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CHAPTER III
QUANTITY OF SEWAGE

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17. Dry weather Flow.—Estimates of the quantity of sewage flow to be expected are ordinarily based on the population, the character of the district, the rate of water consumption, and the probable ground-water flow. Future conditions are estimated and provided for, as the sewers should have sufficient capacity to care for the sewage delivered to them during their period of usefulness.

18. Methods for Predicting Population.—Methods for the prediction of future population are given in the following paragraphs.

The method of graphical extension. This is the quickest and most simple of all. In this method a curve is plotted on rectangular coordinates to any convenient scale, with population as ordinates and years as abscissas. The curve is extended into the future by judgment of its general tendency. An example is given of the determination of the population of Urbana, Illinois, in 1950. Table 4 contains the population statistics which have been plotted on line A in Fig. 8 and extended to 1950. The probable population in 1950 is shown by this line to be about 21,000.

The method of geometrical progression. In this method the rate of increase during the past few years or decades is assumed to be constant and this rate is applied to the present population to forecast the population in the future. For example the rate of increase of population in Urbana for the past 7 decades has varied widely, but indications are that for the next few decades it will be about 20 per cent. Applying this rate from 1920 to 1950 the population in 1950 is shown to be about 17,800. It is evident that this method may lead to serious error as insufficient information is given in the table to make possible the selection of the proper rate of increase.

TABLE 4
Population Studies
YearUrbana, IllinoisPopulation of
PopulationAbsolute Increase for Each DecadePer Cent Increase for Each DecadeDecaturDanvilleChampaignKankakeePeoriaBloomingtonAnn, Arbor Michigan
18502107365,0951,594
18602,038182885.63,8391,6321,7272,98414,0457,0755,097
18702,27723910.57,1614,7514,6255,18922,84914,5907,368
18802,94266522.69,5477,7335,1035,65129,25917,1808,061
18903,51156916.216,84111,4915,8399,02541,02420,4849,431
19005,728221738.720,75416,3549,09813,59556,10023,28614,509
19108,245251730.531,14027,87112,42113,98666,95025,78614,817
192010,230198519.443,81833,75015,87316,72176,12128,63819,516

Fig. 8.—Diagram Showing Methods for Estimating Future Population.

The method of utilizing a decreasing rate of increase. This method attempts to correct the error in the assumption of a constant rate of increase. After a certain period of growth, as the age of a city increases its rate of increase diminishes. In applying this knowledge to a prediction of the future population of a city the population curve is plotted, as in the graphical method and a straight line representing a constant rate or increase is drawn tangent to the curve at its end. The curve is then extended at a flatter rate in accordance with the rate of change of a similar nearby larger city. This method has not been applied to any of the cities included in Table 4, as none has reached that limiting period where the rate of increase has begun to diminish.

The method of utilizing an arithmetical rate of increase. This method allows for the error of the geometrical progression which tends to give too large results for old and slow-growing cities. This method generally gives results that are too low. The absolute increase in the population during the past decade or other period is assumed to continue throughout the period of prediction. Applying this method to the same case, the increase in the population during the past decade was 2,000. Adding three times this amount to the population in 1920, the population of Urbana in 1950 will be about 16,000.

The method involving the graphical comparison with other cities with similar characteristics. In this method population curves of a number of cities larger than Urbana but having similar characteristics, are plotted with years as abscissas and population as ordinates, with the present population of Urbana as the origin of coordinates. The population curve for Urbana is first plotted. It will lie entirely in the third quadrant as shown by the heavy full line in Fig. 8. The population curves of some larger cities are then plotted in such a manner that each curve passes through the origin at the time their population was the same as that of the present population of Urbana. These curves lie in the first and third quadrants. The population curve of the city in question is then extended to conform with the curves of older cities in the most probable manner as dictated by judgment. Such a series of plots has been made in Fig. 8. The results indicate that the population of Urbana in 1950 will be about 25,500.

The last method described will give the most probable result as it is the most rational. For quick approximations the geometrical progression is used. The arithmetical progression is useful only as an approximate estimate for old cities.

19. Extent of Prediction.—The period for which a sewerage system should be designed is such that each generation bears its share of the cost of the system. It is unfair to the present generation to build and pay for an extensive system that will not be utilized for 25 years. It is likewise unfair to the next generation to construct a system sufficient to comply with present needs only, and to postpone the payment for it by a long term bond issue. An ideal solution would be to plan a system which would satisfy present and future needs and to construct only those portions which would be useful during the period of the bond issue. Unfortunately this solution is not practical, because, 1st, it is less expensive to construct portions of the system such as the outfall, the treatment plant, etc., to care for conditions in advance of present needs, and 2nd, the life of practically all portions of a sewerage system is greater than the legal or customary time limit on bond issues.

A compromise between the practical and the ideal is reached by the design of a complete system to fulfill all probable demands, and the construction of such portions as are needed now in accordance with this plan. The payment should be made by bond issues with as long life as is financially or legally practical, but which should not exceed the life of the improvement.

The prediction of the population should therefore be made such that a comprehensive system can be designed with intelligence. Practice has seldom called for predictions more than 50 years in the future.

20. Sources of Information on Population.—The United States decennial census furnishes the most complete information on population. Unfortunately it becomes somewhat old towards the end of a decade. More recent information can be obtained from local sources. Practically every community takes an annual school census the accuracy of which is fairly reliable. The general tendencies of the population to change can be learned by a study of the post office records showing the amount of mail matter handled at various periods. Local chambers of commerce and newspapers attempt to keep records of population, but they are often inaccurate. Another source of information is the gross receipts of public service companies, such as street railways, water, gas, electricity, telephone, etc. The population can be assumed to have increased almost directly as their receipts, with proper allowance for change in rates, character of management, and other factors.

21. Density of Population.—So far the study of population has been confined to the entire city. It is frequently necessary to predict the population of a district or small section of a city. A direct census may be taken, or more frequently its population is determined by estimating its density based on a comparison with similar districts of known density, and multiplying this density by the area of the district. In determining the density, statistics of the population of the entire city will be helpful but are insufficient for such a problem. A special census of the area involved would be conclusive but is generally considered too expensive. A count of the number of buildings in the district can be made quickly, and the density determined by approximating the number of persons per building. Statistics of the population of various districts together with a description of the character of the district are given in Table 5.


Fig. 9.—Density, Area, and Population, Cincinnati, Ohio. 1850 to 1950.

TABLE 5
Densities of Population
City Character of District Area, Acres Density per Acre
Philadelphia Thomas Run. Residential. Mostly pairs of two and three-story houses. 1204 acres settled. 1,840 59
Pine Street. Residential. Mostly solid four to six-story houses. 156 acres settled. 160 97
Shunk Street. Residential. Mostly pairs of two and three-story houses. 539 acres settled. 539 119
Lombard Street. Tenements and hotels, 145 acres settled. 147 113
York Street. Residential and manufacturing. 354 acres settled. 358 94
New York City Residential. Three-story dwellings with 18–foot frontage, and four-story flats with 20–foot frontage. 100
Residential. Five-story flats. 520–670
Residential. Six-story flats. 800–1000
Residential. Six-story apartments. High class. 300
Chicago 1st Ward. Retail and commercial. The “Loop”. 1,440 20.5
2d Ward. Commercial and low-class residential solidly built up. 800 53.5
3d Ward. Low-class residential. 960 48.1
5th Ward. Industrial. Some low-class residences. Not solidly built up. 2,240 25.51
6th Ward. Residential. Four and five-story apartments. A few detached residences. 1,600 47.0
7th Ward. Same as Ward 6. Not solidly built up. Contains a large park. 4,160 21.7
8th Ward. Industrial. Sparsely settled. 13,624 4.8
9th Ward. Industrial and low-class residential. Solidly built up. 640 70.0
10th Ward. Same as Ward 9. 640 80.8
13th Ward. Low-class residential. Solidly built with three and four-story flats. 6,100 36.7
16th Ward. Middle-class residential. Some industries. Well built up. 800 81.5
19th Ward. Industrial and commercial. Some low-class residences. 640 90.7
20th Ward. Low-class residential. Some industries. Entirely built up. 800 77.1
21st Ward. Industrial. Entirely built up. 960 49.9
23d Ward. Industrial and residential. 800 55.4
24th Ward. Residential apartment houses and middle-class residences. 1,120 46.8
25th Ward. Residential. High-class apartments. Wealthy homes. Contains a large park. 4,160 24.0
26th Ward. Residential. Middle-class homes and apartments. Fairly well built up. 4,640 16.1
27th Ward. Residential. Sparsely settled. 20,480 5.5
29th Ward. Low-class residential. Two-story frame houses. “Back of the Yards”. 6,400 12.8
30th Ward. The Stock Yards. 1,280 40.1
32d Ward. Scattered residences. 8,480 8.3
33d Ward. Scattered residences. 12,944 5.5
35th Ward. Scattered residences. 4,960 12.0
General average The most crowded conditions with five-story and higher, contiguous buildings in poor class districts. 750–1000
Five and six-story contiguous flat buildings. 500–750
Six-story high-class apartments. 300–500
Three and four-story dwellings, business blocks and industrial establishments. Closely built up. 100–300
Separate residences, 50 to 75–foot fronts, commercial districts, moderately well built up. 50–100
Sparsely settled districts and scattered frame dwellings for individual families. 0–50

The density of population in Cincinnati from 1850 to 1913 with predictions to 1950 is given in Fig. 9.[18] This shows the densities for the entire city and is illustrative of the manner in which future conditions were predicted for the design of an intercepting sewer. The data given in Table 5 are of value in estimating the densities of population in various districts. The Committee on City Plan of the Board of Estimate and Apportionment of New York City obtained some valuable information on this point, especially in Manhattan. Three-story dwellings with 18–foot frontage, or four-story flats with 20–foot frontage, presumably contiguous, were found to hold 100 persons to the acre. Five-story flats held 520 to 670 persons per acre. Six-story flats held 800 to 1,000 persons per acre, and high-class six-story apartments held less than 300 per acre.

22. Changes in Area.—In order to determine the probable extent of a proposed sewerage system it is important to estimate the changes in the area of a city as well as the changes in the population. With the same population and an increased area the quantity of sewage will be increased because of the larger amount of ground water which will enter the sewers. Predictions of the area of a city are less accurate than predictions of population because the factors affecting changes cannot be so easily predicted. An area curve plotted against time would be helpful in guiding the judgment, but its extension into the future based on past occurrences would be futile. A knowledge of the city, its political tendencies, possibilities of extension, and other factors must be weighed and judged. The engineer, if he is ignorant of the city for which he is making provision, is dependent upon the testimony of real estate men, business men and others acquainted with the local situation.

23. Relation between Population and Sewage Flow.—The amount of sewage discharged into a sewerage system is generally equal to the amount of water supplied to a community, exclusive of ground water. The entire public water supply does not reach the sewers, but the losses due to leakage, lawn sprinkling, manufacturing processes, etc., are made up by additions from private water supplies, surface drainage, etc. The estimated quantity of water used but which did not reach the sewers in Cincinnati is shown in Table 6. The amount shown represents 38 per cent of the total consumption. Unless direct observations have been made on existing sewers or other factors are known which will affect the relation between water supply and sewage, the average sewage flow exclusive of ground water, should be taken as the average rate of water consumption. Experience has shown that water consumption increases after the installation of sewers.

TABLE 6
Estimated Quantity of Water Used but not Discharged into the Sewers in Cincinnati
Expressed in gallons per capita per day, and based on a total consumption of 125 to 150 gallons per capita per day.
Steam railroads. 6 to 7
Street sprinklers. 6 to 7
Consumers not sewered. 9 to 10½
Manufacturing and mechanical. 6 to 7
Lawn sprinklers. 3 to 3½
Leakage. 18 to 21

The public water supply is generally installed before the sewerage system. By collecting statistics on the rate of supply of water a fair prediction can be made of the quantity of sewage which must be cared for. The rate of water supply varies widely in different cities. It is controlled by many factors such as meters, cost and availability of water, quality of water, climate, population, etc. In American cities a rough average of consumption is 100 gallons per capita per day. Other factors being equal the rate of consumption after meters have been installed will be about one-half the rate before the meters were installed. Low cost, good quantity and good quality will increase the rate of consumption, and the rate will increase slowly with increasing population. Statistics of rates of water consumption are given in Table 7.

24. Character of District.—The various sections of a city are classified as commercial, industrial, or residential. The residential districts can be subdivided into sparsely populated, moderately populated, crowded, wealthy, poor, etc. Commercial districts may be either retail stores, office buildings, or wholesale houses. Industrial districts may be either large factories, foundries, etc., or they may be made up of small industries housed in loft buildings.

In cities of less than 30,000 population the refinement of such subdivisions is generally unnecessary in the study of sewage flow, all districts being considered the same. The data given in Tables 8 and 9 indicate the difference to be found in different districts of large cities. The Milwaukee data are presented in a form available for estimates on different bases. These data are shown in Table 10.

TABLE 7
Rates of Water Consumption
From Journals of American and New England Water Works Associations
City Population in Thousands Per Cent Metered Consumption, Gal. per Capita per Day
Tacoma, Wash. 100 11.6 460
Buffalo, N. Y. 450 4.9 310
Cheyenne, Wyo. 13 270
Erie, Pa. 72 3.0 198
Philadelphia, Pa. 1611 4.6 180
St. Catherines, Ont. 17 3.2 160
Port Arthur, Ont. 18 14.7 145
Ogdensburg, N. Y. 18 0.2 140
Los Angeles, Cal. 516 77.9 140
Wilmington, Del. 92 43.7 125
Lancaster Pa. 60 34.6 120
Richmond, Va. 120 75.2 115
St. Louis, Mo. 730 6.7 110
Springfield, Mass. 100 94.4 110
Keokuk, Ia. 14 64.5 105
Jefferson City, Mo. 13.5 34.4 100
Muncie, Ind. 30 23.8 95
Burlington, Ia. 24 4.5 90
Council Bluffs, Ia. 32 75.5 80
San Diego, Cal. 85 100 80
Monroe, Wis. 3 100 80
Yazoo City, Miss. 7 84.1 75
Oak Park, Illinois. 26 100 70
Portsmouth, Va. 75 8.1 65
New Orleans, La. 360 99.7 60
Rockford, Ill. 53 93.0 55
Fort Dodge, Ia. 20 96.0 50
Manchester, Vt. 1.5 69.0 45
Woonsocket, R. I. 47.5 95.6 35

Attempts have been made to express the rate of sewage flow in different units other than in gallons per capita per day. A unit in terms of gallons per square foot of floor area tributary has been suggested for commercial and industrial districts. It has not been generally adopted. The rates of flow in New York City as reported in this unit by W. S. McGrane are given in Table 11.

The most successful way to predict the flow from commercial or industrial districts is to study the character of the district’s activities and to base the prediction on the quantity of water demanded by the commerce and industry of the district affected.

25. Fluctuations in Rate of Sewage Flow.—The rate of flow of sewage from any district varies with the season of the year, the day of the week, and the hour of the day. The maximum and minimum rates of sewage flow are the controlling factors in the design of sewers. The sewers must be of sufficient capacity to carry the maximum load which may be put upon them, and they must be on such a grade that deposits will not occur during periods of minimum flow. The maximum and minimum rates of flow are usually expressed as percentages of the average rate of flow.

TABLE 8
Sewage Flow from Different Classes of Districts
Arranged from data by Kenneth Allen in Municipal Engineer’s Journal, Feb., 1918.
District Gallons per Capita per Day Gallons per Acre per Day
Buffalo, N. Y. From Report of International Joint Commission on the Pollution of Boundary Waters:
Industrial: Metal and automobile plants. Maximum. 13,000
Industrial: Meat packing, chemical and soap. 16,000
Commercial: Hotels, stores and office buildings. 60,000
Domestic: Average. 80
Domestic: Apartment houses. 147
Domestic: First-class dwellings. 129
Domestic: Middle-class dwellings. 81
Domestic: Lowest-class dwellings. 35.5
Cincinnati, Ohio. 1913 Report on Sewerage Plan:
Industrial, in addition to residential and ground water. 9,000
Commercial, in addition to residential and ground water. 40,000
Domestic. 135
Detroit, Mich.:
Domestic. 228
Industrial, in addition to residential and ground water. 12,000
Commercial, in addition to residential and ground water. 50,000
Milwaukee, Wis. 1915 Report of Sewerage Commission:
Industrial, maximum. 81 16,600
Industrial, average. 31 8,300
Commercial, maximum. 60,500
Commercial, average. 37,400
Wholesale commercial, maximum. 20,000
Wholesale commercial, average. 9,650
TABLE 9
Observed Water Consumption in Different Classes of Districts in New York City
From data by Kenneth Allen in Municipal Engineers Journal, for 1918
Hotels Daily Cons. Gals. per 1000 Sq. Ft. Floor Area Tenements Daily Cons. Gals. per 1000 Sq. Ft. Floor Area Office and Loft Buildings Daily Cons. Gals. per 1000 Sq. Ft. Floor Area
Building Max.[19] Avg. Location Max.[19] Avg. Building Max.[19] Avg.
Hotel Biltmore. 470 368 78th–79th St. and B’way. 256 192 McGraw Bldg. 309 206
Hotel McAlpin. 753 694 410 E. 65th St. 350 295 N. Y. Telephone Bldg. 194
Hotel Plaza. 630 578 30th St. and Madison Ave 306 188 Met. Life Bldg. 256
Hotel Waldorf Astoria. 618 482 27 Lewis St. 307 250 42d St. Bldg 271
Hotel Astor. 732 492 258 Delancey St. 267 226 Municipal Bldg. 118
Hotel Vanderbilt. 604 545 Equitable Bldg. 366 268
Average 634 526 Average 297 230 Average 338 219
TABLE 10
Sewage Flow from Different Classes of Districts Based on 1915 Report of Milwaukee Sewerage Commission
Ratio of maximum to average rate for department store district. 1.755
Ratio of maximum to average rate for hotel district. 1.65
Ratio of maximum to average rate for office building district. 1.51
Ratio of maximum to average rate for wholesale commercial district. 2.1
Average and maximum gallons per thousand square feet of floor area: Avg. Max.
For department store district. 232 407
For office building district. 541 891
For wholesale commercial district. 164 344
For all districts except wholesale commercial. 381 618
Average and maximum gallons per day:
For all districts except wholesale commercial. 17,700 29,800
For wholesale commercial district. 9,650 20,000

TABLE 11
Rates of Consumption Predicted for Different Districts in New York City
District Net Bldg. Area in Sq. Ft. per Acre for Ultimate Consumption Avg. Number of Floors Observed Cons. in g.p.d. per 1000 Sq. Ft. Max. Observed Cons. in g.p.d. per 1000 Sq. Ft. Avg. Predicted Mean Cons. Predicted Mean in Million Gals. per Acre per Day Predicted Dry Weather Flow, c.f.s. per Acre Predicted Max. Dry Weather Flow, c.f.s. per Acre Measured Avg. Dry Weather Flow, c.f.s. per Acre Measured Max. Dry Weather Flow, c.f.s. per Acre
Hotel and midtown. 24,800 15 634 526 500 .20 .29 .34 1.04 .146
Midtown and financial. 24,800 15 338 219 300 .12 .18 .23 .078 .110
East and West of midtown. 24,800 10 297 230 300 .074 .12 .15 .057 .097
Apartment, 59th to 155th Sts. 20,400 7 230 300 .043 .06 .09
Manhattan north of 155th St. 20,400 5 230 300 .031 .05 .08
Midtown district consists of department stores, large railroad terminals, industrial and loft buildings, and sky-scraper office building.

It is difficult to set any definite figure for the percentage which the maximum rate of flow is of the average. Fluctuations above and below the average are greater the smaller the tributary population. This relation can be expressed empirically as

M = 500 P⅕,

in which M represents the per cent which the maximum flow is of the average, and P represents the tributary population in thousands. The expression should not be used for populations below 1,000 nor above 1,000,000. Having determined the expected average flow of sewage by a study of the population, water consumption, etc., the maximum quantity of sewage is determined by multiplying the average flow by the per cent which the maximum is of the average. In this connection W. G. Harmon[20] offers the relation

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