the question of excessive 
rains for the purpose of designing sewers for Mobile, Ala., 
found f that the maximum intensity for a storm lasting for thirty 
minutes was 3.1 inches, for sixty minutes, 2.7 inches and for 
1 20 minutes 1.5 inches. He concluded, however, that such 
storms were so infrequent as to be not worth considering and 
he assumed an intensity of 1.5 inches per hour as a practical 
maximum to be cared for in designing the sewers. 

The first extended and detailed study of the excessive 
storms for a single locality was made in 1889 by Emil Kuichling, 
C. E., who included in his elaborate report to the city of Rochester 
on the East Side Sewer a discussion of the probable rainfall, 
and the amount of storm-water to be expected. His work, 
based on the records of the Weather Bureau at Rochester, 
Oswego, and Buffalo, and on other records kept at Cornell 
University, Mt. Hope Reservoir, Hemlock Lake, and by two 
special employes of the city, emphasizes the fact, as just given, 
that the rate of rainfall varies with the unit of time chosen 
for the rain-measurement, and that for the greatest intensities 
a shorter period than an hour must be chosen for a unit. He 
also points out that the area covered by a storm is of limited 
extent, and that the heavier the rate of fall, the less the area 
affected. From his observations, however, he finds that gen- 
erally the clouds which furnish the rainfalls of large rate extend 

*i 33 N. W. Rep. p. 835; 32 N. Y. p. 489. 
t Engineering News, Vol. XL VI, p. 26. 



EXCESSIVE RAINS 39 

farther than any single drainage-area within ordinary municipal 
limits. 

The relation between the intensity of a rain and the duration 
of that intensity, shown by Table III above, was brought out by 
Kuichling very clearly, by means of which he finds a method 
of determining the duration of any rain of a given assumed 
intensity. A similar method is generally applicable. The 
exact relation is unreliable, as it varies in different localities, 
and, the data being uncertain, it is probable that for some time 
to come conclusions will be only approximate. The method 
outlined is, however, the best available for gaining this first 
step in determining the amount of rain to be considered in the 
sewer design. 

The method may be reduced to the following: First collect 
all the rainfall statistics that are available for the city in ques- 
tion and for any other places that are in the same locality and 
under the same meteorological conditions. Unfortunately 
such data are usually defective in accuracy and in the time 
covered, but no other method will ever give as good results 
as a study of past records. With all the available data at hand, 
compute the intensities of all rainfalls whose rate of fall is 
greater than J inch per hour, regardless of the duration of the 
storm, and for every recorded storm, plot a point on cross- 
section paper with the intensity as ordinate and the duration 
of the storm as abscissa. A number of points, each correspond- 
ing to a storm, are thus obtained. The rainfalls of low intensities 
are, of course, most frequent, so that that part of the diagram 
will be well studded with points; but the isolated points repre- 
senting the heavier rains will usually be sufficient in number 
to show that the shorter rains and heavier intensities correspond, 
and that there is some proportionate relation between the two. 
By joining the points by a series of broken lines, selecting those 
points which represent the greatest recognized intensities for 
that time, an irregular envelope is found, the ordinates of which 
give the probable maximum intensities for that locality for the 
corresponding period of time. This envelope is only located 



40 



SEWER DESIGN 



with judgment, and it may be necessary to omit two or three 
uncommon and rarely severe storms. 

Several years ago Prof. A. N. Talbot of the University of 
Illinois made use of the U. S. Weather Bureau records for the 
group of States considered, in making a study of the maximum 






\ 





























\ 
, \ 


























1 
1 




\ 








STORM INTENSITIES 

IN NEW ENGLAND 





! 

f 




\ 

\ 








? ; 





, 


V 




AND ATLANTIC STATES. 


of 










\ 

\^ 











o$ 








* 





\ 

V 




















v 


V 
t\ 











S 
\ 


















* 


J.\ 

, 















X 
N 
























?*; 






? 






> 


> 


x ^^ 






















^ 












. 








*"-- 


. 


^_ 


-. M 










' 



^v 



>. 







\: 


:: : 





" 

























- 


-- 












































DURATION OF STORM IN HOURS. 
FIG. 5. 

intensity of storms, and published his results in the Technograph* 
The records of these stations range from i to 50 years and include 
those from 499 stations. After the storms were plotted as 
indicated above (see Fig. 5), two enveloping curves were drawn, 
one giving what might be called the very rare rainfalls, and the 
other the ordinary maximum. The curves drawn were in 



* Technograph, 1891-1892, pp. 103-117. 



EXCESSIVE RAINS 41 

both cases rectangular hyperbolas. After drawing the two 
curves their equations were determined to be 



for the curve of rare occurrence, and 

y = ^g_ 

for the rains of frequent occurrence, where y is the rate of rain- 
fall in inches per hour, and x is the duration of the storm in 
minutes. The two curves give the following comparisons, 
which Prof. Talbot says are found to hold pretty generally 
throughout the country in spite of great differences in the total 
annual rainfall. 

10 minutes' duration, 9.0 or 4.2 inches rate 
20 " " 7.2 or 3.0 

30 " " 6.0 or 2.3 

45 " " 4.8 or 1.7 

60 " " 4.0 or i. 4 

In checking his two curves it was noted that they were 
drawn so that the rainfall shown by the upper curve of max- 
imum rain would be exceeded once in 83, 107, 100, and 91 years 
for the North Atlantic, South Atlantic, Gulf, and North Central 
States, respectively; and that the other curve would be exceeded 
once in 3.6, 3.1, 3.8, and 3.7 years for the same group of States, 
respectively. 

In commenting on the individual city records, Prof. Talbot 
says: " In summarizing the data of seventy-one years of rain- 
fall of self-recording gages shown on these diagrams, it may be 
noted that the curve of rare rainfall has not been reached in a 
single instance, and that the curve of ordinary maximum rate 
of rainfall for periods of less than forty minutes has not, with 



42 



SEWER DESIGN 



one exception, been exceeded in any marked degree. It is 
further probable that in each of these cities storms giving rates of 
rainfall for any length of storm up to forty minutes will reach the 



values given by the curve y = 



105 



at least as frequently as 



two or three times in ten years." 

In St. Louis Prof. Nipher has used the same method to 



STORM INTENSITIES 

AT 

ROCHESTER, N. Y. 




3 4 5 

DURATION OF STORM IN HOURS. 
FIG. 6. 



determine the probable intensity for a given duration, and has 
plotted the storms of that city in the manner indicated above. 
He also assumed an equilateral hyperbola as the enveloping 
curve, and determined its equation to be ^# = 360. This was 
made up from the rainfall records of St. Louis extending over 
a period of forty-seven years. 

Kuichling plotted (see Fig. 6) the local data of Rochester 
combined with that of two neighboring stations, and used two 
straight lines as, the envelope of the points instead of the hyper- 



EXCESSIVE RAINS 



bola used formerly.* These two lines meet at a point of the 
diagram representing a duration of one hour and an intensity 
of .87 inch. The line to the left of the point of intersection 
is quite steep, while that on the right is more nearly horizontal. 
The combination shows very clearly that the maximum intensity 
of the rainfall diminishes rapidly as the duration increases from 
a few minutes to an hour, and that for rains of uniform intensity 
lasting more than one hour the rate of diminution is quite 



RELATION BETWEEN 

INTENSITY AND DURATION 

OF VARIOUS STORMS 

CHESTNUT HILL RESERVOIR, 
BOSTON 
1879-1901 




1 2 

Duration of Storm in Hours 

FlG. 7. 

slow. By getting the equations of the two enveloping lines, he 
has for storms of less than one hour ^ = 3.730.05060;, and 
for those over one and less than five hours the relation 
;y = 0.990.0020;. Repeating the work for Rochester alone, 
he gets y 2. 10 0.02050;. Kuichling distinctly states that 
no great accuracy can be claimed for this formula, nor can he 
recommend it for general use, despite its great value in the 

* See Trans. Am. Soc. C. E., Vol. XX, p. i. 



44 



SEWER DESIGN 



connection for which it was made. " It is/' he says, " merely 
an attempt to utilize the available data as to the local rainfall 




o o 

jnow J9d sauoui ui iiDiuioy jo 



in a rational manner, and to remove the subject of urban 
sewerage from the realm of vague conjecture." 

Fig. 7 shows a diagram from the paper* by C. W. Sherman 

* Trans. Am. Soc. C. E., Vol. LIV, p. 176. 



EXCESSIVE RAINS 



45 



already referred to, based on rainfall records at Chestnut Hill 
Reservoir at Boston. His equations, in logarithmic form, 

are y = - o687 , for rains of maximum intensity for any period, 

*v 

and y = ' 687 for rains giving the greatest intensity of pre- 

00 



STORM INTENSITY AT 
WASHINGTON AND BALTIMORE 
Washington Storms = 




1 2 

DURATION OF STORM IN HOURS 
FIG. 9. 



cipitation which it would ordinarily be necessary to consider 
in engineering design. 

Figs. 8 and 9 show similar diagrams from the report of the 
Sewerage Commission of the City of Baltimore, 1897. 

Fig. 10, prepared * by Mr. George S. Webster, Chief Engineer, 

* Trans. Am. Soc. C. E., Vol. LIV, p. 210. 



46 



SEWER DESIGN 



Bureau of Surveys, Philadelphia, shows three curves, the 
upper one for the storms of maximum intensity observed for 
the nine years for which self-registering rain-gages made 



m 



s 

o 

a 
I 2 

t! 



exact records possible. The middle curve represents storms 
of extraordinary rainfall, occurring about once a year. The 
lower curve represents the maximum intensity of ordinary 



EXCESSIVE RAINS 



47 



storms. The equations for the three curves are y= 



05253 

00 



y = , and y = > respectively. 

Fig. n, from an article * by J. de Bruyn-Kops, of Savannah, 
Ga., shows even more markedly the variation in the position 
of the curve, depending on the number of infrequent, isolated 



RELATION BETWEEN 

INTENSITY AND DURATION 

OF VARIOUS STORMS 

SAVANNAH, GA. 
1889.1906 




Maximum 

Once in 2 years 
Once in each year 

each year 
3 times each year 
A times each year 
times each year 



30 45 

Duration of Storms in Minutes 

FlG. ii. 

storms of maximum intensity, which are chosen to locate the 
position of the curve on the diagram. In Fig. n there are 
seven curves, each one so drawn as to indicate definitely the 
intensities of. storms of designated frequency, varying from 
storms of such high intensity as to give absolute maxima for 
the seven years considered through those storms occurring once 

* Trans. Am. Soc. C. E., Vol. LX, p. 250. 



48 SEWER DESIGN 

in two years and once a year to storms as frequent as five times 
a year. The equations of Mr. Bruyn-Kops are shown in the 
following table: 

TABLE V 

TABLE SHOWING EQUATIONS FOR RAINFALL CURVES FOR STORMS 
OF VARIOUS FREQUENCY SAVANNAH, GA. 

Maximum storms y = - 

x+ig 

T^-, 

Storms occurring once in two years y- 



04. ' ' I 4 I 

Storms occurring once a year y = j 

Storms occurring twice a year y = 

Storms occurring three times a year y -- 



Storms occurring four times a year y = ~ 



Storms occurring five times a year y = 



#+16 



Fig. 12, from an article * by C. E. Gregory of the firm of 
Hering & Gregory, on " Rainfall and Run-off in Storm Water 
Sewers," shows some of the curves above referred to together 
with one by Edwin Duryea,f and three prepared by himself 
from various records of high intensity storms. His equations 

are y = ~r, y = ~Y an( ^ ^ = ~T f r the curve s numbered 4, 9, and 

*V vV *V 

8 respectively. The last is particularly selected as applicable 
to winter storms, the intensity of which is shown to be less than 
storms at other seasons of the year. By this diagram, it is 
seen that if the curves numbered 2, 10, and 3 are eliminated 
as giving excessive values for ordinary engineering practice; 
the others are similar both as to form and position on the diagram 
and the fact is thus emphasized that the curve must indicate 
to the best judgment of the engineer, not only the existing 
relation between the duration of the storm and its intensity, 
but also the frequency of the storms considered. 

* Trans. Am. Soc. C. E., Vol. LVIII, p. 458. 
t West. Soc. C. E., Vol. IV, p. 73. 



EXCESSIVE RAINS 



49 



The judgment of the engineer in placing the curve on the 
diagram is aided chiefly by a study of the possible damage to 
be done by a storm so great as to overflow the sewers and. 
fill the basements, injuring whatever may be housed there. 
Evidently, if a sewer capable of taking care of the largest storms 
known should cost $25,000 more than one sufficient only for 



1. Kuichling 
. Talbot 

3. Sherman 

4. Gregory 

5. Sherman 
ft, Talbot 

7. Duryea 

8. Gregory 

9. Gregory 
LO. Hering 




1 2 

Duration of Rainstorm in Hours 

FIG. 12. 

the maximum storms coming once a year, the cost of the 
occasional damage due to infrequent rains must not be less than 
the accumulated interest on $25,000 or the larger sewer is not 
worth what it costs. Mr. E. W. Clarke of the Board of Public 
Water Supply of New York City says * that the extent to 

* Engineering News, Vol. XLVIII, p. 388. 



50 SEWER DESIGN 

which the saving in the size of sewers occasioned by assuming 
storms of less than the absolute maximum is carried, must 
be offset by occasional damage suits, including costs, and an 
important factor in the latter is the use made of the buildings 
occupying the area drained. If the watershed were covered with 
business blocks, where extra stock was stored in the basements, 
and were subject to water damage, it might easily happen that 
one suit decided against the city would cost more than would 
justify the construction of the smaller sewer. In residential 
districts, on the other hand, an occasional flooding of the cellars, 
that is, once in three or four years, might cause comparatively 
little damage or even inconvenience. In Kansas City, Mo., 
the practice according to Mr. J. B. Balcomb * is to design the 
main sewers with the expectation of flooding every ten years, 
branch sewers every five years, and laterals every two years. 
The possible future development of a district must, however, 
not be lost sight of, nor the fact that sewers known to be 
inadequate and subject to overflowing may seriously affect 
real estate values and manufacturing enterprises and so indi- 
rectly be a source of loss to the city. 

When the curve has been finally fixed on the diagram show- 
ing rates of fall varying directly with the duration of the storm, 
what rate is to be taken as that by which the sewers are to be 
designed? Following Kuichling, the time by which the intensity 
is made determinate should be equal to that required for water, 
starting from the point on the line of the sewer farthest from 
the outfall to reach that outfall. It is plain that, considering 
the outlet-pipe, a maximum flow will occur when all the laterals 
are discharging their maximum at the same time. But as some 
laterals are near and some far away, it is possible for one set to 
have discharged its volume before the water from the more 
distant pipes has reached the outfall; so that a rain must 
continue at a definite rate for a definite time in order that 
the outfall discharge may represent the maximum discharge 
due to that rain-intensity. The time required must be that 

* Jour. West. Soc. C. E., Vol. XV. p. 706. 



EXCESSIVE RAINS 51 

necessary for water to flow from the farthest laterals. This 
time with its corresponding intensity will give the greatest 
probable discharge at the outfall. A secondary maximum 
may occur as follows: If a part of the contributing territory 
should be steep and near the outfall, it may be that the higher 
rain-intensity corresponding to the shorter time for that section 
will give more storm-water at the outfall than the less intensity 
over the whole section. It can be worked out by trial in a 
few sections and the rain conditions for the real maximum 
determined. The time required for the passage of the water 
from the farthest point to the outfall is a matter of trial and 
judgment. From five to eight minutes is allowed for the rain 
to pass along the ground from where it fell to the nearest inlet 
to the sewer or to the gutter if inlets are not located at each 
block corner. Two feet per second may be taken as a min- 
imum rate of flow in the sewer, and 15 feet per second as the 
maximum, but between the two the rate of flow will depend 
on the 4 surf ace grade and on the size of the pipe. Therefore 
the size and grade of the imaginary sewer must be assumed 
for a preliminary trial. From the surface grade and intensity 
thus established the sizes can be roughly worked out, and if 
very different from those assumed at first, the new intensity 
must be found and the sizes redetermined. It must be remem- 
bered that not all of the rainfall is carried off by the sewers,, 
and that only a certain proportion is to be considered, a subject 
taken up in the next chapter. 

It has been pointed out by some writers * that, since no rain 
can be assumed to flow uniformly for any length of time, but 
that rather it increases in intensity to some maximum and 
then decreases, it is an error to require the theory of the duration 
chosen to depend on the assumption that the entire area is affected 
equally by a storm of any certain intensity. It is argued that 
if a certain time is required for a drop of water to reach the 
outlet from the most distant point, then those distant points, 

* Engineering News, Vol. XL VIII, p. 387, Jour. Assn. Eng. Soc., Vol. XX,, 
p. 204. 



52 SEWER DESIGN 

were affected by rain of a different intensity from nearer points, 
which can discharge their share of the run-off only after the 
crest of the rainstorm has passed. By assuming a number 
of zones around the outfall, an additive method has been 
developed * by which each zone has its approximate duration 
and intensity. The resulting average time of concentration 
Is thus shown to be only about one-half that if the rain were 
assumed to fall uniformly for the entire period. It is believed, 
however, that such a refinement is not justified. There are 
rains falling with a maximum intensity almost uniformly for 
the short period involved in these studies. The rate of rain- 
fall is only one factor in determining the run-off and the other 
factors, such as slope, form of the tributory area, and character 
of the surface introduce such uncertainties that any attempt 
to subdivide the time of concentration into the time by zones 
Is more of theoretical mathematical interest than of real practical 
advantage/ Further, if another rate of rainfall than that 
shown by the observed time elapsing from the beginning of the 
storm to the time of the maximum flow in the sewer, checked 
in the case of Rochester at least by the actual time required for 
water to reach the outfall from the most distant point, is taken, 
then other values than those found in Rochester for the per- 
centage of the rainfall reaching the sewer must be taken. 

For an example of the use of the diagrams described above 
see Chapter XIV. 

PROBLEMS 

14. Using the data of Table II plot a curve similar to that shown in 
Fig. 4 and derive its equation in the form y = .. 

15. Plot the data of Table III, using logarithmic paper, and derive 
the equation of the curve passing approximately through those points 

a 
of the form y = -y. 

* Engineering News, Vol. LXI, p. 265; Engineering Record, Vol. LIX, p. 265; 
Trans. Am. Soc. C. E., Vol. LVIII, p, 458; Vol. LXV, p. 321; Jour. Ass'n Eng. 
Soc., Vol. XX, p. 204. 



EXCESSIVE RAINS 53 

16. Refer to the judicial decisions of p. 38 and summarize the 
opinion of the court in those two cases. 

17. From the publications of the U. S. Weather Bureau, secure data 

on maximum storms covering a period of 10 years for the city of 

Construct an intensity diagram and draw two curves, one for maximum 
storms, and one excluding storms more infrequent than once in 3 years. 

18. Change the form of the equations of Table IV to that of the 
equation for the Philadelphia curves, and judge of the frequency of 
"storms of extraordinary rainfall" by the comparison. 

19. If an extraordinary storm, occurring on the average once in 12 
years, might cause an estimated damage of $25,000, how much money 
might reasonably be spent on enlarging a sewer designed to safely carry 
storm water from maximum storms occurring once in 3 years? 

20. Using data from Monthly Weather Review plot curves for three 
typical storms in order to show the relation between duration and intensity 
for any one storm. 



CHAPTER IV 
PROPORTION REACHING THE SEWERS 

THE maximum intensity of the rainfall to be cared for by 
the sewer having been determined, either by carefully examining 
the tabulated records or by making a diagram of the storms, 
as indicated in the last chapter, the other part of the problem, 
already stated, needs to be solved, viz., what proportion of the 
amount of rain fallen reaches and is carried off by the sewer, 
and at what rate of flow does the discharge take place? Evidently 
these are variable quantities, depending on many unknown 
conditions. The general slope of the surface, its geological 
character, its physical condition, whether paved or unpaved, 
the amount of roof and yard surface compared with lawn 
and garden surface, the grade of the lateral sewers, and the 
temperature of the air as affecting evaporation, will all influence 
that proportion. Perhaps more than any other condition, 
the previous state of the atmosphere will affect this amount. 
If there has been for some time before the excessive rain a steady 
drizzle, so that the ground has been well soaked and made 
partially impervious, the amount afterward absorbed by the 
soil is very small and the sewer receives a correspondingly larger 
amount of water. It is therefore impossible to say, even with 
a surface of known slope or known physical conditions, that 50 
or 70 or 90 per cent of a rainfall will enter the sewer, because 
no account can be taken of the soil permeability.* The only 
absolute conditions occur when there is no exposed surface, 
that is, when the district is entirely covered with roofs; then, 
of course, all the rain is discharged at once into the sewers. 

One method suggested for determining the rate of discharge 
is to compare the time required for discharge with that required 

* Jour. West. Soc. C. E., Vol. IV, p. 152. 

54 



PROPORTION REACHING THE SEWERS 55 

for the rain to fall; but this relation, depending as it does on 
the conditions already mentioned, is uncertain, and therefore 
the method cannot be regarded as reliable. It has, however, 
been stated that, judging from the limited number of observa- 
tions accessible, in none of which was the time for discharge 
from the sewers as short as twice the duration of the storm, 
but rather exceeding this three, four, and five times, it is always 
possible to divide the rate of rainfall by at least two to get the 
rate of discharge. But this must be the result of imperfect 
observations and inattention to details. Col. Adams reports 
using a series of gagings made in London by Mr. Wm. Hay- 
ward, Engineer to the Metropolitan Board of Works, London, 
and designing the Brooklyn sewers to carry off one-half the 
rainfall, believing from his study of those gagings that his 
sewers would have twice as long to discharge the rain as it takes 
to fall. Therefore, having decided that a rainfall of i inch 
per hour was to be expected with sufficient frequency to make 
a provision for it desirable, he made the sewer of such size as 
to take care of half an inch per hour over all the territory drain- 
ing to that sewer. Other English experiments, which are given 
by Baldwin Latham, and on which most of the work done in 
this country has apparently been based, were made in London 
in 1857. Here the Savoy Street sewer, draining an entirely 
built-up part of London, discharged from a rainfall of i 
inch in one and a quarter hours 0.34 cubic foot per second, 
or 34 per cent of the rainfall. Later Sir Jos. Bazelgette, in 
the Savoy Street and Ratcliff Street sewers, determined that 
from rainfalls of 2.9 inches in thirty-six and twenty-five hours 
there was discharged an average amount equal to 64.5 and 
52 per cent respectively. From these gagings and a few 
others the engineers of the London Main Drainage Works 
concluded that a rainfall of 0.25 inch would discharge 0.125 
inch, while one of 0.40 inch might discharge 0.25 inch. In 
1865 Col. Wm. Hayward published a gaging of another Lon- 
don sewer, showing that of a rain of 2.75 inches in thirty-six 
hours 53 per cent was discharged, and in 1858 of a rain of 0.24 



56 SEWER DESIGN 

inch the same sewer discharged 74 per cent; and in the same 
year the Irongate sewer, from a district entirely paved and 
built up, discharged 94 per cent of a rainfall of 0.54 inch in 
five hours, and in August the same sewer discharged 78 per 
cent of a rain of 0.48 inch in 1.67 hours. Kuichling, in citing 
these records, notes the absence of details as to the character 
of the rain, manner of observation, location of gages; and 
suggests possible inaccuracies in the recorded percentages. 
He quotes another gaging by John Rae, C.E., engineer of the 
Holborn and Finsbury sewers, who states that during the con- 
tinuance of a rain of i inch per hour 41 to 54 per cent of the 
precipitation will reach the sewer, according to the amount 
of garden or lawn surface upon the drainage area. Kuichling 
adds: 

" Upon the foregoing indefinite data, which may be found 
quoted more or less extensively in nearly every treatise on 
sewerage, and in most of the elaborate reports, engineers have 
hitherto been content to rely, and thus it has come to be in some 
measure traditional that about 50 per cent of the rainfall will 
run off from urban surfaces during the progress of the storm, 
while the remainder may follow at leisure." Until the recent 
(1889) work of Mr. Kuichling, this has been undoubtedly true, 
and in Providence, Brooklyn, St. Louis, and other cities the 
old sewers, often gorged and overflowing, have proved that 
the old assumptions in regard to rainfall are not accurate, but 
require modification. Of late a German formula has been much 
used, in which the coefficients may be modified for different 
kinds of surface, and the amount of run-off considered in the 
design has thereby been much increased. The discussion of 
this formula is reserved for the next chapter. 

Kuichling proved by his experiments at Rochester that 
these inconsistencies and failures were due to the unit period 
of time used both for the rainfall and for the gagings. He 
observed that the volume of water discharged at different 
stages at the mouth of an outfall sewer increased and diminished 
directly with the intensity of the rain, and that a certain time 



PROPORTION REACHING THE SEWERS 57 

was required in each case before a change in the rate of rain 
was manifested in the outlet. In preparing the design for the 
East Side Sewer an extensive series of observations were car- 
ried out, containing valuable data and contributing largely to 
our knowledge of the subject. The four rain-gages, already 
alluded to, gave him as accurate a knowledge of the rainfall 
as was possible without automatic gages. Simple self-recording 
gages were placed in the principal outlet sewers of the East 
Side, and the cross-sections, dimensions, and slopes of those 
sewers were all carefully determined. It was noted even with- 
out the gage-reading that slight variations in the rate of pre- 
cipitation were quickly felt in the sewers, and the flood-heights 
therefore were due to the maximum intensity of the rain, 
usually lasting but for a few moments, and not to the average 
intensity for the whole period of the storm. Moreover, the 
periods of maximum intensity of rainfall corresponded closely 
with the period of maximum discharge, and in a rain of varying 
intensity the volume of sewer-discharge followed the rain in 
parallel waves. 

The drainage-areas were carefully determined, so that the 
actual volume of the rain falling was obtained, and the amount 
discharged was calculated by Kutter's formula from the height 
of flow in the sewer, as shown by the gage, and from the hydrau- 
lic slope of the sewage. During 1888, 17 storms were gaged, 
their intensities varying from 0.24 inch to 3.20 inches per 
hour in the different sewers. A summary of the results is given 
in the following table, for which Kuichling claims no great 
accuracy, since the amounts of the intermediate showers were 
not always well known, though the totals are reliable. They 
are well worth regarding, however, as being the only careful 
records of the relation of rainfall to sewer-discharge that are 
available. 

It can be seen on inspection that the discharge from District 
X is invariably the largest, accounted for by the fact that it 
has the largest proportion of roof-surface and other impervious 
ground-covering. The effect of a light rain immediately pre- 



SEWER DESIGN 



TABLE VI* 

SHOWING THE COMPUTED PERCENTAGES OF THE HEAVIEST 
RAINFALL DISCHARGED FROM FIVE DIFFERENT CITY DIS- 
TRICTS BY THE RESPECTIVE OUTLET SEWERS DURING 
THE PERIOD OF MAXIMUM FLOW, ALSO THE AVERAGE 
VALUES OF SUCH PERCENTAGES. 

Arranged with reference to duration of heaviest rainfall. 



Date. 


Maximum 
Intensity of 
Rainfall. 
Inches per 
Hour.- 


Duration of Rain at 
Maximum Inten- 
sity. Minutes.' 


Percentage of Rainfall Discharged. 


8>* 

rt K tn 
~ 

'C "0 


rtw 


|| 
Si 


.0 

fi 

^00 > 


.d 

> . c7 

PO Ov . 


H H od 


c M - 


c $ 


Q 


Q 


Q 


Q 


5 


Dec. 10, 1887 
Sept. 16, 1888 


0.31! 
o.47t 


60 
5 


13-8 
19.8 


24.1 
38.2 


58.2 


41 .6 


26.0 

37-2 


Averages 


55 


16.8 


3I-I 


58-2 


41-6 


31.6 


May 9, 1888 


i. 315! to 0.75! 


35 


16.4 


26.2 


52.1 


29.0 


26.0 


April 5, 1888 
May 12, 1888 


0.24f 

0.30! 


30 
30 


iQ-4 15-5 
ii .0 15.8 


35-3 


38.2 
29.6 


20.8 

17.0 


Averages 


30 


10.7 


15-7 


35-3 


34-9 


18.9 


June 24, 1888 
June 28, 1888 


2.62^ 
o.Sot 


20 
20 


6-3 
14-3 


21 . I 

28.7 


35-2 


I3-2H 
35-2 


ii. 8H 
37-4 


Averages 


2O 


10.3 


24.9 


33-6 


24.2 


24.6 


June 2, 1888 
July n, 1888. . . . 
Aug. 16, 1888 


0.40! 

o-76 


15 
IS 
15 


5-5 
7-4 
4-7 


9.0 
I 5 .8 
12-5 


41.2 
24.7 


37-5 

21.8 

18.0 


8.7** 
19.4 

19-ilF 


Averages 


15 


5-9 


12.4 


32-9 


25-8 


19.2 


May 4, 1888 
May 26, 1888 
Aug. 4, 1888 
Aug. 26, 1888 


0.30! 
i .oof 

a'soll 


13 

12 
14 


6.8 
8.6 
4-6 
4.0 


14-4 
25.9** 
IO.O 
12. 2 


64.8** 
31-8 

33*511 


36.1** 
18.7 
15.0 

13-811 


28.2** 

ii. 7 

13-8 

12-311 


Averages 


13 


6.0 


12 . 2 


32.6 


15.8 


12.6 


July 18, 1888 
Aug. 17, 1888.... 


o.7St 
i-33t 


IO 
IO 


7-6 
5-5 


12 . 2 

8.7 


25.0 
18.4 


14.8 
11.9 


10.3 

8.9 


Averages 


10 


6.5 10.4 


21.7 


i3-3 


9.6 


Probable time required for concentration of 
flow at gages. Minutes 


44 


26 


16 


23 


24 



* From Kuichling's Report, p. 165. t Preceded and followed by lighter rain. 

J Sudden shower followed by lighter rain. Heavy shower preceded by lighter rain. 
|| Intensity roughly estimated. 

Tf Sewer here ran under head; percentage is computed from maximum discharge 
without head previous to surcharge. 

** Figures obviously too high or low, and rejected in deriving averages. 



PROPORTION REACHING THE SEWERS 59 

ceding is clearly seen, and the variation in the percentages 
discharged from the same district. From the most urban 
district the maximum discharge was 58.2 per cent of the 
rainfall, and from' the most rural it was as low as 4.0 per 
cent. 

The following gives the general characteristics of the several 
drainage districts (Kuichling's Report, Table XIX). 

District I. About one-half of this area has a dense popula- 
tion, averaging about 35 per acre, and is well developed, while 
the remainder is thinly settled, with much agricultural or 
vacant land. Nearly all of the existing streets are sewered or 
graded, but only a small proportion of the aggregate length is 
improved with macadam, the rest having earthen roadways. 
Soil-surface is generally clayey loam, interspersed with some 
gravel. Surface slightly undulating, the average slope of the 
sewered streets being about 1:150. Sewer-grades range from 
1:47 to i: 910. Outlet sewer is of good rubble masonry with 
flat segmental invert of brick. Length of main and tributary 
sewers at Gage No. 2, is 10.35 miles. 

District IV. Area is generally well developed, beginning in 
the central portion of the city and extending northerly to 
Gage No. 8, in the form of a comparatively narrow strip 
about 4800 feet long by 1 200 feet wide on the average. All 
of the streets are sewered and graded, and about one-third the 
aggregate length is improved with stone block, asphalt, macadam, 
and gravel pavement, the macadam, however, predominating; 
the remainder of the streets have common earthen roadways. 
Along the principal street (North Avenue) many large business 
blocks have been built, but the rest of the territory is occupied 
chiefly by residences. The population may be taken at about 
32 per acre. The houses are generally large, and lots of medium 
size. Below Gage No. 8 few of the streets are improved, 
and there is considerable vacant land. The soil is mainly a 
clayey loam, with muck in the lower portions. The surface 
slopes gently to .the north as far as the N. Y. C. & H. R. R. R., 
and then becomes very flat. The average grade of the streets 



60 SEWER DESIGN 

is about i : 130, and the sewer-grades range from i : 50 to i : 630. 
At the gages the outlet sewer is of good rubble masonry with 
flat and somewhat irregular rocky bottom. Length of main 
and tributary sewers at Gage No. 8 is 4.37 miles. 

Districts IX and X. Discharge measured by Gages Nos. 18 
and 19, in East Main and Alexander Street sewers respectively. 
The former serves a small but densely populated area traversed 
by the principal street, while the latter serves a large and well- 
developed residential district. In District IX the sewer grades 
range from i : 54 to i : 400, and the average surface-slopes of the 
streets is about 1:151; and in District X the sewer-grades range 
from 1:70 to 1:330, the average surface-slope being 1:172. 
From its general character this latter district should give the 
greatest percentage of rainfall-discharge, as the amount of 
roof-surface is here proportionally the greatest. The length 
of main and tributary sewers at Gage No. 18 is 0.76 mile. 

District XVII. Discharge measured by Gages No. 30 
and 31 in the Griffith Street sewer. The tributary area is well 
sewered and developed, and the average density of population 
may be estimated at about 35 per acre. Every street has an 
improved roadway, about one-fifth of the total street-surface 
being asphalt, one-fourth stone block, and the remainder 
macadam and gravel pavement. Numerous large business 
blocks and apartment-houses are found on the territory, but 
the greater portion of it is occupied by residences, standing 
generally on lots of medium size, although in about twenty- 
five acres of the area the lots are very deep and afford oppor- 
tunity for additional streets. The surface-grades in about 
one-half of the area are of good inclination, while in the remainder 
they are rather flat, the average being about i : 240 for Gage 
No. 30 and i: 175 for Gage No. 31. Sewer-grades vary from 
i: 100 to 1:350. The soil is generally a clayey loam, and much 
of the rainfall is as yet absorbed into the ground. Length of 
main and tributary sewers at Gage No. 30 is 2.56 miles. 

In an article on flood-waves by Alvah Grover in the Trans. 
Am. Soc. C. E., Vol. XXVIII, an apparatus is described for 



PROPORTION REACHING THE SEWERS 



61 



automatically measuring the height of waves in sewers.* The 
heights thus obtained, plotted on the same sheet and to the 
same scale as the depths of rainfall, give at a glance the relation 
between the two. The article in question is largely devoted to a 
description of the apparatus, but the relation between five 
storms and the resulting sewage-flow is given. The largest 
percentage found is as follows: 



Date. 


Duration by 
U. S. Weather 
Bureau. 


Amount of 
Rainfall by 
Writer's 
Gage. 


Duration of 
Disturbance 
in Sewer in 
Seconds. 


Per Cent of 
Total Rainfall 
Discharged 
Reg. by Gage. 


Sept. 27, '92. .. 


2 hr. 55 min. 


0.32 inches 


22,853 


60.6 



Fig. 40 shows the daily record of sewage-flow as recorded by 
the apparatus. 

It is interesting in this connection, although the percentages 
have no bearing on the present question, to compare the results 
of the gaging of the Sudbury River watershed, as given in 
the Geol. Report of N. J., Vol. II, p. 6, with like data of 
many other streams (see Table VII). 

The tables following illustrate a relation between the rain- 
fall and the discharge of a watershed of 78 square miles, very 
similar to that at first thought to exist between the same 
quantities in the case of sewers, and show that while the annual 
average holds not far from 50 per cent, the monthly relation is 
much more variable. In the case of sewers, in order to reach 
the true relation between the rain and the discharge, the unit 
time must be reduced from the month not only to the day and 
hour, but to the five-minute or minute interval. 

Baumeister in considering this subject says: "In England 
from o to 70 per cent of the rainfall reaches the drains, averaging 
about 50 per cent. In different districts of London from 
53 to 94 per cent has been registered. It required from three 
to four times the duration of the storm to carry off the water, 
and the maximum flow per second in the sewers rose as high as 

* At Omaha, Neb. 



62 



SEWEK DESIGN 



2.4 times the average, obtained by dividing the total effluent 
due to the storm by the number of seconds of flowing. Hence 

it will be seen that the necessary capacity will be 0.5 X =J 

o o 
of the rainfall per second. 

TABLE VII 

TABLE SHOWING THE RAINFALL AND STREAM-FLOW ON THE 
SUDBURY RIVER 



Month. 


1880 1881. 


1881 1882. 


18821883. 


1883 1884. 


1884 1885. 


December . 


2.83 0.31 


3.96 1.38 


2.30 0.56 


3-55 0.35 


5-17 1-65 


January . . . 


5-56 0.74 


5-95 2.21 


2.81 0.60 


5.09 1.76 


4.71 2. 2O 


February . 


4.65 2.49 


4-55 3-87 


3.87 1.66 


6-54 4-74 


3.87 2.18 


March .... 


5-73 7-14 


2.65 5.06 


1.78 2.87 


4.72 6.75 


1.07 2.81 


April 


2.OO 2.67 


1.82 1.50 


1-85 2.33 


4.41 4.93 


3-6i 3-13 


May 


3-5 1 i-72 


5.07 2 . 30 


4.19 1.67 


3-47 1-84 


3-49 2.38 


Tune. . 


C 40 2 31 


i .66 0.91 


2 . 40 0.52 


2 AX O 72 


2 8? O 7A 


July 


o *r w ^ o 
2.35 0.49 


1.77 0.15* 


2.68 0.21 


O * T"0 / ^ 

3.65 0.40 


* w / w . 1 1\ 

i . 43 o . i i 


August. . . . 


1.36 0.26 


1.67 o.io 


0.74 0.14 


4.65 0.46 


7.19 0.43 


September . 


2.62 0.34 


8-74 0.53 


1.52 0.16 


0.86 0.08 


1.43 0.21 


October. . . 


2.96 0.33 


2.07 0.53 


5 -60 0.33 


2.48 o. 5 


5.10 0.60 


November . 


4 . 09 o . 68 


1.15 0.36 


1.81 0.35 


2.65 0.30 


6.10 2.03 




43.06 19.48 


41.06 18.90 


31.55 11.40 


45.52 22.48 


46.04 18.47 


Month. 


1885 1886. 


1886 1887. 


1887 1888. 


18881889. 


1889 1890. 


December.. 


2.72 2.09 


4.98 1.82 


3-88 i. 15 


5-40 5-43 


3.14 4-00 


January. . . 


6.37 2.61 


5.20 4.62 


4.15 1.88 


5-37 4-96 


2.53 2.24 


February. . 


6.28 7.73 


4.78 4.56 


3.69 3.26 


1.66 1.93 


3.51 2.46 


March .... 


3.61 3.67 


4 . 90 5.12 


6.02 5.76 


2.37 2.39 


7 . 74 6 . 50 


April 


2.23 3.36 


4.27 4.52 


2-43 4-57 


3-4i 2.43 


2.65 3.24 


May 


3.00 1.29 


1.17 i . 80 


4.83 2.91 


2-95 i-57 


5-21 2.44 


Tune. 


I 47 O 35 


2 .65 O. 71 


2 . =54 0.73 


2 .80 I . 13 


2 .03 0.98 


July 


X ' *T / ^ * O3 

3.27 0.21 


3.76 0.20 


* OT- ** / O 
I .41 O. 21 


8-94 1-13 


2.46 O.I9 


August. . . . 


4.IO O.I7 


5.28 0.38 


6.22 0.68 


4-i8 2.55 


3.87 0.24 


September . 


2.91 0.2O 


1.32 0.19 


8.59 1.99 


4.61 1.42 


6 . oo o . 79 


October . . . 


3.24 0.26 


2.84 0.34 


4-99 3-57 


4.26 2.19 


10.51 4.05 


November . 


4.65 1.16 


2.67 0.64 


7.23 4.76 


6-29 3.35 


I . 2O 2.10 




43.85 23.104 


3.82 24.90 


55.98 31.47 


52.24 30.48 


50.85 29.23 



In a table for European cities the percentage of the rain- 
fall provided for varies from \ of a rainfall of 0.9 inch for 



PROPORTION REACHING THE SEWERS 63 

suburban territory in Berlin to J of a rainfall of 2.9 inches in 
Koningsberg 

After a careful study of his records Kuichling formulated 
the following conclusions: 

" i. The percentage of rainfall discharged from any given 
drainage-area is nearly constant for rains of all considerable 
intensities and lasting equal periods of time. This can be 
attributed only to the fact that the amount of impervious 
surface on a definite drainage-area is also practically constant 
during the time occupied by the experiments. 

" 2. The said percentage varies directly with the degree 
of urban development of a district, or, in other words, with the 
amount of impervious surface thereon. This fact is clearly 
shown by the large percentage derived from the relatively 
most developed district, X, in contrast with the smaller per- 
centages from the relatively less developed districts, IX, IV, 
and XVII, and the least improved district, I. 

"3. The said percentage increases directly or uniformly 
with the duration of the maximum intensity of the rainfall 
until a point is reached which is equal to the time recorded for 
the concentration of the drainage-waters from the entire tributary 
area at the point of observation; but if the rainfall continues at 
the same intensity for a longer period, the said percentage will 
continue to increase for the additional period of time, but at a 
much smaller rate than previously. In other words, the pro- 
portion of impervious surface slowly increases with the duration 
of the rainfall. 

" 4. The said percentage becomes larger if a moderate 
rain has immediately preceded a heavy shower, thereby partially 
saturating the permeable territory and correspondingly increas- 
ing the impervious surface. 

"5. The sewer-discharge varies immediately in all appre- 
ciable fluctuations in the intensity of the rainfall, and thus 
constitutes an exceedingly sensitive index of the rate and its 
variations of intensity. 

"6. The diagrams also show that the time when the rate 



64 SEWER DESIGN 

of increase in the said percentages of discharge changes abruptly 
from a high to a low figure, agrees closely with the computed 
lengths of time required for the concentration of the storm- 
waters from the whole tributary area; and hence the said 
percentages at such times may be taken as the proportion of 
impervious surface upon the respective areas." 

Since the early work of Kuichling in Rochester no similar 
work on a generous scale has been reported to the engineering 
world. In 1908, a committee of the Boston Society of Civil 
Engineers was appointed * to compile available data and to 
direct experiments to be made by members of the society, on 
this subject. Some work has been done, but no report published. 
Similarly, the Sanitary and Municipal Section of the Western 
Society of Engineers has undertaken to collect data from their 
members. The engineers in charge of sewer work in Phila- 
delphia, in St. Louis, in Cleveland, and doubtless in many 
other cities, have on hand experimental data giving valuable 
comparisons for those particular cities and is much to be hoped 
that they will some day allow them all to be published. The 
time may come when the uncertainties of the percentage of 
run-off to rainfall will be recognized as so great as to make 
values based on it useless. Then if accumulated records 
will allow, storm-water flow can be referred directly to area and 
surface conditions. Until such data are available, at all events, 
a percentage of the rainfall is the only known method of approx- 
imating to the truth. 

Three large districts of Chicago have been studied, the 
sewage measured and the rainfall gaged. L. K. Sherman 
presented the results f to the Western Society of Engineers, 
Jan. 15, 1912. The unit of time used however was the day 
so that the effect of short storms of high intensity is not shown. 
It was demonstrated that while the maximum rainfall was 
such as to deliver water to the area at rates of 95, 47, and 48 
cubic feet per second per square mile, the run-off was 50, 15, 

* Engineering News, Vol. LIX, p. 219. 

f Jour. West. Soc. Engrs., Vol. XVII, p. 361. 



PROPORTION REACHING THE SEWERS 65 

and 38 cubic feet per second, or 52, 32, and 78 per cent. These 
districts are 22 square miles, 8.3 square miles and 0.15 square 
mile in area, and the densities of population are given as 
19, 5.3, and 35 per acre, the last being in the centre of the 
business district of South Chicago. This verification of the 
work of the engineers of 1860 is a tribute to the work of those 
pioneers. 

Mr. Parmley, after much experience in Cleveland, believes* 
that, for safety in business districts, 100 per cent of the rainfall 
should be expected to reach the sewers. For residence districts, 
he suggests 20 to 50 per cent, although he says that where 
the lots are not large and the district is well built up, the per- 
centage of the rain entering the sewer may be 70 per cent. 

In Kansas City, approaching the problem from the other 
side, Mr. Balcomb f has assigned values to the amount of 
rain in inches per hour that may be expected to be absorbed 
by surfaces of various soils. Thus he assumes that paved 
streets absorb 0.50 inch per hour at the beginning of a storm, 
decreasing to 0.25 inch at the end of fifteen minutes, and that 
garden soils absorb i.oo inch at the beginning, decreasing to 
o at the end of 120 minutes. Most engineers, however, prefer 
the direct percentage, although absorption is undoubtedly 
one of its important factors. 

Some experiments were carried on by students { of the 
College of Civil Engineering (Cornell) in 1910, in which it was 
found that from a residential area of 42 acres on a steep side- 
hill, the maximum percentage of rainfall intensity shown in the 
sewage flow was 34.8. The resident population, exclusive of 
students, was 22 per acre, and was not different from other sub- 
urban property where there is one house and a lawn to every 100- 
foot lot with occasionally one not built on. In the thesis based 
on these experiments, it was pointed out that the needs of 
growing vegetation should be considered, since the amount 

* Jour. Assn. Eng. Soc., Vol. XX, p. 212. 
t Jour. West. Soc. Engrs., Vol. XV, p. 707. 
J Thesis by P. Z. Horton and R. Taylor, 1910. 



66 SEWER DESIGN 

of rain absorbed by grasses and vegetation generally was an 
important factor quite distinct from the amount of percola- 
tion into the ground. 

Mr. Alvord, who has had a long practical experience in the 
application of the theory of run-off to actual construction, 
lays great stress on the absorption capacity of the soil.* He 
believes that the earth becomes a great storage reservior after 
a dry season and may entirely absorb the water from a short 
storm. He shows that a certain district of Chicago, of an average 
residential character, would require by theory a sewer 8| feet 
diameter, but by reason of the soil conditions, the existing 
sewer 4 feet diameter, J the capacity, is found to be large enough. 

Mr. J. H. Fuertes f has reported that by actual measure- 
ments of rainfall and run-off, he found the percentage on an 
open field, of hard clay soil, covered with grass, on a 5 per 
cent slope to be 29 per cent, a high ratio for grass land. 

Perhaps no better summary can be had than that given 
by Professor Marston, who says: J " The most important part 
of this paper (by C. E. Gregory) seems to the writer to be the 
general presentation of the following principles: 

" First. The water falling on the so-called impervious area 
of an ordinary sewer watershed does not all run off as fast 
as it falls, but part of it accumulates in increasing quantities 
on the surface during downpours of moderate length, such as 
cause the maximum discharges from sewer districts of ordinary 
size. 

" Second. As the storm continues at the same rate, the ratio 
of run-off from the impervious area to the rate of rainfall 
increases, owing to the increased depth and velocity of the sur- 
face flow toward the sewer, until, finally, if the storm lasts long 
enough, the rate of run-off from the impervious areas becomes 
equal to 100 per cent of the rate of rainfall. 

" Third. The pervious area becomes more and more 

* Jour. West. Soc. Engrs., Vol. IV, p. 154. 
f Jour. West. Soc. Engrs., Vol. IV, p. 170. 
I Trans. Am. Soc. C. E., Vol. LVIII, p. 498. 



PROPORTION REACHING THE SEWERS 67 

saturated with water as the storm continues, and there will 
be a percentage of run-off from pervious areas increasing from 
o for short storms to quite a large percentage for storms last- 
ing several hours. 

" There can be no question as to the general truth of these 
three principles, but when the author (Mr. Gregory) attempts 
to go further and present definite curves and formulas, purport- 
ing to show the exact laws of change in the percentage of run- 
off with relation to the time elapsed since the beginning of the 
storm, the writer believes he is going beyond what the present 
meagre data from gagings of storm-sewers warrant. 

" These data are not very extensive, and the author himself 
points out their many defects. For many years engineers have 
been criticising the old run-off formulas, and new formulas, 
based on insufficient data, should be avoided. 

" All that engineers are at present warranted in doing is to 
make some deduction from 100 per cent run-off from the imper- 
vious areas for short storms in favorable cases, and some increase 
above o per cent (say varying up to 20 per cent for one-hour storms 
with average soil and slopes) in the run-off from the pervious 
areas for long storms, both the deduction and the addition being 
at present left to the judgment of the engineer, in view of his 
general knowledge and his familiarity with local conditions." 

To still further emphasize the fact that there is no infallible 
rule for predicting the percentage of rainfall for which sewers 
are designed, Mr. C. B. Burdick has prepared * the diagram 
shown in Fig. 13, which gives the practice of the various cities 
named in the matter of sewer capacity. Since the difference 
between the rainfall curves of various cities is rather a cjuestion 
of position on the diagram than of actual difference in rate of 
rainfall, the figure shows for a district of 100 acres (about 
20 blocks) a minimum run-off of 0.18 cubic foot per second at 
Gary and a maximum of 1.9 at Baltimore. If the time of 
concentration be taken at forty minutes for such a district 
(distance of flow would be about 4000 feet) and, from Fig. n> 

* Trans. Am. Soc. C. E., Vol. LVIII, p. 507. 



68 



SEWER DESIGN 



the rate of rainfall be taken at 2 inches, then the percentage 
for Gary is only 9^, while in Baltimore it is 95 and in St. Louis 
it is 70. With such variation in values, it seems hopeless to 




COO}" lOOTcOt COiO-*CO<M'-IOC"CC>t-COiO-*CO 
<M*. <M* J OJ r-5 r-5 r-5 rH rH r-5 r-5 r^ rH rH 

aao Y agd'oog aad.jgg.i oiqno tn^o-uny; 



extend efforts on perfecting details of any one factor while the 
combined factors give such widely different results. 

A proper solution of the problem calls for a careful study 
of the district to be drained, with careful attention to the soil, 
the shape, the slope, the relative amount of impervious area, 
all uncertain and not susceptible of mathematical expression. 



PROPORTION REACHING THE SEWERS 69 

With the effect of the size of the district, i.e., the time of con- 
centration, upon the rate of rainfall in mind, a proper value 
for the latter can readily be selected, but the proper percentage 
of this to be used in determining the size of the sewer is far 
more uncertain. The methods developed in the next chapter 
will be of service for such a purpose. 

PROBLEMS 

21. Show that for a rainfall of i\ inches per hour on an impervious 
area, the run-off is approximately 2\ cubic feet per second. 

22. From any city plan available, scale not less than 200 feet to the 
inch, determine the percentage of some district, of about 100 acres, that 
is devoted to street surface. 

23. In a residential district of a city, inspect three selected blocks, 
pacing distances between street centre lines and estimating as closely 
as possible the areas of roofs, determine the percentage of roof area and 
street pavement area to total areas of the blocks. 

24. Assume an area of 100 acres to be of three different shapes, wide 
and shallow, square, narrow and deep. Assume further that the path of 
the sewer may be either around the edge of the area or along a diagonal. 
Show how such changes would affect the time of concentration if the 
velocity remained the same. 

25. Assume a square area of sides equal \ mile and assume that 
this area has varying slopes from o to 10 per cent (take i per cent, 
2 per cent and 5 per cent as intermediate values). Assuming a rainfall 
to follow Fig. 6 (lower curve) with 35 per cent of the area impervious 
and the rest not contributing. Show the effect of the slope on the time 
of concentration and on the sewage flow. Establish a relation between 
Q and S. 



CHAPTER V 
RELATION OF DENSITY TO PERCENTAGE 

WHILE it is evident that more rain will be discharged into 
a sewer from a closely built-up territory than from an open and 
agricultural district, yet so far as the data of the last chapter 
go, no light has been thrown on the proper variation of the 
percentage as determined by the relative amounts of pervious 
and impervious surface. Our knowledge on this subject is 
due to Mr. Kuichling. 

If it is assumed, as indeed seems reasonable, that the 
density of population bears a direct ratio to the percentage of 
impervious area in a given district, and if that ratio is once 
determined under general conditions, the determination for 
other places of their population-densities will serve approx- 
imately, at least, by means of the same ratio, to determine 
the percentage of impervious surface also, and so the percentage 
of the rainfall discharged through the sewers. The relation 
between the population and the impervious surface was found 
by a laborious compilation of the amount and character of 
street-surface, roofs, lawns, gardens, etc., and of the population, 
all in typical districts, and by a reduction of all the areas of 
semi-impervious nature to the areas of impervious surface, 
equivalent in discharging power. It was assumed that the 
duration of the storms was such that even from impervious 
pavements not all the rain was discharged an assumption 
only justifiable in dealing with storms of great magnitude, 
whose duration is expressed in minutes. For long rains even 
garden or lawn surfaces may reduce the losses due to evapora- 
tion and surface inequalities, so that if the duration of the 
storm is sufficient, the surface becomes practically impervious; 
but in general such soils will absorb nearly all the rain falling. 

70 



RELATION OF DENSITY TO PERCENTAGE 71 

In some German practice it is customary to deduct such surfaces 
from the contributing area. 

The various kinds of relatively impervious surface found 
on urban territory were classified by Kuichling as follows: 

1. The different varieties of roofs from which nearly all 
water runs off. 

2. The first-class sidewalks and pavements, such as asphalt, 
and cut-stone blocks or brick with asphalted joints. 

3. The second-class sidewalks and pavements, such as the 
common Medina blocks with large open joints. 

4. The third-class sidewalks and macadam or gravel 
pavements. 

5. Ordinary graded roadways and similar surfaces. 

From the best pavements and sidewalks a considerably 
less proportion of water is discharged than from roofs because 
of the irregularities of surface and because of the absorption 
by the dust and dirt, even if the surface itself is practically 
non-absorbent. The other classes, of course, retain a still 
larger percentage, owing to deeper depressions and ruts and to 
the greater absorptive power of the material itself. 

By an analysis of the conditions in cities like Buffalo, Syracuse, 
and Rochester it was found that in well-developed city dis- 
tricts there are on an average 32 persons per acre.* With an 
assumption of 5.6 persons per dwelling, there should be therefore 
about six dwellings per acre in such territory. In the cities 
investigated it was further found that about 27 per cent of the 
entire area was occupied by public streets and alleys, of which 
43 per cent, or one-tenth of the entire surface, was provided 
with some kind of pavement varying in quality with the char- 
acter of the district. In the growth of cities this proportion 
is likely to increase, it was observed, until all of the 27 per 
cent has some more or less impervious pavement. A certain 
roof-area was assumed for the six dwellings, and that for an 
assumed business block or tenement added, with something 
more for possible barns or sheds for each acre, the result being 

* In Ithaca, N. Y., by actual count there are 26.2 in the residential district. 



72 



SEWER DESIGN 



that 1 8 per cent of the acre would probably be roof-surface. 
To this was added the impervious surface of the streets, which, 
with due allowance for the future, was taken as 16 per cent 
of the acre, making in all 34 per cent impervious, the rest being 
well-compacted earthen surfaces of back yards and courts 
which are specially drained. These last were taken to be of 
such a character and amount as to discharge rain-water from 
an area equal to 25 per cent of the whole. For a density of 50 
persons per acre it was assumed that there were no vacant 
lots, that both the dwellings and the business and apartment 
buildings were more crowded together, since the land is more 
valuable, and that therefore the roof-surface amounts to 28 
per cent of the acre. The amount of street-surface will not 
differ materially from the amount previously estimated, but 
nine-tenths of it, or 25 per cent of the whole, may be regarded 
as impervious. Since the yards are more likely to be paved, 
they may be considered to discharge an amount equal to 28 
per cent of the whole. Similar analyses were made for other 
densities, and the final relations determined on are as follows: 

TABLE VIII 



Average 
Number of 
Persons per 
Acre. 


Percentage of 
Roof-surface 
per Acre. 


Percentage of 
Improved 
Street-surface 
per Acre. 


Percentage of 
Hard-earth 
Streets and 
Yards per 
Acre. 


Total Percentage 
of Relatively 
Impervious 
Surface per 
Acre. 


15 


8.4 


7-4 


15.0 


30.8 


25 


14.0 


12.5 


21-5 


48.0 


32 


18.0 


16.0 


25.0 


59-0 


40 


22.5 


20.0 


27.5 


70.0 


5 


28.0 


25.0 


28.0 


81.0 



If the population-densities increase beyond 50 persons 
per acre, the roof and impervious street-surface will also increase 
up to a maximum, while the hard-earth surface will increase 
up to a certain point and then rapidly decrease, being replaced 
by a larger value of the other two factors, the open-earth space 
being taken up entirely with paved yards. The amount of 



RELATION OF DENSITY TO PERCENTAGE 73 

roof-surface and improved street-surface and paved yards 
seldom reaches 100 per cent, as there are always a few open 
spaces, gardens, small parks, etc., so that for areas of any 
magnitude, even in the largest cities, the limit may be set at 
90 per cent. The street-area cannot exceed 27 per cent of the 
entire area unless yards be included, when it may amount to 
40 per cent; and the roof-area will reach 60 per cent, as a 
maximum, for cities like Rochester. 

But the paved streets are not absolutely impervious, only 
relatively so, and the hard-earth yards, while allowing some 
rain to run off, also retain some, so that the percentages given 
above are only of the areas to be considered. It remains to 
determine what proportion runs off from the four classes. The 
loss of water by absorption and evaporation from roofs is gen- 
erally so small in heavy rains that it may be neglected, so 
that the roof-surface may be taken as truly impervious. As 
to the percentages furnished from pavements and sidewalks 
the amount varies with the quality of the pavement; and while 
no record of exact experiments was available, it was estimated 
that from a well-paved stone or asphalt pavement 80 per cent 
of the rain ran off. From well-kept macadam or gravel roads 
from 30 to 50 per cent of the rain was obtained, and, inter- 
polating for other pavements, for second-class sidewalks and 
stone pavements the discharge would be 60 per cent; for the 
best macadam, 50 per cent; and for inferior macadam and gravel 
roads not more than 40 per cent would reach the sewers during 
a hard storm. The proportion to be expected from the hard- 
earth surfaces of streets and yards is evidently subject to 
great variation, but it was assumed that it would be 20 per cent 
of the rain falling. 

Correcting Table VIII by these percentages of discharge, 
and assuming, as indicated by the Rochester studies, that the 
quantities of the different classes of pavement were divided 
as given, in proportion to the different densities, we obtain the 
following table: 



74 



SEWER DESIGN 
TABLE IX 



Average 
Number 
of 


Total- 
Percent- 
age of 


Subdivided into Pave- 
ments of 


Proportion Considered 
as Fully Impervious 


Equiva- 
lent Per 
Cent of 


Persons 
per Acre. 


Improved 
Street 
Surface. 


ISt 

Class. 


2d 

Class. 


3d 
Class. 


ISt 

Class. 


2d 
Class. 


3d 
Class. 


Fully Im- 
pervious 
Surface. 


15 


7-4 




1-5 


5-0 




O.6o 


0.40 


3-3 


25 


12-5 


4.0 


2 .O 


6-5 


0.80 


0.6o 


0.40 


7.0 


32 


16.0 


8.0 


3-o 


50 


0.8o 


O.6o 


0.40 


10.2 


40 


20. o 


13-3 


6.7 




O.So 


O.6o 




14.7 




50 


25.0 


20. O 


5-o 




0.8o. 


0.6o 




19.0 



Then assuming that the hard earth yields 20 per cent of the 
rain, and reducing from Table VIII, we get finally the amount 
of water discharged from a given rain in terms of the varying 
densities, as follows: 

TABLE X 





Percentage of Fully Impervious Surface. 




Average Number 
of Persons per 
Acre. 




Total Percentage 
of Fully 
Impervious 
Surface per Acre 


Roofs. 


Improved 
Streets. 


Unimproved 
Streets and 
Yards. 


15 


8.4 


3-3 


3-0 


14-7 


25 


14.0 


7.0 


4-3 


25-3 


32 


18.0 


10. 2 


5-o 


33-2 


40 


22-5 


14.7 


5-4 


42.6 


50 


28.0 


ig.O 


5-6 


52-6 



By plotting the final percentages as ordinates with the 
corresponding densities as abscissae, a curve may be drawn 
which will express the relation between these two variables 
(see Fig. 14). The equation of this curve may also be found 
if desired. 

A small amount of additional data may be added as corrob- 
oration to the results of Mr. Kuichling. In Ithaca, 1910, the 
two seniors already referred to carefully measured the various 
surfaces in a district of 42 acres that had a normal population 
of 22 per acre, with a house on every lot but one, with results 
given in the following table : 



RELATION OF DENSITY TO PERCENTAGE 
TABLE XI 



75 



TABLE SHOWING PERCENTAGES OF DIFFERENT KINDS OF SUR- 
FACES IN A TYPICAL DISTRICT OF ITHACA, N. Y. 



No. Persons 
per Acre. 


Percentage 
of Roof 
Surface per 
Acre. 


Percentage 
of Impervious 
Road Surface 
per Acre. 


Percentage 
of Hard Earth 
and Macadam 
Road per Acre. 


Total Per- 
| centage of 
Relatively 
Impervious 
Surface. 


Percentage 
of Lawns 
and Flower- 
beds per 
Acre. 


22 


I? 


8 


15 


40 


60 



If this be reduced to the total amount of impervious surface, 
by assuming that 80 per. cent of the rain was delivered from 
the improved streets and 40 per cent from the hard-earth and 
macadam roads, and nothing from the lawns and flower-beds, 
amount becomes 29.4, while the maximum percentage 




i 40 

r 
r 

10 

( 




















^ 


X 




















^X 


^^ 




















^ 


^ 




















^x 


' 




















^X 




IAGRAM OF RUN-OF 

BASED ON 

KUICHLING'S STUDIES. 
[ 


'Ft ~~ 










// 




D 








// 












^ 














/ 


















3 10 iO 30 40 .50 6( 



Proportion of RainfallReacmnq Sewers 
FIG. 14 

foundj in the experimental work was 34.8, an earlier rain prob- 
ably adding a small run-off from the grass. 

In another thesis by Mr. H. E. Green, '06, a portion of the 
campus was studied and the run-off measured by a weir across 
the small creek that furnished drainage for this particular district. 
The percentages of relatively impervious areas were as follows: 



Roof Surfaces. 


Sidewalks and 
Macadam. 


Gravel Roads and 
Walks. 


Open Ground. 


5-5 


3-5 


4-2 


86.8 



76 SEWER DESIGN 

By reference to Table VIII it is plainly seen that if it were 
residential area, the roof surface and road area would accord 
with a population of less than 15 per acre, and that therefore 
by Table X there should be somewhat less than 15 per cent 
the intensity of rain found in the rate of run-off. The max- 
imum storm measured had a flow of thirty-five minutes at the 
rate of 0.78 inch per hour, the duration being that for 
concentration. The rate of rainfall was 46.0 cubic feet per 
second for the entire area and the maximum run-off was 2.5 
cubic feet or 5.4 per cent. The entire storm lasted 3^ hours, and 
the ratio of the entire volume of run-off to the entire rainfall 
was 19.3, the run-off, however, lasting sixteen hours. 

In New York City in 1888, gagings * by Rudolph Hering 
were made of the run-off from a district in the lower part of the 
city containing 221 acres. The time of concentration was 
probably about forty-five minutes. The percentages of rela- 
tively impervious area were as follows: 



Roof. 


Paved Area. 


Grass Area. 


43-5 


46.5 


IO 



That is, assuming 70 per cent of the paved area and 20 
per cent of the grass area to be relatively impervious, 78 per 
cent of the rainfall should reach the sewer. The actual per- 
centages reported range from less than 10 to 75 per cent. A 
percentage of 65 was common, and one rain following a snow 
storm appeared to discharge even more than 75 per cent. It 
is, however, worth noting that the greatest flow per second 
in the sewer was due to a very heavy thunder shower, lasting 
thirteen minutes, 38 per cent of which gave the maximum 
sewage flow recorded. 

In applying the relation to cases where greater densities 
of population occur than are given in Table X, it must be 
remembered that the rate of increase of the reduced imper- 

* Trans. Am. Soc. C. E., Vol. LVIII, p. 464. 



RELATION OF DENSITY TO PERCENTAGE 77 

vious surface diminishes until that surface reaches a limit of 
80 or 90 per cent, corresponding to a density of about 75 per- 
sons per acre. Beyond this density there can be no material 
increase of such surface, since then the whole available area 
becomes covered with pavements and buildings, and any 
additional population is accommodated by crowding more 
persons into the houses. It is also proper to remark that the 
figures given refer only to certain average urban conditions 
and are therefore subject to such modifications as may be 
appropriate under different conditions. For example, in a 
rapidly growing suburban village the amount of water delivered 
from the surface twenty years hence may be very different from 
what the present indications would show. The measured 
amounts of water, in the case of Rochester, served to check 
the assumptions made, and have shown that they are very 
near the truth, so that there can be no doubt that the method 
as given will furnish, except under very exceptional conditions 
of building or surface, results nearer the truth than can be 
obtained in any other way. 

PROBLEMS 

26. Assuming 5 persons per house, determine from a count of the 
number of houses in a given district the number of persons per acre. Pace 
the distances needed to determine the area. 

27. By noting where additional houses might be built arid where 
business blocks might be put, estimate the possible future density of popu- 
lation of this same district. 

28. On a given area of 240 acres, 50 acres are under roof, 36 acres 
are brick pavement, 15 acres are stone block, 12 acres are bituminous mac- 
adam, and 60 acres are hard earth streets and yards. What is the per- 
centage of reduced fully impervious surface in percentage and what 
population per acre does it correspond to? 

29. In a part of Ithaca, population 26.2 per acre, the lots are 66' 
X 132', and the blocks are 10 lots long and two deep (660' X 2640. Esti- 
mate the size of a house and the amount of street surface in a block to 
compare with Table VIII . 



CHAPTER VI 
MATHEMATICAL FORMULA 

WE have seen how the amount of rainfall to be provided 
for in a sewer depends on the rate of rainfall and on the dura- 
tion of the storm; that this amount is an uncertain quantity, 
and that its value is generally made to depend more on a long- 
established custom than on any experimental certainty. We 
have seen that the rate of rainfall may vary from the least 
dampness through rates of an inch per hour, which is the rate 
usually given in the text-books, up to 4, 5, or even 6 inches per 
hour. We have further seen that the maximum rate is a func- 
tion of the length of the storm, and that it is not possible to 
make a determination of a rain rate unless the length of the 
storm considered is also known. It has been pointed out that 
while high rates are usually only for short periods, they may 
nevertheless be more troublesome than a more moderate rain 
lasting a longer time and yielding a larger volume. We have 
seen that the period of time adopted as a unit is of importance 
for calculating the intensity of the storm, and that the size of 
the district from which the run-off is to be determined governs 
the choice of this. period. The fact that the condition of the 
ground, its slope, porosity, degree of saturation, all have an 
influence on the proportion of rainfall furnished to the sewers 
has also been pointed out. And the evident conclusion is 
that there is a wide latitude for judgment, that it is not possible 
to make a design with the precision used in other engineering 
constructions, but that the size of the storm-sewer can only 
be properly designed by carefully considering the district to 
be served, and by basing the judgment, which must be used, 
on as thorough an acquaintance with the district as possible. 

In spite of all the uncertainty as to the data of the problem, 

78 



MATHEMATICAL FORMULAE 79 

various attempts have been made at different times to express 
in mathematical terms the relation existing between the rain- 
fall, the general slope of the surface, the drainage-area, and the 
storm-water discharge, but experience has proved them all more 
or less unsatisfactory. Could the coefficients of these formulae 
be well known by experiment, and then could they be used 
by the same investigator on similar territory, doubtless the 
results would be sufficiently accurate; but the coefficients are 
made by one engineer and their values used by another, whose 
knowledge of the original conditions can be at best very limited. 
As to the density or character of the district, often nothing 
more is known than that the territory is " urban." 

The best-known formulae are those of Hawksley, Biirkli- 
Ziegler, Adams, and McMath. The following analytical com- 
parison is taken from a lecture by Emil Kuichling delivered 
before the Association of Civil Engineers of Cornell University 
in 1893.* 

Hawksley's formula was probably established some time 
between the years 1853 an d 1856, and was the result of an 
endeavor to find the relation existing between the diameter 
of a circular sewer and the other factors above named, on the 
assumptions of a rainfall of i inch per hour, one-half reaching 
the sewer, with the sewer-grade parallel to that of the street. 
This formula expressed analytically the relations brought out 
in a table prepared by John Roe, showing the measured dis- 
charges from a number of sewers in the city of London, during 
and after rain-storms of different intensities and under other 
different conditions. An intensity of i inch per hour was 
regarded as the maximum for which provision should be made, 
as rains yielding more than that are exceedingly rare in Lon- 
don. Hawksley considered that this rate was general, and 
concluded, therefore, that a formula based on the measurements 
made would serve for any other sewer to be constructed in 
that vicinity a fair conclusion, except that it omits any con- 
sideration of the character of the soil or of the relative amount 

* See also Trans. Am. Soc. C. E., Vol. LVIII, p. 458. 



80 SEWER DESIGN 

of impervious surface. The formula was first published in 
this country in the report of James P. Kirkwood on the Water- 
works of Brooklyn. It was used by Sir Joseph Bazelgette and 
Mr. William Haywood in preparing the plans for the main 
drainage-works of London, and has been much used elsewhere 
both in this country and in England. 
In its original form it was 



log 



10 
or, divested of its logarithmic form, 



where d = diameter of sewer in inches; 
A = number of acres drained ; 

N = length in which the main falls one foot, which equals 
i/s, where s is sine of slope, 

If i/s be substituted for N, and D in feet for d in inches 



or 



mo 

D w = = 0.0001010 

98135 



This formula is still used by the Borough of Brooklyn 
except that the term 6.8 in the formula is changed to 8, making 

A3 



Since the rainfall is assumed to be i inch per hour, and 
since half of it is assumed to enter the sewers, these two factors 
are really understood, so that if r = the rainfall in inches per 
hour reaching the sewers, which is equal to the actual rainfall 



MATHEMATICAL FORMULAE 81 

multiplied by some constant, depending mainly on the char- 
acter of the surface, the substitution of this gives 

A 3 

D 10 = o.oooioigr 3 , 

with c = ^, and r i ; but 



and 

v = 

assuming the constant 100: R is the hydraulic radius and s 
is the slope; but R for a circular pipe flowing full D/^. There- 
fore 

Q= -50 VD.S =39.27 Vn 5 s, 

4 
whence 

W-2-V.i. 



,39- 2 7/ 
or 



39- 2 7 

Equating this value of D 10 with that from the formula 
given above, 

Q Y i AW 

. = 0.0001010 , 

,39.277 s 2 s 

or 



which is a modified form of the Hawksley formula. 

Adams, on the ground that experience showed that, while 
this formula was sufficiently satisfactory for small districts, 
it gave sewers of inadequate dimensions in the case of larger 
areas, proposed a modification of the ordinary formula for 



82 SEWER DESIGN 

flow in pipes in order to secure a satisfactory capacity for all 
sizes. 

Taking the formula as deduced above, 

Q 



39.27 s 1542.$ 

he changed the exponent of D from 5 to 6 in order to get a larger 

value for the amount of run-off: 

^4 
Then substituting -- for <2, on the assumption that ^ of 

a precipitation of r, =i inch per hour, will reach the sewer 
during this period of time, he has 




6168.5 



Ar 
For any other value of r than unity, - - would have to be 

substituted for Q, giving 

D = 



6168.5 
But for the flow in the conduit, as above, 




and equating the two values of D, 



Biirkli-Ziegler published in 1880 a paper on the discharge 
of sewers,* and in it proposed a variation of Hawksley's for- 

* Introduced into this country in 1881 by Rudolph Hering in his classic report 
to the National Board of Health. 



MATHEMATICAL FORMULAE 83 

mula, to allow its use under other conditions than those of 
the London districts. In French units his formula was 



T Vi ; 

where g = volume of storm-water (in liters) reaching the sewer 

per second from each hectare of surface drained; 
c = constant varying with the character of the surface; 
r = average rainfall in liters per hectare per second during 

the heaviest fall; 

S = general fall of the surface per thousand ; 
A = area drained in hectares. 

Biirkli-Ziegler recommended that for ordinary conditions 
c be made 0.60 for thickly populated urban districts and 0.25 
for suburban ones, with an average value of 0.50, and that the 
maximum rainfall assumed be taken at 125 to 200 liters per 
hectare per second. 

One liter per hectare per second equals 0.0143 cubic foot per 
second, so that the rainfall corresponding to 125 to 200 liters 
per hectare = 1.79 to 2.86 cubic feet per acre per second, or 
rainfalls of 1.79 and 2.86 inches per hour. 

Transforming the whole formula into English units, reading 
Q in cubic feet per second per acre, r in inches per hour, A 
in acres, s for S, and making, by definition, s = S/iooo, we have, 



Q = c 7.05?- .0143 4; 

\ * 

the values of c corresponding to 0.25 and 0.60 will be in English 
measure 1.76 and 4.23, and for the mean 3.52, so that the formula 
in English, if Q = the total discharge, is 



84 SEWER DESIGN 

where c has the values just given, and r is taken at values of 
1.79 to 2.86 inches per hour. 

In 1887 Robert E. McMath of St. Louis published in the 
Transactions of the Am. Soc. C.E.* a paper on the necessary 
size of sewers to discharge the run-off from the excessive rains 
of St. Louis, and deduced a formula which by actual experience 
was so framed as to answer every purpose for that city. It 
was derived by observing, during periods of excessive jrains, the 
sewers which were overcharged, and plotting them as points 
on a diagram whose abscissae were the areas drained in acres, 
and whose ordinates were the calculated capacities of the sewers, 
computed by Kutter's formula. By drawing a curve that should 
pass above these points of surcharge and below or among the 
other plotted points taken from sewers of known capacity, 
the constants and coefficients for the curve were used as those 
to represent the run-off to be expected. The equation of the 
curve taken was. 

= 0.75X2.75^7^ 

Q being the quantity of water reaching the sewer in cubic feet 
per second, and A the area drained. In symbols it would be 



where c' is the proportion of the rainfall reaching the sewers, 
after making the proper allowance for evaporation, absorption, 
and retention. The value taken at St. Louis, probably for the 
built-up part of the city, was 0.75. The symbol r stands for 
the number of cubic feet of water falling on an acre per second, 
or practically the rainfall in inches per hour. It was assumed 
by Mr. McMath to be 2.75 inches per hour, s is taken as the 
mean surface-slope in feet per thousand, and in the diagram 
is made 15. The form of the Biirkli-Ziegler formula was taken, 
and if S be changed to s, whence S equals looos, so that c = 
c' 1 1000, it will be comparable with the others. Mr. McMath 

* Vol. XVI, p. 179. 



MATHEMATICAL FORMULAE 85 

adds that the improvement over the Biirkli-Zeigler formula 
lies in the fact that the latter, based as it is on observations 
of small areas, is inapplicable to districts containing 1000 acres 
or more, while the St. Louis coefficients make the formula good 
to 10,000 acres. 

In a report to the city of Baltimore by the Sewerage Com- 
mission (1897) is a report by Rudolph Hering and Samuel M. 
Gray, Consulting Engineers. The four formulae given above are 
discussed therein, together with a fifth deduced from diagrams 
prepared for the Department of Public Works of New York 
in 1889. This discussion is as follows (the formulae are here 
repeated for convenience) : 



Hawksley: Q = c-A*r*s*\ for r = i, ^ = 3.95. 

Adams: Q = c-A*rh**\ for r = i, ^ = 1.03. 

Blirkli-Zeigler : () = c rA f s* . 

for ^ = 2.75, cr = n.6i for built-up areas; 

cr= 9.59 for average city areas; 

^ = 4.79 for rural areas. 
McMath: Q = cr-$*A*', 

for 7 = 2.75, cr = 8.2i for built-up areas; 

^ = 3.39 for suburban areas. 
N. Y. diagrams : Q = cr A 8 V 7 ; 

cr = 10.59 ^ or completely built-up areas; 

7 = 8.97 for well-built-up areas; 

cr = 6.59 for suburban areas. 

Rainfall. Assuming all the factors except the run-off and 
the rainfall to remain constant, the formulae become: 

Hawskley : Q = const. X r 76 . 

Adams: Q = const. X r 83 . 

Blirkli-Ziegler: Q = const. X r. 
McMath: Q = const. X r 

N. Y. diagrams: Q = const. X r. 

Hering and Gray say: " There is hardly a question that, 



86 SEWER DESIGN 

all other factors being equal, the run-off from such small areas 
as are considered for city drainage should vary directly with 
the rainfall in all cases of heavy storms, and also for short periods 
if absorption and evaporation can be neglected. Therefore, 
as these assumptions can generally be made for city work, the 
three latter formulae, which have a direct variation with the 
rainfall, are preferred. 

Slope. " When the maximum rate of fall does not cease 
before the run-off from the entire area has reached its lowest 
point, then for this area the run-off will be independent of the 
slope. But when the maximum rate ceases before this takes 
place, the slope will have a decided influence upon the amount 
of water accumulated. The greater the slope of the surface, 
that is, the steeper the territory, the more rapidly will the water 
run off and accumulate along the lowest lines. It is not prac- 
ticable at this time to state how large the area must be before 
the variation of the slope should be considered. It depends 
upon the maximum rate of rainfall, upon the steepness of the 
area, and upon other local conditions. Assuming that the 
run-off increases with the slope, what is the ratio between 
these two quantities? If all factors except these two are assumed 
to be constant, then the ratio in the different formulae is shown 
as follows: 

Hawksley: Q = const. Xs' 25 . 

Adams: Q = const. X^ 083 . 

Burkli-Ziegler: Q = const. Xy 25 . 
McMath: Q = const. Xr 20 . 

N. Y. diagrams: Q = const. Xs' 27 . 

" The exponent showing little variation indicates that there 
is but slight difference in the formulae as to the weight attached 
to the slope, but that the N. Y. diagrams with the largest 
exponent give it the most importance. 

Area. " The larger the area the greater is the total run-off. 
But the larger the area the smaller is the run-off per unit of 
area. This variation is important and demonstrates that a 



MATHEMATICAL FORMULAE 87 

drain taking the water from a large area, say 100 acres, does 
not require to have ten times the capacity of one taking the 
water from only 10 acres. 

" If it is assumed that all the factors are constant excepting 
the run-off and drainage-area, then the above formulae give the 
following values : 

Hawksley: Q = const. XA' 75 . 

Adams: Q = const. 

Biirkli-Ziegler: Q = const. 
McMath: Q = const. 

N. Y. diagrams: Q = const. 

" From this it is seen that the coefficients fail to show any 
great difference in the formulae. 
" All the formulae have the form 

Q = c-r x A z S x . 

" From what was said above, the only formulae giving any 
other exponent than unity to r are those of Hawksley and Adams, 
and it is as well to ignore such variation. Therefore the pre- 
ferred formulae have the form 

Q = c-r-A x S x . 

As they are practically derived independently of a knowledge 
of the exact maximum rainfall, we may substitute for c-r the 
one value C and write 



In the Biirkli-Ziegler formula we may therefore write, 
for the greatest storms, values for c-r or for C, modifying the 
numerical values to correspond with the slope in feet per 
thousand : 

C = n.6i for built-up areas; 
C= 9.59 for average city areas; 
C= 4.79 for rural or suburban areas. 



88 SEWER DESIGN 

McMath's formula for St. Louis gives: 

C = 8.2i for built-up areas; 

C = 3.3 9 for rural and suburban areas. 

On the N. Y. diagrams the values are: 

C = 10.59 for built-up areas; 
C= 8.97 for average areas; 
C= 6.59 for rural areas. 

In the design of the Walworth Run Sewer in Cleveland, 
use was made of an original formula : 



fs* 

Q-ACRjfc 



or in the form of p. 85 



a somewhat lower value of the exponent of s, but otherwise 
very similar to the others. The values of c-r chosen range 
from 3 to 7, the latter being for the most densely built-up part 
of the city. Fig. 13 already referred to shows that the form 
of the equation is not the important factor but rather the value 
assigned to the constant C. This has already been shown to 
vary not only with the amount of impervious surface, but 
with other factors, so that an engineer in one city might properly 
assume 75 per cent of the rainfall to enter the sewers while in 
another city, with the same rain intensity and impervious area, 
50 per cent might be ample. It is impossible to reduce a ques- 
tion of judgment and experience, such as the assignment of a 
proper value to C becomes, to the fixity of a mathematical 
table. The opinion of an experienced engineer on this point 
should always be sought by a young engineer with no previous 
experience who is designing storm-sewers. 

As a further example of work done in this direction, Fig. 



MATHEMATICAL FORMULA 



89 



1 I 



I I 



R= 



oo cr 












I I I 



O t/f 

5 g 2 

o o 

? 






\ 



>A 



\ 



\\ 



\ 



8 



oiqno ui 



UJOJJMOU 



^- *o 
I : 

e 
i 







90 SEWER DESIGN 

15 is given, taken from the report on the drainage of the city 
of the surveys, gagings, and observations made by the city 
of New Orleans, 1895. These curves are based upon the results 
engineer's department under the advice of the advisory board 
during the years 1893 and 1894, and upon a comparison of 
these results with those of similar observations in other cities 
presenting like conditions. 

Fig. 1 6 shows an ingenious arrangement which converts the 
solution of the McMath formula into a mechanical process. 
The logarithms of the quantities involved are taken and plotted 
to form the runner and scale of a slide-rule. The device is 
the invention of Mr. A. S. Crane, formerly of the Department 
of Sewers, Brooklyn, N. Y., and has recently been largely 
used in determining the sizes of storm-water sewers for that 
city. 

By either of the two ways just outlined, viz., by estimat- 
ing the probable future population of each district of the city 
and, by Table IX of Chapter V, noting the percentage of rain- 
fall that may be expected to run off, the rainfall having been 
determined by the diagrams explained in Chapter III; or else, 
more quickly but less intelligently, by using one of the formulae 
or diagrams of this chapter, the amount of storm-water to be 
cared for by the sewer can be found. In the report already 
alluded to, Mr. McMath shows that, according to the experience 
at St. Louis, the Biirkli-Ziegler formula gives, except in the case 
of small areas, insufficient amounts. Comparisons might be 
made in a similar way for all the formulae and diagrams extant, 
but as each has been made to accord with some special data, 
a discrepancy only shows that the amount of run-off varies in 
different cities and localities. From the method of construc- 
tion, the formula of Mr. McMath must give the best possible 
results for St. Louis, and similar formulae might be built up for 
other cities having an equally long sewer experience. Except- 
ing only the use of a formula made up in the manner of that 
for St. Louis, no method can give as intelligent and reliable 
results as that detailed in Chapter V. 



MATHEMATICAL FORMULAE 



91 



Hi 



El 



E- 



S i 



FIG. 16. 



92 SEWER DESIGN 

Before considering the relation between the amount of water 
finally determined on and the resulting size of the sewer, other 
sources of sewage are to be considered. 

PROBLEMS 

30. Show that by changing 6.8 to 8 in the Hawksley formula, the 

A 3 

value of D l becomes .001615-. 

o 

31. Show that the numerical value of the constant in the Biirkli-Ziegler 
formula is changed from 0.60. to 4.23 by substituting English units of 
measure. 

32. Taking the five formulae of p. 85, plot curves for each equation, 
taking areas up to 1000 acres for abscissae and run-off in cubic feet per 
second per acre for ordinates. 

33. Determine the probable run-off from some definite district or 
area. Use all the methods and compare results and make a final decision 
in the light of all the evidence. 

34. Show by numerical explanation how the constant of a formula 
representing the method of Chapter V, viz., Q = C-vA can be reconciled 
with the constants of Chapter VI. 

35. Show by a diagram how much effect the term S' 25 has in the math- 
ematical formula, that is, plot two curves with run-off per second per 
acre for ordinates, and values of S for abscissae, with A = 500, and = 50 
acres, and with assumed values of C and r. 

36. Plot curves from the 5 formulae of p. 85, with run-offs as ordinates 
and areas as abscissae in order to show the effect of the exponent of A. 
Take a fixed value for C-r, and the values of S, i.e., 5 = .ooi, 6* = . 005 and 
5" = . 05. 



CHAPTER VII 
ESTIMATING FUTURE POPULATION 

THE amount of storm-water reaching a sewer, and the con- 
sequent size of the sewer, bear only an indirect relation to the 
population on the area drained, but the number of people in a 
given district is a direct function of the amount of domestic 
sewage to be cared for. In order to determine, therefore, the 
amount of house-sewage which a system of sewers must carry, 
it is primarily essential to determine the population on the area 
to be sewered. 

The number of persons on a given area may be approximately 
determined at any time in several ways. The U. S. Census 
reports, published every ten years, furnish a basis for an estimate 
of the population for intermediate years, but as a sewer system 
has always to be designed for use during an indefinite number 
of years in the future, some method of predicting the popula- 
tion for that future time must be devised. It is usual to base 
the prediction on two things. First, after noting the past 
growth of the city in question, it is assumed that it will con- 
tinue to increase regularly according to the law of its past. 
Thus in Chicago, at the time of the first report of the Sanitary 
Commission, the future population of the Sanitary District 
was estimated in this way, as shown in Fig. 17. Curves were 
drawn for other large cities and used as a guide, but they proved 
of little value. Messrs. Hering and Gray used the same method 
in their Baltimore report as shown in Fig. 18. They had recourse 
to other sources of information besides the U. S. Census reports; 
the police estimates of population, made every year, and obtained 
by multiplying the voting population by a constant, were made 
the basis of the prediction quite as much as the more authen- 
ticated U. S. reports. 

93 



94 



SEWER DESIGN 



The values of these predictions can now be tested and shown 
to be reasonably accurate. 



I I I I I I I 

POPULATION CURVE 

DRAWN FOR 

CHICAGO, ILL. 




ST.LDUI 



m 



in 



/ / 



not 



1800 



1850 



1900 



YEAR. 

FIG. 17. 



2,500,000 



,000,000 



1,500,000 



1,000,000 



200,000 



POPULATION CURVE 










/ 


// 




000,000 
800,000 
700,000 
600,000 
500,000 
400,000 
300,000 
200,000 
100,000 


i 
BALTIM 

o - Pol 


70R 

ORE, MD. 

ice Census. 
S. Census. 










'// 


2 










// 


M 








= U. 






^ X 


/// 


i^J. 

























"^ 


'// 
























*) 


/$ 
























j 


^. 
























S 


j^ 






















^ 


^ 


















I. * 


^- ^ 


-^ 


























FIG. 1 8. i0 HK> " 



The census population for 1900 and for 1910 for Chicago 
was 1,698,575 and 2,185,283, while the lower branch of the 



ESTIMATING FUTURE POPULATION 



95 



curve predicts for those years populations of 1,690,000 and 
2,250,000. For Baltimore the agreement between prediction 
and census are equally good. The census figures for 1900 and 




8 

NouvindOd 



1910 are 508,957 and -670, 5 8 5- and the predicted values, scaled 
from the diagram, are 520,000 and 650,000. 

The other method assumes that the city in question is like 
other cities of the same size as regards its rate of increase, and 
that it will follow, approximately at least, the same law. This 
method was followed in Appendix No. i to the report of the 



96 SEWER DESIGN 

Chief Engineer of the Metropolitan Water-supply made to the 
State Board of Health of Massachusetts in 1895, and is described 
as follows (see Fig. 19). First, ignoring the city limits and 
taking the metropolitan area within 10 to 15 miles radius 
from the centre of business, the U. S. Census for Boston was 
found to give 269,754 population in 1850, gradually increasing 
to 844,814 in 1890. Then, by using partial and incomplete 
censuses, such as assessed polls, names in directory, enumera- 
tion of school-children, and making a compilation of other 
statistics which indicate, to some extent, the growth of com- 
munities, such as the number of buildings erected and the 
number of water services added, and comparing these quantities 
with the known population in census years, it was possible to 
obtain the population of the district for the years 1891-1894 
with much greater accuracy than could have been done by 
projecting ahead the previous rate of growth. In this way the 
probable population for 1894 was found to be 967,000. On 
the diagram given, which is taken from the report mentioned, 
are plotted population curves of Boston and five other cities, 
with five-year spaces for abscissae and population for ordinates, 
and all the curves are so placed as to coincide at a point cor- 
responding to a population of 967,000 on each. Philadelphia 
and Chicago are of little value in showing the tendency of the 
curve, but London, Berlin, and New York show the rate of 
growth of those cities beyond the point where they had Boston's 
population, and by assuming that Boston's future growth would 
be influenced by no tremendous shock of pestilence, war, or 
business disaster its population line was drawn to follow approx- 
imately these other cities. 

The check which the 1910 census has given to this work 
shows it to have been surprisingly accurate. Thus in 1910, 
sixteen years after the diagram was made, the census showed 
a population in this district of 1,520,470, while the diagram 
gives 1,500,000. 

The same method was followed in the smaller city of Brock- 
ton, as found in the Report of the Sewerage Commission of 1893 



ESTIMATING FUTURE POPULATION 



97 



prepared by the engineer, Mr. H. F. Snow (see Fig. 20). Here 
all cities in the United States reaching a population of 27,000 
between 1851 and 1870 were plotted, together with the past 
records of Brockton, whose population in 1890 was 27,294. 

The growth of all these other cities being plotted (some 
extending for 40 years), and making due allowance for natural 
advantages possessed by some cities and not by Brockton, and 
giving due weight to the municipalities existing under the same 



POPULATION CURVE 

drawn for 
BROCKTON, MASS. 



1850 



Rl 



mbusC 



1900 



rfni 



mi 



BroiKTcn 



Rjcf iflon J Va 



qto 



Ma! 5. 



nd 



JH( rtfo tl C )na 



Me. 



50000 



00000 



50000 



1940 



FIG. 



conditions as nearly as could be, the probable future population 
of Brockton was obtained. 

The actual growth of this city has been more than was 
expected, so that the discrepancy is greater in this case between 
the prediction and the reality than in any of the other cities 
noted. Thus the diagram indicates in 1900 and 1910, popula- 
tions of 39,000 and -^fcooS, while the census gives values of 
40,063 and 56,878. 

Rafter and Baker in a discussion of this subject give some 
tables taken from Census Bulletin No. 52, showing the increase 



SEWER DESIGN 



in population during the years 1881-1890 for cities of 8000 
to 50,000 inhabitants, and also for cities of over 50,000 inhab- 
itants; and while the increase for the first series varies from 4 
to 267 per cent, and for the second from 7 to 360 per cent, 
they conclude as a rapid generalization, first, that in American 
towns having a population less than 50,000 the present rate of 
increase may be taken at about 100 per cent in from 15 to 20 
years; and second, that in the larger towns the increase will be 
about 50 per cent in the same time. They further say that 

TABLE XII 

TABLE SHOWING RATES OF INCREASE IN POPULATION FOR CITIES 
OF DIFFERENT SIZES 



TfTViA-, fl,^ 


Number of 
Cities 
Considered in 


Range of Rates of 
Annual Increase. 


Average Annual Rate of 
Increase in Per Cent. 


w nen LiiG 
Population is 


Deriving 
Average Rate 
of Increase. 


Maximum 
Per Cent. 


Minimum 
Per Cent. 


Average of 
all the Dif- 
ferent Values. 


Probable 
Average 
Value. 


IOOOO 


9 


30.50 


6.50 


14.82 






2OOOO 


I CJ 


24. 2O 


4. IO 


II.I7 




30 300 


A 
19 


18.00 


2 .40 


8-34 




4OOOO 


20 


I5-50 


2.60 


6-45 




50000 


2O 


13.00 


2-35 


6.05 


6.05 


60000 


15 


10.40 


1 .40 


5-50 


5-60 


70000 


13 


9. 10 


3-oo 


5-57 


5-30 


8000O 


12 


8.30 


2 . IO 


4-95 


5-03 


QOOOO 


II 


7-95 


I . IO 


4.80 


4-85 


IOOOOO 


IO 


7-30 


2-35 


4-93 


4.66 


I IOOOO 


9 


8.25 


2.80 


5-21 


4-52 


I 20000 


7 


6.40 


3.10 


4-38 


4.40 


130000 


5' 


6.05 


3.10 


4-37 


4.26 


I4OOOO 


5 


5-75 


3-07 


4-30 


4.15 


150000 


4 


5.65 


3-43 


4.62 


4.04 


160000 


4 


6.00 


3-40 


4-5i 


3-93 



analyses of 400 towns given in the Census bulletin referred 
to above show that about 25 per cent have doubled in the 
decade 1880-1890, and that the towns showing this large 
increase are situated in all parts of the country, many of them 
in the older settled States where fixed conditions may be sup- 
posed to have been reached. In the case of towns of over 



ESTIMATING FUTURE POPULATION 



99 



50,000, the number increasing from 50 to 100 per cent is smaller, 
only 14 per cent of 56 towns given increasing more than 100 
per cent. 

Mr. Kuichling extends this study farther, and suggests 
that the rate of increase is so well fixed to correspond with the 
size of town that the relation once established may in most 
cases be used to predict the future growth of any town of known 
size. He bases the relation which he believes to exist on a 





\ 




1 


I 




1 1 I 




1 




V 






CURVE SHOWING RATE OF 
INCREASE OF POPULATION 
VARYING WITH SIZE OF CITY. 

(From Kuichling.) 






\ 
\ 






- 




\ 
\ 








\ 










\ 








\ 










\ 






























\ 
































*fc 
































% 
































^"^ 


<i^ 
































-^ 







\ 
\ 








-" _ 





























\~ 


~m*. 



































10,000 



5U.OOO 100,000 

POPULATION. 
FIG. 21. 



150,001) 



detailed study of the Census reports, where the rate of increase 
for towns of varying sizes seems to continually decrease as the 
size of the town increases, the average per cent of increase for 
towns of the same size agreeing very closely. The preceding 
table is taken from his report as compiled from the U. S. 
Census of 1880, and shows average rates of annual increase for 
cities of the United States. 

The table shows very plainly (see Fig. 21 for the graphical 
representation) a law of decrease in the annual rates as the size 



100 



SEWER DESIGN 



of the city increases, which law, as shown in the report, holds 
if cities of from 160,000 to 900,000 be included in the com- 
parison. As a check on the law and for comparison, the author 
has taken the Census report for 1910 and computed the rates 
of increase in a similar manner for cities of between 10,000 
and 200,000, with results as shown in Table XIII and in Fig. 22. 

TABLE XI 

TABLE SHOWING RATES OF INCREASE IN POPULATION FOR CITIES 
OF DIFFERENT SIZES 



When the 
Population is 


Number of Cities 
Considered in 
Deriving 
Average Rate 
of Increase. 


Range of Rates of Annual 
Increase. 


Average Annual 
Rate of Increase 
in Per Cent 
of All the 
Different Values. 


Maximum 
Per Cent. 


Minimum 
Per Cent. 


1 0000 


44 


I9-I39 


0.288 


5-7I5 


20000 


S3 


10.691 


o.ooo 


2.714 


30000 


37 


23.223 


0.092 


4.814 


40000 


25 


20.599 


0.405 


3-858 


50000 


16 


II . 260 


1.680 


5-652 


60000 


10 


9-785 


1.803 


3-873 


70000 


ii 


7-655 


1.846 


4.483 


80000 


5 


6.OI2 


1-425 


3-741 


90000 


7 


8.119 


2.167 


4-449 


IOOOOO 


4 


4-375 


0.648 


i .906 


I I 0000 


4 


3.661 


1.376 


2.885 


I2OOOO 


4 


5.006 


1.942 


2.994 


130000 


3 


2.813 


2.368 


2.615 


140000 


i 


2.327 


2.327 


2.327 


150000 


2 


12.427 


7.229 


9.828 


160000 


I 


2.782 


2.782 


2.782 


180000 


I 


4.456 


4-456 


4.456 


2OOOOO 


I 


3.416 


3-416 


3.4i6 



In this latter comparison the law seems to be lost, the increase 
in the annual rate depending apparently not so much on the 
size of the city as on other unknown factors. In both diagrams, 
populations are plotted as abscissae, and the average annual 
rate of increase in per cent as ordinates. The broken irregular 
line shown is obtained by joining the points thus plotted, and 
if a continuous regular curve be drawn between the points, 
as nearly as may be, it will represent the probable general law 



ESTIMATING FUTURE POPULATION 



101 



of growth of American cities of the class under consideration, 
and will give the general percentages found in the sixth column 
of Kuichling's table. No such curve was drawn for the growth 
in 1900-1910, as the points plotted were so irregular as to show 
rather the lack of any general law than the evidence of the law 
itself. Kuichling makes the diagram give a method of esti- 
mating a future population as follows: Take from the diagram 



10,000 





CURVE SHOWING RATE OF 
INCREASE OF POPULATION 












(1910 Census) 




| 


1 






































1 
1 






































1 
1 










t 






/ 


\ 




















t 










I 

I 


; 


\ 


/ 


\ 
\ 


/ 


\ 


/ 












l 
f 


\ 




/ 


\ 




t 
t 
\ 
t 


/ 
/ 
/ 
i 












f 


\ 

\ 

\ 










1 


\ 


/ 


/ 




\ 


















\ 
\ 


/ 




\. 


\ 






/ 















































50,000 



100,000 
Population 

FlG. 22. 



150,000 



200,000 



or table the rate of increase corresponding to the present popula 
tion, interpolating if necessary; add that increase to the present 
population; take the rate for that sum; find the increase cor- 
responding; add the latter to the former sum, and continue 
this for as many years as desired. The method is rather tedious 
and gives only the general and probable law, with a result 
which must be modified by such conditions as the previous 
rate of growth, locality, facilities for manufacture, and trade 
would suggest. 



102 SEWER DESIGN 

This law and the discussion must be used with great caution 
in the case of any particular city, the general law being often 
very wide from the truth. From Table XIII it is seen that cities 
of 10,000 inhabitants increased in population in 1900-1910 
from o.o to 10.7 per cent per year, while the general law would 
indicate about 1 1 per cent. Cities of 30,000, however, apparently 
may, as a maximum, increase at the rate of 23 per cent. Should 
the city in question not be an average city, a large error would 
evidently result from trying to apply the general law. 

No law or estimate can be found for new cities such as 
spring up in the western part of the United States. There 
may be cited as an example San Diego, which, in January, 
1887, when the plans were made for its sewer system, had a 
population of 5000. In February, 1888, there was a population 
of 33,000, and by the Census of 1890 the town had a population 
of 16,129. In 1910 the population was 39,578. 

To further illustrate the method of securing an idea of the 
future population, Fig. 23 is given from a thesis on the sewerage 
of Ithaca, by Mr. W. E. Truesdell, C.E., Cornell University, 
1896. The city population of Ithaca was given by U. S. Census 
for 1880 and 1890, and there was also available an unofficial 
census in 1892 which did not, however, check with the other 
two. The following additional records were consulted and 
plowed on the same diagram as the Census figures : the maximum 
vote in city elections for every five years from 1855 to 1897; 
the yearly public-school registration from 1879 to 1897; the 
school population from 1871 to 1891. The rate of increas- 
of the population of the city was taken as the mean of the 
rates of increase in votes, in school registration, in school popula- 
tion, and in the Census reports, weighting the different records 
as the peculiar condition seemed to justify. In the figure, 
the long broken line shows the apparent increase as indicated 
by the local censuses, while the long heavy line shows the 
adopted line, modified by the two government censuses of 1880- 
1890. By Kuichling's method the population in 1920 will 
be 113,000, while by Mr. TruesdelPs it will be only 18,500. 



ESTIMATING FUTURE POPULATION 



103 



104 SEWER DESIGN 

In the design of sewers for the place, Mr. Hering assumes the 
future population as 30,000, not stating, however, when this 
number is to be expected. The actual population by the 1910 
Census was 14,802. 

The result of this study into methods of forecasting the 
population of any city at some definite future time is that it 
is a matter for the judgment of the engineer. That while he 
may make use of certain auxiliaries, such as census reports 
for past growth and for the growth of other cities, while he 
may consult the local reports of growth in various municipal 
directions, while he may construct diagrams and tables, these 
are all only aids. The actual determination of the future 
population must be made by the individual judgment, based 
and guided by such methods as have been outlined, but modified 
by an intimate knowledge of the local conditions of situation 
and enterprise, and of the other often unknown factors which 
govern the growth of a modern city. 

PROBLEMS 

37. By reference to the publications of the U. S. Census Bureau, 
find the average numbers of persons per house in five cities of New York 
State. Choose cities differing in location, size, and kind of industry. 

38. Collect records of population as given by U. S. Census Bureau 
for years 1860-1910 inclusive for City of Rochester, N. Y., and by plotting 
the curve of its growth, estimate the probable population for 1950. 

39. Take a city directory for 1900, and by comparing the 

number of names with the census population, get the ratio of names to 
total population. Multiply the number of names in the 1910 directory 
by this ratio and compare the result with the census population. 

40. Using census populations for 1900 and 1910 for the city of , 

compute the annual ratios, assuming both an arithmetical and geometrical 
law of increase. Using both ratios determine the populations for 1905 
and for 1915. 

41. Find the probable population of Elmira in 1950, by comparing 
with population of Syracuse, Rochester, Cambridge, Lowell, and Newark, 
after method of Fig. 20. 



CHAPTER VIII 
AMOUNT OF SEWAGE PER CAPITA 

THE probable future population of the city for whose use 
the sewers are designed being determined, it remains to assume 
a daily sewage-flow per capita, with such variations from hour 
to hour from the average flow as may be found to be usual. 
The amount of sewage contributed per head per day is a 
quantity variable in different parts of the country and in 
different cities, depending on the variation in the water-supply, 
and it has been customary in this country to assume that the 
daily water-supply of a place is all converted into sewage, 
and that a determination of the amount of sewage is made 
when the amount of water-supply is found. This undoubtedly 
approaches the truth, although it is more in accordance with 
sewer-gagings to say that the hourly and daily variation in 
flow of sewage corresponds closely to that of the water-supply, 
while the actual amount of sewage is something less. That 
the records show the volume of sewage always less than that 
of the water used is partly due to the fact that the houses 
supplied by city water-works generally exceed in number those 
connected with the sewers. And, further, since the water- 
connections precede the sewer-connections, there can never be, 
as long as connections with either water- or sewer-pipes are 
being made, an equal flow of water and sewage. Nor can there 
be any fixed relation between the two volumes until the final 
number of houses and buildings in a city are supplied with both 
connections. 

Fig. 24 * shows the pumping records of the water-supply, 
and the relation between the two volumes, at Atlantic City, 
N. J., for the several months of the year 1892, with the water- 

* From Engineering News, Vol. XXIX, p. 124. 

105 



106 



SEWER DESIGN 




WATER CONSUMPTION AND SEWAGE 
FLOW AT ATLANTIC CITY, 

1892. 



1.5 M. 



1M. 



! t 



! 1 1 



FIG. 24. 



AMOUNT OF SEWAGE PER CAPITA 107 

consumption for 1896. Fig. 25 shows the two curves for Des 
Moines, Iowa, for 1895.* Both diagrams show the sewage- 
flow to be about 35 per cent less than the water-consumption. 

The variation in the water-supply of a city is almost incred- 
ible, cities of the same size and character often having a 
difference in daily consumption of as much as 150 gallons 
per head. To what cause this is due it is hard to say, as there 
seems to be no law as to the relation between the consump- 
tion and the size of the city. Nor does any one cause seem 
responsible. Probably the largest factor is leakage, caused 
by poor construction of the main line, and in the house-fixtures, 
and by carelessness on the part of the house-holder and by 
neglect on the part of the water-works superintendent in 
making proper repairs. Any discussion (notably such as have 
taken place in the New England Water-works and in the 
American Water-works Associations) on the question of leakage 
brings out its importance very plainly, and the reports on the 
various devices for detecting water-waste make their efficiency 
unmistakable. For example, in his annual report for 1802, 
Mr. Trautwine mentions that in Philadelphia, out of 782 appli- 
ances in 142 houses inspected for waste, 22 were leaking slightly 
and 32 running continually. The daily consumption per capita 
for these houses was found to be 222 gallons, of which 192 
were wasted, 30 only being used. It is generally in the smaller 
cities that municipal oversight is most lax, the increased con- 
sumption in the larger cities making a total volume of waste 
so large as to demand investigation; yet this has so many 
exceptions as to be of little value. 

The following tables are given to show what amounts of 
water are actually used per head per day in typical cities of 
the United States. Most of the figures given are derived 
from the records of pumping-plants, because actual measure- 
ments of the amount of water used in gravity supplies are very 
few. From the meager data available there seems to be no 
reason to believe that the fact and cost of pumping offers 

* The data supplied through the kindness of Professor Marston, Ames, Iowa. 



108 



SEWER DESIGN 




1 I 1 I I 
11111 



AMOUNT OF SEWAGE PER CAPITA 109 

any restriction on the unlimited use of water, even though 
the use of each additional gallon of water means additional 
expense. The first table (Table XIV), is based on a report by 
the Municipal Engineering Magazine (Vol. XXXVII, pp. 258, 
330), with populations from the 1910 Census. Table XV 
is from a report of Mr. E. C. Bailey, then superintendent of 
the Albany filter-plant, and represents conditions in 1905. 
It seems plain from a study of these two tables that there is 
no relation between the amount of water used and either the 
size of the city, or its location, but that rather there must 
be a special inquiry for each city whose water-supply is to be 
determined. It should also be noted that in many cities, 
particularly where the water flows by gravity, no method of 
measuring the flow is provided and the quantity named in the 
city reports or by the water-works superintendent is little 
more than a wild guess. If, in addition, the proportion of the 
population using the municipal supply is uncertain, the per 
capita consumption may be sadly in error. 

As an example of the method of analyzing the probable 
amount of water to be provided in a given city, the following 
extract is made from Appendix II of the report by Dexter 
Brackett on the Metropolitan Water-supply, Massachusetts 
State Board of Health: 

" The water used in any city or town may be subdivided 
under four heads: 

" i. Quantity used for domestic purposes. 

" 2. Quantity used for trade and manufacturing purposes. 

"3. Quantity used for public purposes. 

" 4. Quantity wasted." 

Under the first head should be included not only the amount 
used for household purposes, but also the quantity required 
for stores, stables, laundries, and all requirements of a purely 
residential community. 

The following table (XVI), from the report, shows by 
actual measurement the per capita consumption for purely 
domestic use by different classes of people in a number of cities. 



110 



SEWER DESIGN 



TABLE XIV 

SHOWING CONSUMPTION OF WATER IN VARIOUS SMALL CITIES 
OF THE UNITED STATES 1910 



Name of City. 


Source of Supply. 


Popula- 
tion. 


Daily 
Consump 
tion. 


Daily 
Con- 
sumption 
Per 
Capita. 


Petersburg, Va 


Creek, pump, filter 


24 127 


4^4 080 


10 


Pensacola, Fla 


Wells, pumps 


22,082 


5OO,OOO 


22 


Charlotte N. C 


Creek pump 


24. 014. 


I 324 s67 


4O 


Wilmington, N. C . . . . 
Tampa F^a 


River, pump, filter 
Spring wells pump 


25,748 
37 782 


I,O22,OOO 

i 700 ooo 


40 

4C 


Maiden, Mass 
Battle Creek, Mich . . . 
Lincoln Neb 


Boston Supply, gravity. . . . 
Lake, stream, pump 
\Vells pump 


44,404 
25,267 
A'i 073 


2,019,500 
1,226,000 

-7 192 OOO 


45 
49 

CQ 


Jacksonville, Fla .... 


Wells pump . ... 


C7 6OQ 


2 o c6 200 


ei 


Gloucester, Mass 


Streams, pump 


24,308 


1,246,149 


Cl 


Superior Wis . . 


Wells pump 


4O 384. 


2 226 7OO 


re 


Taunton, Mass 
Newport, Ky 


Ponds, pump 
River, pump 


34,259 

30,300 


1,903,935 
1,843,000 


56 
60 


Madison Wis . . . 


Wells pump 


2C Z-II 


I <64 08^ 


61 


Salem, Mass 
Waltham, Mass 


Lake, river, pump 
Wells, pump 


43,697 

27,834 


2,987,000 
I,Q29,72$ 


68 
70 


South Bend, Ind. . . 


Wells pump 


f-2 684. 


4 064 ^2Q 


7q 


Everett, Mass 
Rockford 111. 


Boston Supply, gravity. . . . 
\Vells pump 


33,484 

At 4OI 


2,592,400 
3 ^ ^ ? OOO 


77 
78 


Fitchburg, Mass 
Ft Wayne Ind 


Boston Supply, gravity. . . . 
W^ells pump 


37,826 

63 O3 3 


2,9OO,OOO 
r T 31 833 


80 
80 


Macon Ga 


River pump filter 


4.0 66^ 


3 373 OOO 


83 


Columbia, S. C 
Springfield, 111 


River, pump, filter 
River, pump " . . 


26,319 

51,678 


2,369,720 
4 738,000 


90 
91 


Quincy, Mass 


Surface water, reservoir. 


32 642 


30 co ooo 


03 


McKeesport, Pa 
Peoria 111 


Wells, pump 
\Vells pump 


42,694 

66 OsO 


4,031,281 
6 806 ooo 


94 

IOI 


Norfolk, Va 


Creeks pump, filter . 


67,4^2 


6 cK2 7 ^6 


IO3 


Haverhill, Mass 
Roanoke, Va 


Ponds, pump, and gravity. 
Spring pump 


44,115 

-7A 874 


4,65i,779 

4 O76 83O 


1 06 
117 


Chelsea, Mass 
Atlantic City, N. J . . . 
Binghamton, N. Y. . . 


Boston Supply, gravity. . . . 
Wells, pump 
River, filter pump 


32,452 
46,150 

48 44^ 


4,O9I,2OO 
5,874,000 

6 313 ooo 


126 
128 
I3O 


Houston, Texas 
Bangor, Me . . . 


Wells, pump 
River filter pump. 


78,800 

24 80^ 


1 1 ,000,000 

3 6oQ 2 ^4 


140 
I4 1 ? 


Auburn, N. Y 


Lake, pump . 


34 668 


6 ooo ooo 


173 


Newburgh, N. Y 
Lewiston, Me 


Stream, pump and gravity. 
Lake pump 


27,805 

26 247 


5,000,000 
4 900 ooo 


1 80 
187 


South Omaha, Neb . . . 


Omaha Water-works . . . 


26 2=JQ 


4 077 OOO 


1 88 


Muncie, Ind 


River wells pump 


24 OCX 


53OO OOO 


221 


Anderson, Ind 


River, filters, pump . 


22 476 


5 ooo ooo 


222 













AMOUNT OF SEWAGE PER CAPITA 



111 



TABLE XV 

SHOWING CONSUMPTION OF WATER IN VARIOUS LARGE CITIES 
OF THE UNITED STATES 1905 



Name of City. 


Source of Supply. 


3 opulation. 


Daily 
Consump- 
tion. 


Daily 
Con- 
sump- 
tion Per 
Capita. 


Birmingham, Ala 
Fall River, Mass 
New Orleans, La 


Creek, pump, filters 
Lake, pump 
River, filter, pump 


132,683 
104,863 
287,100 


5,028,900 
3,805,000 
13,820,000 


37 
36 
48 


St. Paul, Minn 
Providence. R. I 


Lakes, wells, gr., pump. . 
River, pump 


163,065 
175,597 


8,337,000 
10,130,000 


51 
58 


Worcester, Mass 
San Francisco, Cal. . . . 
Indianapolis, Ind 
Rochester, N. Y 
Milwaukee Wis 


Imp. Res., gravity ...... 
Streams, gravity, pump . . 
River, filter, pump 
Lakes, gravity 
Lake pump 


118,421 
342,800 
169,164 
162,608 
28^ 3OO 


7,920,000 
25,000,000 
13,400,000 
13,500,000 
^4 ooo ooo 


6 7 
73 
79 
83 
84. 


Minneapolis, Minn . . . 
Newark, N. J 
Memphis Tenn 


River, pump 
River, gravity 
Wells pump . . 


202,718 
246,070 
102,3^0 


18,813,000 
24,000,000 
10,000,000 


92 

97 
98 


Syracuse, N. Y 


Lake, gravity 


108,^74 


11,000,000 


IOO 


Baltimore Md 


Creeks gravity . ... 


tCOQ OOO 


56 ooo ooo 


no 


St. Louis, Mo 


River, pump 


575,2OO 


63,530,000 


no 


Paterson N T 


River pump 


IO5 171 


I 2 6OO OOO 


1 20 


Cincinnati, O 
Boston, Mass 
Jersey City, N. J 
Detroit Mich 


River, filter, pump 
Creeks and river, pump . . 
River, gravity 
Lake pump 


325,900 
560,900 
206,433 
28s 7OO 


39,600,000 
80.000,000 
32,020,000 
44 800 ooo 


121 
141 

155 

1^7 


Los Angeles, Cal 
Pittsburgh Pa 


Springs, gravity 
River filters pump 


102,479 
321 600 


17,000,000 
54 ooo ooo 


166 
1 68 


Washington, D. C. . . . 
Omaha, Neb 


River, filter, gravity. . . . 
River, pump 


287,700 
102,555 


50,000,000 
18,000.000 


174 
175 


Cleveland, O 
Columbus O 


Lake, pump 
River filter pump 


381,000 

12s 1 ^60 


66,900,000 
23 ooo ooo 


175 
183 


Albany, N. Y 
Philadelphia, Pa 


River, filter, pump 
Rivers, filters, pump .... 


94,15! 

I203,7OO 


18,100,000 
287,188,000 


192 

222 


Buffalo N. Y 


Lake, pump 


3 ? 2 AOO 


02 36^ OOO 


262 













The examples cited in Boston are generally apartment- and 
boarding-houses, the average number of persons per house 
being 40. The consumption per capita varied from 59 gallons 
in the more modern and expensive houses to 16.6 gallons in the 
cheaper apartment-houses. 

Brookline, a wealthy residential suburb with a large number 
of private stables, conservatories, and lawns, had the large 
consumption of 44.3 gallons. 



112 



SEWER DESIGN 



TABLE XVI 



CONSUMPTION PER CAPITA FOR DOMESTIC USE IN BOSTON, 
BROOKLINE, NEWTON, FALL RIVER, AND WORCESTER, AS 
DETERMINED BY METER MEASUREMENT 



City 
or 
Town. 


dumber 
of 
louses. 


lumber 
of Fami- 
lies. 


lumber 
of 
Persons. 


Consumption 
Gallons per 


Remarks. 


Family. 


Capita. 


Boston 


3i 

46 
223 
39 
339 

40 


402 

628 
2,204 
413 
3,647 

' ' 828' 
490 
619 

278 
34 

148 

20,514 
81 
37 
93 

245 
229 


1,461 

2,524 
8,432 
1,844 
14,261 

1,699 
4,140 

2,450 
3,005 

1,390 
170 

740 

90,942 
327 
187 
447 
1,104 
809 


221 

185 
123 
80 
139 

221.5 
132.5 


59 

46 
32 
16.6 
35-6 

46. i 
44-3 

26.5 
6.6 

6.9 
25-5 

8.4 

16.8 
19 9 

23-4 
19.8 

12. 2 
15-6 


Highest-cost apartment-houses in 
the city 
First-class apartment-houses 
Moderate-class apartment-houses 
Poorest-class apartment-houses 
Average of all apartment-houses 
supplied by meter 
Boarding-houses 
Average of all dwellings supplied 
by meter 
All houses sup lied with modern 
plumbing 
These families have but one 
faucet each 
Ditto 
The most expensive houses in the 
city 
Average class of houses generally 
with bath and water-closet 
Whole domestic consumption 
Woodlan St., best class of houses 
Cedar St., best class of houses 
Elm St., houses of moderate cost 
Southbridge St., cheaper houses 
Austin St., cheaper houses 




Brookline. 


Newton .... 


490 


<( 




34-5 
127-5 

42.0 

80.2 
118. i 
95-0 
55.1 
55 


Fall River . . 
Worcester. . 


28 
64 



















In Newton, 490 families, averaging five in a family, had 
an average consumption of 26.5 gallons per capita. The 
houses are modern, with every plumbing convenience, but 
small grounds. 

The amounts used in Fall River and Worcester are very 
much less, partly from the manufacturing character of the 
cities and the resulting class of residents. 

For the future water-supply of Boston the quantity required 
for domestic use, based on the table and facts above given and 
on the known local conditions, proportions, and numbers of 
the various classes of residents, and with due regard for future 
growth of each class, was assumed to be 30 gallons per capita. 

Elaborate studies made in New York City upon the con- 



AMOUNT OF SEWAGE PER CAPITA 



113 



sumption of water in separate residences, seems to indicate 
that even the Brookline figures may be largely exceeded. Thus 
in 1900, Mr. J. J. R. Croes was .permitted by the owners of 
25 residences in Manhattan and of 12 residences in Brooklyn, 
to measure the amounts of water used in each house. Meters 
were used to secure the records, but no penalty was attached 
to the discovery of careless waste or wilful leakage. Table XV * 

TABLE XV 

SHOWING RECORD OF TWENTY-FIVE WATER-METERS IN RESI- 
DENCES IN MANHATTAN. AVERAGE FOR THREE WEEKS 
IN JANUARY AND FEBRUARY, 1900. 



No. 


Nearest 
Street. 


Nearest 
Avenue. 


Gallons 
per Day. 


Number 
of Oc- 
cupants. 


Gallons 
per 
Capita. 


Baths. 


Water- 
closets. 


Faucets. 


I 


121 


Manhattan 


138.68 


4 


34-67 


I 


2 


21 


2 


73 


Boulevard 


205.34 


4 


51-34 


2 


2 


25 


3 


30 


Lexington 


205 . 70 


7 


29-39 


2 


3 


12 


4 


88 


Amsterdam 


221 . 15 


5 


44-23 


I 


2 


II 


5 


38 


Third 


236. 10 


5 


47-22 


I 


2 


15 


6 


15 


Lexington 


243 08 


7 


34-72 


I 


2 


14 


7 


40 


Park 


286.05 


4 


71.51 


2 


3 


21 


8 


69 


Columbus 


318.51 


7 


45-50 


3 


3 


21 


9 


84 


Eighth 


354-35 


4 


88.59 


2 


3 


25 


10 


48 


i ( 


364.70 


6 


60.78 


2 


3 


13 


ii 


IO 


Fifth 


369-38 


10 


36.94 


2 


3 


17 


12 


18 


Third 


37I-9 1 


8 


46.49 


I 


2 


9 


13 


44 


Fifth 


387-68 


8 


48.46 


5 


6 


29 


14 


8 


Greene 


399-68 


6 


66. 61 


i 


4 


4 


15 


55 


Sixth 


480. 21 


8 


60.03 


3 


4 


13 


16 


72 


Riverside 


577-43 


ii 


52-49 


2 


4 


22 


17 


18 


Third 


578.21 


ii 


52.57 


2 


3 


7 


18 


77 


Riverside 


622 .64 


IO 


62.26 


3 


4 


27 


Average of 18 houses 


353.38 


6-95 


50.84 








19 


121 


Lenox 


519-33 


6 


86.56 


2 


3 


23 


20 


48 


Madison 


743-68 


9 


82.63 


2 


3 


28 


21 


94 


West End 


914-28 


8 


114.29 


2 


3 


24 


22 


71 


Boulevard 


916. 70 


9 


101.86 


3 


4 


15 


23 


88 


Riverside 


1303 . 76 


9 


I4 4-86 


3 


4 


16 


24 69 

25 |Houst'n 


Eighth 
First 


235I-74 
4521.91 


6 

21 


391 .66 

215-33 


3 


4 
3 


23 
6 


Average of 7 houses 


1610. 20 


9.71 


165-75 








Average of 25 houses 


705 . 28 


7.72 


91.36 









* Report to the Merchants' Association, p. 132. 



114 



SEWER DESIGN 



gives the results of the measurements for Manhattan, and is 
so arranged that the last seven houses only are guilty of excessive 
and unnecessary water consumption, as determined by careful 
inspection of the premises. It will be seen that the per capita 
consumption varied from 29.39 to 88.59 gallons, the latter 
according to Mr. Croes being neither abnormal nor excessive. 
In the last seven houses, the leakage and waste was unmis- 
takable. In No. 20, a leak was found in a flushing- tank, the 
repairing of which reduced the water used from 82.63 to 38.6 



12500 



75000 



7500 




5000 

a 
S 

2500 

I 



RECORD OF 25 WATER METERS ON RESIDENCES IN 
MANHATTAN, NEW YORK 

FIG. 26. 

gallons per capita per day. A similar leak in No. 23 caused 
a reduction in the use of water from 144.86 to 66.2. In the 
case of Nos. 24 and 25 water was found to be running con- 
tinuously through water-closets, and the stoppage of these 
leaks reduced the flow from 392 and 215 to 73 and 40 gallons 
respectively. Fig. 26 shows these data, expressed graphically, 
The heavy line is drawn so that its inclination indicates the aver- 
age rate of consumption, viz., 50.84 gallons per head per day. The 
relative inclination of the other line shows thus at a glance the 
agreement or non-agreement of the various houses. The effect 
of stopping the leaks in Nos. 23 and 24 is plainly seen, and that 



AMOUNT OF SEWAGE PER CAPITA 115 

in the case of No. 25, 'the waste which was curtailed for two 
days was allowed to continue. It is pointed out also that 
the marked change in rate in- the case of No. 5 was due to a 
visit of a small boy who delighted in sailing a toy steamboat 
in the bathtub of the house. During the ten days of his stay, 
he was drawing water for this purpose at the rate of 800 gallons 
per day, or he was instrumental in changing the per capita 
rate from 47 to 146 gallons per day. 

From this table, Mr. Croes concluded that since the reason- 
ble use, as indicated by the meter readings of the first 18 houses, 
was 351.9 gallons per house, the amount wasted was the 
average for the 25 houses, viz., 705.3 gallons less that amount, 
or 351.9 gallons, practically 50 per cent. 

In the large tenement-houses of New York, however, the 
consumption per head is much less than the above would 
indicate. Thus the next house to No. 25 above, was a tenement 
with 36 occupants and the water-consumption was 10.6 gallons 
per head per day. Another tenement on the west side made 
from two old residences, had 50 occupants and used water at 
the rate of 5.6 gallons per day per capita. 

The use of water for trade and manufacturing purposes 
shows a great variation in different communities. Brackett's 
report gives the actual amounts used in Boston; but without 
the number and size of the manufacturing industries his figures 
are of little value. The table is given, however, to show the 
relative amounts of water used by the different industries. 

In New York it was found that the amount of water used 
in buildings where some business was carried on was remarkably 
uniform, after the well-known largest consumers had been 
required to install meters. It was considered safe to estimate 
that on the average each metered tap in New York would 
deliver 1450 gallons per day, this amount having been found 
to hold almost exactly, year after year. 

After duly considering all the available data, Mr. Brackett 
found that the amount used in the Boston Metropolitan District 
for trade and mechanical purposes was about 25 gallons per 



116 



SEWER DESIGN 



capita. But he judged that, in view of the constantly increas- 
ing demand for water for these purposes, and also considering 
that an allowance of about 10 per cent should be made to cover 
shortage on meter measurements, at least 35 gallons per capita 
per day should be provided for these purposes. It is, of course, 
understood that this is applicable only to Boston, and that the 
amount will vary in different cities. Residential towns, for 
example, require little beyond that needed for domestic use. 
Other cities, with industries using large amounts of water, 
may require more than 35 gallons adopted for Boston. Of 



TABLE XVI 

METERED WATER USED FOR TRADE AND MECHANICAL PUR- 
POSES IN BOSTON, CHELSEA, SOMERVILLE, EVERETT, AND 
CAMBRIDGE IN 1892 



Name of Business. 


Daily 
Average 
in Gallons. 


Name of Business. 


Daily 
Average 
in Gallons. 


Offices, stores and shops .... 
Steam railways 
Factories 


2,458,700 
1,783,400 
1,414,000 


Saloons 
Laundries 
Chemical works 


120,500 
91,660 
87,270 


Elevators and motors 


I 337 700 


Iron works 


83 73O 


Sugar-refineries . ... 


O2O.2OO 


Mills and engines 


62 680 


Hotels (transient) 
Slaughter-houses 


596,200 
512,800 


Marble and stone works . . 
Wharves 


52,950 
39,8OO 


Street railways 


422,900 


Theatres 


36 100 


Electric companies. 
Breweries and bottling 


422,100 
420 040 


Fish stores 
Oil works 


18,200 

172 ^O 


Gas companies 


zccc^o 


Tanneries. . . . 


I6,8OO 


Shipping 


351,700 


Bakeries 


I3,O3O 


Stables 


309,600 


Markets 


I 2 050 


Miscellaneous 


2ZZ ,OOO 


Distilleries 


10,780 


Restaurants 


164 800 


Greenhouses 


9r ?Q 











course, the amount of water used in the various industries 
of a city has no relation to the population, and should be 
estimated from the amount and kind of manufacturing, 
although it can afterwards be reduced to a per capita basis 
for convenience. 

For public purposes Mr. Brackett has divided the use of 



AMOUNT OF SEWAGE PER CAPITA 117 

water as follows, the amounts being partly estimated and partly 
meter measurements: 

Public buildings, schools, etc 2 . 30 gals, per capita 

Street-sprinkling i.oo " 

Flushing sewers o.io " 

Fountains 0.25 

Fires. . . o.io " 



3-75 

Of this amount 4 gallons per capita was allowed for public uses. 

The amount of water wasted, that is, ignorantly allowed 
to escape from the mains and negligently allowed to escape 
from faucets and leaks, is very large. 

A very striking proof that the pumping records do not 
show the amount of water used is furnished by one of the 
towns in the Metropolitan District. All the water used in 
the town was measured by a meter on the supply-main, and 
every service-pipe has a meter. The works were but four 
years old, had 18 miles of cast-iron mains, 376 services supply- 
ing about 2300 persons, and, with the exception of the water 
used for flushing mains, street-construction, street-sprinkling, 
and for fires, all of the water used was measured by the meters 
on the service-pipes. . In 1893 the daily average amount 
registered by the meter on the supply-main was 128,560 gallons, 
while the total recorded by the service-meters was 65,380 
gallons. Allowing 2000 gallons per day for blowing-off pipes 
and for fires, there remains 61,380 gallons, or nearly 50 per cent 
of the whole consumption, unaccounted for. In Newton 46 
per cent of the water pumped was not accounted for by the 
service-meters, after making proper allowances for water not 
so registered. In Fall River, during the same year, with the 
most careful system of inspection to prevent waste, 37 per 
cent of the water pumped ^ould not be accounted for. 

In West Orange, N. J., the water company buys all its water 
by meter from, another water company and then sells it by 



118 



SEWER DESIGN 



meter to its various consumers. According to Mr. J. H. 
Fuertes,* the company is never able to account for more 
than 80 per cent of the water, although by rigid inspections 
and immediate stoppage of all leaks they are able to keep 
close to this limit. If a small supply, distributed through only 
about 30 miles of street mains, with every inducement for 
both water company and consumer to keep down the leaks, 
is subject to such a loss, it may be regarded as ideal when 
80 per cent of the water-consumption is accounted for. The 
following table from Mr. Fuertes' reportf gives other data, 
showing how, from the best evidence possible, the amount not 
accounted for varies from 16 to 43 per cent. 



TABLE XVII 

SHOWING PERCENTAGES OF WATER-SUPPLIES WASTED OR 
ACCOUNTED FOR BY REASONABLE USE 



NOT 



City. 


Water Used by 
Consumers. 


Public 
Uses. 


Total. 


Amount 
of Water 
Supplied 


Unac- 
counted 
for. 


Percen- 
tage. 


Per Cent 
of 
Services 
Metered. 


Manu- 
fac- 
turing. 


Domes- 
tic. 


Brockton 
Boston 
Cleveland 
Hartford 


5-5 
25.0 
40.0 

3-o 
37-0 
81.0 

II .0 

45-o 

39-3 
14.7 
0.4 
24.0 


16.6 
30.0 
26.0 
30.0 
30.0 
30.0 

15-0 
25.0 
31.0 
21.5 
28.6 
20.0 


3-0 

2 .O 
10. O 

5-o 
5-o 
5-o 
5-o 
5-o 
18.0 
3-o 

2-5 
2.0 


25.1 
57-o 
76.0 
38.0 
72.0 
116.0 
3i-o 
75-o 
88.3 
39-2 
3i-5 
53-5* 
39-o 


37-1 
86.0 
96.0 
62 .0 
138.0 
146.0 
54-0 
89.0 
108.3 
64.0 
55-o 
94-0 
68.0 


12 .0 
29.0 
20.0 
24.0 
36.0 
30.0 
23.0 
14.0 
20.0 
2 4 .8 
23-5 
40-5 
29.0 


32 
34 

21 

39 
33 

21 

42 

16 
19 
39 
43 
43 
42 


90 

49 
99 
about 80 
about 90 

84 
79 

72 

45 

IOO 
100 

95 


Harrisburg (1891) 
(1904) 
Lawrence 
Milwaukee 


Syracuse 


Taunton 
Wellesley 


Yonkers 


Worcester 











* So given by Mr. Fuertes. 



By measuring the flow of water through the water-mains 

* Report of James H. Fuertes, C.E., on "The Waste of Water in New York 
and its Reduction," p. no. 

t Pp. 45-47- 



AMOUNT OF SEWAGE PER CAPITA 119 

in Boston it was found that between i and 4 A.M., when little 
water should be used, there was still a consumption at the rate 
of from 30 to 35 gallons per capita. In Brookline, where the 
taps are nearly all metered, from June to December, 1891, the 
consumption from midnight to 4 A.M. was 44 per cent of the 
total consumption, or at the rate of 25.8 gallons per capita, 
and a careful inspection of every fixture only reduced this to 
17.7 gallons. Other methods of comparison between the night 
flow and that used properly for domestic and city purposes 
led Mr. Brackett to sum up the question of waste as follows: 

" That there exists a waste of from 40 to 50 per cent of 
the total consumption in most cities and towns where meters 
are not generally used is a fact accepted by those who have 
studied the question, but it is, I think, the popular idea that 
this enormous waste can be, and is, almost entirely prevented 
by the use of water-meters on the services. But the results 
obtained in the cities and towns where the largest number of 
meters are in use show that while the consumption per capita 
is smaller than in unmetered places of the same general 
character, still a very large proportion of the water supplied 
by the reservoirs or pumps does not pass through the service- 
meter." 

His conclusion for Boston was that it is not possible even 
with the use of meters to reduce the waste below 15 gallons 
per capita ; and that if some efficient system of waste-prevention 
is not adopted, the amount wasted will become, as it is now 
in some of our large cities, from 30 to 60 gallons per inhabitant. 

As the result of this painstaking work, Mr. Brackett con- 
cluded that the future water-supply of Boston would need to 
provide 100 gallons per capita per day for the daily con- 
sumption, made up as already indicated: 35 gallons for domestic 
use, 35 gallons for trade and manufacturing, 5 gallons for 
public purposes, and 25 gallons for waste, the last amount 
being taken in view of the uncertainty of securing strict pre- 
vention of waste. 

A common method of estimating the constant leakage and 



120 



SEWER DESIGN 



Water Consumption per Head per 
Day in Gallons 

:*> e o> -i oo o o P to w 
oooo oooooo 



k 






K 



Midday 

6P.M. 

Midnight 

CA.M. 

Midday 

6P.M. 

Midnight 

6A.M. 

Midday 

6P.M. 

Midnight 

6A.M. 

Midday <M 

6 

6P.M. 

Midnight 

6A.M. 

Midday 

0P.M. 

Midnight 

CA.M. 

Midday 

6P.M. 

Midnight 

6A.M. 

Midday 

6P.M. 

Midnight 

6 A.M. 

Midday 



waste from a water sys- 
tem is to measure the 
night flow and assume 
that all that amount ex- 
ceeding a small quantity 
for night use and un- 
avoidable or incurable 
waste is a constant waste 
that can be cured if proper 
measures are adopted. 
Thus Mr. Freeman in his 
report to Hon. Bird S. 
Coler on the water-supply 
of New York determined 
the rate of flow from hour 
to hour, as shown in Fig. 
27,* and showed graph- 
ically what a large part 
of the city's water-supply 
served no purpose, but 
was altogether wasted. 
In figures, his conclusion 
was that at the times 
when the demands for 
water were practically 
zero, that is, between 2 
and 4 in the morning, the 
consumption still existed 
at the rate of 94 gallons 
per head per day. Mak- 
ing the liberal allowance 
of 19 gallons for night use 
and 10 gallons for incur- 
able waste, Mr. Freeman 

* Redrawn from Diagrams 
Nos. 5 and 6. 



AMOUNT OF SEWAGE PER CAPITA 



121 



concluded that the needless waste 
in New York City was 75 gallons 
per head per day. His conclusion 
seemed to be justified by a com- 
parison of the consumption curves 
of New York with those of Fall 
River and Woonsocket, Fig. 28,* 
the similarity being very marked, 
except for the constant excess in 
length of the New York ordi- 
nates. 

Mr. Fuertes,! on the other 
hand, believes that a large night 
flow is a necessary accompaniment 
of a large, progressive, manufactur- 
ing city. He cites the night-con- 
sumption in Chicago (165 gallons 
per capita) for comparison and 
compares it with a night flow of 
1 06 gallons per capita in a certain 
district in the Bronx. It was 
known that in this last, the mains 
were new, the buildings generally 
metered, and that this large night 
flow was due to its use in manu- 
facturing. Mr. Fuertes says that 
it appears to him that data con- 
cerning night-consumption in large 
cities are really of little practical 
value in forming a foundation on 
which to build up demonstrations 
of excessive wastage. 

But there can be little doubt 
of the value of this sort of study 

* Redrawn from Diagrams Nos. 5 and 6. 
t Fuertes' Report, p. 124. 



Rate of Consumption, 
Gallons per Cap per Day 







(i 


-^ 
















\ 




Noon 
1 








^/ 
















I 








-f 
























; 


















y 






y. 


















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/ 
















/ 








Mid- 
n ght 
















/ 










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lit 


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^ 


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, y 
















s- 








































r^ 










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Mid- 
night 














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O 




















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t~ 




























ra 




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J< 
















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5 


















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s 


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x^ 




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B 

d- 

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r 






(y 
















/ < 








M 

in 


i; 














/ v 










\ 








































^ 












*"* 1 


*" 


-^ 














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) ; 
















; 








x 


8 














, 




Noon 




c 


<- 



























> r ; 














s 






p 

X 

g 






^ 
















i 








> X 










































































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^ ^_ 




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4 





FIG. 28. 



122 



SEWER DESIGN 



in fixing on the waste in strictly residential cities, and it 
would seem that if large night flows are due to manufacturing, 



INCREASE IN CONSUMPTION 

OF 

WATER PER INHABITANT 

FROM REPORT TO COMPTROLLER 
OF NEW YORK CITY 
BY JOHN R. FREEMAN 
1900 








ouu 
290 

280 
270 
260 
250 
240 
230 
220 
210 
200 
190 

Q 

180 t! 
170 * 
160-2 

150 g 

a 

140 " 
8 

130 a 

120 1 

3 

110 
100 
90 
80 
70 
60 
50 
40 
30 
20 
10 









1 


\ 
> 




j 


, 






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/ 


V 






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ffalo 








f 1 
p / 


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iladelphia 






f T' 





t 






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/ /'\ 


," x 
/ 


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5bington 








2 


/ \ 


/ s 










7 


/ Jl 

/ 5 


Q?f 










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/ / 

/ / 


w 


Y O ^- Chi 


sago 








/ v / 


Q 'j 


</ 


\ ..Average 
>'? 






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tf 


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' \/ Detroit 




/ 


\jC/ x ' 


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S New York 




I 


/ , 


^v 


/., 


* 


S/^J 


Tewark 




7JL 


/ 




/.- 


^ 








TL* 


i ./ 


"* 


/ ] 


i * 








-M^- 


^Vs- 


*" 

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/ V 


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b*zzy 








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-4 


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l>> t-. GO GO C^ C5 O 



FIG. 29. 



such industries as are concerned might be determined and 
allowed for. 



AMOUNT OF SEWAGE PER CAPITA 123 

Another factor, affecting the per capita consumption of 
water, and particularly noteworthy because sewers to carry 
the waste water are designed for the water-consumption at 
some distant time in the future, is that there is a tendency 
for all cities to increase the rate of per capita consumption, 
as they increase in size. Fig. 29, from the Freeman Report,* 
shows this tendency unmistakably, although the exact rate 
varies largely in different cities and in a few cities the law is 
apparently contradicted. Nor is this inconsistent with the 
statement already made that there seems to be no relation 
between the per capita consumption and the size of cities. 
In any one city, the rate increases as the city grows, and the 
figure would indicate that, as an average value for large cities, 
the increase is about 30 gallons every 10 years. Even in cities 
where meters are generally used, the law holds, though the 
rate of increase is smaller. 

The possible effect of a general introduction of water-meters 
and the effect of their use on the rate of consumption must 
be considered also in predicting future water-consumption. 
To actually say that a city in which water-waste has been 
abnormal will instal meters and that, as a consequence of this 
predicted action, the sewers may be made only a fraction of 
the size otherwise necessary, would not be a safe engineering 
venture. But the probable result of installing meters may 
be pointed out and the consequent saving in the cost of 
building sewers used as an argument in favor of their purchase 
and use. Fig. 30, from Freeman's Report, f shows in a general 
way the effect upon the per capita consumption of the use 
of meters. The curve of the average is not exact, but is drawn 
as summing up the general tendency and as a convenient guide 
to the eye in studying the comparative effect of various per- 
centages of meters in the different cities. The effect of meters 
is unquestionably to reduce the careless waste of water that 
occurs in about 25 per cent of the house-services. At first, 
it has a tendency to reduce the reasonable consumption, but 

* Diagram No. 4. f p. 70. 



124 



SEWER DESIGN 



such a tendency is soon suppressed, or offset by the effect of 
the growth of the city. Thus Fall River, as shown by the 
diagram of Fig. 31,* had in 1874, a per capita consumption 



ZDU 

225 














EFFECT OF THE USE OF METERS 

UPON THE 

CONSUMPTION OF WATER IN SEVERAL CITIES 

FROM REPORT TO COMPTROLLER 
NEW YORK CITY 
COMPILED BY JOHN R. FREEMAN 
1900 
















































\ 












per Day 


1 








\1 








\ 








\ 


"1 


fA\b 


my 


v\ 










\ 










Inhabitanl 


\ \ 




1 








1l 




l 








' ' 1 


\ 


I 










\ 


I 




























| \ 


(!) 










Consumption in Gallons per 

& S S 8 1 I 


A 


n 
















ti 
















\\ \ 


















\\ 


Detr 


oit 














s 




















\ 


. 
























\\ 




















t 




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V. 




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* 


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V, 


--^ 








\ 


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9 








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V 




k 














s . 




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chme 


nd 
















































x . 


























"*s x 














\ 


New 


Yorl 
























k -< 


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T,o 


well 




^*^ 




















I 






/ 


'^ 


P/> 


*s^ 


<""- 


-o 


^ 







^ 


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fe 


^ 




r f 


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k 


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Pong 


hkee 


psie 




t 


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*-, 


s/ 


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t< 












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,on 














t 


















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- -_ 




u 





























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r 


















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4 f 






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w 




Fa 


1 Kiv 


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* 






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ton 






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Low 


ell 































































































































































10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 
Percenttv-o nf TapsMetered 

FIG. 30. 

of 84.5 gallons. This decreased steadily with the introduction 
of meters until in 1887, with 70 per cent of the services metered, 



* From figures quoted by Mr. Fuertes, p. 155. 



AMOUNT OF SEWAGE PER CAPITA 



125 . 



the consumption was only 26.9. Since 1887, there has been 
a slight but nearly constant increase in the rate. Fig. 32, 




O 190 



C -*-> 



170 



100 



120 



1900 



Me 



30 40 50 60 70 80 90 

Percentage of Meters to Service 

FlG. 31. 




1903 



FIG. 32. 



1904 



25000 SS 
Bo 
20000 2 a 



15000 -g ^ 

l! 



5000 



from Fuertes' Report,* shows the effect upon the water con- 
sumption of the gradual installation of meters in Cleveland 

* p- 143- 



126 



SEWER DESIGN 



The decrease in the per capita water-consumption as the number 
of meters in use increases is clear evidence of the effect of the 
latter in eliminating leakage and waste. 

As a further example of a method of ascertaining the relation 
between the amount of water used and the character of the 
population, reference is made to Vol. VI, No. i, of the Journal 
of the New England Water- works Association, where the rela- 
tion is shown between the number of fixtures in a house and 
the amount of water used. The following table, since partly 
amended, is taken from that report. It shows that bv actual 



TABLE XVIII 





Per Cent of 
First-faucet Flow. 


Gallons per Capita 
per Day. 


First faucet 




7 


Second faucet 


2O 


I A. 


First bath 


CQ 


7 r 


Second bath 
First water-closet 


15 
IOO 


I . I 

7 O 


Second water-closet 
Set tubs 
Hose 


40 

20 
I 


2.8 

1.4 

I . I 


Stores, etc 
Schools 
Churches 


50 
50 

IO 


3-5 
3-5 

O 7 


Boilers 
Laundries 


130 

2OO 


9.1 

14 o 


Greenhouses 


QO 


6 3 


Stables 


50 


3-5 



meter-readings in Newton, on houses having but one faucet, 
7 gallons per capita per day was the average amount used, 
the minimum being 5 and the maximum 1 1 ; that when a house 
has two faucets, 20 per cent of additional water is used; for 
the first bath, 50 per cent additional, etc. All these are based 
on a family of five, the average number in Newton. If boarding- 
houses or tenements are considered, these numbers will be 
increased by about 7 per cent per person. 



AMOUNT OF SEWAGE PER CAPITA 127 

The average water-consumption, however, no matter how 



-H 



# 







D O ~ 






SNOTIVQ 



carefully estimated, is not a sufficient guide to the rate of 
sewage-flow. Further knowledge is needed on the subject of 



128 



SEWER DESIGN 



the variation of flow from hour to hour. Evidently more water 
is used and the flow to the sewers is greater during the day 
than during the night, and if the size of the sewer was based 



Aug. 25-26 
1890 



Aug. 10-11 

















WATER 
HEMI 
ROCHE 


CONSUMPTION 

FROM 

.OCK LAKE 

AT 

:STER, N. Y., 
1890. 

II 


^ / 

\ / 
\^/ 





\ 
\ 



















-* 


N 


\ 
\ 


/ 
i 

/ 


i 
\ 

\ 








^/ 


X*" 


\ 


/" 


x, 




\ 








\ 
\ 


















DJ 












^\ 


\ 






^^ 


\ 


















1 
















\ 


1 




\ 


Y 

\ 
\ 


\ 










































\ 


I 


\ 


* 


y 


/ 
/ 






































\ 


/ 























































450000 



400000 



350000 



300000 



250000 



200000 



150000 



100000 



50000 



FIG. 34. 

only on the average flow through the twenty-four hours, it 
would be too large at some times and altogether too small 
at others. To fulfil its purpose, the sewer must plainly be 
large enough to readily carry off the water, at that time of 
the day when the rate of flow is largest, even if it requires 



AMOUNT OF SEWAGE PER CAPITA 



129 



an area two or three times that necessary for the average 
flow. 

To show actual examples of hourly and daily variation 
in the water-supply, the following diagrams are given: 

Fig. 33 shows the variation in the daily water-consumption 
of the city of Binghamton, N. Y., the details being furnished 
to the author through the kindness of Mr. John Andersen, 
secretary of the Water Board. The average daily rate for 



Sunday 



Monday 



Tuesday 



Wednesday 



Thursday 



Friday 



Gallons per Capita perDay 

sl__|__i___J 


1 


1 1! 


1 1 


1! 


i! 


1 1 


! 1 


II 


1! 




n 


n 


I 


1 1 


ii 


ii 


i 


n 




'1 


n 


1 1 


1 1 




Ii 




1 1 


i 


! 






| 




i 








\ 




"T TT 




















































































































































































































































































































































y v 




^ 












K, 












f 


u - 


v^. 
















^ 












>- 




A 


{\ 


. 


















V 






/ 






x 










f 










N 






f 









\ 








/ 




J 


L 




^/ 








/ 










1 




I 


3hi 


aj. 


'0 


V. 


A 


r 




f 


la 


n 


i: 


-8 


\ 


19( 


1,, 










Vj 


^ 




















1 




/ 










I/ 


X 


7 












J 


^ 














A 














(, 




^ 




* 















V* 




















































































































































































































































































































































































































































































































































































































































































































































































f. 
















































v 


\ 












11 




^ 










1 


\ 




\ 












\ 


f 


> 



















^ 


















\ 














y 












V 


. 
































/ 


\ 


A 










/ 






i 
















\ 




F 


* U J 


R 


Vt 


r 


V 


A 


[>r 


il 


z 


. 


M; 


A 


2, 


11 


00 






7 




i 


^~ 


\ 






/ 






I 


^ 






/ 








v 






/ 














f 










s 








w 












\, 


J^ 












._ 


^ 












S 


^ 


z 










\, 


X 


^ 












\ 


ZE 






i 


u 


n 


^ 






nil! 






iL 














u 


1 


1 1 


|| 


,1,, 


i] 


M 


IL 




\\ 


| 


-LL 


IL 


1 1 


| 


i 


1 


! 


Ml' 


Ii ii 



g 
s s 



FIG. 35- 



the five days is 220,440 gallons per hour, as shown by the heavy 
straight line; the average daily maximum (272,400) being 
24 per cent more than the average daily consumption. 

Fig. 34, from a table given by Rafter and Baker, shows the 
water-consumption in Rochester from Hemlock Lake. As 
before, the average rate of consumption is added and the 
maximum consumption is thus shown to be 46 and 58 per 
cent more than the average, for the two days shown. 

In Fig. 27, the variation in the water-consumption has 
already been shown. The maximum rate there is 143 gallons 



130 



SEWER DESIGN 



per capita, and the average 115, for the maximum rate is only 
24 per cent more than the average. If, however, 65 gallons 
of waste were to be eliminated, so that the average rate would 
be 50 gallons and the maximum 78 gallons, the latter would 
then be 56 per cent greater than the average. 

TABLE XIX. 

GAGINGS OF DRY-WEATHER FLOW OF SEWAGE AT DES MOINES 
AND ELSEWHERE 







Popula- 


Sei 


vage Flo 


w. 


Per 

Cent 


Per 
Cent 
Max. 


Sewer. 


Date. 


tion. 
Tribu- 
tary. 


Mini- 
mum. 


Aver- 
age. 


Maxi- 
mum. 


Max. 
above 
Aver- 
age. 


above 
Aver- 
age. 
Min. 
madeO. 


Compton Av., St. Louis. . . . 
College St., Burlington, Vt. . 
Huron St., Milwaukee, Wis. 
Memphis, Tenn 


1880 
1880 
1880 
1881 


325 
3,174 
2O,OOO 


65 
65 

61 


102 

US 


149 
140 
1 2O 
140 


46 
30 


130 
70 


13 sewers Providence, R. I. 


1884 


? 9 82 ^ 




78 








16 sewers, Toronto, Can .... 
Hospital, Weston, W. Va. . . 
Schenectady, N. Y 
Canton Ohio 


1891 
1891 
1892 
1803 


168,081 
I,OOO 

* 1 0,000 
40 ooo 


40 
72 

CA 


87 
91 
86 

1 2O 


151 
103 

1 80 


66 

20 
40 


118 

71 

68* 


Chautauqua 
Iowa Agricultural College. . . 
Des Moines, Iowa, East side 
11 West side 
Cadillac, Mich 


1894 
1894 
1895 

1895 
1906 


7,000 
289 
3,100 
19,400 
2,992 


6 
o 

22.5 

54 
152 


2O 
32 

74 
129 
202 


30 

77 
142 
1 80 
2 53 


50 
141 
92 
40 
15 


7i 
141 

131 
68 

IOO 


Gloversville, N. Y : 


1908 


20,642 


61 


IOI 


143 


42 


105 



* Estimated. 

The variation shown in the next to the last column is evidence of the effect of 
ground-water flow. The larger the minimum flow, the smaller the effect of the 
daily variation. The last column shows the percentage by which the maximum 
is greater than the average if the minimum flow be made zero and the average 
and maximum flows reduced by the same amount. 

Fig. 35 * shows the hourly variations in the cities of Chicago 
and Fall River. In the former, the leakage is very large, 
and the maximum rate of consumption only 15 per cent more 



Fuertes' Report, p. 12, 



AMOUNT OF SEWAGE PER CAPITA 131 

than the average. In the latter the leakage is very small 




SNOTIVO 



and the maximum rate is at least 100 per cent more than the 
average. 



132 



SEWER DESIGN 



A list of actual sewer-gagings, so far as have been made 
public, was compiled and published in Engineering News, Vol. 
XXXV, p. 131, in a paper on sewer-gaging of Des Moines. 
The table is given on p. 130, Table XIX, with gagings of the 
outlet sewer at Canton, O., Chautauqua, N. Y., Cadillac, 
Mich., and Gloversville, N. Y., added. Two columns have 
been added to the table, one giving the percentage by which 
the maximum flow is greater than the average, and the second 
the same percentage, should the quantities involved be reduced 
by the amount required to make the minimum zero. The 
percentage will be affected largely by the amount of ground- 
water running in the sewer and by the amount of water used 



Z5000 



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SEWAGE FLOW 

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10 \t IMA 4 



for manufacturing purposes and discharged into the sewer. 
No definite information on this point, however, is to be 
found. 

Fig. 36 shows a sewage-pumping diagram for Atlantic City, 
N. J., for the year 1892. The effect of the summer season 
is plainly seen, as well as of the other holidays of the year.* 

Fig. 37 shows a diagram prepared from the results of a 
gaging of the outfall sewer of Canton, 0., in the spring of 1893.1 
The average daily amount (21,100 gallons) has also been 
calculated and added, the maximum amount being 43 per 
cent greater than the average. 

* Engineering News, Vol. XXIX, p. 123. 
t /&*., Vol. XXX, p. 61. 



AMOUNT OF SEWAGE PER CAPITA 



133 



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134 SEWER DESIGN 

Fig. 38 shows the results of the gaging of the Schenectady 





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outfall sewer as given by Mr. Landreth.* The average line is 

: * Engineering News, Vol. XXVII, p. 305. 



AMOUNT OF SEWAGE PER CAPITA 



135 



added (35,500 gallons), and the maximum found to be 59 per 
cent greater than the average flow. 

Fig. 39 shows the results of the gaging of the sewer at the 
Insane Hospital at Weston, Va., made under the direction 
of Mr. Rafter and quoted in Rafter and Baker's " Sewage 
Disposal." The maximum here is found to be 22 per cent 
greater than the average. 

Fig. 40 is a diagram taken from the paper of Mr. Grover 
already alluded to. 

Fig. 41 gives a diagram of the sewage-pumping records at 




anks 



s Flush Tanks 



: 



18 Sew 



i\ 



Tune 2G, 



July 3, 



Chautauqua, N. Y., on the days indicated.* Here the average 
for the four days is 5700 gallons, the average maximum flow 
being 50 per cent more than the average. 

In Fig. 40 the effect of constructing poor pipe-lines is plainly 
seen from the large flow at the times of day when there should 
be little or no flow in the sewers. While the maximum flow is 
only 56 per cent greater in amount than the average flow, yet 
it is 117 per cent greater than the average if the flow at 3 A.M. 



* Ibid., Vol. XXXI, p. 87. 



136 



SEWER DESIGN 




AMOUNT OF SEWAGE PER CAPITA 137 

be called nothing, and the flow for the rest of the day reduced 
correspondingly. 

Fig. 42 shows three curves based on gagings made of the 
two main sewers of the small city of Cadillac, Mich. The lower 
curve is for the 1 2-inch main, serving 475 persons. The middle 
curve is for the i8-inch main, serving 2517 persons. The 
upper curve is the result of adding together the measurements 
in these two sewers but correcting for the discharge of thirteen 
flush-tanks. The 1 2-inch pipe, without flush- tank water, had 
a minimum flow of 221 gallons, an average of 318 and a max- 
imum of 558, the latter being 75 per cent greater than the 
average even with the high minimum flow. For the 1 8-inch 
pipe the minimum rate was 138 gallons, the average, 178, 
and the maximum, 239, or 34 per cent above the average. 
The large flow is said to be due almost wholly to defective 
plumbing, and the results are interesting as indicating the large 
amount of waste in a relatively small place. 

Fig. 43* shows a long-time measurement of the flow of 
sewage in the intercepting sewer at Gloversville. The large 
flows in the spring of both years is undoubtedly due to ground- 
water entering the pipes, although the system is intended 
strictly for house sewage only. The minor variations from day 
to day are very marked and the excess in March is plainly 
responsible for a flow more than double the average. 

Fig. 44, also of Gloversville, shows the hourly variation for 
a typical day. The effect of the mill wastes is most striking 
and serves, in this city at any rate, to show that the high night 
flow of sewage is not due to manufacturing use. 

For the sewage alone, the average hourly rate was 62,000 
gallons and the maximum 78,000, or 26 per cent increase. 
With the mill wastes added, the average flow is 84,000 gallons 
and the maximum 119,000, an excess of 42 per cent. 

It follows from a study of the tables and diagrams given 
above that while the amount of flow or the per capita flow 
varies between wide limits, affected largely by the amount of 

* Report of Harrison P. Eddy and Morrell Vrooman to Mayor of Gloversville. 



138 



SEWER DESIGN 



water wasted, a law of daily variation is to be found for all 
places, and that the maximum flow is from 50 to 100 per cent 
greater than the average flow. The obvious method, then, 
for determining the proper amount of house-sewage flow is to 
determine the probable daily water-consumption per capita at 
the future time for which the sewers are designed. About 
75 per cent of this might then properly be assumed to be the 



TYPICAL HOURLY QUANTITY 
OF SEWAGE 

GLOVERSVILLE, NEW YORK 

QUANTITY OF DOMESTIC SEWAGE, MILL 

WASTES AND DOMESTIC AND MILL SEWAGE 

COMBINED, DISCHARGE PER HOUR 




A.M. 



P.M. 



FIG. 44. 



sewage flow. It will be safer, however, to assume that the 
maximum water rate will be the maximum sewage flow, and 
that any extraordinary excess in water rate will be partly com- 
pensated for by the fact that really only about three-quarters 
of such excess will reach the sewers. Therefore, add 100 per 
cent to the average water-consumption for the maximum rate 
of flow, and the result is the amount of flow for which the sewer 
must be designed if it is to be limited to house-sewage. This 



AMOUNT OF SEWAGE PER CAPITA 139 

does not include, it is to be noted, any ground- water flow nor 
any large manufacturing enterprises which may affect the 
daily variation. 

Analyses, more in detail, have been made of the variation in 
the flow, considering not only the daily maximum, but also 
seasonal variations, taking the monthly maximum and adding 
it to the weekly maximum, to the daily maximum, and to 
the hourly maximum. This method was given by Fanning in 
his " Water-supply," and was quoted by Staley and Pierson. 
Baumeister says that the days of greatest consumption require 
one and a half times as much water, and hence the sewers 
must be designed to carry off one and a half times the normal 
flow. The hourly maximum is one and a half times the hourly 

mean. Hence the capacity of the sewer must be such as to 

ji \/ j JL j 
remove hourly - - of the average daily quantity, or 

more than twice the amount calculated on the supposition 
that the same quantity was supplied each hour of the year. 
In one of the recent German books on water-works by Franzius 
and Sonne the daily maximum is fixed at ij and the hourly 
at if, making the average between the latter and the daily 

average - - = approximately.* 

A common method of defining the maximum flow is to say 
that one-half of the daily flow will run off in 6 to 8 hours, 
and the sewer must be designed for this rate of flow. From 
the diagrams given, and taking the midday hours when the 
flow is greatest, the number of hours required to carry off 
one-half of the daily flow is as follows: 

Binghamton, August 9 loj 



10 IOJ 

" ii gi 

" 12 10 

" 13 IOJ 



Baumeister. 



140 SEWER DESIGN 

Rochester, August 10 gj 

" 25 8| 

Canton g| 

Schenectady 1 1 

Hospital, Weston 9 

Chautauqua, July 24 8J 

" 3i 81 

August 16 9! 

" .18 9* 

indicating that to assume that one-half of the daily flow will 
flow off in 8 hours is a safe assumption. It further indicates 
that a capacity of twice the average flow is a larger allowance 
than necessary. 

What the daily average will be must be left to the judgment 
of the engineer. By Table XII it varies from 19 to 222 gallons 
per capita per day, according to published records. Mr. 
Brackett shows that for the vicinity of Boston from 11.2 gallons 
to 44.3 gallons per capita per day are legitimately used for 
domestic purposes, and that these amounts must be increased 
for public purposes and for manufacturing and trade. 

Mr. Whitney of Newton shows that the amount of water 
for domestic use varies with the number of fixtures in the 
house, from 7 gallons per capita per day for one faucet to 22.8 
gallons for two faucets, two water-closets, and two baths, and 
that other uses increase the amounts as given in Table XVIII. 

It remains for the engineer, after studying the character of 
the population and the possibility of manufacturing interests, 
to fix such a per capita allowance as is appropriate for that 
community. 

PROBLEMS 

42. From Fig. 24 determine the ratio of the sewage flow to the water- 
consumption for the months of July and September. 

43. From Table XIII, plot points showing the relation between total 
population and per capita consumption. See if the relation follows any 
law. 



AMOUNT OF SEWAGE PER CAPITA 141 

44. If 75 gallons per head per day in New York City are wasted, 
and can be eliminated, what would be the ratio of the maximum daily 
rate to the average, after the waste is stopped? What is it now, by 
Fig. 27? 

45. From Fig. 33 determine the average and maximum rates, if they 
are corrected on the assumption that the night flow is hiefly waste and 
can be reduced to 1000 gallons per hour. What percentage then will the 
maximum be of the average? 

46. The average daily water-consumption of a city is found to be 
5,000,000 gallons. What rate of flow, in cubic feet per second, should 
be taken for the sewage flow? Use Baumeister's rule, and then compare 
with the suggestions of p. 138 and p. 139. 



CHAPTER IX 
GROUND-WATER REACHING SEWERS 

THE amount of rain-water entering a sewer has been dis- 
cussed, and also the amount of water from domestic uses, the 
latter including the amount used for manufacturing and other 
municipal purposes. It now remains to determine the amount 
likely to come from the ground-water through which the sewer- 
line passes. This amount will depend on the material of which 
the sewer is made, on the kind of joints, on the method used in 
making them, and on the distance and head of ground-water 
in which the sewer is exposed to the infiltration. The last 
condition has considerable variation even in the same line, 
both because of irregular variation due to rain and because of 
periodic seasonal changes. In constructing the filter-beds at 
Brockton, it was found that there was a seasonal variation 
of 4 feet in the height of the ground-water, the height being 
greatest in May and least in November. Such a rise in the 
elevation of the ground-water might increase the length of 
sewer exposed to ground-water by some miles, especially if 
the hydraulic grade of the underground stream followed nearly 
parallel to the sewer-grade. 

In his report on the Sewerage of Ithaca, Mr. Hering says: 
" In addition thereto [60 gallons per capita per day, assumed 
for average water-supply], 10 per cent of this quantity has 
been added to allow for ground-water which will probably find 
its way into the sewers in spite of the most careful workman- 
ship." 

In the report on the Sewerage of the Mystic and Charles 
rivers, January, 1889, the engineer, Mr. F. P. Stearns, has 
collected the following information: 

142 



GROUND-WATER REACHING SEWERS 143 

" Kalamazoo, Mich. Some ground-water finds its way into 
the system, estimated from data taken before the sewers were 
open for public use, to be 20 per cent of the capacity of the 
sewers. 

" Norfolk, Va. No accurate estimate made, but ground- 
water forms at least 60 per cent of pumping. From informa- 
tion given elsewhere in the returns, the maximum flow is found 
to be about 167 gallons daily per inhabitant connected with the 
sewers. Of this, the ground-water, estimated at 60 per cent, 
equals 100 gallons. 

" Schenectady, N. Y. The sewers are laid through wet 
ground and quicksand in some instances. The Erie Canal 
seepage also affects them to a small degree. Measurements 
made at about the time that the system was completed indicate 
that the infiltration of ground-water amounts to about 5 per 
cent of the capacity of the mains." 

Mr. Stearns also says that he has recently examined two 
new systems of pipe sewers which were built with the intention 
of excluding the ground-water, and in both cases the amount 
of water collected by the sewers was considerable. In one of 
the cases, where the population connected with the sewers 
was small, the amount of ground-water was probably in excess 
of the sewage proper. 

In the sewerage works of Canton, O., built in 1893, a 20-inch 
outfall with no connections was gaged for subsoil water, and in 
a length of 2400 feet a flow was found, due to infiltration, of 
31,712 gallons in 24 hours, or at the rate of 70,000 gallons 
per mile per day. In the same system of about n miles 
there was a flow to the disposal works between midnight and 
6 A.M. of about 73,000 gallons, which is at the rate of 26,500 
gallons per mile per day (Engineering News, Vol. XXX, 
p. 61). 

In the design for Taunton, Mass., 20 per cent for infiltra- 
tion was added to the estimated flow in a 24-inch pipe passing 
through a swamp. 

In North Brookfield, Mass., 1580 feet of 1 2-inch pipe was 



144 SEWER DESIGN 

found to leak at the rate of 2500 to 5000 gallons per day, a 
rate of about 17,000 gallons per mile per day. 

At Rogers Park, 111., Mr. Broughton, engineer for The 
Shone Co., by means of special precautions (deep sockets and 
careful ramming) reduced the leakage in 9200 feet of 6-inch 
pipe under a head of from i foot 6 inches to 9 feet 6 inches 
of water, to 15 gallons per minute, or 1240 gallons per mile 
per day. 

In Winona the same engineer made all sewers, which lay in 
water with a head of more than 5 feet, of cast iron. 

At Brockton, Mass., the ground-water flow was said to be 
400,000 gallons from 16 miles of sewers, or 25,000 gallons per 
mile per day. 

At Altoona, Pa., the flow from 6100 feet of 27-inch pipe 
was 47,181 gallons, or at the rate of 40,814 gallons per mile 
per day. 

From 3190 feet of 3o-inch pipe the flow was 52,352 gallons, 
or at the rate of 86,592 gallons per mile per day. 

From 5030 feet of 33 Jx 44-inch brick and concrete sewer 
the ground-water flow was 252,342 gallons, or at a rate of 
264,000 gallons per mile per day. It should be noted, however, 
that this last flow has since been largely reduced by the con- 
tractor working under the direction of the engineer. 

In the East Orange sewerage works,* where the conditions 
for producing a water-tight sewer were unusually severe, a 
large part of the line being 10 feet or more under water and 
laid in quicksand, but where at the same time unusual pre- 
cautions were taken to prevent leakage, the amount of ground- 
water entering the sewer from 29 miles was found to be 650,000 
gallons. The house-sewage flow after three years' use was 
620,000 gallons, and the flush-tank flow 30,000 gallons. 

Rafter and Baker, after noting that at East Orange some 
of the sewers were laid under 20 feet of ground-water, and that 
a brick sewer with its many joints and porous material was 

* Trans. Am. Soc. C. E., Vol. XXV, p. 125. 



GEOUND-WATER BEACHING SEWERS 145 

used for 4000 feet in a location most unfavorable for tight work, 
and that with these exceptionally adverse circumstances the 
infiltration was only 50 per cent of the total quantity, or an 
amount equal to the domestic flow, say: " The results obtained 
under the extremely unfavorable conditions existing at East 
Orange of a leakage of only 2.5 gallons per second (215,000 
gallons in 24 hours) from 25 miles of vitrified-tile sewers, with 
66,000 joints, is indicative that, under favorable conditions 
and with careful workmanship, a system of such sewers may 
be made nearly impervious, though in designing disposal work 
it will probably be safe to allow for an infiltration of 15 per 
cent of the flow of sewage proper." 

In connection with studies made on the pollution of Boston 
Harbor, the State Board of Health of Massachusetts had tests 
made on the infiltration of ground-water into sewer systems 
of recent construction. These showed * that into 137 miles 
of sewers, ranging in size from 8 inches to 36 inches diameter, 
the leakage was at the rate of 40,000 gallons per mile per 
day. 

In the course of his report, Mr. Goodnough, the chief 
engineer, said that so far as he could judge by determinations 
of the amount of night flow throughout the State, the leakage 
into any large sewer system might easily amount to 70,000 
gallons and at times when the leakage is extraordinary to as 
much as 80,000 gallons per day per mile of sewer. He adds 
that, in extensions of the Metropolitan Sewer System it seems 
desirable to make provision for a leakage of as much as 80,000 
gallons per day per mile of sewer. 

In the case of the joint trunk sewer from Elizabeth and 
Newark to Staten Island Sound, unusual care was taken in 
the construction, special jointing material (sulphur and sand) 
being used instead of cement and in the 150 miles of main 
sewer and tributary systems, the infiltration was at the rate 
of 25,000 gallons per mile per day.f 

* Special Report on the Discharge of Sewage into Boston Harbor, 1900. 
f Report Passaic Valley Sewerage Commission, Dec., 1907, p. 13. 



146 SEWER DESIGN 

Mr. J. N. Hazlehurst,* refers to a lawsuit, entered into 
because while the specifications limited the leakage into a 
sewer system under contract to 5000, measurements made 
after all the pipes were laid showed an average leakage of 
44,600 gallons per mile per day. In the course of this article, 
he refers to measurements made at Maiden, Mass., where 
tests made directly after the completion of the sewerage system 
showed a leakage at the rate of 50,000 gallons per mile per day. 
-This was, he intimates, in spite of the fact that all the work 
was underdrained and cement used almost extravagantly in 
the hope of securing water-tight work. 

Mr. Hazlehurst also refers to the measurements made in 
New Orleans, where an original estimate of 31,800 gallons 
per mile per day (0.003 cubic foot per second per acre) was 
found to be approximately correct after the sewers had been 
built. 

Such values as have been given above seem to establish 
the fact that many sewers can be found that are imperfectly 
constructed and that as a consequence admit more or less 
ground-water into the pipes. It is, moreover, probable that 
the measurements recorded are the results of attempts to 
reduce leakage to more moderate and reasonable figures and 
are therefore unduly high. 

Mr. Hazlehurst implies, however, that these leakages are 
characteristic and says definitely that there can be no such 
thing as a water-tight pipe line and that if an engineer, in 
his specifications, sets a limit to the amount of leakage, it 
behooves him to " be very sure of his ground, both literally 
and figuratively." 

Granted, however, that it is doubtful whether a sewer can 
be made water-tight under ordinary conditions and methods 
of construction, it remains to be seen what is a reasonable 
amount of infiltration. 

If the sewer is of brick, assuming first-class construe tion, 

* Engineering News, Vol. L, p. 179. 



GROUND-WATER REACHING SEWERS 147 

the amount of ground-water entering may be restricted to that 
due to the porosity of the brick and mortar. Various methods 
are found in pocket-books for making brick walls impervious, 
and many statements are made to the effect that brick masonry 
in engineering construction allows considerable water to pass 
through. No definite data, however, seem available for the 
exact amount of such percolation under different conditions of 
construction. In the case of sewers, experience seems to show 
that in the same ground more water comes through a brick 
than through a pipe sewer; but nothing definite is known on 
the subject. 

The author has seen water under a head of a few feet pass, 
in numberless small streams, through a 1 2-inch brick wall. 
He has experimented with tanks of brickwork, with 8-inch 
walls, with and without plaster coats, and is convinced that, 
with the work of ordinary housemasons, it is beyond all reason 
to expect an 8-inch brick wall to be water-tight, even with 
an ordinary plaster coat. It is essential for water- tightness 
that the voids of the plaster coat be filled either with several 
coats of cement wash, with asphalt, or with some one of the 
many water-proofing paints or plasters available. Mr. John 
N. Brooks * has suggested that a more suitable unit for infiltra- 
tion for brick or concrete sewers is gallons per day per square 
yard of interior surface, and from some experiments of his 
own on a concrete sewer 9 miles long, he finds the leakage 
for 4- to 6-foot sewers, in first-class ^condition with special 
waterproofing of three-ply felt and pitch, to be at the rate of 
0.8 gallon per square yard, or 6000 gallons per mile for the 
4-foot sewer. 

The only two instances on record of leakage through the 
walls of brick sewers, are at Orange, N. J., and at Maiden, 
Mass., already referred to, and instanced by Mr. A. P. Folwell,f 
secretary of the American Society of Municipal Improvements. 
The leakage was found to be at the rates of 570,000 and 800,000 

* Proc. Am. Soc. C. E., Vol. XXVIII, p. 1705. 
f Municipal Engineering, Vol. XXV, p. 348. 



148 SEWER DESIGN 

gallons per mile for the two places, respectively, or 122 and 
136 gallons per square yard. It is absurd, however, as Mr. 
Folwell himself points out, to expect that such leakage as this 
is reasonable, and it only serves to illustrate what large flows 
may occur through badly built brickwork. 

If the sewer is of vitrified pipe, ground-water enters the 
pipe through the joints, and the amount to be expected depends, 
assuming perfect workmanship, on the kind of cement, depth 
of joint, and other details of construction of the joint. In 
Vol. XIII, p. 71, of the Journal of the Association of Engineer- 
ing Societies, are given the results of some tests by Freeman 
C. Coffin, C. E., made to investigate this very point. His 
results are given as follows: 

" In the standard form of pipe-socket, with well-made 
joints of either Portland cement, neat or i : i, or of Rosendale 
cement i : i, with over-filled joints, the leakage would not be 
serious, probably not exceeding 1000 gallons per mile per day, 
with the level of the ground-water from 2 to 8 feet over the pipe. 

" In pipe with deep sockets the tests indicate that if the 
joints are well made the leakage will be about as follows: In 
Rosendale cement neat it will be very large, perhaps over 
100,000 gallons per mile per day. In Rosendale cement mixed 
with sand i : i the leakage would not exceed 700 to 800 gallons 
per mile per day. In Rosendale i : 2 it would approximate 
1000 or 1200 gallons per day; with Portland cement neat, 
about 150 gallons per day; with Portland i : i, about 500 or 
600 gallons." 

The sockets of these pipes were very small to reduce the 
area of cement as much as possible, and Mr. Coffin thinks 
that even with the best intentions the difficulty of filling these 
joints in a trench would be insurmountable, and he therefore 
gives the figures above as representing only what can be done 
in a laboratory experiment. 

In the discussion of the above conclusions, Mr. Cofiin says 
that it would seem that Portland cement,~either neat or mixed 
i : i, or Rosendale i : i, would make work that was suffi- 



GROUND-WATER REACHING SEWERS 149 

ciently tight for all practical purposes, provided the joints 
could be well filled and could remain undisturbed by water 
or jarring until sufficiently set to resist. Unfortunately, in 
practical construction joints in a sewer-pipe are never made 
with the same care as in a laboratory experiment; and further, 
it seldom happens that the joints are allowed to stand from 
12 to 48 hours before being covered with water, as was done 
in these experiments. In a wet trench the cement is not always 
forced into the joint, and water is admitted to the joint before 
the cement is thoroughly set, tearing off the coating and leaving 
an opening into the pipe. 

To approximate actual conditions as nearly as possible, 
F. S. Senior, as his thesis work, under the direction of the 
author, made some experiments in which water was admitted 
to the joint at various intervals from the time of making. 
His experiments* brought out the following points: First, that 
there is to be expected a gradual improvement in the tight- 
ness of cement-joints from the time that they are first laid, 
amounting to from 40 to 80 per cent, and that the decrease in 
leakage is greater for Rosendale cement than for Portland. 
Second, that there is more leakage under high heads, and 
that the increase with the head is nearly proportional to its 
square root. Third, that there is a great advantage in using 
quick-setting cement if there is any probability of having the 
joints covered with water; and further, that a quick-setting 
cement will reduce the length of time necessary to pump from 
a wet trench, since the amount of infiltration after the cement 
has taken a hard set is inconsiderable. Fourth, that in a wet 
trench a gasket is of great value; and whereas without it a 
line on which water has risen before the cement in the joints 
was hard would admit water to the extent of half filling a 
6-inch pipe, yet with gaskets the leakage would be no more than 
if the water had been kept off till the cement had set. This 
last is in contradiction to Mr. Coffin, who concluded that a 

* Trans. Ass'n Civil Eng'rs, Cornell Univ., 1897, p. 113. 



150 SEWER DESIGN 

gasket, by taking up in the joint space that should be filled 
with cement, was a detriment rather than a benefit. Mr. 
Senior's experiments were all made on six 2-foot lengths of 
6-inch pipe, and the mortar all mixed i : i. His results in 
detail were as follows: 

When the water was turned onto the joints within 3 or 4 
minutes after the cement had begun to set (15 minutes after 
the first joint was made), the leakage through Rosendale 
cement was at the rate of 150,000 gallons per mile per day, 
decreasing to 30,000 after 72 hours. The Portland cement, 
under the same conditions, showed a first leakage of 120,000 
gallons, decreasing to 4500 after 72 hours. 

When, however, the cement was allowed to stand 30 minutes 
before water was admitted, the leakage through Rosendale 
joints was at first 70,000, reduced to 25,000 after 72 hours, 
and for Portland the leakage was 60,000, which became 4,000 
after the same time. 

In using gaskets, water was turned on in 10 minutes, or 
before the cement was set, so that the full benefit of the gaskets 
was brought out. With Rosendale the first leakage was only 
26,000 gallons, and after 72 hours it had decreased to 8000 
gallons per mile per day. With Portland, while the first leak- 
age was 11,000 gallons, after 72 hours it was but 5500 gallons, 
or a small and insignificant amount. The results of this last 
work as well as that of Mr. Coffin show that even under the 
best conditions there is some leakage; but that if the joints 
are well made this amount can be reduced to about 4000 gallons 
of water per mile per day for a 6-inch pipe. (Compare with 
p. 144.) For larger pipe the increase would probably be pro- 
portional to the area of the joint. 

If the joint space increased regularly both in width and 
length, this area would be approximately proportional to the 
square of the diameter. But the widths are uniform at f inch 
up to and including zo-inch pipe and all other sizes have a 
^-inch space for standard pipe. For deep and wide socket 
pipe, the space is always f inch. The area then depends on the 



GROUND-WATER REACHING SEWERS 151 

circumference or directly as the diameter, except that there 
is an abrupt change between the 10- and 1 2-inch pipes. 

As an example, a 1 2-inch pipe 2 miles long, laid in water, 
might be reasonably expected to carry as a minimum amount 
of subsoil infiltration 4000x2x2 or 16,000 gallons of water, 
while the capacity of the pipe flowing half-full at a velocity of 
2 feet per second is 650,000 gallons per day, or the leakage 
is about i\ per cent of the capacity of the pipe. This might 
be somewhat reduced by allowing 12 hours for the cement 
to set before the water is turned on, but it takes into account 
not a single bad joint nor one which is not fully filled, of which 
there are always many in actual construction. If the leak- 
age were at the rate of 10,000 gallons for a 6-inch, or 20,000 
gallons for the 1 2-inch pipe, it would be less than most of the 
examples cited and would be only 6 per cent for the 2 miles. 

In Vol. XIX of the Journal of the Association of Engi- 
neering Societies is a valuable paper by Mr. F. A. Barbour 
of Brockton, Mass., on the strength of sewer-pipe, and inci- 
dentally on some tests of the tightness of pipe-joints. He gives, 
however, no conclusions as to amounts, saying that the results 
have been decidedly unsatisfactory from the standpoint of a 
written report, and no tabulations of the figures will be given. 

The evident lesson so far as ground- water is concerned is 
that, instead of adding a certain percentage to the desired 
capacity of the sewers, a more rational method is to consider 
in detail the lengths of pipe to be laid under a head of ground- 
water, and to increase those lines and the mains lower down by 
a certain amount of leakage per mile, the amounts to be 
arrived at by actual experience and by the experiments quoted. 

Mr. Alexander Potter, Engineer of the Joint trunk sewer 
of New Jersey, concludes* that even with rigid inspection it is 
not safe to count on less than about 25,000 gallons per mile 
per day leakage with cement joints, but with sulphur-sand 
joints it may be reduced to about 5000 gallons per day. These 

* Engineering Record, Vol. LX, p. 377. 



152 SEWER DESIGN 

amounts seem large in view of the experimental data, but it 
must be remembered that the amounts given in the experi- 
mental data are for leakages through perfect joints, and that 
in construction any workmanship except the best, which it is 
practically impossible to secure in trench-work, will materially 
modify and increase the amounts given. 

PROBLEMS 

47. The annular space for the joint in a lo-inch pipe (3 -foot lengths) 
is f inch. If the thickness of the pipe is inch and the leakage is at the 
rate of 15,000 gallons per mile per day, determine the rate of infiltration 
through the cement in gallons per square yard of area. 

48. The annular space of a 6-inch pipe is f inch and for a 1 2-inch pipe 
^ inch. If the thickness of the pipes are f inch and i inch respectively, 
compute the relative permeability, assuming the latter to depend on the 
area of the joint. 

49. If the leakage through the walls of a brick sewer, 4 feet 6 inches 
diameter, is at the rate of 5 gallons per square yard of interior surface, 
compute the leakage per mile of sewer. 

50. If the leakage into a sewer system is at the rate of 25,000 gallons 
per mile per day under a certain head, what would be the probable leakage 
if the head is doubled, judging by Senior's experiments. 

51. Assuming the leakage into 6-inch pipe to be at the rate of 8000 
gallons per mile per day, determine the total leakage into 10 miles of 
6-inch pipe, 5 miles of 8-inch pipe, 2 miles of lo-inch pipe, and 0.75 mile 
of i2-inch pipe, 



CHAPTER X 
GRADES AND SELF-CLEANSING VELOCITIES 

IN the early days of sewer-construction the fact that sewers 
could be kept clean by any other method than by periodic 
sweeping was scarcely appreciated. Sewers were a subject 
not fit even for discussion, much less for the professional inter- 
ests of any except the meanest laborers. Sewers were neces- 
sary, were to be taken for granted, but were not to be made a 
topic of public conversation. To this public attitude towards 
sewers it is undoubtedly due that the principles of hydraulics, 
early studied in the case of rivers by the most eminent scien- 
tists, have been so tardily applied to sewage-flow, and have only 
recently been recognized in determining the size, shape, grade, 
etc., to make the sewer best suit its intended purpose. 

Baldwin Latham gives examples of defective house-drains 
said to be still in use in London houses. Fig. 45 shows a 

defective section of a sewer car- . _^ 

rying storm-water and sewage, 
which has been in use in 
Ithaca for many years. Many 
examples could be found of 
similar faulty construction, of 
broad flat inverts, of rough sur- ,, 

rlG. 45* 

faces, of open joints, and of 

grades not sufficient to carry along the matter in suspension. 
It is, however, enough to point out that such imperfectly con- 
structed sewers have been the rule in the past, and that only 
within the latter half of the last century has the relation 
between the hydraulic elements concerned and a clean non- 
depositing sewer been recognized. Now it is known that 

with a sufficient velocity and depth any material that has 

153 





154 SEWER DESIGN 

been deposited there may be scoured out from the bed of a 
sewer or stream, or it may be held in suspension and so pre- 
vented from accumulating deposits. To what laws or by 
what means this power of water to hold material of greater 
density in suspension is due is not clearly known. The sub- 
ject, however, is of great importance, because if a sewer is to 
be kept clean without intermittent hand labor, it must be 
through the transporting power of the water which hurries 
along with and in itself all solid matter. The admirable com- 
pilation by Mr. E. H. Hooker on this subject, presented as a 
thesis at Cornell University in 1896, and published later in 
the Trans. Am. Soc. C. E., gives the following propositions, 
applicable to sewers, as expressing the main facts so far as they 
are known and necessarily underlying any broad theory of the 
cause of the suspension of sediment: 

" i. The movements of solids by water may take place 
by dragging, by intermittent suspension, or by continuous 
suspension. 

" 2. Motion in each of the three ways is increased with 
increase of depth; yet the depth itself can only affect the inter- 
mittent suspension. 

" 3. Motion in each of the three ways is increased by 
increase in the mean velocity. 

"4. The presence of the sediment in the stream-flow 
decreases its mean velocity. 

"5. Dragging as well as suspending power increases with 
heaviness of the liquid and with its greater coefficient of 
viscosity. 

" 10. Increase of vortex motion increases the power of 
transport. 

"13. Bodies suspended in flowing water, either inter- 
mittently or continuously, tend to acquire a velocity greater 
than that of the water surrounding them." 

The theories offered to explain the facts or propositions 



GRADES AND SELF-CLEANSING VELOCITIES 155 

just given are summed up by Mr. Hooker with the state- 
ment that the suspension of sediment in flowing water may be 
attributed to three causes acting together, or in rare cases 
separately : 

" First. The resultant upward thrust due to eddies, con- 
ditioned upon the fact that the earth's (bed of stream) pro- 
file offers more rugosities than the air profile, and the effort 
exerted by a current upon a solid varies as the square of the 
relative velocities. 

" Second. The resultant upward motion of solids due to the 
fact that an immersed body tends to move faster than the 
mean velocity of the displaced water, and in such motion tends 
to follow the line of least resistance. 

" Third. The viscosity of the water." 

The law of Airy, that the transporting power of flowing 
water varies as the sixth power of the velocity, Mr. Hooker 
passes over without comment, but he gives curves showing the 
increase of suspending power with velocity. 

By these laws as given, it is evident that a certain velocity 
and depth are necessary to keep material from sedimentation. 
The exact relation between velocity and depth to secure the 
best transporting power is not known. In the case of sewers 
it is generally assumed that for a given quantity of water the 
maximum transporting power is secured with the maximum 
velocity, and that therefore a sewer section in which the vol- 
ume of flow is variable should be designed so as to keep the 
velocity of flow for all depths equal, or as nearly equal as pos- 
sible, to that obtainable from the section most favorable for 
that quantity if considered alone. Since the maximum velocity 
for a constant quantity is obtained when area divided by 
wetted perimeter is a minimum, the section generally used as 
giving the greatest velocity is circular, and in sewers of vary- 
ing flow the section is egg-shaped as being the best possible. 
Should it, however, be found that the depth of flow is more 
important as a function of the transporting power than is now 
thought, the maximum velocity will be no longer sought, since 



156 



SEWER DESIGN 







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GRADES AND SELF-CLEANSING VELOCITIES 



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158 



SEWER DESIGN 



now it is used only as an index of the transporting power. 
As Mr. Hooker intimates, the whole subject is far from being 
on a satisfactory basis, and observation and experiments are 
much needed to put the matter in its true light. 

The available experiments on the velocity required to take 
up into suspension or to drag along material in running water 
are not many. Table XX, taken from Mr. Hooker's article, 
gives what there are. 

It is seen that a velocity varying from 16 to 60 inches per 
second is required to take up material, and Baldwin Latham 
gives the following table showing how the specific gravity of 
the material affects that velocity. The experiments on which 
this is based were made by Mr. T. E. Blackwell, C.E., for the 
government referees, in the plan of the Main Drainage of the 
City of London. 

TABLE XXI 



Material. 


Specific 
Gravity. 


Commenced to Move at a 
Velocity of 


Coal 


1.26 


1.25 to i . 50 ft. per sec. 


i 


i . 33 


i .50 to i . 75 


Brickbat 


2.OO 


i . 75 to 2.00 


Chalk 


2 .CX 


i . 75 to 2.00 


Oolite stone 
Brickbat 


2.17 

212 


1 


Chalk 


2 .OO 


> 2.OO tO 2. 25 


Broken granite 


2.66 


j 


Chalk 


2. 17 


j 


Brickbat 


2.l8 


> 2 . 25 tO 2 .50 


Limestone 


I .46 




Oolite stone 


2.32 


1 


Flints 


2.66 


L 2 . 50 to 2 . 75 


Limestone 


3 .00 











Evidently other conditions than the specific gravity are 
concerned, and as no dimensions are given, it is probable that 
there was a variation in the size of the pieces tested and, what 
is probably of more active importance, in the shape of the 
pieces. In a thesis on Flushing- waves, in 1894, Messrs. Fort 



GRADES AND SELF-CLEANSING VELOCITIES 159 

and Filkins of Cornell University note that a piece of brick 
nearly cubical in shape, weighing 22 ounces and having a 
volume of over 16 ounces, was carried by a flushing- wave more 
than 1000 feet, while under the same conditions a mere flake 
of the same brick, having a volume of not more than 2 cubic 
inches, could not be moved more than 600. feet. Also a piece 
of limestone nearly cubical, weighing 7.75 ounces, was car- 
ried 1400 feet, while a piece weighing 4.75 ounces, but nearly 
flat in shape, was carried only 470 feet. 

It is seen, then, from the above old, meagre, and variable 
data that a flow of water requires a certain velocity to carry 
along solid material, and that the suspension of the material 
depends also on its size, shape, and specific gravity. 

Material deposited at the same place will be lifted by a 
flow of water and carried to different distances; those pieces 
whose shapes are such as to withstand the current, offering 
a thin and sloping edge to it, being last taken up, as the velocity 
increases, and soonest dropped. In a similar way a large stone 
too heavy to be carried along has been found to shelter smaller 
ones which otherwise might have been taken up by the cur- 
rent. Small irregularities in the channel serve as shelters for 
the fine material, and piles of sand, etc., are likely to accumulate 
behind projecting bits of mortar. It is plain, then, that 
neither theoretical determinations of the velocity required to 
carry matter in suspension, nor yet the results of experiments 
on different materials of varying sizes and specific gravities, 
are sufficiently like the conditions prevailing in sewers to deter- 
mine the velocities required in the latter, and it is only from 
experience in sewers themselves, where the material to be 
transported is that natural to a sewer and where the condi- 
tions of rugosity of bed and variation in the velocity in the 
different laminae are those peculiar to a sewer, that any reli- 
able recommendations must come. 

As an indication of the extreme lower limit of the range 
of velocities, reference may be had to the recent work on sedi- 
mentation where studies have been made on the velocity of 



160 SEWER DESIGN 

settlement of particles of varying size. Thus, Hazen has 
found* that in still water particles i mm. in diameter settle at 
the rate of .33 foot per second, but that particles .1 mm. in 
diameter reduce this rate to .028 foot per second and those 
.01 mm. to .005 foot per second. That is, the size of par- 
ticle, particularly in the case of fine suspended matter, plays 
an important part in the rate of settling and it is quite pos- 
sible for the particles to be so small that they will not settle 
at all. In the separate system the size of the suspended parti- 
cles is continually changing on account of the organic decom- 
position of the material and at the lower end of a long line the 
reduction in size may be so great that a much smaller velocity 
will suffice to keep the sewer clean than would be needed at the 
upper end. The relatively low velocities in Table XX shown 
in the cases of soft earth and clay are undoubtedly due to the 
small size of the particles involved. Experiments with more 
finely divided material might show even lower velocities. The 
question then is not merely what velocities will prevent sedi- 
mentation, but what are the sizes of particles of suspended 
matter found in sewage and what velocities are necessary to 
prevent sedimentation of such particles. 

Since the size of particles carried in suspension in sewers, 
either for storm water or for domestic wastes, is largely con- 
jectural, it follows that it is hopeless to attempt to apply any 
definite law of hydraulics to the problem, but that rather the 
engineer must be contented to accept the results of experience 
and secure in new work such velocities as have been found 
adequate to prevent undesirable subsidence. 

The following required velocities are those suggested by 
different prominent engineers and have been tabulated by 
Staley and Pierson: 

Baldwin Latham 2 to 3 ft. per sec. 

Beardmore 2.5 to 3 

Phillips 2.5 to 3 " " 

* Trans. Am. Soc. C. E., Vol. LIII, p. 63. 



GRADES AND SELF-CLEANSING VELOCITIES 161 

Rankin i to 4.5 ft. per sec. 

Adams 2.5 to 3 " " 

Philbrick 2.5 to 3 " " 

Gebhard 2 to 3 " " 

Baldwin Latham gives a little more detail, saying that in 
his experience he has found that in order to prevent deposits 
in small sewers or drains, such as those of 6 or 9 inches diam- 
eter, a velocity of not less than 3 feet per second should be 
secured. Sewers from 12 to 24 inches diameter should have 
a velocity of not less than 2\ feet per second, and in sewers of 
larger diameter in no case should the velocity be less than 
2 feet per second. This statement would evidently imply an 
expected or experienced increase of transporting or scouring 
power in the current with an increase of depth. 

A fact still further contributing to the general uncertainty 
of this subject is that the velocities given above are those for 
the pipes flowing full or half full. Since a small pipe sewer 
rarely flows half full, and since the velocity decreases rapidly 
as the depth in the pipe decreases, it follows that the bottom 
velocity on which the scouring power depends must be much 
less than the 2\ or 3 feet per second which by the table seems 
necessary. For example, an inch flow in an 8-inch sewer, laid 
on such a grade that it has a velocity of 3 feet per second 
when flowing half full, has with the less depth a velocity of but 
1.6 feet per second, which, by the table on p. 156, is not sufficient 
to move anything except the smallest gravel. 

When it is remembered that sewers are designed for a period 
of years in advance and that the full capacity of the sewer is 
to be reached only at that future time and then only at that 
hour of that day throughout the entire year when the flow will 
be the greatest, it is readily seen that in fact at all times the 
flow is less than that estimated and that therefore the velocity 
will always be less than that assumed to exist. 

In examining in the Ithaca sewers the velocities with small 
depths, the author has found velocities of 0.98 foot per second 



162 SEWER DESIGN 

apparently carrying along the solid matter and requiring no 
more flushing than is usual. It would seem, then, that the stated 
velocities are not the actual flow velocities, but are those required 
at half-depth in order to get the needed velocities with the usual 
flow, the actual velocities needed being from i foot to if feet 
per second. 

The velocity required being known, it can only be secured 
by sufficient grade, and the minimum grades are those just 
sufficient to produce the velocities given above. By the 
rule of Latham, the larger the sewer the less need be the 
velocity and grade, but it assumes that the amount of flow 
is sufficient to keep the sewer flowing half full. 

Thus it is possible to carry away a definite amount of 
sewage either by a large pipe and a small velocity or by a 
small pipe and a correspondingly high velocity. According to 
Latham, the following sewers laid at the grades given will all 
have the same velocity flowing half full, but the amounts 
carried must be in the ratios of 100, 25, 4, and i: 

A sewer of 10 ft. diameter, grade .038 per cent 
11 " 5 " " .076 

" " 2 " " .190 



The velocity required is therefore a function of the quan- 
tity as well as of the grade. 

The fact that large sewers may be laid on a light grade and 
yet maintain the necessary velocity is sometimes responsible 
for an attempt to reduce the necessary grade for a small pipe 
by the substitution of a larger one. Thus one of the author's 
students in a Thesis design planned 24-inch pipes for a number 
of laterals, because his grades were very light and he mis- 
takenly thought that by using a larger pipe, the grades for 
that pipe if half full, could be used. The error is at once appar- 
ent, a small flow in a large pipe requiring a greater slope for the 
pipe than if the flow was confined in a smaller cross -section. 



GRADES AND SELF-CLEANSING VELOCITIES 163 

An ingenious arrangement was adopted some years ago by Mr. 
J. H. Fuertes in the case of the Paxton Creek intercepting 
sewer for Harrisburg, Pa. The permissible grade for this 
pipe line was so light that the resulting velocity was altogether 
inadequate, so the diameter was increased from about 18 
inches to 5 feet and a full cross-section was insured by auto- 
matically admitting water from the creek so that this water 
added to the sewage would secure the needed velocity. The 
increased cost of the sewer was here justified by the elimination 
of pumping which would otherwise have been necessary. 

For sewers flowing constantly, either full or half full (the 
velocity is the same at both points, increasing at a point A full 
to a maximum of 112 per cent), at a velocity of 2 feet per second, 
there are required, according to Kutter's formula, grades as 
follows (# = .013): 

6" 8" 9" 10" 12" 15" 18" 20" 24" size 
.7 .5 .4 32 .22 .16 .11 .10 .09 grade 

Latham's tables, based on Weisbach's formula, give the 
following : 

6" 8" 9" I0 " 12" 15" 18" 20" 24" size 
.34 .26 .23 .20 .18 .14 .11 .10 .09 grade 

showing a large difference for the smaller sizes as explained 
in the discussion of the two formulae (see p. 167). 

Staley and Pierson say that a 6-inch lateral laid on a rV per 
cent grade works in a fairly satisfactory way, but Hering 
advises y 5 cr per cent is possible. At Ithaca, where all the sewage 
has to be pumped and where all the sewers in the valley are 
laid on the minimum grade, the grades adopted were: 

6" 8" 10" 12" 15" 18" 20" 24" size 
.5 .5 .45 .40 .35 .25 .20 .20 grade 

Examination of the plans of engineers throughout the coun- 
try discloses that fact that there is considerable latitude in the 



164 SEWER DESIGN 

grades adopted as the minimum, implying either that the 
knowledge of the grade needed for the minimum velocity given 
above is indefinite, or that ideas of what the minimum velocity 
is, vary. At the lower end of a main where there are no 
house-connections and where, should the sewer get blocked, 
backing up of the sewage would do no harm and would prob- 
ably accumulate a head which would force out the obstruc- 
tion, a grade or velocity less than those given might be toler- 
ated. And at the upper ends of laterals where, although the 
amount of flow is probably small, a flush-tank can be placed to 
wash out periodically whatever might form a stoppage, light 
grades can be used, however undesirable. Between these two 
extremities of the line, grades less than those given are unwise 
and a source of continual trouble. Advantage is sometimes 
taken of natural aids to get intermediate flushing, as proximity 
to some stream, or to breweries or swimming- tanks, and on this 
account the grades are lessened. The whole subject gives 
an excellent opportunity for experimental work in sewers 
actually in use, and is open to much more enlightenment. 

PROBLEMS 

52. If a i2-inch sewer flowing half-full has a velocity of 3 feet per 
second, what would be the velocity of flow with a depth of i inch? (Use 
tables from Trautwine's or Kent's Pocketbooks for values of area and 
wetted perimeter.) 

53. If a combined sewer, 4 feet diameter, is so laid as to secure a velocity 
of flow of 2.5 feet per second flowing full, what would be the velocity 
of flow for the house-sewage with a depth 0^4 inches? 

54. Using the Chezy formula (v c\/R-S), find the value of S to give 
a velocity of 3 feet per second in a 24-inch pipe, half-full (c = 100). 

55. If the estimated sewage-flow is 2 cubic feet per second and the 
available fall is only f inch in 100 feet, find the necessary diameter of 
sewer, flowing full, to give a velocity of 2.5 feet_ per second, assuming 
creek-water can be added. Use formula v =c\/R-S with = 120. 

56. If a 6-inch lateral is laid on a T% per cent grade, what is the theo- 
retical velocity? (Use v = c \/R 5 with c = 70.) 



CHAPTER XI 
DEVELOPMENT OF FORMULA FOR FLOW 

THE first attempts to discover the law by which the velocity 
of running water depends on the fall and cross-section of the 
channel is supposed to have been made in 1753 by Brahms, 
who observed that the acceleration which we should expect 
in accordance with the law of gravity does not take place in 
streams, but that the water in them acquires a constant veloc- 
ity. He points to the friction of the water against the wet 
perimeter as the force which opposes the acceleration, and 
assumes that its resistance is proportional to the mean radius, 
Rj that is, to the area of the cross-section divided by the wet 
perimeter, o v = CRVH, with C equal to a fraction multi- 
plied by \/2g. 

In 1775 Brahms and Chezy, the latter a celebrated French 
engineer, whose most famous work was the Burgundy Canal, 
made the next advance, and altered the relation between the 
velocity and the mean radius. These engineers are to be 
regarded as the authors of the well-known formula usually 
known as the Chezy formula, viz., 




or velocity equals a constant multiplied by the square root 
of the hydraulic radius and by the square root of the slope. 

Dubuat, 1779, undertook to determine experimentally 
some of the laws governing flowing water, and for that purpose 
he made an elaborate series of gagings of some French canals 
and of artificial channels. His results are summed up in 

these two laws: 

165 



166 SEWER DESIGN 

1. The force which sets the water in motion is derived 
solely from the inclination of the water-surface. 

2. When the motion is uniform the resistance which the water 
meets, or the retarding force, is equal to the accelerating force. 

He also showed that the resistance is independent of the 
weight or pressure of the water, so that its friction upon the walls 
of pipes and channels is entirely different in its nature from 
that existing between solid bodies. 

Coulomb's investigations, a little later, indicated that the 
resistance offered by the perimeter of a channel is represented 
by two values, the first of which is proportional to the velocity, 
and the second to the square of the same. Upon this principle, 
de Prony based his formula 

R-S^av+bv 2 ; 

in which a and b are constants to be derived from experi- 
ments. From thirty measurements by Dubuat and one by 
Chezy, de Prony found, for metric measures, that a equals 
0.000,044 and b equals 0.000,309. Somewhat later, Eytel- 
wein, after comparing the above thirty-one experiments with 
fifty-five others by German hydraulicians, suggested that a 
should equal 0.000,024 and b equal 0.000,366. 

This formula of Eytelwein is a familiar one, and reference 
is made to Proc. Inst. C. E., Vol. XCIII, p. 383, for extensive 
tables on sewer design, based upon it. 

Many authorities, seeking to simplify the expression, held 
that it would be permissible to shorten the formula by neglect- 
ing the term aXv } which is very small for large streams espe- 
cially, reducing the form to that of the Chezy formula again. 

For this modified formula the value of b is given as 0.0004, 
later taken by Eytelwein as 0.000,386, and it has been much 
used in Germany and Switzerland until recently. It gives 
in metric units 

and in English units 



DEVELOPMENT OF FORMULAE FOR FLOW 



167 



It was noticed, however, that while this formula agreed 
with the experiments for certain conditions of slope and 
velocity, it would not hold for others; so that, as an improve- 
ment, Ruhlman and Weisbach deduced from the same experi- 
ments varying values of the constant to correspond with the 
varying values of velocity. The following table gives the 
values of c varying with v as given by Weisbach. 

TABLE XXII 



Veloc. V = 
ft. per sec. 


0-3 


0.4 


0.5 


0.6 


0.7 


0.8 


0.9 


I.O 


i.S 


2.0 


3-0 


5-0 


7.0 


IO.O 


15.0 


Const. C = 


72.8 


76.6 


79-3 


81.1 


82.6 


83.8 


84.6 


85.4 


87.8 


89.1 


90.4 


9i.S 


92.0 


92.4 


92.7 



The table shows the values of c, for velocities common to 
sewers, to lie between 89 and 91, which are undoubtedly cor- 
rect for certain kinds of channels. But, as will be seen later, 
the physical conditions of the channel also affect the values 
of c, so that, without knowing the conditions of the experi- 
mental channels on which these values of c are based, the 
results are uncertain for general use. 

Baldwin Latham gives very elaborate tables based on these 
values of c, giving grades necessary to produce velocities of 
from 2 to 10 feet per second in pipes flowing f , J, f , and full, 
the pipes being both circular and egg-shaped. Similar tables 
are given for discharge. Except that diagrams are now so 
largely used, a reproduction of these tables with better values 
of v might well be made, for their convenience and general 
adaptability are remarkable.* 

According to Dubuat, de Prony, and all hydraulicians 
up to their time, differences in roughness in the wet perimeter, 
or irregularities in the direction of the stream, had no effect 
on the value of the coefficient. It was assumed by Dubuat 
that a layer of water adheres to the walls of the pipe or chan- 
nel, and is therefore to be regarded as the wall proper sur- 

* The elaborate treatise on Sanitary Engineering, by Col. E. C. S. Moore, 
published early in 1899, contains such tables as are here suggested. 



168 SEWER DESIGN 

rounding the flowing mass. According to Dubuat's experi- 
ments the adhesive attraction of the walls seems to cease at 
this layer, so that differences in the material of the walls pro- 
duce no perceptible change in the resistance. That this reason- 
ing is not good we now know; but since the early experiments 
on the value of the coefficient were made under conditions in 
which the wall-surfaces differed but little, and since no new 
experiments were made until the middle of this century, engi- 
neers, however much convinced of the unreliability of these 
early formulae, were not in a position to construct a more 
accurate one. It was left to M. Darcy, Inspecteur General 
des Fonts et Chaussees, to whom the city of Dijon owes her 
excellent water-supply, to open the way to a better under- 
standing of this subject. In the Dijon water-pipes M. Darcy 
noticed,* as had been observed by others, that those pipes 
which presented the smoothest inner surface furnished the 
greatest quantity of water in a given time, or, in other words, 
that the greatest velocity was found in the smoothest pipes. 
He argued that a similar phenomenon must take place in open 
channels, and undertook to make a thorough and extensive 
series of experiments upon this point. By special authority 
of the government, he had constructed near Dijon, on the 
Canal de Bourgogne, a special canal 6 feet wide, 3 feet deep, 
and about 1850 feet long. It received its water from the 
canal and discharged it into the River 1'Ouche. The water was 
supplied by two reservoirs at a constant head, and the amounts 
were measured by a series of carefully calibrated weirs. The 
canal was furnished successively with different linings, viz., 
neat cement, i : 3 mortar, boards, brick, fine and coarse peb- 
bles, and laths, nailed transversely to the direction of the cur- 
rent, .01 and .05 metre apart. The grades were varied from 
.001 to .009 per unit of length. Besides these experiments, 
all known data were collected and compared. Just as M. 
Darcy had completed these arrangements, most of them pre- 

* Recherches exp6rimentales relatives au Movement de L'Eau dans les Tuyaux, 
par Henry Darcy, 1857. 



DEVELOPMENT OF FORMULAE FOR FLOW 169 

liminary, he died, in 1860, and the carrying on of the experi- 
ments and drawing up of the conclusions fell to his assistant, 
M. Bazin. It was the latter who arranged and conducted the 
gagings and extended them to several branches of the Canal 
de Bourgogne, who collected and digested the numerous results, 
and who has written an elaborate book on the subject, embody- 
ing the results of years of investigation and study.* Bazin 
made two general deductions: 

1. The coefficient c of the formula for the determination 
of the mean velocity in canals and rivers of uniform flow varies 
with the degree of roughness of the wetted surface. 

2. These coefficients c vary much more nearly with R than 
with v. 

He further noticed a change in c corresponding to a change 
in 5, but he did not consider it of sufficient importance to be 
taken into account. 

From his study and the knowledge thus gained M. Bazin 
established a new formula, making it applicable to his experi- 
ments and having v change with the differences in the rough- 
ness by having four classes of surfaces, with special coefficients 
for each class, and putting every channel into one of these four 
classes. He takes the abbreviated formula of Eytelwein, 



and makes the constant 

or 

n\ I j 

|)^ } or v = I -VRS. 




. To determine values of a and g, M. Bazin plotted for con- 

* Recherches Hydrauliques, entreprises par M. H. Darcy: continues par 
M. H. Bazin, 1865. 



170 SEWER DESIGN 

slant slope and constant roughness a series of experiments, 
using formula in the form 



2 R' 

DC 1 

the ^y-ordinates being values of or , and the #-ordinates, 

values of . a then gives the distance of the origin from the 
R 

point where the F-axis is cut by the straight line, drawn as 
nearly as may be through the points; and g is the tangent of 
the angle which the line makes with the X-axis. 

In this way four sets of coefficients were obtained, here 
given in English measure. 

I. Cement and carefully planed wood: 

a = .000,046 ; g = .000,0045 . 
II. Smooth ashlar, brick, and wood: 

a = .000,058 ; g = .000,0133. 

III. Rubble masonry: 

a = .000,073 j = ^.000,0600. 

IV. Earth: 

a = .000,085 ; g = .000,3 5. 

V. Carrying detritus and coarse gravel: 
a = .000,122; g = . 000,7000. 

The last class was added later by Kutter. 

In his treatise M. Bazin says: " One must regret the sub- 
stitution for a single simple formula of a new formula with 
variable constants in the coefficients; but the indeterminate 



DEVELOPMENT OF FORMULAE FOR FLOW 171 

character of the coefficients is an inconvenience peculiar to the 
nature of the phenomena, and further progress in hydraulic 
theory can never remove it. There are, moreover, very few 
physical laws the formulated expression of which does not 
include like inde terminates." 

The experiments of M. Bazin and the coefficients derived 
from them are standards in hydraulic history, whose accuracy 
has never been questioned, and are to-day used throughout 
France in determining the velocity in open channels. Tables 
based on this formula are given by Flynn in his Hydraulic 
Tables (p. 180). 

About the same time that M. Bazin was making these 
important experiments in France, Humphreys and Abbot were 
making their well-known experiments on the velocity of flow 
in the Mississippi River.* They deduced the following formula: 



v= \\Jo. 



* 



o.ooSim-\- * 22 RiV s 



where m= -= for small streams and m = 0.1856 for large 



streams. 

By experiments made more recently in which this formula 
has been tested, it has been proved to be not generally applic- 
able, both from the fact that the limits of m are not wide enough 
and that the influence of slope as introduced is not accurate. 

The variation in the velocities of different laminae of the 
stream were, however, well brought out by the work on the Mis- 
sissippi River, and the earlier results of M. Bazin verified. It 
appeared, especially from the later and more extensive work, 
that the velocities in a longitudinal vertical plane would form 
the abscissae of a parabolic curve with the axis parallel to the 
surface and at the depth of maximum velocity. This depth, 
when the air is still, is, according to the Mississippi work, 
about fV of the entire depth below the surface. A wind blowing 

* Report on the Mississippi River, 1876. 



172 SEWER DESIGN 

down-stream affects the shape of the parabola, bringing the 
axis nearly to the surface, so that the surface velocity is the 
maximum velocity, while an up-stream wind drops the axis 
below the mid-depth. In the last case the bottom and top 
velocities were about the same, while the up-stream wind 
reduced the bottom velocity to about 85 per cent of that at 
the surface. 

It is to be noticed that before the construction of the 
Kutter formula the most advanced development of the primi- 
tive formula v = cVRS was embodied in the formula of M. 
Bazin, who made the coefficient c vary with (i) the degree of 
roughness of the wetted perimeter, decreasing with the increase 
of roughness; (2) the value of the hydraulic mean radius, increas- 
ing with its increase; and (3) the slope, decreasing with its 
increase in large channels and increasing with its increase 
in small channels. 

It remained for Ganguillet and Kutter to combine all 
these variables into one algebraic expression for the value of 
c, a discussion of which follows in logical order. 

Before taking up the discussion of the Kutter formula, 
however, the two latest English formulae may well be noticed. 
The first, by Henry Robinson, was arrived at, says the author, 
by Mr. Edgar Thrupp, the author's chief assistant, and is 
said to be based on the results of direct experiments in sewers, 
made by himself and by a great many other observers during 
the last forty years and up to the present time. 

The formula is 



R* 

v = 



where v is the velocity in feet per second ; 
R is the hydraulic radius; 

S is the length of sewer in which it falls one foot; 
C is a coefficient of roughness; and 
x and n constants. 



DEVELOPMENT OF FORMULAE FOR FLOW t 173 

The index x, the root n, and the coefficient C depend on the 
nature of the surface of the channel. For brick sewers in good 
condition the value of the index x is .61, n is 2, and C is .00746. 
For cement plaster x is .67, n is 1.74, and C is .004. A dia- 
gram given at the end of the book on " Sewage Disposal," 
by Mr. Robinson, allows velocities and discharges to be read 
directly. 

The other English formula, Santo Crimp's, is given as 



the same meaning being given to the letters, except that S 
is the fall divided by the length. It would seem that, with 
no possible variation for the coefficient, this formula could 
not equal the others in accuracy, though it is suitable for 
conditions similar to those upon which it was founded, that 
is in brick sewers. 

With the use of logarithmic plotting, a new interpreta- 
tion of old data was possible and it remains to refer to two 
exponential equations based on the old experiments but made 
possible only by the aid of logarithmic paper. 

Sullivan's formula, presented to the world by Mr. M. E. 
Sullivan of Denver, Colorado, in a small book called " The New 
Hydraulics," expresses the relation between the three varia- 
bles in the form z = CR- 75 S' 60 in which C varies only as the 
roughness and as nothing else, and so is absolutely, accord- 
ing to Mr. Sullivan, a correct index of the roughness. For 
cast-iron and for terra-cotta pipe, a numerical value of 141 is 
advised for C, and for brick conduits a value of 120. 

Messrs. Williams and Hazen soon after produced their 
little book, explaining their slide rule for solving the various 
problems of water-flow, and deriving their exponential equa- 
tion which has the form v = CR~ Q3 S' 54: . They say that if expo- 
nents could be selected agreeing perfectly with the facts, the 
value of C would depend on the roughness only, and for any 
degree of roughness C would then be a true constant. They 



174 SEWER DESIGN 

advise in their formula a value of 140 for new cast-iron pipe, 
of 100 for old cast-iron pipe, no for vitrified pipe and 100 for 
brick conduits. 

PROBLEMS 

57. With the aid of Table XXII (first assuming a value of C and 
deriving v in order to select a proper C from the table) determine values 
for v when d = 6 inches and $ = .5 per cent and for ^ = 36 inches and s = .i 
per cent. 

58. If Latham's book on Sanitary Engineering is available, look up 
values in those tables for comparison with results of Problem 57. 

59. Compute, using Table XXII, the value of v when ^ = 48 inches and 
5 = 6 inches in 100 feet. Compare result with tables in Moore's " Sani- 
tary Engineering." 

60. Determine the value of C from Bazin's formula, using the con- 
stants for brick and assuming that D = i2 inches. Compare with the 
constant obtained for Table XXII. 

61. In the Williams-Hazen formula, take C = no, D = $o inches and the 
fall of the water surface 7.98 feet in 4160. What is the velocity of flow 
and what the discharge with the pipe half-full? 

62. In the Sullivan formula, take C = i25, D = 2.$ feet and the hydraulic 
grade, 11.85 f eet m 6170. What is the velocity of flow and what the dis- 
charge, if the pipe flows full? 

63. Determine the values v and Q, by the Santo Crimp formula if 
the slope and diameter are respectively .00192 and 30 inches. 

64. Determine the values of v and Q in the Robinson formula if C = .004, 
n = i.74 and # = .67, the other data being identical with Problem 62. 



CHAPTER XII 
KUTTER'S FORMULA 

IN the endeavor of Ganguillet and Kutter to construct 
a new formula which by proper variation of its constants should 
be applicable to all streams, small as well as large, to pipes as 
well as to rivers, the original Chezy formula was used as a basis. 
The way in which their complicated formula was made up is 
here roughly outlined, both to indicate more clearly the mean- 
ing of and reason for its terms, and also to show a method by 
which other empirical formulae can be constructed. Their 
method was to assume and demonstrate that the value of 
" c " would be best formulated by an expression of the form 
used by M. Bazin, but into which the element of roughness 
should be introduced. M. Bazin's formula was 




or, making i/a equal y and g/a equal x, it would read 




Ganguillet and Kutter at first thought that y could be made 
constant, that is, independent of roughness, which would be 
made a function of x, equal to n-y, or n-y 2 , etc. To check 
this assumption and at the same time find the value of y, a num- 
ber of the gagings of Bazin were selected and curves drawn 
with values of i/VR for abscissae and i/c as ordinates. Aver- 

175 



176 SEWER DESIGN 

age lines were then drawn through the points thus plotted. 

Then, since the expression c equals - , can be trans- 

i % 

71 

formed by taking the reciprocal of each side, the expression 
becomes 

I I X I 



or it has the form of an equation of the first degree and of a 
straight line in which if values of i/c are plotted as ordinates 
and of il\f~R as abscissae, then i/y must be the constant term 
and x/y the tangent of the angle of inclination. If i/y is 
constant, it will appear by all the lines passing through the 
same point on the axis of y. Far from doing this, the lines 
plotted cut the axis at points unmistakably far apart, and 
the divergence was especially noticeable when small flows 
with steep grades and large flows in rivers with low grades 
were compared. It seemed then that, in the formula, y must 
be made a variable as well as x. After repeated trials to get 
the plotted points to agree with the curves drawn by the 

formula, y was made equal to a4 , and x to a-n, so that C 
equals 



n 

. an 
i +--/= 

VR 

the above values or relations being determined by series of 
gagings made with the same slope as nearly as possible. Up 
to this point in the development, c had been made to vary 
with R and with n, and it remained to make it vary with S. 
It was known from the experiments of Bazin and from those 
of Humphreys and Abbot that it must be brought in in such 
a way that c would increase as the slope decreased for large 



KUTTER'S FORMULA 177 

rivers, and would decrease as the slope decreased for small 
channels and pipes. In other words, there must be a point 
or a certain value of R or a certain sized stream in which the 
slope had no effect on c, but that for that size the value of 5 
could increase or diminish without affecting the value of c. 
From the available data a series of points were plotted with 
values of c and R as variables, and all with the same slope 
as near as possible. In this way a series of lines were obtained, 
each representing a certain slope, and it was found without doubt 
that they intersected at a point whose value for i/vR was one 
metre approximately, or whose value of i/c was .027 in metric 
units. The element of slope was introduced, arbitrarily, by 
making y equal to a+l/n-\-m/S' t then, preserving the relation 

x = ny l, x was made equal to (a-\--L)n. Then, to deter- 

\ *-V 

mine the values of /, points were plotted from streams whose 
value of i/VR was i, and the roughness of whose channels 
was similar, and the value of / was found to be i.oo. Then, 
to get a, points were plotted with values of i/S as abscissae and 
of y as ordinates, and the point where the line intersected the 
axis gave a equal to 23, and m, or the tangent of the angle, 
equal to .00155. The constants a, I, and m being determined, 
it remained to find values for n for different channels. This 
was done by again plotting points of actual gagings for differ- 
ent streams and finding corresponding values of n. In this 
way the values were found to range from .009 to .040. 
To sum up, then, from the original formula 



in which c equals 



where y equals 



l.m 

a-\ +-^, 
n S 



178 SEWER DESIGN 

and where x equals 



R-S in metric units, 



or 



,, . i.8n . .00281 

41.66+ h =r- 

n S 



VR'S in English units. 



or 



The values given for n are as follows : 

I. Channels lined with carefully planed boards or with 

smooth cement ............................... oio 

II. Channels lined with common boards or surfaces care- 

fully plastered with cement-mortar, one- third sand, in 
good condition, also for iron, cement, and terra-cotta 
pipes, well jointed and in best order, and for other 
surfaces equally rough ........................ on 

III. Channels lined with unplaned timber or rough cement- 

mortar .............................. ........ OI 2 

IV. Channels lined with ashlar and well-laid brick-work, 

ordinary metal, earthenware, and stoneware pipe in 
good condition but not new, cement and terra-cotta 
pipe not well jointed nor in perfect order, plaster, and 
planed wood in imperfect or inferior condition, and 
other surfaces equally rough ................... 013 

V. Channels in rubble masonry ...................... 017 

VI. Channels in earth; rivers ....................... 025 

VII. Streams with detritus ......................... 030 



KUTTER'S FORMULA 179 

The unwieldy nature of the formula given above has led to 
almost general use of graphical methods of solution. In the 
first notice of the formula in the Swiss exhibit in Philadelphia, 
1876, there was shown with the printed exposition a diagram 
familiar to- us in its English units, by means of which c could 
be graphically determined. It is printed in the back of the 
translation of Kutter's book by Hering and Trautwine, and can 
be found in some of the pocket-books. Mr. Hering in his 
translation gives tables for x and y, by means of which the 
diagram can be replotted at any time. Similar tables are 
given in Jackson's translation. 

But even with this diagram to aid in finding c, several 
algebraic reductions need to be made before the real purpose 
of the formula, that is, the value of v, is known. Trautwine 
in his pocket-book devotes four pages to tabulating c for 
different values of S, R, and n, when values of v might have 
been given. After c is known the square root of the product 
of R and S must be multiplied by c to get v. 

In Vol. VIII of the Transactions of the Am. Soc. C. E., p. i, 
Mr. Hering gives a method by which the velocity can be at 
once read from the diagram constructed for c. His reasoning 
is very simple. The equation 



can be written 



R 



or the four terms are in a simple proportion, so that by plot- 
ting the values of c and of Vi/5 on one side, and of v and of 
V R on another side, of an angle, the corresponding relations 
will be represented by similar triangles. In Kutter's diagram 
the coefficients c are already plotted on the vertical and the 
values VjR on the horizontal axis; by plotting an additional 
scale of grades on the former and of velocities on the latter 
axis the graphical solution is complete by merely drawing 



180 SEWER DESIGN 

parallel lines. The article referred to gives the diagram with 
tabulated values of x and y, and of the relation of V i/S to g, 
or the grade per hundred. Several numerical examples are also 
given. 

But even this graphical determination of v is not enough. 
In sewer-design, except at the limits, the value of v is useful 
only as it enters into the value of Q. A diagram, then, to be 
thoroughly useful should give at once the value of Q from 
the physical data, viz., slope and size of pipe, and the next 
chapter is devoted to the construction and use of such dia- 
grams. It remains in connection with Kutter's formula to 
mention the set of tables which, except in the form of a graph- 
ical diagram, give the formula most conveniently for use. 
Reference is made to Flynn's tables, published as Nos. 67 and 
84 o f Van Nostrand's Science Series. These are made possible 
in their form by establishing the fact that, within the ordi- 
nary limits of use for pipes, sewers, and conduits, the value 
of s affects the value of c almost not at all, and therefore s may 
be taken as constant, c then varies only with R and n. Tables 
are calculated for any one value of n, values of c being 
given for values of R. Instead of tabulating the values of c, 
however, it is noted that the equivalent of Q, viz., AcVR-S 
can be broken up into the two factors AcV R^nd Vo, and the 
value of v can be taken as the product of cVR and VS. 

Further, since for pipes flowing full the value of R is pro- 
portional to the diameter of the pipe, diameters are written 
instead of values of R', the tables then give (for a certain value 
of n) diameters of pipes from 5 inches up to 20 feet, and for 
those diameters the corresponding values of A, of R, of c\/R, 
and of Ac VR. 

For any slope^ its square_ root, given in another table, 
multiplied by c \/R or A - cVR for the desired diameter gives 
the resulting velocity or discharge. 

No. 67 gives tables for circular sewers from 5 inches to 
20 feet in diameter with ^ = .015; tables for egg-shaped sewers 
(old form) i'Xi'6" to 12' Xi8/ flowing full, two-thirds full, 



KUTTER'S FORMULA 181 

and one-third full, with ^ = .015; tables of 5* and V5, ranging 
from 5 = i in 4 to 5 = i in 2640, or from 25 to .028 per cent. 

No. 84 gives, with other tables and discussions, tables 
for circular pipes flowing full, the diameters ranging from 

5 inches to 20 feet, and with values for n of .on, .012, and .013. 
A table of slopes is given varying from 5 = i per cent to 5 = .053 
per cent, decreasing by small amounts, so that the table is very 
convenient. 

To illustrate the use of Flynn's tables the following examples 
are given, using No. 84: 

1. What are the velocity and discharge of an 8-inch sewer 
flowing full on a grade of .4 per cent, n being assumed at .013? 

From the table for ^ = .013, and for a value of d = 8, c^R 
is 31.00 and Acvlt is 10.822. From a table of square roots, 
V5 is .06325. Then v equals 3i.ooX.o6325, or 1.96 feet per 
second, and Q is 10. 822 X. 06325, or .68 cubic foot per second. 

2. What will be the size of sewer required to carry off a 
flow of 3.6 cubic feet per second, the grade being .125 per cent, 
n being taken at .013? 

From the table for ^ = .013 a value of AcV R must be found 
which multiplied by \/.ooi 2 5 shall equal 3 .6. This is 3 .6 divided 
by .0354, or 101.7, which corresponds to a diameter of i foot 

6 inches, the value required. Similarly the velocity will be 
the product of cVR found in the same line, or 5 7. 80 X. 03 54, 
that is, 2.05 feet per second. 

3. On what grade must a 24-inch pipe be laid to secure a 
velocity of 2.5 feet per second, n being taken at .on? 

From the table for n = .on, and a diameter of 24 inches, 
cV R is found equal to 87.36, which multiplied by V5 must 
be 2.5. VS is therefore .0285, and 5, .0008, or .08 per cent. 

4. What grade is necessary to discharge 8.5 cubic feet of 
sewage through a 20-inch pipe, and what will be the velocity, 
n being .012? 

From the table for ^ = .012, and a diameter of 20 inches, 
Ac\/R is 150.61, which multiplied by Vs must be 8.5; 
must therefore be .05637 and 5 is .00267, or .267 per cent. 



182 



SEWER DESIGN 



*st 



,,99 



e 



In using Kutter's formula, or tables or diagrams pre- 
pared from it, it must be 'remembered that 
the resulting value of v depends, even with 
known values for 5 and R, upon the judgment 
of the engineer in selecting the proper value 
for n. Kutter gives a value of .on for 
cement and terra-cotta pipe in good condi- 
tion, and .013 for stoneware pipe in good 
condition but not new, and for cement and 
terra-cotta pipe not well jointed. These 
values, from experiments made by the author 
in pipe sewers, seem to be true only for per- 
fectly clean pipes; and whenever accumula- 
tions of silt occur, or in pipes with any 
projecting cement, these values are too small. 
Probably .013 for pipes and .015 for brick- 
; work would agree more closely with actual 
sewer-gagings than the values given above. 

It may, however, be well to note that 
there is some evidence tending to show that 
the values of n as just given are not constant, 
but change with the depth of flow. In a 
thesis by Glenn D. Holmes written in 1897 
under the direction of the author, are given 
some values of n found experimentally for 
clean sewer-pipe on different grades. The 
values found varied from .007 to .021 for the 
differing grades (.56 to 2.51 per cent) and for 
the varying depths. As the depths increased 
in the experiments, reaching the half-full 
point as a limit, the values of n were in- 
creased for the higher grades and decreased 
for the lower, with the evident meeting-point 
at n = .013, agreeing with the common assump- 
tion. Further experiment in this direction would seem desirable. 
As a convenient and ingenious method of finding values 



s ^ 



^ 



KUTTER'S FORMULA 183 

of Q from the grade and size of pipe, " Colby's Sewer Com- 
puter " is of value. Based on Kutter's formula, with n = .oi$, 
the logarithms of the grades, discharges, and diameters are 
laid off on the rule and runner, so that by proper setting of 
grade and diameter the discharge can be at once read off. 
No velocity is given, although the runner could have addi- 
tional divisions for this purpose. The rule is shown in Fig. 46. 

PROBLEMS 

65. Determine numerically the difference in the value of C between 
values of = .oi3 and ^ = .015; for values of 5 between .005 and .0005, and 
for values of R between ^ = .125 and ^ = 1.25. 

If a diagram is based on a value of ^ = .013, by what per cent would v 
be increased or diminished for ^ = .015. 

66. For ordinary range of values used in sewer work show numerically 
how much variation in s would affect the value of c. 

67. Compute average values of C for ordinary sizes of pipes, and for 
ordinary range of s, with n = .013. 

68. Given an open ditch section, of side slopes 2 horizontal to i vertical 
with bottom an arc of 18" radius tangent to the sides, determine the 
depth of flow, on a grade of .005 per cent, to carry 35 cubic feet per 
second. Ditch is lined and n may be taken at .015. 

69. Find the size of a trough whose width is double its depth that 
will deliver 180 cubic feet per minute. Assume the slope to be 2 feet in 
TOCO feet and the coefficient of roughness, n, to be .013. 

70. An outfall flume is to discharge 40 cubic feet of sewage per 
second. It is to be built of plank (n = .01 1) on a slope of i in 3000. What 
should be the dimensions to give the minimum amount of lumber. 

71. If a 36-inch brick sewer has a coefficient of roughness ft = .015 
and a 36-inch pipe sewer one of .013, compute the grades in the two cases 
necessary to give velocities of 2 feet per second. If the sewer were a mile 
long, how much deeper in the ground would the brick sewer be? 



CHAPTER XIII 
SEWER DIAGRAMS 

WHILE the earlier formulae were not so complex that their 
solution was especially tedious, the later ones, and especially 
Kutter's, are of that nature. It is therefore not only in keep- 
ing with the general tendency of the times to reduce all com- 
putations to graphic or other approximate and time-saving 
methods, but it is almost a necessity if the formulae are to be 
of practical use. 

Diagrams, to be of service, must fulfil the following condi- 
tions: they must deal directly with the quantities of interest, 
not with some function of those quantities; they must be on 
a scale large enough so that the error of reading may be within 
the allowable error of the result; they must be equally service- 
able for all sizes, velocities, etc.; they must be so constructed 
as to give well-defined intersections at all parts. An advan- 
tage of the diagram, besides the time and labor saved, lies in 
the possibility of comparing of the quantities involved, and this 
should not be overlooked. 

The diagrams that have already been printed may 
divided into two classes: first, those based on Latham's tables 
or Eytelwein's formula; and second,' those based on Kutter's 
formula or on modifications of it, such as Flynn's tables. 

Of the first class may be cited the extensive diagrams of Mr. 
W. T. Olive printed in the Proc. Inst. C. E., Vol. XCIII, p. 383, 
very elaborate and complete and models of the sort. 

In the same publication, Vol. XCVI, p. 268, are diagrams 
giving discharges as before, and also giving the relations between 
the velocities and discharge at different depths in both circular 
and egg-shaped sewers. 

The diagrams in the " Separate System of Sewage," first 

184 



SEWER DIAGRAMS 185 

edition, by Staley and Pierson, are made up from Latham's 
tables, and the difference between these values and those 
from Kutter's formula are well shown in the second and later 
editions, where Kutter's lines are printed in red on the same 
plate. 

Among the diagrams compiled by J. Leland FitzGerald, 
reprinted on a plate in Baumeister's " Sewerage " (First 
Edition), is one also based on Latham's tables, giving the 
discharge of circular and egg-shaped sewers. (Engineering 
News, Vol. XXIV, p. 212.) 

The first diagram based on Kutter's formula was that 
published in the Trans. Am. Soc. C. E., Vol. VIII, p. i, by 
Rudolph Hering, and reprinted by the Society for general 
use. It has discharges for ordinates, and slopes in feet per 
hundred for abscissas. The intersecting curves are those for 
velocities and diameters, and a separate sheet is required for 
different values of n. One such sheet (^ = .013) is given in 
Engineering News 7 Vol. XXXII, p. 449. 

A diagram computed by Mr. Moore of St. Louis is given 
in the Journal of the Association of Engineering Societies, 
Vol. V, p. 360, whose ordinates are diameters, and abscissae 
discharges in cubic feet per second. The intersecting curves 
then are velocities and grades, given in fall per hundred feet. 
This is not as well adapted for use as the first, both in that 
the intersections are more oblique and that in order to read 
for small pipe a supplemental diagram of the corner has to be 
redrawn on a larger scale. 

In the Engineering News for August n, 1892 (Vol. XXVIII, 
p. 127), is a carefully drawn diagram by Professor Talbot of 
the University of Illinois. Here the discharges were made 
ordinates, and the gradients in per cent the abscissae. The 
square roots of the gradients were plotted instead of the 
gradients themselves, and in order to get better intersections 
the axes of the diagram are inclined towards each other. The 
line of equal diameters becomes a straight line, and in order 
to get the 6- and 8-inch pipes on the diagram their discharges 



186 



SEWER DESIGN 



are made ten times the true value. The diagram is supple- 
mented by Mr. F. S. Bailey, in order to show larger sizes and 
is published in enlarged form in Engineering News, Vol. XXXII, 
p. 403, the construction being as before except that the value 
of n is taken at .015. 

A rather complicated set of formulae has been published by 
Messrs. Adams and Gemmell (see Engineering News, Vol. 
XXIX, p. 396) for sewers from 6 inches up to 5 feet in diameter. 
All the values are kept in one diagram by placing one part 
of the diagram to a certain scale over another part already 
drawn to a larger scale, and by reading ordinates for one part of 
the diagram on one side and for another to a different scale 
on the other. The result is a very compact diagram, but one 
likely to lead to confusion. These are the diagrams given 
in the very convenient " Sewerage Engineer's Note-Book " 
by Albert Wollheim, London, who thinks them the " most 
handy diagrams yet printed." 

In the Paving and Municipal Engineer, Vol. VII, pp. 116 
and 119, are two diagrams by John W. Hill. 

In order to make more definite the errors involved by 
using the tables of Latham or diagrams based on those tables, 
values of v, for various slopes and sizes of pipes have been 
computed and ave shown, side by side, in Table XXIII. 

TABLE XXV 

SHOWING VALUES OF v, FOR DIFFERENT SLOPES AND SIZES OF 
PIPE BY FORMULA OF WEISBACH AND KUTTER 



Slope. 


6" 
Diameter. 


12" 

Diameter. 


18" 
Diameter. 


24" 

Diameter. 


36" 

Diameter. 


48" 
Diameter > 


60" 
Diameter 




rt 

,0 


n 


.D 


CD 


X) 


* 


o 


g 


1 


CD 


A 


b 


1 


u 








8 









'5 





5 





'a; 


"3 


.2 

u 


g 







M 




M 





M 




M 


^ 


M 


^ 


M 


'^ 


M 


i : 10 


II . I 


8.0 


14.9 


13.6 


17-6 


15.0 


















i : 100 


3-6 


2-5 


5.1 


4-3 


6.2 


5-9 


7-2 


7-2 


8.7 


9.8 


10. 




II . I 




i : 200 


2.4 


1.8 


3-6 


3.1 


4-4 


4-i 


5.1 


5.1 


6.2 


6.8 


7-2 


8-3 


8.0 


9.6 


i : 500 




i . i 


2. 2 


1.9 


2-7 


2.6 


3.1 


3-2 


3-9 


4-3 


4-5 


5-2 


5.1 


6.1 


i : 1000 


0.9 


0.8 


1.4 


i-3 


1-7 


1.8 


2. 2 


2.3 


2.7 


3-o 


3-2 


3-7 


3-6 


4-3 



SEWER DIAGRAMS 187 

It will be noticed that for values of ^ = .5, i.e., for 24-inch 
pipe, the velocities are identical, but that for smaller sizes, 
Weisbach's formula gives velocities that are too large, and for 
larger sizes, velocities that are too small. The difference is 
more marked in a comparison of quantities, especially for the 
larger sizes. For example, the difference for a 6o-inch sewer 
on a grade of i : 500 is that between a discharge of 100.2 
and 119.8 cubic feet per second, or nearly 20 cubic feet per 
second, which is about the capacity of a 24-inch pipe. 

A recent book (1910) on water supply and sewerage, in spite 
of the discrepancies between the values of the old formulae 
and the more modern ones, has included in its text a plate 
giving values of v and Q for varying values of d and s, basing 
the diagram on Latham's old tables. From the diagram, the 
values given in Table XXV in the columns marked Weis- 
bach can be checked and the differences shown there would 
be found also in any designs based on the diagram referred to. 

All the diagrams consider the four quantities, size of pipe, 
velocity of flow, grade, and discharge, while the element of 
roughness is left out, considering that it is the same for all the 
quantities included in the diagram; and if, as when the sewer 
changes from pipe to brick, it is necessary to change n, 
another diagram has to be made. It is possible to construct a 
diagram having any two of the above quantities as ordinates 
and abscissae, while the other two quantities appear as curves 
crossing the axial lines, and each other at various angles. 
Further variations can be made by constructing the dia- 
grams in parts, each to a different scale; by using a logarithmic 
scale for one or both axes; by laying off, instead of the diam- 
eters or the corresponding values of R, the values of the square 
root of R. The grade may be expressed and drawn in per cent, 
in feet per mile, or in number of feet for a fall of one foot. 
Separate diagrams have to be prepared for brick sewers and for 
pipe, for circular sewers and for egg-shapes, so that for com- 
pleteness three diagrams, however made, should be provided. 

The diagrams in Plates 3, 4, and 5 are given with the idea 



188 SEWER DESIGN 

that they will serve all purposes of actual design. The abscissae 



esj 

8 

CX 
0^3 

CO 



ft 



<*>. 



% 



x. 



V^_ 



-& 



)D P9jpunn 



-* o 

N *>* 



8 



^ 

J9M9S JO,OOI o o 

J9d SUOSJ9J ^ 



x 



X 






X 



13 



10 Q o o 

co <*-< 

5101 JO U1PIM 



8 S g R 



are grades in per cent, and the ordinates discharge in cubic 
feet per second, the logarithms of both quantities being plotted 



SEWER DIAGRAMS 189 

instead of the numbers themselves. The advantage of this 
method of plotting, shown in the good intersections, is evident. 
The diagram shown in Fig. 47 is given as being convenient 
for laying out laterals. By its use the greatest length possible 
for a 6-inch pipe flowing full to be laid for contributing house- 
drains can be read off at once. As the diagram shows, the 
first factors are the width of lots and the probable number 
of persons per lot. This is changed into the number of per- 
sons for one hundred feet of sewer and combined with an 
assumed number of gallons per head per day. This gives gal- 
lons per hundred feet of sewer, which, taken with the grade 
of the sewer, gives gallons capacity of length of sewer, to which 
the assumed contribution is made. A similar diagram can 
easily be made for 8-inch pipe. 

PROBLEMS 

72. Using values found in Flynn's Tables, construct a diagram on 
cross-section paper, having slopes in feet per thousand for abscissae and 
discharge in million gallons per day for ordinates. 

73. Construct three curves, showing the relations between sizes of 
pipes and slopes in per cent by which velocities of 2.0, 2.5 and 3.0 feet per 
second may be obtained according to Kutter's formula. 

74. Construct a diagram on logarithmic paper for circular pipes 
flowing half -full, with slopes in feet per thousand for abscissae and dis- 
charge in cubic feet per second for ordinates. Show curves for both 
sizes of pipes and for velocities. 

75. Using the Williams-Hazen formula, construct a diagram to show 
relation between slopes and discharges for pipes 6 to 24 inches diameter 
on logarithmic paper. 

76. Construct a diagram for elliptical pipe (or for a basket-handle 
section) showing discharges for various sizes and slopes. 

77. Construct a diagram for conduits whose section is a right tri- 
angle, vertex down, showing discharges for various depths and slopes. 



CHAPTER XIV 
USE OF DIAGRAMS 

IN order to understand better the use of Kuichling's 
method for determining the amount of rain-water to be consid- 
ered and the proportion of the fall reaching the sewers, the 
following hypothetical example is given of its use in Ithaca, 
N. Y., the plan of which city is given on Plate I. 

It is assumed that the surface-water above Eddy Street 
will be taken care of by a drain discharging from the end of 
that street into Six Mile Creek, and that all the storm-water 
falling on the area between Eddy Street and Aurora Street 
at the foot of the hill is to be taken care of by a drain run- 
ning from State Street north to Cascadilla Creek. Evidently 
three main laterals will lead into this drain one coming down 
the hill on State Street, one on Seneca Street, and one on Buffalo 
Street; while a fourth line, smaller than the others, will enter 
from Mill Street. 

To determine the rate of rainfall the duration required 
for a maximum flow at the outfall is necessary, that is, the 
length of time for rain to get from the upper end to that point. 
The point farthest from the outfall is at the corner of State 
and Eddy streets, and, scaling from the map, it is 2375 feet 
to the corner of Aurora and State streets and 1325 feet on 
Aurora Street to the creek. Down the hill the average grade, 
from the contours, is about 7 per cent, and if we assume a 1 2-inch 
pipe, according to the diagram on Plate 3 the velocity will be 
10 feet per second. That is, it will take water about 2375^10 
= 237 seconds, or four minutes, to reach the bottom of the hill. 

On the flat there are 1720 feet, and the velocity will be 
that due to a fall shown by the contours to be 10 feet in that 
distance, a .58 per cent grade. 

190 



USE OF DIAGRAMS 191 

By the diagram on Plate 4, assuming that a 3-foot pipe 
will be needed, we find the velocity to be 6 feet per second, 
so that it will take 254 seconds, or a little more than 4 minutes, 
for the water to get to the creek a total time from the 
farthest point of 8 minutes. Adding 3 minutes for the time 
necessary after the storm starts for the rain to reach the 
gutters and catch-basins, the duration of the storm which will 
give a maximum discharge is n minutes. 

Now consulting Kuichling's diagram, Fig. 6, we find the 
maximum rate of a storm lasting n minutes to be 3.18 inches 
per hour. 

On larger areas it will be necessary to determine the time 
of concentration separately for the different parts of the same 
area in order that the rate of rainfall may decrease as the 
combined parts give larger and larger total areas. In the 
present case, however, the entire area is so small and the time 
of concentration to the bottom of the hill is so short that no 
greater accuracy would be secured by computing the rate of 
rainfall separately for the smaller district. For large areas, 
however, the times of concentration must be completed in 
order. 

We assume, then, that there is a rain falling at the rate 
of 3.2 inches per hour which is to be cared for, and note that 
by the topography no water from the upper side of Eddy 
Street or above will enter this drain; and that as the velocity 
is high and the buildings are residences, so that a temporary 
filling of the gutters will not be an annoyance, the pipe need 
not begin until the water has reached the corner of Stewart 
Avenue and State Street. At that point there is a contrib- 
uting area, scaling it from the map, of 1750X580=1,015,000 
square feet, or 23.3 acres. An inch an hour is practically the 
same as a cubic foot per acre per second, so that the discharge 
from these 23.3 acres will be 23.3X3.2 = 74.5 cubic feet per 
second, provided it all flows off. The area has a population 
of about 25 per acre, and, by the table given on p. 74, 25.3 
per cent of the rainfall will flow off. 74.5X25.3 equals 18.8 



192 SEWER DESIGN 

cubic feet per second, or the amount of run-off to be cared for 
by the drain at that point. It may be noted here that on steep 
hillsides 5 to 10 per cent is sometimes added, but as this area 
is entirely unimproved and likely to remain so, having a large 
proportion of lawn and no paved streets, nothing need be 
added. 

By diagram on Plate 3, to discharge 18.8 cubic feet per 
second on a grade of 10 per cent, which the hill from this 
point down is seen to be, will take a 1 5-inch pipe, which will 
run to Spring Street. Here an area of 540,950 square feet, 
or 12.4 acres, discharging 25.3 per cent, adds 10.0 cubic feet 
per second. Since the diagram does not show the intersection 
of the 30 cubic-foot line with the 10 per cent grade line, the 
size must be computed. It is found to be an 1 8-inch pipe. 
At the foot of the hill, 400 feet from Aurora Street, the grade 
changes to 0.5 per cent, and on this grade a 3O-inch pipe is 
required, which will run the 400 feet to the corner. Here the 
drainage of 7 acres, or 5.6 cubic feet per second, enters, making 
34.4 cubic feet in all. On the same grade of 0.5 per cent this 
takes about a 33-inch pipe. At Seneca Street will enter the 
water from the area between Seneca and State streets and west 
of Stewart Avenue. This amounts to 11.2 cubic feet per 
second, making 45.6 in all, requiring a 39-inch pipe. This 
may be taken from the diagram on Plate 4 and will be either 
brick or concrete. At Buffalo Street the contributing area 
is 13.7 acres, or 10.9 cubic feet per second, making a total of 
56.7 cubic feet, requiring a 42-inch sewer. On account of 
the amount of sediment brought down the hill, and the large 
deposits where the velocity is so retarded, it will be wise to 
increase the size from here to the creek, making it 48 inches 
for the remaining distance. 

Reviewing the velocities, the farthest point is at the corner 
of Quarry and Buffalo streets. From here to State Street, 
with a grade of 6 per cent, the water flowing in an open 
gutter will have a velocity of about 9 feet per second, requir- 
ing, for the 1085 feet, 120 seconds or 2 minutes. Still flowing 



USE OF DIAGRAMS 193 

in the gutter it will take about three-fourths of a minute more 
to reach Stewart Avenue. In the 1 5-inch pipe on the 10 per 
cent grade the velocity is between 1 2 and 1 5 feet per second for 
300 feet, adding a quarter minute, or 3 minutes in all. For the 
remaining distance the time will be 6 feet per second, requiring 
nearly 5 minutes more, or 8 in all. This agrees with the time 
assumed, and therefore a second rate of rainfall based on this 
time just found will not be necessary. 

For a possible maximum with a shorter storm, if the 
Buffalo Street lateral is considered, it will take only about 
6 minutes for its water to reach the outfall, including the time 
necessary for the water to reach the gutter, and the corre- 
sponding rainfall is 3.4 instead of 3.2 as used before. For the 
limited area drained by this lateral it is plain that there can 
be no maximum flow brought down by this pipe. 

To illustrate the method of determining the sizes of pipes 
for domestic sewage, assume that it is required to find the size 
for the Northern Main in the city of Ithaca, that is, the pipe 
coming directly to the pumping-station and taking the sewage 
from the region north and east of Cascadilla Creek. According 
to the map this is an area of 138 acres, and is populated at the 
rate of about 30 per acre. The area taken is all that can ever 
drain into the system, and represents all the future population 
in the district. The population to be considered is 4140. After 
studying the water-supply it is assumed that a future provision 
of 70 gallons per head per day should be provided, that is, an 
average daily flow of 289,800 gallons. If half of this is sup- 
posed to flow off in 8 hours, the rate of flow in those hours 
will be 18,110 gallons per hour, or 302 gallons per minute, equal 
to 40 cubic feet per minute. A knowledge of the territory 
will justify the assumption that fully 2 miles of the pipe-line 
will be covered with ground-water, which, at the rate of 
20,000 gallons per mile per day, will add 4 cubic feet per minute 
to the flow, making 44 in all. By the topographical conditions 
the grade will be the minimum, and will be determined by the 
requirements of velocity. Looking on Plate 3, we find that 



194 SEWER DESIGN 

for 44 cubic feet per minute, with a velocity of 2.0 feet per 
second, a 1 2-inch pipe is required. This pipe will run from the 
lower end to the first lateral, where the volume of flow will 
be diminished by the amount there contributed. The smaller 
pipe is continued until the next lateral is reached, and so on. 
It is to be noted that while the size of pipe as just taken 
is calculated so that the estimated flow will fill the pipe only 
half full, this factor of safety is not always necessary, and in 
the lower ends of large mains, where the flow is large and 
comparatively constant, the size of pipe as determined for the 
exact flow is taken, or the pipe increased by one or two sizes 
only, as it is evidently bad engineering to require the expendi- 
ture of a large amount of money unnecessarily. In studying 
the grades and sizes for a city, various ways of tabulating 
and simplifying the large amount of computation can be 
devised. The relative effect of the grades of one line on another 
is best seen by plotting the profiles one above another so that 
the lower end of every lateral is in a straight line directly above 
the starting-point. 

PROBLEM 

78. Design the size and grades for an outfall sewer along the route 
shown on Plate VI. The following suggestions should be followed: 

Determine the volume of storm-water and domestic sewage that will 
have to be taken care of at the point A from District I. Assume that the 
sewer will be 10 feet below the surface at this point and that it will be 
laid on a slope to give a velocity of 2.5 feet per second to B. Assume the 
drainage from all of District II to enter at B. Assume a minimum grade 
again to E, and that the drainage from three-quarters of District III will 
enter at D. From E to F the grade will be greater, the elevation of the 
invert at E being +5. From F to G, the grade is i per cent and the 
drainage of one-quarter of District III will enter at G. From G to the 
river the grade is that necessary to give a velocity of 2 feet per second. 
Assume a ground water leakage of 8 cubic feet per day per square foot 
of interior surface. 



CHAPTER XV 

SEWER PLANS 

THE location of the outfall is the prime element among 
the factors brought together to decide how the mains and laterals 
of a city shall be arranged. The outfall itself, leading to the 
place of disposal, is located to agree with the method of disposal 
chosen, a discussion of which is not here taken up. The outfall 
may lead to the seashore, to the banks of a stream or lake, to 
broad farm-lands for irrigation, to a well-adapted area for 
nitration, or to some low out-of-the-way place for chemical 
treatment. If the place of disposal is the sea, tides, currents, 
and winds largely determine the location of the outfall. If 
onto irrigation-fields, the sewage must be taken wherever suit- 
able land is available, whether down the valley from the town 
or on the top of a hill above it. The filtration-area must be 
chosen where proper soil is to be found; unless the area is arti- 
ficial, when it can be placed more advantageously as regards 
distance and grade. If chemical treatment is to be practised, 
only enough land for the buildings and tanks is necessary, and 
a location to which the sewage can be led by gravity should be 
obtained if possible. Thus the position of the outfall is not 
in all cases to be decided by the topography, but is conditional 
on the final disposal. However, when the sewage is to be turned 
into a river or lake, the valley lines to the shore are usually 
followed. If the combined system is used, provided the sewage 
has to be treated or led away from the nearest point of the 
river to a point farther down-stream, it is usual to let the storm- 
water overflow into the river, while the house-sewage is carried 
along to the desired point. This is done by automatically 
arranged outlets. By an ingenious device the height of the 
overflow-weir is so arranged that the overflow begins to dis- 

195 



196 



SEWER DESIGN 



charge when the amount of dilution has reached that point 
previously decided to be allowable. It is advisable, and these 
relief-outlets make it practicable, to discharge the storm-water 
at as many points as possible, keeping the size of the storm- 
sewers small, carrying the water on the streets as long as pos- 
sible and avoiding the pouring of a large mass of water and 
sediment into the river at one point. 

The outfall being located, it is possible to arrange the mains 
and laterals according to one of five systems;* and although 




FIG. 48. 

there may be combinations of these, so that it is sometimes 
difficult to recognize the system adopted, yet in the first study 
of the topography it is advisable to keep these separate arrange- 
ments in mind. 

(A) Perpendicular system. When the city lies on the bank 
of a large river or bay, as New York, Philadelphia, or Portland, 
Me., where the volume of flow in the stream or the change of 
water at each tide is sufficient to keep the sewage diluted so 
as to be inoffensive, the only aim is to get the sewage into the 
water by the shortest path. In this we have what is called 

* Baumeister. 



SEWER PLANS 



197 



the perpendicular system (Fig. 48).* The mains follow down 
the beds of the separate valleys with laterals running from the 
ridge-lines between. There are as many mains as there are 
subordinate valleys, the grades are the best possible, and the 
sections of the sewers are small. Wherever a flat area is adjacent 
to the stream, and sewers from higher land must cross this to 
reach the water, it is possible that in heavy rains the low land 
may be flooded from the gorged sewers; this, however, is a 
question of the design and can be avoided. 

(B) Intercepting system. If the stream is not large enough 
for satisfactory dilution and the sewage has all to be carried 



int 



jrcept 



nqSe 



/ver 



FIG. 49. 

to a single point for treatment, or if the river-water is used for 
domestic purposes, so that the sewage has to be carried down- 
stream below the intake of the river-water, then the ends of 
the mains of system " A " are picked up by an intercepting 
sewer, the combination making the intercepting system, Fig. 49. 
This is sometimes an after-thought (as in Milwaukee and 
Chicago), in which case the different elevations of the main 
ends makes the construction of the intercepting sewer very 
difficult. Sometimes this intercepting sewer may be designed 
on such a scale as to pick up the ends of outfall sewers from 
separate villages or cities. Thus along the Charles River, 
just outside of Boston, is an intercepting sewer which takes 

* Report of the National Board of Health, 1881, page 117 et seq. 



198 



SEWER DESIGN 



the sewage from Waltham, Newtonville, and other places 
which formerly had sewer systems discharging directly into the 
river. Similarly, in New Jersey along the Passaic River and 
in New York, along the Bronx River, are sewers which act as 
interceptors for villages and cities instead of for lines of sewers 
all within one city. The first system, i.e., the perpendicular, 
can always be designed so that, when the necessity occurs, the 
interceptor may be put in with the elevations of the mains 
properly adjusted. This large sewer is usually expensive to 
build, being in the lowest ground, often below the stream-level, 
in gravel or soft mud. Besides preserving the stream from 
pollution, this system has the further advantage of allowing 




High Level Sewer. 



Low Level Sewer. 



FIG. 50. 

all the sewage to be brought to one point for pumping in case 
this is necessary, so that one large pump can take the place of 
several small ones. 

(C) Zone system. In case the sewage has to be pumped 
it may happen that a large part of the contributing territory 
is high enough so that the sewage from that part will flow to 
the outfall by gravity, and in this case the sewers may be 
arranged to form the Zone system, that is, a double intercept- 
ing system. An intercepting sewer is laid nearly following a 
contour so that it may discharge all the sewage from the land 
above it to the outfall by gravity, while the second interceptor 
collects only that part of the sewage which would in any case 
have to be pumped (Fig. 50). The advantages are the reduced 



SEWER PLANS 



199 



amount of water to be pumped, the decreased probability of 
flooding the lowest part of the city, and, in the case of land- 
disposal, the possibility of using the sewage at the place of 
treatment at different levels, as is done in England at some of 
the irrigation-areas. In this case, as in " B," the sewers leading 
into the interceptors may be arranged according to the per- 
pendicular system or to the fan system. 

One of the best examples of the Zone system may be seen 
in the city of London, England, where three different zones 
have been arranged to be drained by a low-level sewer, a mid- 




FIG. 51. 

die-level sewer, and a high-level sewer. The sewage from the 
low-level district has to be pumped three times, that from the 
middle-level only once, and that from the high-level sewer not 
at all. 

It should be noted that the possibility of making use of the 
zone system economically depends upon the cost of the high- 
level intercepting sewer being less than the capitalized cost of 
pumping the sewage not so intercepted. It is easily possible 
for a high-level intercepting sewer to cost so much for construc- 
tion as to far exceed the expense of handling the relatively small 
amount of liquid by pumps or otherwise. 



200 



SEWER DESIGN 



(D) Fan system. In this the mains radiate from the out- 
fall to serve different parts of the city, each main having its 
own branches and laterals (Fig. 51). Whether this or the 
perpendicular system is used will evidently depend on the topog- 
raphy and on the requirements of the outfall. 

(E) Radial system. In this system, of which Berlin is the 




FIG. 52. 

only city offering a good example, the sewage is cared for at a 
number of points in the circuit of the outskirts, and the sewage 
is brought to these points by different mains. The drainage 
is thus from the centre outward in several directions, and the 
sewage is cared for on filtration areas in these several localities 
(Fig. 52). Baumeister notes the great advantage of this method 
in that the sewers in the centre of the city are laid after that 



SEWER PLANS 201 

part is built up, so that there is little possibility of the section 
growing and needing larger sewers, while the part on the out- 
skirts which will grow is near the pumping-stations or disposal 
works and can be served at comparatively small cost and with- 
out interference with the rest of the system. In the other 
systems, as the outskirts away from the outfall grow, the whole 
system must be increased, the intermediate lines being designed 
to carry off only the amount first considered. 

The ideal topography for the radial system would be a 
gently sloping conical hill with the city at the apex. Such an 
ideal condition is really never found, so that the practical use of 
this system is limited to level areas for the drainage of which 
pumping will have to be resorted to by any system. At Berlin 
the outfall sewers leave the city in four different directions and 
the sewage is lifted by pumps and discharged onto the several 
irrigation fields which constitute the celebrated sewage farm of 
Berlin. 

Many combinations of these systems occur, and the out- 
lines given are to be considered only as guides to judgment in 
the individual case. The arrangement and combination must 
be adjusted to the topographical conditions. In the intercept- 
ing system, if there are a number of subordinate mains and 
one of those farthest up-stream is low, it follows that the inter- 
ceptor in order to take the sewage from this and still have a 
grade down-stream must at the last contributing main reach 
a point much lower than otherwise necessary. 

It is also often possible to take up a few hundred feet of the 
original subordinate main and, by relaying on a lighter grade, 
be able to raise the intercepting sewer throughout its entire 
length and thereby considerably reduce its cost. A small 
auxiliary pumping-station may sometimes be introduced to 
care for the sewage from the single low main and so reduce the 
entire cost of construction. In the new intercepting sewer 
for Chicago, where the depth is determined both by the depth 
of the present mains and by the requirements of grade, tunnel- 
work is resorted to as being cheaper than open cut, and large 



202 



SEWER DESIGN 



intermediate pumping-plants are required to avoid excessive 
depths at the outfalls. 

When possible, the laterals should be laid to reach the mains 




FIG. 53. 

in the shortest path, though topographical conditions do not 
always admit of this. In Fig. 53 it is more expedient to build 
two sewers from c to the water at a and b than to take the 



V 

FIG. 54. 

sewage from the whole area from d, both because the grades 
would be greater from the centre both ways than from water 
to water, and because the longer sewer would require greater 
size and greater depth of cutting. Where there are a number 



SEWER PLANS 



203 



of laterals and lines of equal size it is best to combine them 
into a main as soon as possible, rather than to have a number 
of lines of about the same capacity. In algebraic terms, it is 
cheaper to build a single line of nx capacity than to build n lines 
of x capacity. 

Figs. 54 and 55 illustrate the point, the length of the sewers 
being the same in both cases; but as the length of the small 
laterals is greater and that of the mains less in Fig. 55 than in 
Fig. 54, the former is the more economical arrangement. Further, 
the laterals will have a better grade, that is, the grade will be 



V 

FIG. 55. 

placed where it is most needed, this resulting from the fact 
that, since the main in Fig. 54 is larger than that in Fig. 55, 
it will not require as great a grade for the same velocity. Com- 
pare also in Fig. 56 the two sides of the diagram, illustrating 
two ways of laying out the pipes. 

On the other hand, in order to maintain in the sewers as 
uniform a velocity as possible, and in order to avoid deposits, 
wherever the sewage from a hillside discharges into a flat it is 
better to carry the sewage along contours than perpendicular 
to them. This will not increase the length nor, as a rule, the 
sizes of the sewers, since every street must have a sewer, and 
since where this arrangement is desirable the grades are ample 



204 



SEWER DESIGN 



for an almost indefinite length. In the case of storm-water, 
the circuitous path has the further advantage that the gradual 
accumulation of storm-water in the lower parts of the city will 
not require such large sewers as if the sewage were brought down 
in the short time required on the steepest streets. 
Other points that may be noted are as follows: 
Since manholes or flush-tanks are usually built at the ends 
of laterals, it is often possible to run the ends of two laterals 
into the same manhole, thereby saving the cost of one manhole 
and flush-tank, though increasing the length of the sewer. 



\ 



FIG. 56. 

The comparative cost is here to be considered, though the 
single manhole or flush-tank probably gives better ventilation. 
It is generally recommended that, since the flow of air is 
along the top of the pipes, wherever the sizes of the pipes are 
changed the smaller pipe be raised enough to bring the crowns 
of the pipes on a continuous line, in order to have a continuous 
ventilation upward through the sewer. For example, a 1 2-inch 
pipe emptying into a 1 5-inch pipe should be 3 inches higher on 
account of the ventilation. On long lines laid on a minimum 
grade this is a serious matter and requires that the lower end 
of a main be a foot or more deeper than the grades themselves 
would call for. Since the pipes are expected to run only half 
full, leaving half of the pipe for ventilation, it seems to the 



SEWER PLANS 205 

author that both of these factors of safety are not necessary, 
and that, except in rare cases where the pipes are expected to 
run full, where the cutting is deep and the line long, this require- 
ment of grade can be omitted. 

The Rawlinson principle of straight lines between manholes 
is rigidly insisted upon except for sewers large enough for a 
man to walk through, and all curves and changes of direction 
are made in the manholes. It has been recently recommended 
that even the house-drains, which are generally made to enter 
the sewer through a Y branch, should connect through a T in 
order to facilitate inspection. The direction of the flow imparted 
by a Y branch is said to be imperceptible, especially when the 
branch has a fall of 6 inches or more, and the possibility for 
inspection is very desirable. 

To compensate for the increased resistance to the flow in 
the short curves made in the manholes, it is usual to add a small 
fall in this curve, amounting to an inch or so for an 8- to 1 5-inch 
pipe. 

Recently in one of the engineering periodicals, there has 
appeared a theoretical consideration of the actual loss of head 
incurred by the flow of sewage around such curves. The varia- 
tion in the conditions such as the relative height of the flow 
line in the main sewer and in the lateral, and in the clean con- 
dition of the pipes is such that no exact solution can be hoped 
for. Probably an inch fall in the bend is more than enough, 
but it does no harm and prevents deposition of sediment at the 
end of the lateral. 

In order that the streams from two or three sewers meeting 
at the same manhole may have as little eddy-forming effect as 
possible and may meet and continue to flow with the least 
deposit of sediment, it is desirable that the streams all have the 
same velocity in order that in no one shall the velocity be 
checked. It is desirable also that the sewage-level in each of 
the joining sewers shall be at the same height. This last of 
course is not possible for all stages of all intersecting lines, but 
it may be so for the depth of flow for which the sewers are 



206 SEWER DESIGN 

designed. At the manholes the confluent streams are made to 
merge gradually by means of tongues formed in the bed of the 
manhole by which means the streams are guided together as 
smoothly as possible. If one sewer at a small depth enters a 
main at great depth, it is better to allow the lateral a straight 
drop with a bend at the bottom than to let the flow shoot down 
a steep incline to have its solid matter deposited at the foot. 
When two laterals enter the main from opposite sides it is 
especially desirable that the streams be guided into the main 
rather than that their opposing currents meet and form eddies 
which will tend to the formation of deposits. 

It is sometimes possible to use the volume of water brought 
down by a lateral as a source of flushing, a gate or storage 
reservoir in the manhole being arranged, and in this case an 
incline is better than a straight fall. 

PROBLEMS 

79. Consult collections of plans of sewer systems such as may be found 
in the report of the New York State Department of Health, 1900-1904, 
and select distribution systems to illustrate, as well as possible, the dif- 
ferent systems described in this chapter. 

80. Make a numerical comparison of the results to be obtained by using 
designs of either Figs. 54 or 55. Assume the length of each square of 
the figure to be 500 feet, that the amount of contributing sewage is 
10,000 gallons per day for each such unit distance. Assume a uniform 
velocity of flow of 2 feet per second and compare the relative elevations 
of the two outfalls. 

81. If a flush tank installed costs $60, and two sewers are leaving a 
ridge street on the same cross street, would it be more economical to start 
the two lines from one flush tank in the middle of the ridge street or to 
build two flush tanks 180 feet apart on the cross street? Assume the pipe 
to be 8 inches, costing 14 cents a foot, and the excavation to cost 60 cents 
per cubic yard. 



CHAPTER XVI 
SEWER CROSS-SECTIONS 

As has already been stated, in this country sewer-pipe are 
invariably made circular, though attempts have been made 
in England to make pipe of oval form. Experience shows 
that the difficulties of burning (any eccentricity or deformation, 
which in a circular pipe can be avoided by turning axially, spoils 
the oval pipe), will probably prevent any similar attempts in 
this country. The general advantage of circular pipe lies in 
the fact that when half full or full there is a greater velocity 
for the same grade than in any other pipe-section, and for the 
amount of material in the pipe the circular section has the 
greatest area; or, geometrically, for the same perimeter the 
circle, of all polygons, has the greatest area. If, therefore, 
sewers were always to flow full, they should, whether of pipe 
or brick or concrete, be built of circular form, in order to econo- 
mize material. But with a variable flow the circular section 
loses its value, and the less the flow the poorer the section for 
its purpose. According to the equation of flow, v = c \/RS, 
the velocity varies with the square root of the hydraulic radius, 
and in a sewer where the depth of flow changes from hour to 
hour the velocity decreases as the depth decreases, since the 
ratio of A : p continually decreases. This applies especially 
to the combined system, where the sewers are large to accom- 
modate the rainfall, so that the house-sewage flows in a wide 
shallow stream with a velocity much less than that at the half- 
full point. To avoid this difficulty the cross-section of the 
brick sewer has been changed in an attempt to make the ratio 
of A : p as nearly constant as possible for every depth, that is, 
to make the area of flow nearly semicircular for every depth. 
The gain over the circular sewer in increased velocity for low 

207 



208 



SEWER DESIGN 



depths is considerable, although the velocity can never be made 
constant, since with the same grade the larger circle will have 
the greater velocity. 

Many different shapes have been tried, though there are now 
but two in common use for this purpose. The egg-shape 
shown in Fig. 57 was introduced in England by Mr. John Phillips 
in 1846, and is used to-day with the same proportions then 
advised. The vertical height is equal to one and a half times, 




FIG. 57. 

the radius of invert is equal to one fourth, and the radius of the 
sides to one and a half times the transverse diameter. The 
other form of egg-shape, Fig. 58, has a smaller invert and is 
therefore better adapted to sewers where the depth of flow may 
at times be very small. The vertical height is one and a half 
times the transverse diameter as before. The radius of invert 
is one-eighth of the transverse diameter, and the radius of the 
sides one and a third times. Latham says that this new form 
is stronger than the old, and that with small volumes of flow 
it is better adapted to be self -cleansing than the earlier form. 



SEWER CROSS-SECTIONS 



209 



In order to obtain some comparison between the value of 
egg-shaped and circular sewers when the flow is small, the 




FIG. 58. 




V 




FIG. 59. 

author has plotted two sections, reduced in Fig. 59, one of a 
circular sewer 6 feet in diameter showing depths of flow of 3, 
6, 12, and 24 inches, and one of an egg-shape, with the same 
discharges in both cases. The grade was assumed at .03 per 



210 



SEWER DESIGN 



cent for both sections, and by repeated trials the depths in the 
egg shape necessary to give the same discharges as the circular 
were found. The benefit then is seen in the increased value of 
v in the former case. 





Circular Sewer 


Egg- shape 


. I 


ii 


III 


IV 


I 


II 


III 


IV 


Depth 


o-35 
0.41 
0.56 
o. 16 
0-39 

y 


o-5 

.1.12 

0.66 
0.64 

0.56 


i .00 

3-n 
0.86 

3-53 
1.14 


2.00 
7.24 
O.Q7 
12 .00 

1.66 


0.32 

0-37 
0.64 
0.18 
0.50 
.0.28 


0.58 
0.87 

o.73 
0.63 

0-73 
0.30 


I . 20 
2.08 
0.82 
3.20 
I. 4 8 
0.30 


3-87 
7.04 
0.96 
11.32 
1.63 


Area 


(i r* 


Discharge 
Velocity 


Per cent gain in velocit 



According to the table, a gain of about 30 per cent in the 
velocity is obtained by using the egg-shaped sewer. 

Since egg-shaped sewers are less stable and substantial 
than circular sewers, since for the same area of cross-section they 
require more masonry, and since they are more difficult of 
construction, it is of value to note the alleged advantage in 
velocity of this form and compare it with the increased cost of 
construction. 

Fig. 60 shows a diagram by which the discharge and the 
velocity of flow in the circular pipe can be read directly in 
terms of the discharge and velocity when the pipe is flowing 
full. The ordinates give the proportionate depths of flow and 
the horizontal line through any given or desired proportionate 
depth extended to meet the two curves given show by the 
abscissae the proportions of the discharging velocity when the 
pipe is flowing full. Similar curves may easily be made for the 
two forms of egg-shaped sewer referred to above or for any 
other section which is being used. 

Interesting curves of this sort applied to the sections sug- 
gested for the main intercepting sewers at Boston and called 
respectively, the basket-handle section, the gothic section, and 
the catenary section, will be found in the report on the Boston 



SEWEK CROSS-SECTIONS 



211 



Metropolitan sewerage systems, by Howard Carson, Chief 
Engineer. 

While the circular section is always employed for terra 
cotta pipe, in the case of larger sewers, made of brick or concrete, 
there is not the same necessity for adhering to the circular 
section. It is sometimes economical not to do so and a large 
number of peculiar and interesting sections may be found by 
reference to the larger text books and to the files of the periodi- 
cals. A floor of nearly flat area saves on the cost of forms. 



1.0 



p 

30.6 



30.3 

o 



0.1 



0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 

Proportional Velocities and Discharges 

FIG. 60. 



these floors being laid very much like sidewalks. Then, in firm 
earth where good lateral support may be had, light sidewalls 
can carry an arch cover at the minimum of expense. In deep 
cuttings, sometimes elliptical or oval sewers have been used 
with a view of saving excavation by limiting the width of the 
trench. Where, in other places insufficient head room has 
been encountered, the circular form has been changed to an 
ellipse with the long axis horizontal or to a section having very 
short sidewalls and with flat arcs for the top and bottom. 

It is not possible in these pages to take up in detail the 



212 SEWER DESIGN 

particular uses of the various sections which have been used 
or the needs of various conditions nor would it be desirable 
to consider the hydraulic properties or the structural weak- 
nesses of such sections without reference to their uses. It is 
only possible, therefore, here, to point out that these various 
sections are used and that for large outfalls where the flow of 
sewage is reasonably uniform, the economy of construction of 
other forms should be compared with the economy of material 
which for the same capacity always remains as an advantage 
to the circular form. 

PROBLEMS 

82. Compare the velocities and discharges of two conduits laid on 
the same grade (s =.0003), one being circular, 6 feet diameter, flowing full, 
and the other of the same area but rectangular with width twice the depth. 

83. Using the diagram of Fig. 60, determine the velocities of flow in a 
36-inch tile sewer, laid on a 0.2 per cent grade, with depths of flow varying 
by 2-inch intervals from o depth to half-full. Plot a curve showing variation 
of velocity with depth. 

84. A brick sewer is to be laid on a .0002 grade and is to carry 100 cubic 
feet per second flowing half full. If the flow sometimes drops to 5 cubic 
feet per second, how much gain in velocity would be had by using an old- 
style egg-shaped sewer? 

85. Using Kutter's formula, find the value of V, for a conduit of wooden 
plank nailed together edgewise to form a trough of triangular section. 
Assume the depth at the centre to be 12 inches and the grade to be .05 
per cent. 

86. An outfall sewer has a section formed by a semicircular invert, 
surmounted by vertical side walls. If the radius of the invert is 3 feet 
and the total depth of flow 6 feet, find the slope, by Kutter's formula, 
necessary for a velocity of 2 feet per second. 



CHAPTER XVII 

FLUSHING 

NOTWITHSTANDING the fact that of late years the grades 
and sizes of sewers have been more carefully determined and 
more accurately proportioned to the work required of them, 
and that they are now so built that the scouring and suspending 
power of the running sewage at no time gets below a prede- 
termined minimum, yet accumulations of silt and filth often 
occur which must be cared for by some special means. There 
are two ways by which such deposits may be removed, by 
flushing or working out the obstruction with a strong flow of 
water, and by scraping or dragging it out with a suitably 
designed hoe or scraper. 

The water for flushing may be obtained in several ways. 
Where the topography admits of it, water from some stream 
may be introduced at the upper parts of the system and dis- 
charged into the same stream at a lower level; in the case of 
a seaside city the high tide may be allowed to enter the sewer 
and flow out at some point where the tide is lower; a reservoir 
may be filled at high tide, and discharged after the tide has 
fallen; rain-water, waste water from baths, factories, etc., 
may be accumulated for a time, and then discharged into the 
sewer; the public water-supply may be used; or, finally, the 
sewage itself may be dammed up and made to act as flush- 
water. In planning the flushing arrangements, it must be borne 
in mind that a quiet flow of sewage or water, however large, 
is of little effect in removing obstructions once formed, and 
that to be effective the flush-wave must be sudden, of large 
volume, and introduced within a short distance of the obstruc- 
tion. This wave-action, in all cases except where the stream- 
flow is always sufficient to fill the pipes, must be formed by 

213 



214 SEWER DESIGN 

a sudden discharge through a gate or other device. This may 
be done either automatically, or by hand; at fixed intervals, 
or whenever deemed necessary. In this country a reservoir 
accumulating water from the public water-supply and discharg- 
ing through an automatic gate (the so-called automatic flush- 
tank) is the flushing method in general use. In many cases, 
however, it would seem a sad lack of judgment to neglect to 
provide, when it can be easily and cheaply done, other means 
of washing out the mains and laterals of a system. 

When hand-gates are used, limited, on account of weight, 
to pipes of about 20 inches diameter, either the water-supply 
or sewage may be used. For this purpose the brickwork on the 
lower side of the manhole beyond which it is suspected that 
deposits may occur is brought up in a plane around the pipe 
from the bottom, and a bearing-surface for the gate bolted on; 
or a frame in which the gate may slide up and down may be 
secured to the manhole wall. The end of the pipe may form 
'the bearing-surface, or the pipe may be closed by a plug. 

Large sewers, especially storm-water sewers in which the 
flow-volume varies largely, require gates too large and heavy 
to be raised directly by hand, and a screw or windlass must be 
provided. If such a gate is located at a point in the sewer 
where an overflow into some stream can be arranged, it provides 
for the contingency of a gate sticking or broken mechanism or 
the negligence of attendants. 

Automatic flush-tanks, generally used with 6- and 8-inch 
sewers, in this country are of two types, viz., operating through 
some movable part or through the starting up of a large siphon. 
Of the first type is that made in Schenectady, N. Y., by the Van 
Vranken Flush-tank Co., the following description and drawing 
of which is taken from the circular (see Fig. 61): 

" The tank consists of a siphon, of which the interior diam- 
eter ranges from 5 to 8 inches in the various sizes, a trap at the 
bottom, and a cast-iron case connected with the sewer or drain. 
It is this trap that forms the essential feature of the Van Vranken 
siphon. Instead of being fixed, it is hung on trunnions under 



FLUSHING 215 

the longer leg, being so balanced that when nearly full its 
centre of gravity is brought forward and a portion of the con- 
tained water poured out. As the water had previously risen 
in the outside reservoir to a height above the lower bend of the 
siphon equal to the depth of water in the trap, the sudden 
change of level in the latter causes the longer leg to be imme- 




FIG. 61. 

diately filled with a stream under about 4 inches head, so that 
the siphonic action commences at once without waste of water." 

The siphon-tank was invented by Mr. Field, so far as its 
present form is concerned, was afterwards improved by Col. 
Waring, and is known as the " Field- Waring Tank." The 
following description, together with a sectional drawing, is taken 
from the circular (see Fig. 62). 

" The siphon invented and patented by Rogers Field and 
improved by Col. George E. Waring, Jr., consists (in the form 



216 



SEWER DESIGN 



shown) of an annular intaking limb, and a discharging limb 
at the top of which is an annular lip or mouthpiece, the bottom 
of which is tapered to less diameter. The discharging limb 
terminates in a weir-chamber which when full to its overflow- 
point just seals the limb. Over the crest of the weir is a small 
siphon whose function is to draw the water from the weir- 
chamber and thus unseal the siphon. At the lower end of the 
small siphon is a dam or obstruction to retard its breaking. 







FIG. 62. 

The main siphon is brought into action (on the tank being filled) 
by means of a small stream of water flowing over the annular 
mouthpiece and falling free of the sides of the discharging 
limb. As soon as the lower end of the discharging limb has 
been sealed by filling the weir-chamber the falling stream of 
water gathers up and carries out with it a portion of the con- 
tained air, thus producing a slight rarefaction. 

" This rarefaction causes the water to rise in the intaking 
limb higher than in the basin outside, and hence increases the 
stream of water flowing over the mouthpiece, which in turn 



FLUSHING 217 

increases the rarefaction, and the siphon is soon brought into 
full play. 

" On the tank being emptied to the bottom of the intaking 
limb the flow is checked, and the small siphon over the crest 
of the weir draws the water from the weir-chamber, air enters 
the discharging limb, and the siphon is vented ready for the tank 
to again fill. 

" These siphons are largely in use and are giving excellent 
satisfaction; made in two sizes for flushing sewers." 

A slight modification of this tank was made by Benezette 
Williams, and the improved tank was manufactured under the 
name of " The Rhoads- Williams Siphon." It has been much 
used in the West and has proved very satisfactory. The cata- 
logue gives the following description and table, which latter will 
serve as a general index of the capacity of flush- tanks: 

" The Rhoads- Williams Siphon, as illustrated in Fig. 63, 
consists of an annular intaking limb or bell, and a discharging 
limb terminating in a deep trap below the level of the sewer. 
Below the permanent water-line in the discharging limb is con- 
nected one end of a blow-off, or relief trap, having a less depth 
of seal than the main trap, the other end of which joins the main 
trap on the opposite side at its entrance to the sewer and above 
the water-line of the trap. 

" The bell has a vent-pipe terminating at a given point 
above the bottom of the bell, and extends above the high- 
water line. The pipe which extends above the bell has a cap 
on it with the proper size sniff-hole for venting the siphon. 

" As the tank fills (the main trap being full) the water 
rises in the intaking limb or bell, even with the level of the 
water in the tank, until, reaching the end of the vent-pipe, a 
volume of air is confined in the two limbs of the siphon between 
the water in the intaking limb and the water in the main trap. 
As the water rises higher in the tank the confined volume of 
air is compressed, and the water is depressed in the main trap 
and in the blow-off trap. This process goes on until the water 
in the tank reaches its highest level above the top of the intaking 



218 



SEWER DESIGN 



limb, at which time the water is depressed in the blow-off trap 
to the lowest point and the confined air breaks through the 
seal, carrying the water with it out of the trap, thus releasing 




FIG. 63. 

the confined air and allowing an inflow from the tank, putting 
the siphon into operation. 

" On the tank being discharged to the bottom of the intak- 
ing limb the flow is checked, and the siphon is vented by the 
admission of air to it through the vent-pipe." 



FLUSHING 



219 



TABLE XXVI 

RHOADS-WILLIAMS AUTOMATIC SIPHON 







Size and Capacity of Tanks, with 






Diameter 
of Dis- 
charging 
Limb. 
Inches. 


Diameter 
of Sewer. 
Inches. 


Siphons of Standard Length. 


Water re- 
quired to 

fill IOO 

Lineal Feet 
of Sewer. 
Cubic Feet. 


Price at 
Factory for 
Siphons of 
Standard 
Length. 


Diameter. 
Feet. 


Discharging 
Depth. 
Inches. 


Discharging 
Capacity. 
Cubic Feet. 


5 


6 


4 


26 


27 


2O 


$26.00 


6 


8 


4* 


31 


40 


35 


30.00 


8 


IO 


5 


36 


59 


55 


40.00 


10 


12 


6 


36 


85 


79 


60.00 


12 


15 


7 


40 


128 


122 


QO.OO 



The Miller tank is the latest development and is probably 
the best and most reliable tank to be had to-day. The follow- 
ing description from the catalogue explains the workings of the 
several parts: 

" The Standard Design Miller Siphon, as shown by accom- 
panying illustration (see Fig. 64), consists of but two parts: 
the discharging limb or deep-seal trap (with the discharge 
mouth integral therewith), and the intaking limb or bell, which 
is placed over the longer leg of the siphon and held securely 
in place by its own weight, both parts being plain castings 
with no machine work whatever. 

" This siphon has no moving parts to get out of order, no 
joints to leak, and no small tubes to clog up or choke, and is 
universally acknowledged to be the simplest and most durable 
device of its kind ever made. 

[From London Engineering.] 

" ... The action of this siphon is as follows: As the 
water entering the tank rises above the lower edge of the bell 
it encloses the air within, the lower portion of the trap being, 
of course, filled with water. As the water-level of the tank 
rises the confined air gradually forces the water out of the long 
leg of the trap, until a point is reached when the air just 
endeavors to escape around the lower bend. Now as the dif- 



220 SEWER DESIGN 

ference of water-level in the two legs of the trap equals the 
difference of the levels between the water in the tank and the 
water within the bell, it will be seen that the column of water 




FIG. 64. 

in the short discharge leg has practically the same depth as the 
head of water in the tank above the level at which it stands in 
the bell. The two columns of water therefore counterbalance 
each other at a certain fixed depth in the tank. As soon as 
this depth is increased by a further supply, however small, 



FLUSHING 



221 



a portion of the confined air is forced around the lower bend, 
and by its upward rush carries with it some of the water in the 
short leg, thus destroying the equilibrium and the siphon is 




FIG. 65. 

brought into full action immediately. The water is then 
drawn out of the tank to the bottom of the bell, the siphon 
vented by the admission of air through the sniff-hole, and the 
operation repeated. The secret of this invention is the free 
projection of the overflow edge of the short leg of the trap, 



222 SEWER DESIGN 

which allows of the instantaneous escape or falling away of the 
heaved-up water. Thus if the discharge mouth were formed 
as an ordinary bend, the siphon would not act (although the 
confined air rushes around the lower bend), for the simple 
reason that the heaved-up water has no means of instantaneous 
escape, and therefore the equilibrium is not sufficiently dis- 
turbed. It will thus be seen that the action of this siphon 
depends, not on the escape of air, but on the sudden reduction 
of a counterbalancing column of water. 

" Repeated trials with a 6-inch (Miller) siphon have shown 
that it will discharge full bore a 5oo-gallon tank, fed so slowly 
as only to be filled in fourteen days. 

" There being no internal obstruction, the discharge is 
extremely rapid. 

" We have had the opportunity of seeing one of these siphons 
at work in the excellent Sanitary Museum at Hackney, and, 
though severely tried, the siphon worked perfectly." 

A special form of the " Miller Tank," designed by Andrew 
Rosewater for use in the city of Omaha, Neb. (see Fig. 65), is 
now manufactured. It is claimed that it discharges 40 per cent 
faster than any other siphon of the same size. It does not 
take the place of the inspection manhole, but affords easy access 
for inspection during the working of the siphon. 

Fig. 66 * shows an automatic discharging siphon made by 
the Merritt Company, of Camden, N. J., and embodying a 
different principle. The main discharge pipe is built in the 
form of a " U " tube, the longer leg containing an auxiliary 
small air pipe, with a return bend at its lower end. When the 
chamber starts to fill, this small pipe bend or seal is filled with 
water, so that the rising water confines and compresses air in 
both the large and small " U " pipes. In time, and at any 
desired height, determined by changing the relative lengths of 
the parts of the small -pipe siphon, the seal is broken and the 
air escaping draws air enough from the large pipe to start it 

* From Ogden and Cleveland's ' Practical Method of Sewage Disposal." 



FLUSHING 



223 



in action. The method has an advantage in that it requires 
no deep excavation, and the mechanism can be set after the 
manhole is built. 

Of late years the Pacific Flush-tank Co., having obtained 




FIG. 66. 
Single " Merritt " Automatic Siphon. 



control of the Rhoads- Williams Tanks, and having made a num- 
ber of modifications, combinations and improvements on its 
own tanks, is able to supply flush- tanks of a great variety of 
forms and sizes. The use of automatic siphon control in con- 



224 SEWER DESIGN 

nection with the discharge of sewage onto filter beds has given 
a great impetus to the use of flush-tanks, and their reliability 
has been much improved. The question of the propriety of 
their use for the purpose of cleaning the upper ends of laterals 
is discussed in the next chapter. 

PROBLEMS 

87. In the tipping bucket of the Van Vranken flush-tank, assume a 
definite geometrical shape and locate the proper centres of support, con- 
sidering the bucket both empty and full. 

88. In the Miller tank, determine the relation between the head of 
water in the tank and the length of the lower limb of the siphon. Is 
any other factor involved in fixing the depth of water in the tank at the 
instant of discharge? 

89. Determine the time (approximately) for the discharge of a flush- 
tank, 4 feet diameter, 2\ feet deep through a 6-inch siphon. (Consult 
-catalogue for dimensions). 



CHAPTER XVIII 
USE OF FLUSH-TANKS 

THE following paper, read by the author before the American 
Society of Civil Engineers, in May, 1898, offers a discussion 
on the suitable use of flush-tanks, their proper capacity, fre- 
quency of discharge, etc. 

The use of flush-tanks in connection with small pipe sewers, 
which has been made an integral part of the " Separate System " 
and generally adopted in systems caring only for house-sewage, 
is attended with much uncertainty. In such systems it is gen- 
erally specified that a flush-tank be placed at the head of every 
lateral, each tank being so regulated as to discharge at least 
once in 24 hours. The relation between the size of the sewer- 
pipe and the amount of water used in a flush is not given, nor 
is the influence of grade discussed. The general law is laid 
down that all laterals, regardless of size, grade, or contributing 
population, must be supplied with flush-tanks in order to secure 
a self-cleansing flow in the laterals and to maintain the integrity 
of the system. 

The financial burden of such a requirement is evident. 
As an example, it may be cited that in the plans for the sewerage 
system of Ithaca, N. Y., in which plans this requirement of flush- 
tanks was thoroughly complied with, even for the 12 per cent 
grades, no less than 131 flush- tanks were required in 25.3 miles 
of sewers, or one for every 1020 feet. The relative importance 
of the flush-tanks may also be seen by comparing the actual 
cost of the sewers with the estimated cost of the tanks. The 
cost of the sewers, viz., the sum of the amounts of the several 
contracts, was $81,000, and, estimated at $50 each, the flush- 
tanks would cost $6550, or more than 8 per cent of the cost of 
the system. It would seem, then, that the cost of flush- tanks 

225 



226 SEWER DESIGN 

is by no means insignificant, but that their use increases the 
cost of the separate system by nearly one-tenth, besides intro- 
ducing a permanent charge, both for water used and for intelli- 
gent care in maintenance. That these annual charges are 
no bagatelle will be apparent by again referring to the case 
of Ithaca. Assuming that the tanks required are of a capacity 
of 150 gallons, a minimum amount, discharging but once a day, 
the water required is 19,650 gallons a day. Twenty cents per 
1000 gallons (the amount charged in Ithaca *) is a fair average 
amount, and at that price the daily charge for water is $3.93, 
or $1434.45 per year. Adding to this $600 per year as the wages 
of a mechanic, whose constant attention is found by experience 
to be necessary in examining and readjusting the tanks, the total 
annual charge is $2034.45. This, capitalized at 6 per cent, 
gives $33,908, and, added to the $6550, gives $40,458 as the 
total expenditure on account of flush-tanks in a sewer system 
costing for pipe laid $81.000. Surely the item of flush-tanks 
is an important one, and should be carefully examined, so that 
if the conditions of the sewer-grade, for example, modify the 
necessity for tanks, or if the amount of water is a function of 
the time-interval between flushes, or of the size of the pipe, 
it may be known in order that the large proportionate cost of 
flushing may be reduced to what has been found by careful 
investigation to be an absolute minimum. 

That the requirement given above is felt by present-day engi- 
neers to be largely in excess of necessity is sufficiently evident 
from a study of the paper by F. S. Odell, M. Am. Soc. C. E., 
entitled " The Separate Sewer System without Automatic 
Flush- tanks," | an d the subsequent discussion, in which the 
author says that at Mt. Vernon, N. Y., no flush- tanks are 
used, and that, while hand-flushing by means of fire-hose is 
practised at intervals of six months, even this infrequent flush- 
ing does not appear necessary, as examination of the sewers 
invariably shows a very wholesome and satisfactory condition. 

* " Manual of American Water-works," 1897. 
f Trans. Am.' Soc. C. E., Vol. XXXIV, page 223. 



USE OF FLUSH-TANKS 227 

In the discussion very little positive evidence is given, but the 
experiences recorded go chiefly to show that while automatic 
flush-tanks do not in themselves make the separate system 
practicable, there is, nevertheless, a need, under certain con- 
ditions, for flushing, those conditions being as yet not fully 
determined. 

The questions, answers to which are essential for an intel- 
ligent disposal of flush-tanks on a sewer system, are four, viz.: 

1. What is the relation, if any, between the grade of the 
sewer and the necessity for automatic flush-tanks? 

2. Assuming a need for automatic tanks, how does the 
grade of the sewer affect the amount of water required, and 
what is the proper amount to be used? 

3. How often should tanks be discharged? 

4. What effect does the substitution of a 6-inch for ah 8-inch 
lateral have on the necessity for tanks and on the amount of 
water to be used? 

Before attempting to answer these questions, it will be well 
to look at the subject broadly, and consider the hydraulic 
problem involved. Sewage is water carrying in suspension 
less than i part in 1000 of solid matter, and sewers are supposed 
to be so laid that the resulting velocity of flow is sufficient 
to keep this solid matter in suspension. This suspending 
and scouring power probably depends on the velocity, and 
on the depth, of the sewage stream, and if either gets below 
a certain point, sedimentation will follow and a deposit take 
place. It is generally stated that a velocity of about i\ feet 
per second is required; but the effect of depth is neglected. 
At the lower end of a 6-inch lateral the depth and velocity are 
assumed to be sufficient to prevent this sedimentation, but as 
the contributing population grows less toward the upper end, 
the depth and velocity decrease and the transporting power of 
the stream falls so low as to allow the solid matter, brought 
into the sewer by the house-drains, to become stranded. This 
deposit increases by gradual accumulation until the sewer is 
blocked, until the head from the backed-up sewage is sufficient 



228 



SEWER DESIGN 



to carry away the obstruction, or until the discharge of the flush- 
tank (and here is seen its true function) takes up the obstruction 
and carries it to a point where the depth and velocity of the 
sewage will hold it in suspension. Table XXVI and the dia- 



,040 

IE 

o OUfl 


























































/ 




























/ 






1 

* 
f> non 
























/ 


























^ 


/ 










010 














^*" 


^^ 


^ 


























- 






















*"*1500 1250 1000 750 500 400 300 200 100 
DISTANCES FROM DEAD END IN FEET. 



.72 



1.085 



1.50 
1.92 
2.25 
2.76 



FIG. 67 

gram (Fig. 67) are given to show the requirements in grade to 
maintain a velocity of i\ feet per second in a 6-inch lateral, 
assuming a constant contributing population of 76 persons 
per 100 feet of sewer, with a daily flow of 60 gallons per capita, 
and with the assumption of one-half flowing off in 6 hours. 

TABLE XXVI 



Distance from Dead 
End in Feet. 


Discharge in Cubic 
Feet per Second. 


Slope in Feet per 
Foot. 


Depth of Flow in 

Inches. 


1750 


0.245 


0.0103 


3.00 


1500 


O. 2IO 


0.0104 


2. 7 6 


1250 


0-175 


0.0123 


2.25 


1000 


o. 140 


0.0140 


1.92 


7SO 


0.105 


0.0174 


1-50 


500 


0.070 


0.0225 


I.I4 


400 


0.056 


0.0256 


1. 08 


300 


0.042 


0.0302 


0.96 


200 


0.028 


0.0342 


0.72 


100 


0.014 


o . 0400 


O.6o 



The diagram (Fig. 67) shows that, taking n equal to 0.013, 
and computing velocities by Kutter's formula, a grade of i per 



USE OF FLUSH-TANKS 229 

cent is required for a 6-inch pipe half full for a velocity of 2.5 
feet per second, and that if the amount of flow constantly de- 
creases, the depth of flow decreases also, and the grade, in order 
to maintain the same velocity, must be increased according to 
the diagram. The diagram is given for two reasons: first, 
to show that by the accepted laws governing the transportation 
of material in flowing water, lateral sewers could be laid, theo- 
retically, on such grades that no flushing would be necessary, 
since, with grades which continually increase toward the upper 
end, the corresponding velocities will always be equal to that 
required to transport matter in suspension; second, to show 
that as the grade of the sewer increases, the distance from the 
upper end to the point where the stream reaches the velocity 
required to carry matter in suspension decreases, and so the aid 
required from flush- tanks is less. No value can be placed on 
the grades given, as the diagram is based on the assumption 
of a house with five persons every 66 feet, and this is not always 
the case; but it is believed that there is a grade at or beyond 
which flush- tanks are not required, and if the distance to which 
the flushing power extends is a function of the amount of 
water discharged, then this amount should be less on steep 
grades. 

Referring again to Mr. OdelPs paper, it is first noted that 
at Mt. Vernon, with grades of from 0.5 to 6 per cent, no flush- 
tanks are used, and a good hand-flushing twice a year answers 
every purpose. 

In the discussion, Mr. Hering says that on light grades 
flushes of 200 to 300 gallons generally lose their flushing power 
after passing a few hundred feet through the pipe, and that some- 
times after 500 feet he has been unable to detect any differ- 
ence in the flow due to the discharge of the tank. 

Mr. Kiersted writes that in one system designed by him 
he recommended flush- tanks only on laterals of less than 0.5 
per cent grade, and for five years the system has been in opera- 
tion with but few stoppages. 

Mr. Folwell writes that in his experience he has omitted 



230 SEWER DESIGN 

flush- tanks on grades from 6 to 12 per cent, and on the 6 per 
cent grades no stoppages were discovered, nor were there any 
odors. 

Mr. Le Conte intimates that flush-tanks as built do not 
answer their purpose, for where grades are light and the flush 
most needed, they do the poorest work; and the large quantity 
of water needed to be effective must be obtained by some other 
means. 

Mr. Odell maintains that flushes of 200 gallons or less fail 
to flush a sewer properly, especially on flat grades where flush- 
ing is most needed. 

A table by Mr. Allen shows that on grades greater than 
0.5 per cent a velocity of more than i\ feet per second is main- 
tained over 1000 feet from the flush-tank, but on lesser grades 
the velocity drops to 2 feet or less within 600 feet. 

In order to obtain an insight into general engineering prac- 
tice in the matter, and, at the same time, .reap the benefit of 
any experience which was to be had, the author sent out, on 
January iyth, 150 reply postals, reading as follows: 

" ITHACA, N. Y., January 17, 1898. 

"DEAR SIR: 

" To aid me in deciding as to the necessity for flush- tanks 
for our sewer system, will you kindly answer the following: 

" I. Do you find flush-tanks a necessity, or is periodic 
hand-flushing sufficient to keep sewers clean? 

" II. Does the element of grade affect the question, and 
within what limits of grade are tanks required? 

" III. Does your experience show any relation between 
the minimum amount of water required for effective flushing 
and the grade of the sewer? 

" Thanking you in advance for your kind assistance in this 

matter, 

" I am, yours very truly, 

" H. N. OGDEN, 
" Engineer, Ithaca Sewer Commission" 



USE OF FLUSH-TANKS 231 

These postals were sent to those cities of between 10,000 
and 60,000 population, in the New England and Middle Atlantic 
States especially, which were reported in the " Manual of 
American Water- works " for 1897 as having separate or sani- 
tary sewers. Eighty answers were received, and the courtesy 
and good- will expressed in all was much appreciated. It was 
the same story in nearly all cases. " I would be pleased to 
answer your questions fully, but this is the best that I can do 
for you," or " This is only my idea, while I can readily under- 
stand that what you want is the result of actual experience," 
or " I cannot give you the desired information, but would be 
thankful to you if you would let me know the result of your 
inquiry." The results given below in a brief summary show 
chiefly how uncertain and vague is the knowledge on the sub- 
ject, and how necessary are some experiments and investi- 
gations. 

Of the eighty engineers who sent replies to question No. i, 
whether flush-tanks are necessary, seventeen had no opinion 
on the subject; twelve had experience only with combined 
systems, but had, according to their replies, found no trouble 
in keeping the ends of their 10- and 12 -inch laterals clean with 
rain or with hand-flushing; twenty-six of the eighty used 
periodic hand-flushing and found it to answer every purpose , 
keeping the sewers clean and free from obstructions; twenty- 
five either used flush-tanks or considered them a necessity for 
small pipe sewers. It was not possible in these last answers to 
separate actual experience from personal conjecture on the 
question, so that this number may include many hearsay 
opinions. 

The evidence is not very clear. The fact that twenty- 
six used hand-flushing satisfactorily indicates that such flush- 
ing is sufficient. That it must be properly and regularly done, 
however, is made plain by the fact that, out of twenty-five 
believing in flush-tanks, nine had tried periodic hand-flushing, 
found it uncertain and irregular, and had put in flush-tanks, 
to secure proper attention. On the other hand, of the twenty- 



232 SEWER DESIGN 

six believing in hand-flushing, two came to that opinion after 
becoming disgusted with the uncertainty of tanks. 

On the second question, only twenty-three of the eighty 
ventured an opinion. Of these, eight thought that the grade 
did not affect the question, but that flush-tanks were as neces- 
sary on steep as on flat grades. One engineer explained his 
position by. saying that while the velocity on the steep grades 
might be greater, yet as the depth would be less, the trans- 
porting power would be less, and therefore tanks were equally 
necessary. Of the fifteen who thought that tanks are not 
needed above a certain grade, six merely ventured it as an 
opinion, and nine fixed the limit at from 0.5 to 3 per cent; four 
of these gave i per cent as the limit; one, 3 per cent; and the 
other four less than i per cent. 

Only six replies were given to the last question, whether 
the amount of water in the flush-tank should be varied with 
the grade of the sewer. Of these six, two engineers thought 
that no difference should be made; three thought that less 
water could be used on the steep grades, but had no definite 
opinion as to the relative amounts; while one well-known 
engineer, who has thoroughly studied the workings of the 
sewer system under his care, writes that he finds one flush 
daily on a 2 per cent grade as effective as two flushes daily on 
a 0.5 per cent grade, each flush of 300 gallons. 

The general conclusion from the replies is that on low grades, 
probably below i per cent, occasional flushing is needed at the 
upper ends of laterals; that this may be accomplished either 
by hand-flushing or by the use of automatic tanks; that if 
tanks are used, less care and vigilance are required in inspec- 
tion and oversight, but, on the other hand, the periodic exam- 
ination of the system, which should not be omitted, is apt 
to be irregular, and if a tank fails to work or if an obstruction 
occurs below the effect of the flush, a serious nuisance may 
result; that if hand-flushing is used, a constant and regular 
inspection must be practised, although actual flushing may be 
required but once a month or even less. The amount of water 



USE OF FLUSH-TANKS 233 

needed in flush-tanks is not known, nor the relation between 
amount and grade. 

With a view of obtaining more information on this appar- 
ently unstudied subject, the author carried on some experi- 
ments in the spring of 1897, in which he was assisted by Mr. 
I. W. McConnell, C.E. The results of the experiments have 
been recorded by Mr. McConnell in a thesis for the degree of 
Civil Engineer in Cornell University. 

The sewers on which the experiments were made, chosen 
so as to afford a variety of grade, with as long lines as possible, 
were all 8-inch pipe, and each had at the upper end a manhole 
about 4 feet in diameter at the bottom. Flush-tanks of the 
usual commercial size discharge at a rate of about i cubic foot 
per second, and, by repeated experiment, the opening from the 
manhole into the sewer was reduced to such a size (about 5 
inches) that the rate of discharge varied from 0.89 cubic foot 
per second for 4 feet head in the manhole to i.i cubic feet per 
second for 6 feet head. These conditions it was thought approx- 
imated closely enough to the workings of a flush-tank. A 
5 -inch opening was cut in a pine board held firmly against 
the end of the 8-inch pipe; then a flat rubber-faced cover, 6 
inches in diameter, was placed over the opening and held there 
by a light stick braced against the back of the manhole, mak- 
ing an effective plug. The manhole was filled to any desired 
depth by means of fire-hose attached to neighboring hydrants, 
and then, by means of a cord fastened to the stick and to the 
cover, the contents of the manhole were discharged into the 
sewer. The capacity of the manholes at depths varying by 
6 inches was determined by measurement, so that by filling to 
the proper depth any desired amount of water could be dis- 
charged. The effect of the flush-waves was then noted at the 
successive manholes down the line. No determinations of the 
velocity of the wave were made, the effect being judged by the 
depth of the wave, and by the force shown in moving gravel, 
etc., placed in the different manholes. The wave-depths were 
read by observers stationed in the manholes, where they re- 



234 



SEWER DESIGN 




6 8 10 12 14 16 18 30 22 24 'M 28 30 & 34 36 
TIME SCALE IN MINUTES. 

FlG. 68. 



GREEN ST. 

FORM OF FLUSH WAVE. 
QUAN.OF WATER=40 C. F 
AVERAGE OF 3 FLUSHES 




10 12 14 16 18 20 22 24 26 38 30 32 34 36 

TIME SCALE IN MINUTES. 



FIG. 69. 






i 




































| 

QU 
A 


CAYUQA ST. 

ORM OF FLUSH WAVE. 
AN. OF WATER=40 C. Fl 
/ERAGE OF 3 FLUSHES. 


















\ 














































/ 






\ 










































/ 










5 






























































^ 




















' 


$20.2 


" 












i 










/ 








v 








^ 


^^ 














3 


895.4 





iO 












EE 






i 


4. 












N, 


x 


v 


^ > 


^*- 




- 


^! 


^^ 


~ 
















-^-^ 


-^ . 




1 , 






o 






/. 














,, 


-^ 




\ 






































^^1 


C 




/ 


* 












s^ 








\ 






































Jo-, 




/o 












/ 


r 












\ 


^ 








































~ 




> v 


















\ 




















































N - 


^ 




























/ 1 


y 








^ 
























































LL 










X 

























































26 

TIME SCALE IN MINUTES. 

FIG. 70. 



30 32 34 



USE OF FLUSH-TANKS 



235 



corded as rapidly as possible (usually every seven seconds) the 
depth as marked on a thin vertical scale placed in the sewer. 
Figs. 68 to 71 show the wave-forms and the progressive flatten- 
ing as the wave gets farther and farther from the flush-tank. 

To test the transporting power of the wave small brickbats 
and gravel of various sizes, coated with paint so as to be recog- 
nizable, were placed in the inverts at the manholes. A consid- 
able growth, apparently of vegetable origin, had become at- 
tached to the sides and bottom of the pipe, and the value of the 
flush in removing this growth was also noted. The order of pro- 
cedure was to examine and note the condition of the line, and, 
after placing the gravel, etc., in the manholes, to make a number 




10 20 



40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 
TIME SCALE IN SECONDS. 

FIG. 71. 



of flushes, each of 20 cubic feet, and note the results. Then, in- 
creasing the amount discharged to 30, 40, 50, and 60 cubic feet, 
the respective results were noted. Then either the whole pipe 
was scraped by a rubber-edged piston-like cleaner, or merely 
the manhole inverts and about 6 feet each way into the pipe, 
and the flushing repeated. Tables XXVII-XXX give the 
results on the different lines. 

Before commencing the work, the examination of the Green 
Street pipe showed it to be practically clean, with no ground- 
water, except between the third and fourth manholes, where 
there was a stream about one-fourth inch deep. No house- 
connections had been made, but there was a small depth of silt, 
and bits of cement left from construction, also a slight vegetable 



236 



SEWER DESIGN 



TABLE XXVII 

GREEN STREET SEWER 



TT_|--_^, _* 


Effects at 


XJ_ -f 


Volume 01 
Flush. 


Manhole 


Manhole 


Manhole 


Manhole 


IN O. OI 

Flushes. 




No. i. 


No. 2. 


No. 3. 


No. 4. 




25 cu.ft. 


Scoured clean 


Scoured clean 


No effect 


No effect 


I 


30 " 


" 


" 


" 


" 


I 






, 


Several stones 


. 




40 " 


" 


{ 


started 


} 


8 


(( 


(( 


f 


Small gravel gen- 


\ < 




60 




I 


erally started 


} 


2 


80 " 


11 


" 


do 


" 


2 


120 " 


ft 


tl 


" 


lt 


3 



growth on the sides and bottom of the pipe. Gravel of all 
sizes placed in the pipe at the flush-tank was carried through to 
manhole No. i in two flushes of 25 cubic feet each, the first flush 
alone not being sufficient. The gravel scoured out of the bottom 
of manhole No. i by the first flush was not brought to No. 2 
until the So-cubic-foot flush was put in, and no gravel scoured 
out of No. 2 was brought to No. 3 by any of the flushes. After 
the seventeenth flush as above, the pipe was thoroughly scraped 
and cleaned, and flushes eighteen to twenty-eight were made. 
Similar results were obtained, except that the flushes carried 
the gravel about 200 feet farther than before and seemed effec- 
tive for that distance. 

TABLE XXVIII 

CAYUGA STREET SEWER 



Volume 
of Flush. 


Manhole 
No. i. 


Manhole No. 2. 


Manhole No. 3. 


Manhole 
No. 4. 


No. of 
Flushes. 


30 cu.ft. 


Scoured clean 


No effect 


No effect 


No effect 


3 


40 


( ( 


| Disturbed but \ 


< i 


< < 


7 






I not cleaned / 














( Some vegetable } 






60 " 


( ( 


Partly scoured 


\ growth passed > 


< 


2 








[ through J 






80 " 


< < 


Cleaned 


" 


i ( 


3 


r. 













USE OF FLUSH-TANKS 



237 



In Cayuga Street there were a few connections and little 
flow, so that the condition of the pipe was very foul; there was 
also a heavy vegetable growth in the pipes. 

On Linn Street no comparative records could be made. The 
pipe was clean from the flush- tank to manhole No. i, and in 
this length there were no connections. From No. i to No. 2 it 
was slightly foul, and very foul the remainder of the length. 
There were two house-connections on the line. Five flushes of 
20 to 60 cubic feet were made. Each was very effective, one 
apparently as much so as another. All obstructions introduced 
were removed at once from manholes Nos. i and 2. A steady 
flow i inch deep from the hose carried everything forward at 
once to a point beyond No. 2 and to the flatter grade. 

TABLE XXIX 

AURORA STREET SEWER 



Volume 
of Flush. 


Manhole 
No. i. 


Manhole 
No. 2. 


Manhole 
No. 3. 


Manhole 
No. 4. 


No. of 
Flushes. 


40 cu.ft. . . . 
60 " 
80 " 


Cleaned 

< < 

< <. 


Cleaned 

1 1 

t 1 


No effect 

Disturbed 
< < 


No effect 
( Water dirty; some 1 
j vegetable growth j- 
1 came through J 
A few stones disturbed 


3 
7 

2 



TABLE XXX 
FIRST STREET SEWER 



Volume of 
Flush. 


Manhole 
No. i. 


Manhole 
No. 2. 


Manhole 
No. 3. 


Manhole 
No. 4. 


No. of 
Flushes. 


40 cu.ft 


Cleaned 


No effect 


No effect 


No effect 


5' 


60 " 


< 





( ( 


i ( 




80 " 





" 


i ( 


( ( 


2 



On the Aurora Street line the pipe was very foul, chiefly from 
a hospital connection at the upper end. The vegetable growth 
was excessive, and the accumulations of organic matter very 
evident. 



238 



SEWER DESIGN 



On Buffalo Street, where the grade is about 12 per cent, 
the effective of the flush was amazing. Where any sewage 
at all flows in the pipe, it is sufficient to remove all obstruc- 
tions. A flush of any volume rushes down the hill at a 
high velocity, with piston-like action, and sweeps everything 
before it. 

Table XXXI gives the distances and grades between man- 
holes on the lines used in the experiments. 

TABLE XXXI 
DISTANCES AND SLOPES BETWEEN MANHOLES 





Green St. 


Cayuga St. 


Aurora St. 


First St. 


Linn St. 




rt 


, 


c 


, 


g 




c 


, 


d 


, 


Description. 


8^ 


v So 
p*rt 


l| 


& 


S^ 


<u aj 

O.M 


D . 
O -|J 


i 


c "S 


Jl 




oj *^ 


g 




lj S 


rt J^ 


'O C 


rt r ^ 


^ "d 




"g G 




.2 

Q 


o 


5 


O 


Q 


5" 


S 


o u 


5 


o 8 


Dead end to man- 






















hole No. i 


298 


1-31 


320 


0.89 


177 


3-14 


371 


I .CX) 


331 


2-94 


Manhole No. i to 






















manhole No. 2 . . 


231 


0.52 


316 


0.50 


390 


1.28 


341 


0.50 


278 


2.70 


Manhole No. 2 to 






















manhole No. 3 . . 


290 


0.52 


259 


0.60 


413 


1 .02 


394 


0.57 


317 


0.50 


Manhole No. 3 to 






















manhole No. 4 


3O^ 


o 52 






4.IO 


o 40 


3Q3 


I OO 






Manhole No. 4 to 






















manhole No. 5 . . 


296 


0.75 






417 


0.80 



















The manager of the Van Vranken Flush-tank Company 
gives his practice in proportioning the sizes of flush-tanks 
for any particular sewer as follows: The capacity of the reser- 
voir should be equal to one-half that of a length of sewer in 
which the grade produces a rise equal to the diameter of the 
pipe; so that the Green Street line, 8 inches diameter and 
0.5 per cent grade, should have a discharge of half the volume 
of the pipe, -fXioo in length, or 23 cubic feet; and for a i per 
cent grade one-half of that, or 11.5 cubic feet. He says, further, 
and the statement has been confirmed by the author's work, 



USE OF FLUSH-TANKS 239 

that an 8-inch pipe on a 0.4 per cent grade will flow one-third 
full at a distance of 300 to 400 feet from the tank discharging 
the above amount; and that on a 5 per cent grade the water 
will come down as a solid piston for any dischrage greater than 
14 cubic feet. 

The manager of the Pacific Flush-tank Company writes 
that as a rule he does not interfere with engineers in their design 
for tanks, but, in his opinion, a flush of 175 gallons on a i per 
cent grade is sufficient, and on any flatter grade twice that 
amount of water should be used, or, as he says, " long lines or 
flat grades require greater capacity of tanks than steep grades 
or short lines." 

Conclusions. The following conclusions are based upon 
previously published data on this subject; upon the experi- 
ence of engineers in different parts of the country; upon the 
flushing diagrams recently published by J. W. Adams, and upon 
observation and the special experiments made in Ithaca; and 
it is believed that they are justifiable and a safe guide in the 
use of flush-tanks. 

(1) Flushing of some sort is required at the upper ends 
of laterals, the frequency and amount depending on the num- 
ber of house-connections, on the carefulness or prodigality in 
the use of water by the house-holders, on the grade and size 
of the sewer, on the character of its construction, and on a 
mysterious something which defies definition, but which pro- 
duces frequent accumulations in one line and does not affect 
another, apparently like the first. 

(2) This variety in the conditions prevents any exact state- 
ment of a relation between the quantity of water which should 
be discharged from a flush-tank and the grade of a sewer, but 
it plainly indicates that the advantage of automatic flush- 
tanks lies in a general guarantee or insurance against accumula- 
tions in the upper part of the laterals, while periodic hand-flush- 
ing must be depended on only when in charge of a responsible, 
indefatigable, and intelligent caretaker. 

(3) Judging by the experience at Ithaca, and despite the 



240 SEWER DESIGN 

statements of other engineers, it seems to the author that on 
grades of less than i per cent automatic flush tanks are an 
economic necessity, even where water has to be paid for, the 
added expense of frequent hand-flushing more than offsetting 
the possible discharge of flush-tanks when not absolutely 
necessary. 

(4) The volume of water discharged should not be less than 
40 cubic feet, and the effect of the flush can hardly be expected 
to reach more than 600 or 800 feet. Below this point accumu- 
lations may occur which must be removed by hand-flushing and 
carried on to a point where the sewage-flow has the necessary 
transporting power. 

(5) On flat lines and where obstructions occur below the 
influence of the flush-tank, a second flush-tank, placed about 
800 feet from the first, will be more effective than increasing 
the first tank to a capacity of three times its original discharge. 

(6) The frequency of discharge should depend on the local 
conditions, but it is probable that the maximum interval 
depends on the practical working of the siphon, so that the 
usual prescription of once in 24 hours is a safe rule. 

(7) If tanks are used on grades greater than i per cent, 
15 to 20 cubic feet give as good results as larger amounts, with 
the same rule as to frequency of discharge. 

(8) However, economy is best served, on grades above i 
per cent, by omitting flush-tanks, and resorting to periodic 
hand-flushing at such intervals as experience shows to be neces- 
sary on the different lines. In most cases semi-annual or 
quarterly flushings, with a hose, are sufficient. 

(9) On grades greater than 3 per cent flush-tanks are unnec- 
essary, and their installation is a waste of money. 

(10) Hand-flushing should be performed and tanks dis- 
charged at night, as a flow of even an inch in a sewer offers a 
large resistance to the flushing action; while with a pipe flowing 
half full the effect of a flush-tank is scarcely visible. 



PLATE I. 



SEWER MAP. ITHACA, N. Y. 




Sewer 
-Underdram 
Surface Dram 
Water Pipe 
Gas Pipe 
5" House Connection 



206-1 



200- 



195- 



190- 



185- 




180 



100 



Iv50 



200 250 300 35 



PRO: 



JohnW. 




Lindsay 



JohnW. Lindsuy 



Susan 



Z;Z4 ! 191.51 



33765 



LENOX 



'6"WbterPipe 



John PLg 




4-Gas' 



PLATE II. 






--- 




_ 










_ 





1 


! 




Q50 per 100 



r-ZlO 



-Z05 



-200 



-195 



-190 



-185 



400 450 500 550 



600 



650 700 



180 



ori 




PLAN. 



PIPES FLOWING FULL 



PLATE III. 




0.2 0.3 0.4 0.5 



.1.0 1.5 2.0 2.5 ao a5 4.0 5.0 6.07.08.0 10.> 



GRADES IN PER CENT. 
DIAGRAM BASED ON KUTTER'S FORMULA FOR VITRIFIED PIPES. 



PIPES FLOWING FULL 



PLATE IV. 




.02 .03 M .05 .00 .10 



.20 .80 .40 .50 .70 1.00 1.50 2.00 aOO 4.CO {100 



GRADES IN PER CENT 

DIAGRAM BASED ON KUTTER'S FORMULA FOR CIRCULAR 
BRICK SEWERS. 



PIPES FLOWING FULL 



PLATE V. 




.10 .15 .20 .25.30 .40 .50.00.70.80.901.0 



GRADES IN PER CENT. 

DIAGRAM BASED ON KUTTER'S FORMULA FOR EGG-SHAPED 
BRICK SEWERS. 



BINGHAMTON, N.Y. 

MAP SHOWING 

TOPOGRAPHY 



PROPOSED OUTFALL SEWER 

FOR THE 

FOURTH WARD. 
1906 



(I / 
III I ' ? DIB 




PLATE VI. 




INDEX 



Adams on Brooklyn sewers 32 

formula for run-off 81 

Adams-Gemmell sewer diagram 1 86 

Altoona, amount of ground- water 144 

Alvord on run-off 66 

Arrangement of laterals 202 

Area as affecting run-off 86 

Atlantic City sewage pumped 132 

water-consumption 105 

Auger for borings 22 

Automatic gages, Weather Bureau 34 

Babcock, S. E., device for admitting ground-water 10 

Bailey sewer diagram 186 

on water-consumption 109 

Baltimore, future population of 95 

rainfall at 45 

report on run-off in 85 

Barbour on sewer-pipe joints 151 

Barometric surveys 14 

Baumeister on maximum sewage-flow 139 

on rainfall discharge 61 

sewer diagrams 185 

Bazin's formula for flow 169 

Binghamton, water-consumption in 129 

Borings, cost of 1 8 

Boston, population 96 

rainfall at 36, 44 

water-supply 115 

Brackett on Boston water-supply 109 

Brahm's flow formula 165 

Brick sewers, permeability of 147 

Brockton, amount of ground-water 144 

population of 97 

rise and fall of ground-water 142 

241 



242 INDEX 

PAGE 

Brookline, water-consumption in 1 1 1 

Brooklyn rainfall, studies 32 

Buildings on urban area 71 

Biirkli-Ziegler's formula for run-off 82 

Cadillac, Mich., sewage-flow at 137 

Canton sewers, amount of ground-water in 143 

Canton, Ohio, sewage gagings 132 

Census reports of population 98 

Chanute on separate vs. combined system 8 

Chautauqua, sewer gaging at 135 

Chezy formula -. 165 

Chicago prediction of population of 94 

run-off, from maximum storms 64 

Clarke, E. C., on separate vs. combined system 3 

Cleveland, maximum run-off 65 

mathematical formula in 88 

Colby's sewer-computer 183 

Coffin on sewer-pipe joints 148 

Combined vs. separate system 3 

Cornell University, experiments on maximum run-off 65 

Fort & Filkins' thesis 159 

Hooker's thesis 154 

Holmes' thesis 182 

McConnelFs thesis 233 

Senior's thesis 149 

Cost of system, separate vs. combined 5, 9 

Crane on slide-rule for run-off 90 

Cross-sections of sewers 207 

Darcy's experiments of flow 168 

Density of population, relation to sewage discharge 70 

Department of Health rules 9> 26 

Des Moines, water-consumption at 107 

Detail maps 15 

Determination of sewer sizes for Ithaca 193 

Diagram of growth of population 99 

for run-off in New Orleans 89 

of rainfall 39 

of Department of Public Works of New York for run-off 76, 85 

of impervious surface per acre 74 

for flow, Staley & Pierson 184 

for lateral design 189 

for sewers, Hill; Wollheim 186 

for sewers, Moore 185 

for sewer design, Talbot; Bailey; Adams and Gemmell 186 



INDEX 243 

PAGE 

Diagram for sewer, Hering 185 

for flow, Fitz Gerald 185 

for sewer computations, Olive's 184 

Discharge o'f rainfall by sewers 54 

Rochester percentages of rainfall 57 

Dubuat, laws of flowing water 165 

East Orange, ground-water at 144 

Egg-shaped sewers 207 

Egg-shape, gain in velocity over circular 208 

Equation of rainfall rate for Rochester 42 

Equations of rainfall rates, comparative table 48 

Examination of soil 20 

Eytelwein's formula 166 

Fan system of laying out 200. 

Faucet, amount of water for one 126 

Field- Waring flush-tank 215 

Fires, amount of water used for 117 

Flow, formula? for 165 

Flushing, separate vs. combined 7, 9 

general methods , 213 

Flushing-sewers, amount of water used for 117, 229 

Flushing- waves, thesis of Fort & Filkins 158 

Flush-tank, Field-Waring 215 

Merritt 222 

Miller 219 

position of 204 

Rhoads- Williams 217 

Flush-tanks, use of 3,5 

Van Vranken 214 

Flynn's tables 180 

Folwell on flush-tanks 229 

Formula, Adams', for run-off < 81 

Bazin's, for flow 169 

Biirkli-Ziegler's, for run-off 82 

Hawksley's, for run-off 79 

Humphreys & Abbot's, for flow 171 

Kutter's, for flow 1 78 

McMath's, for run-off 84 

Robinson's, for flow i? 2 

Santo Crimp's, for flow 173 

Formulas for flow 165 

for run-off 78 

Fountains, water used for 117 



244 INDEX 

PAGE 

Fuertes on preliminary surveys 14 

on run-off 66 

Gagings of Sudbury River : 61 

sewers 132 

Gas-pipe, location 16 

Gloversville, sewage-flow at 137 

Grades, minimum, for sewers 162 

Gray on Providence sewers 32 

run-off in Baltimore 85 

Ground-water in separate system 10 

at Ithaca and other cities 142 

through pipe-joints 148 

brick sewers 147 

Grover, apparatus for measuring flood- waves 60 

Gutters, length of 8 

Hazlehurst on leakage into sewers 146 

House-drain connections 205 

Hawksley's formula for run-off 79 

Hemlock Lake, water-supply from 129 

Hering's gagings in New York City 76 

Hering and Gray on Baltimore population 93 

Hering on run-off in Baltimore 85 

flush-tanks 229 

Kutter's formula 1 79 

minimum grades 1 63 

sewer diagrams 185 

Hill on sewer diagrams 186 

Holmes on value of n 182 

Hooker on suspension of solids 1 54 

Humphreys and Abbot, formula for flow 171 

Impervious surface per acre 72 

Intensity of rainfall, method of fixing 50 

Intercepting system of laying out 197 

Ithaca, calculation of storm-drain for 190 

sewer sizes for 193 

determination of run-off 75 

estimated amount of ground-water 142 

population of 102 

Kansas City, maximum run-off 65 

Kiersted on flush-tanks 229 

Kuichling on relation of density to percentage 70 

run-off formulae 79 



INDEX 245 

PAGE 

Kuichling on population increase 99 

rainfall diagrams 42 

fixing intensity of rainfall 50 

studies of rainfall 39 

Kutter's formula 178 

derivation of 175 

in Flynn's tables 180 

values of n 178, 182 

method for finding c. . . . 1 79 

Laterals, diagram for 188 

Latham on minimum grades 162 

minimum velocity in sewers 161 

sewer sections 153, 208 

Latham's tables 167 

Le Conte on flush-tanks 230 

Levels in survey 24 

Levels of confluent streams 205 

London gagings of storm-sewers 55 

McMath formula on slide-rule 90 

for run-off 84 

Manhole instead of flush-tank 204 

Maps for preliminary study 13 

Maps showing details 15 

Marston on run-off 66 

Maximum flow of sewage 128 

Merritt flush-tank 222 

Meters and water waste 113, 123 

Miller flush-tank 219 

Minimum grades in sewers 162 

velocities in sewers 160 

McConnelPs thesis on flush-tanks 233 

Mobile, maximum rainfall at 38 

Moore on separate vs. combined system 8 

sewer diagrams 185 

n, values of, in Kutter's formula 1 78 

New Orleans, run-off diagrams 90 

New York, water-consumption in 113 

Newton, water-consumption in 126 

Nipher on rainfall intensity 42 

North Brookfield, amount of ground- water 143 

Obstructions in separate and combined sewers 4 

Odell on flush-tanks. . .... 226 



246 INDEX 

PAGE 

Olive, sewer diagrams 184 

Omaha, sewer gaging at 135 

Outfall, sewer system 195 

Paper for maps 16 

Patents, separate system 2 

Pavements, areas of, per acre 72 

classified as to shedding rain 71 

Perpendicular system of laying out . 196 

Philadelphia, rainfall at 46 

water waste in 107 

Pile-driver for borings 21 

Pipe-joints, tightness of " 148 

Plans for sewer system 196 

Population, density of, relation to sewage discharge 70 

studies in, by Kuichling 99 

increase, from Rafter and Baker 97 

predicting future 93 

Potter on leakage into sewers 151 

Profiles on map 24 

de Prony's formula for flow 166 

Providence rainfall studies 32 

Radial system of laying out 200 

Rafter and Baker on population 97 

ground-water 144 

Rainfall, discharge in sewers 54 

intensity of, and duration 39 

diagrams 42 

studies in Brooklyn 32 

Rainfalls reported excessive by Weather Bureau 34 

Rate of rainfall 35 

Rhoads- Williams flush-tank 217 

Robinson formula for flow 172 

Rochester, description of sewer districts 59 

gagings of storm-sewers 56 

rainfall at . . . 42 

water-consumption in 129 

Rock, boring for 20 

Rogers Park, amount of ground- water 144 

Roofs, area of, per acre 72 

Rosewater's design, Miller flush-tank 222 

Run-off diagram for New Orleans 90 

of New York Department of Public Works 76, 85 

from roofs, pavements, etc 73 

from various cities 67 



INDEX - 247 



St. Louis, formula for run-off 84 

rainfall at 42 

San Diego, population of 102 

Santo Crimp's formula 1 73 

Savannah, rainfall at 47 

Schenectady sewer gaging , 134 

Sections detective 153 

Sedimentation in sewers 155 

Senior on sewer-pipe joints 149 

Separate vs. combined system 3 

Sewage, amount per capita 105 

composition, separate vs. combined system 3 

flow of, diagrams of 129 

flow compared with water-consumption 132 

maximum flow of 138 

pumped at Atlantic City 132 

Sewer computer, Colby's slide-rule 183 

Shedd on Providence sewers 32 

Size of city and water-consumption 123 

sewers for Ithaca 190 

Slide-rule for run-off 90 

Slope as affecting run-off 86 

Snow on Brockton population 96 

Sounding for rock, New York 23 

Specific gravity in experiments on suspension 158 

Stearns on ground-water 142 

Staley and Pierson on maximum sewage-flow 139 

minimum grades 1 63 

minimum velocity 1 60 

sewer diagrams 185 

Street-sprinkling, water used for 117 

Subsoil water in separate system 10 

Sudbury River gagings .61 

Sullivan formula 1 73 

Surfaces as affecting run-off 66 

Survey, party for 17 

Suspension of solids in sewage 154 

Talbot on rainfall intensity 40 

sewer diagrams 185 

Taunton, estimated amount of ground- water 143 

Test boring-machine 21 

Trautwine on water waste in Philadelphia 107 

Truesdell on Ithaca population 102 

Van Vranken flush-tank 214 



248 INDEX 

PAGE 

Velocity at different depths in circular sewer 210 

required for suspension by experiment 160 

Velocity, minimum, required in sewers 163 

Ventilation continuous through system 204 

of sewers, separate vs. combined 5,7 

Waring, Col. G. E 2 

Washington, rainfall at 45 

Waste from pipes, water 117, 120 

Water-consumption at Des Moines, etc 107 

causes affecting amount of 109, 122 

compared with sewage flow , 105 

in Chicago and Fall River 113 

in Manhattan 123 

Water meters, effect on consumption 123 

Water-pipe, location 16 

Water waste in Philadelphia 107 

Weather Bureau, excessive rains 34 

Weisbach and Kutter formulae 186 

Weston Hospital, sewer gaging 135 

Williams, Benezette 3 

Williams and Hazen formula 173 

Winona, amount of ground-water 144 

Zone system of laying out 198 



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