  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.
Fig. 8.—Diagram Showing Methods for Estimating Future Population. 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 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, 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.
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
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
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
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 P?, 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 which was used in the design of the Ten Mile Creek intercepting sewer at Toledo, Ohio. For rough estimates and for comparative purposes the ratio of the average to the minimum flow can be Fig. 10.—Daily and Hourly Variations of Sewage Flow.
The fluctuations of flow in commercial and industrial districts are so different from those in residential districts that the formulas given should not be used in the design of sewers other than those draining residential areas. It is reasonable to suppose that fluctuations in rates of flow from industrial districts are dependent Hourly, daily, and seasonal fluctuations in rates of sewage flow are of interest in the design of pumping stations to give knowledge of the rates at which the pumps must operate at various periods. The fluctuations in rates of sewage flow during various hours and days in different cities and districts are shown in Fig. 10. Fluctuations in rate of flow of sewage lag behind fluctuations in rate of water consumption, the time being dependent on the distance through which the wave of change must travel in the sewer. 26. Effect of Ground Water.—Sewers are seldom laid with water-tight joints. Since they usually lie below the ground water level it is inevitable that a certain amount of ground water will enter. Various units have been suggested for the expression of the inflow of ground water in an attempt to include all of the many factors. Some of these units are: gallons per acre drained by the sewer per day, gallons per mile of pipe per day, gallons per inch diameter per mile of pipe per day, etc. Since the ground water enters pipe sewers at the joints, the longer the joints the greater the probability of the entrance of ground water. The last unit is therefore the most logical but the accuracy of the result is scarcely worthy of such refinement and the unit usually adopted is gallons per mile of pipe per day. No definite figure can be given for the amount of ground water to be expected in sewers since the character of the soil and the ground water pressure must be considered. Relatively normal infiltration may be found from 5,000 to 80,000 gallons per mile of pipe per day. The minimum is seldom reached in wet ground and the maximum is frequently exceeded. Table 12 shows the amount of ground water measured in various sewers as given by Brooks. 27. RÉsumÉ of Method for Determination of Quantity of Dry weather Sewage.—The steps in the determination of the quantity of sewage are: determine the period in the future for which the sewers are to be designed; estimate the population and tributary area at the end of this period; estimate the rate of water consumption and assume the sewage flow to equal the water consumption; determine the maximum and minimum rates of sewage flow; and finally, estimate the maximum rate of ground water seepage and add it to the maximum rate of sewage flow to give the total quantity of sewage to be carried by the proposed sewers.
Quantity of Storm Water28. The Rational Method.—The water which falls during a storm must be removed rapidly in order to prevent the flooding of streets and basements, and other damages. The quantity of water to be cared for is dependent upon: the rate of rainfall, the character and slope of the surface, and the area to be drained. All methods for the determination of storm-water run-off, whether rational or empirical, depend upon these factors. The so-called Rational Method can be expressed algebraically, as, Q = AIR,
The area to be drained is determined by a survey. A discussion of R and I follows in the next two sections. An example of the use of the Rational Method is given on page 95. 29. Rate of Rainfall.—Rainfall observations have been made over a long period of time by United States Weather Bureau observers and others. Continuous records are available in a few places in this country showing rainfall observations covering more than a century. Such records have been the bases for a number of empirical formulas for expressing the probable maximum rate of rainfall in inches per hour, having given the duration of the storm. Table 13 is a collection of these formulas with a statement as to the conditions under which each formula is applicable. The formula most suitable to the problem in hand should be selected for its solution.
30. Time of Concentration.—By the time of concentration is meant the longest time without unreasonable delay that will be required for a drop of water The time of concentration can be measured fairly well by observing the moment of the commencement of a rainfall, and the time of maximum run-off from an area on which the rain is falling. A prediction of the time of concentration is more or less guess work. As the result of measurements some engineers assume the time of concentration on a city block built up with impervious roofs and walks, and on a moderate slope, is about 5 to 10 minutes. This is used as a basis for the judgment of the time of concentration on other areas. For relatively large drainage areas such a method cannot be used. The procedure is to measure the length of flow through the drainage channels of the area, to assume the velocity of the flood crest through these channels and thus to determine the time of concentration. Table 14 shows the flood crest velocities in various streams of the Ohio River Basin under flood conditions. The velocity over the surface of the ground may be approximated by the use of the formula V = 2,000IvS,
For areas up to 100 acres where natural drainage channels are not existent this formula will give more satisfactory results than guesses based on the time of concentration of certain known areas. Having determined the time of concentration, the rate of rainfall R to be used in the Rational Method is found by substitution in some one of the rainfall formulas given in Table 13.
I = 0.175t?, but when T is greater than t, I = 0.175 t(T4 3 - (T - t)4 3). Gregory condenses Kuichling’s rules with regard to the per cent run-off, as follows: 1. The per cent of rainfall discharged from any given drainage area is nearly constant for heavy rains lasting equal periods of time. 2. This per cent varies directly with the area of impervious surface. 3. This per cent increases rapidly and directly or uniformly with the duration of the maximum intensity of the rainfall until a period is reached which is equal to the time required for the concentration of the drainage waters from the entire area at the point of observation, but if the rainfall continues at the same intensity for a longer period this per cent will continue to increase at a much smaller rate. 4. This per cent becomes larger when a moderate rain has immediately preceded a heavy shower on a partially permeable territory. Gregory’s formulas have not been generally accepted and are not widely used in practice. Marston stated: All that engineers are at present, warranted in doing is to make some deduction from 100 per cent run-off... the deduction... being at present left to the engineer in view of his general knowledge and his familiarity with local conditions. Burger states In its application there will usually be as many results (differing widely from each other) as the number of men using it. In spite of these objections the Rational Method is in more favor with engineers than any other method. 32. Empirical Formulas.—The difficulty of determining run-off with accuracy has led to the production by engineers of many empirical formulas for their own use. Some of these formulas have attracted wide attention and have been used extensively, The Burkli-Ziegler formula, devised by a Swiss engineer for Swiss conditions and introduced into the United States by Rudolph Hering, was one of the earliest of the empirical formulas to attract attention in this country. It has been used extensively in the form
The McMath formula was developed for St. Louis conditions and was first published in Transactions of the American Society of Civil Engineers, Vol. 16, 1887, p. 183. Using the same notation as above, the formula is, McMath recommended the use of C equal to 0.75, i as 2.75 inches per hour, and S equal to 15. The formula has been extended for use with all values of C, i, S, and A ordinarily met in sewerage practice. Fig. 11 is presented as an aid to the rapid solution of the formula. Fig. 11.—Diagram for the Solution of McMath’s Formula, Fig. 12.—Comparison of Empirical Run-off Formulas. It is to be noted that the only factor taken into consideration is the area of the watershed. It is obvious that other factors such as the rate of rainfall, slope, imperviousness, etc., will have a marked effect on the run-off. There are other run-off formulas devised for particular conditions, some of which are of as general applicability as those quoted. Two formulas which are frequently quoted are: Fanning’s, Q = 200M? and Talbot’s Q = 500M¼, in which M is the area of the watershed in square miles. A comprehensive treatment of the subject is given in American Sewerage Practice, Vol. I, by Metcalf and Eddy. A comparison of the results obtained by the application of a few formulas to the same conditions is shown graphically in Fig. 12. It is to be noted that the divergence between the smallest 33. Extent and Intensity of Storms.—In the design of storm sewers it is necessary to decide how heavy a storm must be provided for. The very heaviest storms occur infrequently. To build a sewer capable of caring for all storms would involve a prohibitive expense over the investment necessary to care for the ordinary heavy storms encountered annually or once in a decade. This extra investment would lie idle for a long period entailing a considerable interest charge for which no return is easily seen. The alternative is to construct only for such heavy storms as are of ordinary occurrence and to allow the sewers to overflow on exceptional occasions. The result will be a more frequent use of the sewerage system to its capacity, a saving in the cost of the system, and an occasional flooding of the district in excessive storms. The amount of damage caused by inundations must be balanced against the extra cost of a sewerage system to avoid the damage. A municipality which does not provide adequate storm drainage is liable, under certain circumstances, for damages occasioned by this neglect. It is not liable if no drainage exists, nor is it liable if the storm is of such unusual character as to be classed legally as an act of God. Kuichling’s studies of the probabilities of the occurrence of heavy storms are published in Transactions of the American Society of Civil Engineers, Vol. 54, 1905, p. 192. Information on the extent of rain storms is given by Francis in Vol. 7, 1878, p. 224, of the same publication. Kuichling expresses the intensity of storms which will occur, once in 10 years as i = 105 t + 20, once in 15 years as i = 120 t + 20, in which i is the intensity of rainfall in inches per hour and t is the duration of the storm in minutes. | |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||||
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