Sewerage and Sewage Treatment

CHAPTER III QUANTITY OF SEWAGE — Quantity of Storm Water

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.

26The 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 27progression 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, 28gas, 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.

31The 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 32average rate of water consumption. Experience has shown that water consumption increases after the installation of sewers.

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 33large cities. The Milwaukee data are presented in a form available for estimates on different bases. These data are shown in Table 10.

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 34to 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.

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

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

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 37taken the same as the ratio of the maximum to the average flow, unless direct gaugings or other information show it to be otherwise.

Fig. 10.—Daily and Hourly Variations of Sewage Flow.

1.

Toledo, O.; Manufacturing average.

2.

Toledo, O.; Manufacturing, Monday.

3.

Toledo, O.; Manufacturing, Sunday.

4.

Toledo, O.; Residential, average.

5.

Toledo, O.; Residential, Monday.

6.

Toledo, O.; Residential, Sunday.

7.

Cincinnati, O., Industrial, average.

8.

Cincinnati, O.; Residential, average.

9.

Cincinnati, O.; Commercial, average.

10.

Average of 7 cities.

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 38upon the character of the tributary industries. A study of these industries will give valuable light on the maximum and minimum rates at which sewage will be delivered to the sewers.

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.^[21]

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.

28. 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,

in which Q =

rate of run-off in cubic feet per second;

A =

area to be drained expressed in acres;

I =

percentage imperviousness of the area;

R =

maximum average rate of rainfall over the entire drainage area, expressed in inches per hour, which may occur during the time of concentration.

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.^[22]

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^[24] to flow from the upper limit of a drainage area to the outlet. Assuming a rainfall to start suddenly 42and to continue at a constant rate and to be evenly distributed over a drainage area of 100 per cent imperviousness and even slope towards one point, the rate of run-off would increase constantly until the drop of water from the upper limit of the area reached the outlet, after which the rate of run-off would remain constant. In nature the rate of rainfall is not constant. The shorter the duration of a storm the greater the intensity of rainfall. Therefore the maximum run-off during a storm will occur at the moment when the upper limit of the area has commenced to contribute. From that time on the rate of run-off will decrease.

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^[25]

in which V =

the velocity of flow over the surface of the ground in feet per minute;

I =

the percentage imperviousness of the ground;

S =

the slope of the ground.

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.

4431. Character of Surface.—The proportion of total rainfall which will reach the sewers depends on the relative porosity, or imperviousness, and the slope of the surface. Absolutely impervious surfaces such as asphalt pavements or roofs of buildings will give nearly 100 per cent run-off regardless of the slope, after the surfaces have become thoroughly wet. For unpaved streets, lawns, and gardens the steeper the slope the greater the per cent of run-off. When the ground is already water soaked or is frozen the per cent of run-off is high, and in the event of a warm rain on snow covered or frozen ground, the run-off may be greater than the rainfall. The run-off during the flood of March, 1913, at Columbus, Ohio, was over 100 per cent of the rainfall. Table 15^[26] shows the relative imperviousness of various types of surfaces when dry and on low slopes. The estimates for relative imperviousness used in the design of the Cincinnati intercepter are given in Table 16.

46C. E. Gregory^[27] states that I, in the expression Q = AIR is a function of the time of concentration or the duration of the storm. If t represents the time of concentration and T represents the duration of the storm, then when T is less than t

but when T is greater than t,

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:^[28]

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^[29] in the same connection:

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, 47in some cases under conditions to which they are not applicable. In general these formulas are expressions for the run-off in terms of the area drained, the relative imperviousness, the slope of the land, and the rate of rainfall.

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

in whichQ =

the run-off in cubic feet per second;

i =

the maximum rate of rainfall in inches per hour over the entire area. This is determined only by experience in the particular locality, and is usually taken at from 1 to 3 inches per hour;

S =

the slope of the ground surface in feet per thousand,

A =

the area in acres;

C =

an expression for the character of the ground surface, or relative imperviousness. In this form of the expression C is recommended as 0.7.

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.

48

Fig. 11.—Diagram for the Solution of McMath’s Formula,

49Other formulas have been devised which are more applicable to drainage areas of more than 1,000 acres.^[30] Such areas are met in the design of sewers to enclose existing stream channels draining large areas. Kuichling’s formulas, published in 1901 in the report of the New York State Barge Canal, were devised for areas greater than 100 square miles. The following modification of these formulas for ordinary storms on smaller areas was published for the first time in American Sewerage Practice, Volume I, by Metcalf and Eddy:

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^⅝ and Talbot’s Q = 500M^¼, 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 50and largest results is over 100 per cent. As these formulas are not all applicable to the same conditions, the differences shown are due partially to an extension of some of them beyond the limits for which they were prepared.

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,

in which i is the intensity of rainfall in inches per hour and t is the duration of the storm in minutes.

CHAPTER IV THE HYDRAULICS OF SEWERS

34. Principles.—The hydraulics of sewers deals with the application of the laws of hydraulics to the flow of water through conduits and open channels. In so far as its hydraulic properties are concerned the characteristics of sewage are so similar to those of water that the same physical laws are applicable to both. In general it is assumed that the energy lost due to friction between the liquid and the sides of the channel varies as some function of the velocity, usually the square, and that the total energy passing any section of the stream differs from the energy passing any other section only by the loss of energy due to friction.

The general expression for the flow of sewage would then be,

in which h is the head or energy lost between any two sections, and V is the average velocity of flow between these sections. It is to be noted in this general expression that the quantity and rate of flow past all sections is assumed to be constant. This condition is known as steady flow. Problems are encountered in sewerage design which involve conditions of unsteady flow, and methods of solution of them have been developed based on modifications of this general expression. The average velocity of flow is computed by dividing the rate (quantity) of flow past any section by the cross-sectional area of the stream at that section. This does not represent the true velocity at any particular point in the stream, as the velocity near the center is faster than that near the sides of the channel. The distribution of velocities in a closed circular channel is somewhat in the form of a paraboloid superimposed on a cylinder.

The laws of flow are expressed as formulas the constants of which have been determined by experiment. It has been found that these constants depend on the character of the material 52forming the channel and the hydraulic radius. The hydraulic radius is defined as the ratio of the cross-sectional area of the stream to the length of the wetted perimeter, or line of contact between the liquid and the channel, exclusive of the horizontal line between the air and the liquid.

35. Formulas.—The loss of head due to friction caused by flow through circular pipes flowing full as expressed by Darcy is,

in which h is the head lost due to friction in the distance l, V is the velocity of flow, g is the acceleration due to gravity, and f is a factor dependent on d and the material of which the pipe is made. A formula for f expressed by Darcy as the result of experiments on cast-iron pipe is,

in which d is the diameter in feet. In using the formula with this factor the units used must be feet and seconds.

Another form of the same expression is known as the Chezy formula. It is an algebraic transformation of the Darcy formula, but in the form shown here, by the use of the hydraulic radius, it is made applicable to any shape of conduit either full or partly full. The Chezy formula is,

in which R is the hydraulic radius, S the slope ratio of the hydraulic gradient, and C a factor similar to f in the Darcy formula.

Kutter’s formula was derived by the Swiss engineers, Ganguillet and Kutter, as the result of a series of experimental observations. It was introduced into the United States by Rudolph Hering and its derivation is given in Hering and Trautwine’s translation of “The Flow of Water in Open Channels by Ganguillet and Kutter.” In English units it is,

53in which n is a factor expressing the character of the surface of the conduit and the other notation is as in the Chezy formula. V is the velocity in feet per second, S is the slope ratio, and R the hydraulic radius in feet. The values of n to be used in all cases are not agreed upon, but in general the values shown below are used in practice.

Kutter’s formula is of general application to all classes of material and to all shapes of conduits. It is the most generally used formula in sewerage design.

The cumbersomeness of Kutter’s formula is caused somewhat by the attempt to allow for the effect of the low slopes of the Mississippi River experiments on the coefficients. The correctness of these experiments has not been well established and the slopes are so flat that the omission of the term 0.0028
S will have no appreciable effect on the value of V ordinarily used in sewer design. The difference between the value of V determined by the omission of this term and the value of V found by including it is less than 1 per cent for all slopes greater than 1 in 1,000 for 8 inch pipe (R = 0.167 feet). As the diameter of the pipe or the hydraulic radius of the channel increases up to a diameter of 13.02 feet (R = 3.28 feet), the difference becomes less and at this value of R there is no difference whether the slope is included or not. For larger pipes the difference increases slowly. For a 16 foot pipe (R = 4 feet) on a slope of 1 in 1,000 the difference is less than 0.2 per cent, and on a slope of 1 in 10,000 the difference is approximately 1 per cent. Flatter slopes than these are 54seldom used in sewer design, except for very large sewers where careful determinations of the hydraulic slope are necessary. It is therefore safe in sewer design to use Kutter’s formula in the modified form shown below in which the term .0028
S has been omitted.

Bazin’s formula is

in which α and β are constants for different classes of material. For cast-iron pipe α is 0.00007726 and β is 0.00000647. This formula is seldom used in sewerage design.

Exponential formulas have been developed as the result of experiments which have demonstrated that V does not vary as the one-half power of R and S but that the relation should be expressed as,

in which p and q are constants and C is a factor dependent on the character of the material. The various formulas coming under this classification have been given the names of the experimenters proposing them. Examples of these formulas are: Flamant’s, in English units, for new cast-iron pipe, which is,

and Lampé’s for the same material which is,

These formulas are useful only for the material to which they apply, but they can be used for conduits of any shape. A. V. Saph and E. W. Schoder have shown^[31] that the general formula for all materials lies between the limits,

55Hazen and Williams’ formula is in the form,

in which C is a factor dependent on the character of the material of the conduit. The values of C as given by Hazen and Williams are,

This formula is of as general application as Kutter’s formula and is easier of solution, but being more recently in the field and because of the ease of the solution of Kutter’s formula by diagrams it is not in such general use. Exponential formulas are used more in waterworks than in sewerage practice.

Manning’s formula is in the form,

in which n is the same as for Kutter’s formula. Charts for the solution of Manning’s formula are given in Eng. News-Record, Vol. 85, 1920, p. 837.

36. Solution of Formulas.—The solution of even the simplest of these formulas, such as Flamant’s, is laborious because of the exponents involved. Darcy’s and Kutter’s formulas are even more cumbersome because of the character of the coefficient. The labor involved in the solution of these formulas has resulted in the development of a number of diagrams and other short cuts. Since each formula involves three or more variables it cannot be represented by a single straight line on rectangular coordinate paper. The simplest form of diagram for the solution of three or more variables is the nomograph, an example of which is shown 56in Fig. 13 for the solution of Flamant’s formula. A straight-edge placed on any two points of the scales of two different vertical lines will cross the other line at a point on the scale corresponding to its correct value in the formula. Such a diagram is in common use for the solution of problems for the flow of water in cast-iron pipe.

Fig. 13.—Diagram for the Solution of Flamant’s Formula for the Flow of Water in Cast-iron Pipe.

Fig. 14 has been prepared to simplify the solution of Hazen and Williams’ formula. The scales of slope for different classes of material are shown on vertical lines to the left of the slope line. For use these scales must be projected horizontally on the slope line. The scales for other factors are shown on independent reference lines.

For example let it be required to find the loss of head in a 12 inch pipe carrying 1 cubic foot per second when the coefficient of roughness is 100. A straight-edge placed at 1.0 cubic feet per second on the quantity scale, and 12 inches on the diameter scale crosses the slope line at .00092 opposite the slope scale for c = 100. It crosses the velocity line at 1.31 feet per second.

Kutter’s formula is the most commonly used for sewer design and has been generally accepted as a standard in spite of its cumbersomeness. Fig. 15 is a graphical solution of Kutter’s formula for small pipes, and Fig. 16 for larger pipes. The diagrams are drawn on the nomographic principle and give solutions for a wide range of materials, but they are specially prepared for the solution of problems in which n = .015. In their preparation the effect of the slope on the coefficient has been neglected. Fig. 17 is drawn on ordinary rectangular coordinate paper and can be used only for the solution of problems in which n = .015. Both diagrams are given for practice in the use of the different types.

57

Fig. 14.—Diagram for the Solution of Hazen and Williams’ Formula.

58

Fig. 15.—Diagram for the Solution of Kutter’s Formula.

For values of n between 0.010 and 0.020. Specially arranged for n = 0.015. Values of Q from 0.1 to 10 second-feet.

59

Fig. 16.—Diagram for the Solution of Kutter’s Formula.

For values of n between 0.010 and 0.020. Specially arranged for n = 0.015. Values of Q from 10 to 1,000 second-feet.

60

Fig. 17.—Diagram for the Solution of Kutter’s Formula.

61

Fig. 18.—Conversion Factors for Kutter’s Formula.

In Figs. 15 and 16 the diameter scales are varied for different values of the roughness coefficient n. The velocity scale is shown only for a value of n = .015. The velocity for other values of n can be determined by the method given in the following paragraphs.

37. Use of Diagrams.—There are five factors in Kutter’s formula: n, Q, V, d (or R), and S. If any three of these are given the other two can be determined, except when the three given are Q, V, and d. These three are related in the form Q = AV, which is independent of slope or the character of the material. There are only nine different combinations possible with these five factors, which will be met in the solution of Kutter’s formula. The solution of the problems by means of the diagrams is simple when the data given include n = .015. For other given values of n the solution is more complicated. Results of the solution of types of each of the nine problems are given in Table 17 and the explanatory text below.

If n is given and is equal to .015, the solution is simple.

For example in Table 17 case 1, example 1; to be solved on Fig. 15. Place a straight-edge at 1.0 on the Q line and at 6 inches on the diameter line for n = .015. The slope and the velocity will be found at the intersection of the straight-edge with these respective scales.

All problems in which n is given as .015 and the solution for which falls within the limits of Fig. 15 or 16 should be solved by placing a straight-edge on the two known scales and reading the two unknown results at the intersection of the straight-edge and the remaining scales.

For example in case 1, example 2 find the intersection of the horizontal line representing Q = 100 with the sloping 62diameter line representing d = 48 inches. The vertical slope line passing through this point represents S = .0065 and the sloping velocity line passing through this point represents 8.5 feet per second.

In general problems in which n = .015, can be solved on Fig. 17 by finding the intersection of the two lines representing the given data, and reading the values of the remaining variables represented by the other two lines passing through this point.

If n is given and is not equal to .015 the solution is not so simple. In Fig. 15 and 16 the diagram is so drawn that the position of the diameter scales for all values of n is fixed on the vertical “diameter” line. The scales of diameter change for each value of n. These scales of diameter are shown for each value of n from .010 to .020 on vertical lines to the left of the “diameter” line. For use, the proper diameter scale for any given value of n must be projected horizontally upon the vertical “diameter” line. The velocity can be determined on Fig. 15 and 16, only 63when the diameter has been determined and then only when the diameter scale for n equal .015 is used, since the only scale shown for velocity is for n = .015.

For example, in Case 1, Example 3 there are given n = .020, Q, and d. Find the intersection of the vertical line for n = .020 with the sloping diameter line for d = 6 inches. Project the intersection horizontally to the right to the vertical “diameter” line. Place a straight-edge at this point and at Q = 1.0 on the quantity scale. The required value of S is read at the intersection of the straight-edge and the slope scale and is equal to 0.13. The intersection of the straight-edge in this position with the velocity scale is not the required value of the velocity since the velocity scale is made out for n = .015 and not .020. It is necessary to change the position of the straight-edge so that it may lie on Q equal 1.0 and on d equal 6 inches for n equal .015. The value of V is shown in this position as 5 feet per second.

The reverse process for Fig. 15 and 16 is illustrated by Case 4, Example 2 in which n = .011 and Q and V are also given. When Q and V are given the value of d is fixed independent of all other factors. Therefore the value of d can be read from the scale with n = .015 and is found to be 12 inches. Now find the value of d = 12 inches on the scale for n = .011 and project on to the “diameter” line. Place the straight-edge at this point and at Q = 2. The required slope is read as .0022.

Fig. 17 is prepared for the solution of problems in which n = .015 only. For problems in which n has some other value it is necessary to transform the data to equivalent conditions in which n = .015. This is done by means of the conversion factors shown in Fig. 18. The given slope or velocity is multiplied by the proper factor to convert from or to the value of n = .015.

For example in Case 1, Example 4 there are given n = .020, Q, and d. With Q and d given the value of V can be read from Fig. 17 without conversion. The corresponding value of S for n = .015 is .0065. It is now necessary to use the transformation diagram Fig. 18. The hydraulic radius of the given pipe is one foot. On Fig. 18 at the intersection of the slope line for R = 1.0 foot and n = .020 the value of the factor is read as 1.92. Since the given n is for rougher material than that represented by n = .015 the required slope must be greater than for n = .015 to give the 64same velocity. It is therefore necessary to multiply .0065 × 1.92 and the required slope is .0125.

In Case 6, Example 1 there are given n = .018, d, and S. The remaining factors are to be solved by Fig. 17. Solve first as though n = .015 in order to find an approximate value of d or R. In this case it is evident that d is greater than 57 inches. The value of R is therefore about 1.25. Referring to Fig. 18 the conversion factor for the slope for n = .018 is about 1.52. Since the given slope for n = .018 is .001, for an equal velocity and for n = .015 the slope should be less. Therefore in reading Fig. 17 it is necessary to use a slope of .001
1.52 = .00066. The diameter is found to be about 80 inches. Since this is nearer to the correct diameter the value of the conversion factor must be corrected for this approximation. The hydraulic radius for an 80 inch pipe is 1.67 feet, and the conversion factor from Fig. 18 is about 1.48. The slope for n = .015 should be therefore .001
1.48 = .000675 and from Fig. 17 the required diameter and quantity are read as 80 inches and 185 second-feet, respectively.

If n is not given but must be solved for, the solution on Fig. 15 and 16 is relatively simple. The desired value of n is read at the intersection of the sloping diameter line representing the known diameter and the horizontal projection of the intersection of the straight-edge with the vertical “diameter” line.

For example in Case 7, Example 1 there are given Q, d, and S. Lay the straight-edge on the given values of Q = 3 and S = .002. At the point where the straight-edge crosses the vertical “diameter” line project a horizontal line to the sloping diameter line for d = 18 inches. The vertical line passing through this point represents a value of n = .019. In order to find the value of V lay the straight-edge on Q = 3 and d = 18 inches for n = .015. The value of V is read as 1.7.

A slightly different condition is illustrated in the solution of Case 8, Example 1 in which Q, V and S are given. Determine first the value of d as though n = .015. Then proceed to determine n as in the preceding examples.

The solution for an unknown value of n on Fig. 17 is not so simple. It must be determined by working backwards from the conversion factor.

65For example in Case 7, Example 2 there are given Q, d, and S. The value of V is read directly as though n = .015 as 7 feet per second. The value of S read for n = .015 is .0075. But the given slope is .005. Since the given slope is flatter than that for n = .015 the conversion factor is less than unity and is therefore .005
.0075 = 0.67. With this value of the conversion factor and the value of R given as 0.75 the value of n is read from Fig. 18 as slightly greater than .012.

38. Flow in Circular Pipes Partly Full.—The preceding examples have involved the flow in circular pipes completely filled. The same methods of solution can be used for pipes flowing partly full except that the hydraulic radius of the wetted section is used instead of the diameter of the pipe. Diagrams are used to save labor in finding the hydraulic radius and the other hydraulic elements of conduits flowing partly full.

The hydraulic elements of a conduit for any depth of flow are: (a) The hydraulic radius, (b) the area, (c) the velocity of flow, and (d) the quantity or rate of discharge. The velocity and quantity when partly full as expressed in terms of the velocity and quantity when full as calculated by Kutter’s formula will vary slightly with different diameters, slopes and coefficients of roughness. The other elements are constant for all conditions for the same type of cross-section. The hydraulic elements for all depths of a circular section for two different diameters and slopes are shown in Fig. 19. The differences between the velocity and quantity under the different conditions are shown to be slight, and in practice allowance is seldom made for this discrepancy.

In the solution of a problem involving part full flow in a circular conduit the method followed is to solve the problem as though it were for full flow conditions and then to convert to partial flow conditions by means of Fig. 19, or to convert from partial flow conditions to full flow conditions and solve as in the preceding section.

For example let it be required to determine the quantity of flow in a 12–inch diameter pipe with n = .015 when on a slope of .005 and the depth of flow is 3 inches. First find the quantity for full flow. From Fig. 15 this is 2.0 cubic feet per second. The depth of flow of 3 inches is one-fourth 66or 0.25 of the full depth of 12 inches. From Fig. 19, running horizontally on the 0.25 depth line to meet the quantity curve, the proportionate quantity at this depth is found to be on the 0.13 vertical line, and the quantity of flow is therefore 2 × 0.13 = 0.26 cubic feet per second.

Fig. 19.—Hydraulic Elements of Circular Sections.

Another problem, involving the reversal of this process is illustrated by the following example:

Let it be required to determine the diameter and full capacity of a vitrified pipe sewer on a grade of 0.002 if the velocity of flow is 3.0 feet per second when the sewer is discharging at 30 per cent of its full capacity, the depth of flow being 12 inches. From Fig. 19 the depth of flow when the sewer is carrying 30 per cent of its full capacity is 0.38 of its full depth. Since the partial depth is 12 inches the full diameter is 12
.038 = 31.6 inches. The velocity of flow at 38 per cent depth is 86 per cent of the full velocity. Since the velocity given is 3.0 feet per second, the full velocity is 3.0
.86 = 3.5 feet per second. With a full velocity of 3.5 feet per second and a diameter of 31.6 inches from Fig. 16 the full capacity of the sewer is 18 cubic feet per second.

6739. Sections Other than Circular.—The ordinary shape used for small sewers is circular. The difficulty of constructing large sewers in a circular shape, special conditions of construction such as small head room, soft foundations, etc., or widely fluctuating conditions of flow have led to the development of other shapes. For conduits flowing full at all times a circular section will carry more water with the same loss of head than any other section under the same conditions. In any section the smaller the flow the slower the velocity, an undesirable condition. The ideal section for fluctuating flows would be one that would give the same velocity of flow for all quantities. Such a section is yet to be developed. Sections have been developed that will give relatively higher velocities for small quantities of flow than are given by a circular section. The best known of these sections is the egg shape, the proportions and hydraulic elements of which are shown in Fig. 20. Other shapes that have the same property, but which were not developed for the same purpose are the rectangular, the U-shape, and the section with a cunette. The egg-shaped section has been more widely used than any other special section. It is, however, more difficult and expensive to build under certain conditions, and has a smaller capacity when full than a circular sewer of the same area of cross-section. Various sections are illustrated in Fig. 22 and 23.

The U-shaped section is suitable where the cover is small, or close under obstructions where a flat top is desirable and the fluctuations of flow are so great as to make advantageous a special shape to increase the velocity of low flows. The proportions of a U-shaped section are shown in Fig. 23 (6). Other sections used for the same purpose are the semicircular and special forms of the rectangular section.

The proportions and the hydraulic elements of the square-shaped section are shown in Fig. 21. This is useful under low heads where a flat roof is required to carry heavy loads, and the fluctuations of flow are not large.

Sections with cunettes have not been standardized. A cunette is a small channel in the bottom of a sewer to concentrate the low flows, as shown in Fig. 22 (7). A cunette can be used in any shape of sewer.

68

Fig. 20.—Hydraulic Elements of an Egg-shaped Section.

d = 6′ 0″ s = .00065 n = .015

Fig. 21.—Hydraulic Elements of a Square Section.

d = 10′ 0″ s = .0004 n = .015

69Sections developed mainly because of the greater ease of construction under certain conditions are the basket handle, the gothic, the catenary, and the horse shoe. Some of these shapes are shown in Fig. 22 and 23. They are suitable for large sewers on soft foundations, where it is desirable to build the sewer in three portions, such as invert, side walls, and arch. They are also suitable for construction in tunnels where the shape of the sewer conforms to the shape of the timbering, or in open cut work where the shape of the forms are easier to support.

Problems of flow in all sections can be solved by determining the hydraulic radius involved, and substituting directly in the desired formula, or by the use of one of the diagrams after converting to the equivalent circular diameter. The determination of the hydraulic radius of these special sections is laborious, and hence other less difficult methods are followed. Problems are more commonly solved by converting the given data into an equivalent circular sewer, solving for the elements of this circular sewer and then reconverting into the original terms, or by working in the other direction. The hydraulic elements of various sections when full are given in Table 18.

70

1. Standard Egg-shaped Section, North Shore Intercepter, Chicago, Illinois.

2. Rectangular Section, Omaha, Nebraska, Eng. Contracting, Vol. 46, p. 49.

3. Trench in firm ground. 4. Trench in Rock.

Note.—Underdrains and Wedges to be used only when Ordered by the Engineer.

7. Brick and Concrete Sewer showing cunette.

5. Soft Foundation. 6. Wet ground.

8. Brick and Concrete Sewer, Evanston, Ill., Eng. Contracting, Vol. 46, p. 227.

1. Tunnel Sections.				2. Open Cut Sections.
Type A.	Type B.	Type C.	Type D.
Where Rock is more than 16′ above Springing Line.	Where Rock is more than 7′ and less than 16′ above Springing Line on both Sides.	Where Rock is between Springing Line and 7′ above Springing Line on both Sides.	Where Rock drops below Springing Line on either Side.	16′ 6″ Sewer. 25′ Fill	Where Rock is above Springing Line
Mill Creek Sewer, St. Louis, Eng. Record, Vol. 70, pp. 434, 435.

3. Circular Concrete Section in Soft and Hard Ground, Eng. Record, Vol. 59, p. 570.

4. Semi-Elliptical Section, Louisville, Ky., Eng. News, Vol. 62, p. 416.

5. Reinforced Concrete Sewer, Harlem Creek, St. Louis, Eng. News, Vol. 60, p. 131.

6. U-Shaped Section, San Francisco, Eng. News, Vol. 73, p. 310.

Fig. 23.

72Equivalent sections are sections of the same capacity for the same slope and coefficient of roughness. They have not necessarily the same dimensions, shape, nor area. The diameter of the equivalent circular section in terms of the diameter of each special section shown is given in Table 18. The inside height of a sewer is spoken of as its diameter.

For example let it be required to determine the rate of flow in a 54–inch egg-shaped sewer on a slope of 0.001 when n = .015. First convert to the equivalent circle. From Table 18 the diameter of the equivalent circle is 1
1.295 times the diameter of the egg-shaped sewer, which becomes in this case 43 inches. From Fig. 16 the capacity of a circular sewer of this diameter with S = 0.001 and n = .015 is 28 cubic feet per second, which by definition is the flow in the egg-shaped sewer.

As an example of the reverse process let it be required to find the velocity of flow in an egg-shaped sewer flowing full and equivalent to a 48–inch circular sewer. Both sewers are on a slope of 0.005 and have a roughness coefficient of n = .015. It is first necessary to find the quantity of flow in the circular sewer, which by definition is the quantity of flow in the equivalent egg-shaped sewer. The velocity of flow in the egg-shaped sewer is found by dividing this quantity by the area of the egg-shaped section. As read from the diagram the quantity of flow is 90 cubic feet per second. From Table 18 the area of the egg-shaped sewer is 0.51D² where D is the diameter of the egg-shaped sewer, and D = 1.295d where d is the diameter of the equivalent circular sewer. Therefore the area equals (0.51) × (1.295 × 4)² = 13.5 square feet and the velocity of flow is 90
13.5 = 6.7 feet per second. This is slightly less than the velocity in the circular section.

Some lines for egg-shaped sewers have been shown on Fig. 17 by which solutions can be made directly. For other shapes, and for sizes of egg-shaped sewers not found on Fig. 17 the preceding method or the original formula must be used for solution. Problems in partial flow in special sections are solved similarly to partial flow in circular sections, by converting first to the conditions of full flow or by working in the opposite direction.

40. Non-uniform Flow.—In the preceding articles it is assumed that the mean velocity and the rate of flow past all sections are 73constant. This condition is known as steady, uniform flow. In this article it will be assumed that conditions of steady non-uniform flow exist, that is, the rate of flow past all sections is constant, but the velocity of flow past these sections is different for different sections. Under such conditions the surface of the stream is not parallel to the invert of the channel. If the velocity of flow is increasing down stream the surface curve is known as the drop-down curve. If the velocity of flow is decreasing down stream the surface curve is known as the backwater curve. The hydraulic jump represents a condition of non-uniform flow in which the velocity of flow decreases down stream in such a manner that the surface of the stream stands normal to the invert of the channel at the point where the change in velocity occurs. Above and below this point conditions of uniform flow may exist.

Conditions of non-uniform flow exist at the outlet of all sewers, except under the unusual conditions where the depth of flow in the sewer under conditions of steady, uniform flow with the given rate of discharge would raise the surface of water in the sewer, at the point of discharge, to the same elevation as the surface of the body of water into which discharge is taking place. By an application of the principles of non-uniform flow to the design of outfall sewers, smaller sewers, steeper grades, greater depth of cover, and other advantages can be obtained.

The backwater curve is caused by an obstruction in the sewer, by a flattening of the slope of the invert, or by allowing the sewer to discharge into a body of water whose surface elevation would be above the surface of the water in the sewer, at the point of discharge, under conditions of steady, uniform flow with the given rate of discharge.

The drop-down curve is caused by a sudden steepening of the slope of the invert; by allowing a free discharge; or by allowing a discharge into a body of water whose surface elevation would be below the surface of the water in the sewer, at the point of discharge, under conditions of steady, uniform flow with the given rate of discharge. The last described condition is common at the outlet of many sewers, hence the common occurrence of the drop-down curve.

The hydraulic jump is a phenomenon which is seldom considered in sewer design. If not guarded against it may cause trouble at overflow weirs and at other control devices, in grit chambers, 74and at unexpected places. The causes of the hydraulic jump are sufficiently well understood to permit designs that will avoid its occurrence, but if it is allowed to occur the exact place of the occurrence of the jump and its height are difficult, if not impossible, to determine under the present state of knowledge concerning them. The hydraulic jump will occur when a high velocity of flow is interrupted by an obstruction in the channel, by a change in grade of the invert, or the approach of the velocity to the “critical” velocity. The “critical” velocity is equal to √(gh), where h is the depth of flow and g is the acceleration due to gravity. The velocity in the channel above the jump must be greater than √(gh₁), where h₁ is the depth of flow in the channel above the jump. The velocity in the channel below the jump must be greater than √(gh₂), where h₂ is the depth of flow below the jump. The jump will not take place unless the slope of the invert of the channel is greater than g
C²,in which C is the coefficient in the Chezy formula. With this information it is possible to avoid the jump by slowing down the velocity by the installation of drop manholes, flight sewers, or by other expedients.

The shape of the drop-down curve can be expressed, in some cases, by mathematical formulas of more or less simplicity, dependent on the shape of the conduit. The formula for a circular conduit is complicated. Due to the assumptions which must be made in the deduction of these formulas, the results obtained by their use are of no greater value than those obtained by approximate methods. A method for the determination of the drop-down curve is given by C. D. Hill.^[32] In this method it is necessary that the rate of flow past all sections shall be the same; that the depth of submergence at the outlet shall be known; and that the depth of flow at some unknown distance up the stream shall be assumed. The shape and material of construction of the sewer and the slope of the invert should also be known. The problem is then to determine the distance between cross-sections, one where the depth of flow is known, and the other where the depth of flow has been assumed. This distance can be expressed as follows:

in which L =75

the distance between cross-sections;

d₁ =

the depth of flow at the lower section;

d₂ =

the depth of flow at the upper section;

H₁ =

the velocity head at the lower section;

H₂ =

the velocity head at the upper section;

S =

the hydraulic slope of the stream surface;

S₁ =

the slope of the invert of the sewer.

In order to solve such problems with a satisfactory degree of accuracy the difference between d₁ and d₂ should be taken sufficiently small to divide the entire length of the sewer to be investigated into a large number of sections. The solution of the problem requires the determination of the wetted area, the hydraulic radius, and other hydraulic elements at many sections. The labor involved can be simplified by the use of diagrams, such as Fig. 19, or by specially prepared diagrams such as those accompanying the original article by C. D. Hill. The solution of the problem can be simplified by tabulating the computations as follows:

At the head of the computation sheet should be recorded the diameter of the sewer in feet, the assumed volume of flow, the area of the full cross-section of the sewer, the velocity of the assumed volume flowing through the full bore of the sewer, and the gradient or slope of the invert. In the 1st column enter the 76assumed depth in decimal parts of the diameter for each cross-section; in the 2nd column enter the same depth in feet; in the 3rd column enter the difference in feet between the successive cross-sections; in the 4th column enter the hydraulic radius corresponding to the depth at each cross-section; in the 8th column enter the velocity, equal to the volume divided by the wetted area, for each cross-section; in the 5th column enter the corresponding velocity head; in the 6th column enter the difference between the velocity heads at successive cross-sections; in the 7th column enter the difference between the quantities in the third and in the sixth columns; in the 9th column enter the hydraulic slope corresponding to the velocity and hydraulic radius of each cross-section; in the 10th column enter the difference between the hydraulic slope and the slope or gradient of the sewer; in the 11th column enter the computed distance between successive cross-sections; in the 12th column enter the elevation of the bottom of the sewer at each cross-section; and in the 13th column enter the corresponding elevation of the surface of the water.

The table should be filled in until the distance to the required section is determined, or if the distance is known, it should be filled in until the depth of flow with the assumed rate of discharge has been checked.

If only the depth of flow at some section is known and it is required to know the maximum rate of flow with a free discharge, or a discharge with a submergence at the outlet less than the depth of flow with the maximum rate of discharge, it is necessary to make a preliminary estimate of the maximum rate of flow in order to fill in the quantity Q at the head of the table. The procedure should be as follows:

1st.

Assume a depth of flow at the outlet.

2nd.

Compute the area (A) and the hydraulic radius (R) at the known section and at the outlet.

3rd.

Determine the area and the hydraulic radius half way between these two sections as the mean of the areas and the hydraulic radii of the two sections.

4th.

Determine the rate of flow through the sewer from the condition that the difference in head at the two sections is the head lost due to friction caused by the average velocity of flow between the sections (equals lV²
C²R) plus the gain in velocity head (equals 77V₂² − V₁²
2g), which then combined and transposed result in the expression:

in which Q =

rate of flow;

A =

the area determined in the 3rd step;

A₁ =

the area at the upper cross-section;

A₂ =

the area at the lower cross-section;

C =

the coefficient in the Chezy formula;

g =

the acceleration due to gravity;

h =

the difference in elevation of the surface of the stream at the two cross-sections;

l =

the distance between the cross-sections;

R =

the hydraulic radius determined in the third step.

5th.

Continue this process by assuming different depths at the outlet until the maximum rate of discharge has been found by trial.

With this rate of discharge and depth of flow at the outlet, the depth of flow at the known section can be checked. If appreciably in error a correction should be made by the assumption of a different depth of flow at the outlet. The approximate character of the method is scarcely worthy of the refinement in the results which will be obtained by checking back for the depth of flow at the known section. It will be sufficiently accurate to assume the rate of flow obtained by trial from the preceding expression, as the maximum rate of discharge from the sewer.

CHAPTER V DESIGN OF SEWERAGE SYSTEMS — Design of a Storm Water Sewer System

41. The Plan.—Good practice demands that a comprehensive plan for a sewerage system be provided for the needs of a community for the entire extent of its probable future growth, and that sewers be constructed as needed in accordance with this plan.

Sewerage systems may be laid out on any one of three systems: separate, storm, or combined. A separate system of sewers is one in which only sanitary sewage or industrial wastes or both are allowed to flow. Storm sewers carry only surface drainage, exclusive of sanitary sewage. Combined sewers carry both sanitary and storm sewage. The use of a combined or a separate system of sewerage is a question of expediency. Portions of the same system may be either separate, combined, or storm sewers.

Some conditions favorable to the adoption of the separate system are where:

a. The sanitary sewage must be concentrated at one outlet, such as at a treatment plant, and other outlets are available for the storm drainage.

b. The topography is flat necessitating deep excavation and steeper grades for the larger combined sewers.

c. The sanitary sewers must be placed materially deeper than the necessary depth for the storm-water drains.

d. The sewers are to be laid in rock, necessitating more difficult excavation for the larger combined sewers.

e. An existing sewerage system can be used to convey the dry weather flow, but is not large enough for the storm sewage.

f. The city finances are such that the greater cost of the combined system cannot be met and sanitary drainage is imperative.

g. The district to be sewered is an old residential section where property values are not increasing and the assessment must be kept down.

79Some additional points given in a report by Alvord and Burdick to the city of Billings, Montana, are:

The separate system of sewerage should be used, where:

1st. Storm water does not require extensive underground removal, or where it can be concentrated in a few shallow underground channels.

2nd. Drainage areas are short and steep facilitating rapid flow of water over street surfaces to the natural water courses.

3rd. The sanitary sewage must be pumped.

4th. Sewers are being built in advance of the city’s development to encourage its growth.

5th. The existing sewer is laid at grades unsuitable for sanitary sewage, it can be used as a storm sewer.

A combined system must be relatively larger than a separate storm sewer as the latter may overflow on exceptional occasions, but the former never.

A combined system of sewerage should be used where:

1st. It is evident that storm and sanitary sewerage must be provided soon.

2nd. Both sanitary and storm sewage must be pumped.

3rd. The district is densely built up.

42. Preliminary Map.—The first step in the design of a sewerage system is the preparation of a map of the district to be served within the limits of its probable growth. The map should be on a scale of at least 200 feet to the inch in the built up sections or other areas where it is anticipated that sewers may be built, and where much detail is to be shown a scale as large as 40 feet to the inch may have to be used. The adoption of so large a scale will usually necessitate the division of the city or sewer district into sections. A key map should be drawn to such a scale that the various sections represented by separate drawings can all be shown upon it. In preparing the enlarged portions of the map it is not necessary to include these portions of the city in which it is improbable that sewers will be constructed, such as parks and cemeteries.

The contour interval should depend on the character of the district and the slope of the land. In those sections drawn to a scale of 200 feet to the inch for slopes over 5 per cent, the contour interval need not be closer than 10 feet. For slopes between 1 and 5 per cent the contour interval should be 5 feet. For flatter 80slopes the interval should not exceed 2 feet, and a one foot interval is sometimes desirable. In general the horizontal distances between contours should not exceed 400 feet and they should be close enough to show important features of the natural drainage. Elevations should also be given at street intersections, and at abrupt changes in grade. For portions of the map on a smaller scale the contours need be sufficiently close to show only the drainage lines and the general slope of the land.

The following may be shown on the preliminary map: the elevation of lots and cellars; the character of the built up districts, whether cheap frame residences, flat-roof buildings, manufacturing plants, etc.; property lines; width of streets between property lines and between curb lines; the width and character of the sidewalks and pavements; street car and railroad tracks; existing underground structures such as sewers, water pipes, telephone conduits, etc.; the location of important structures which may have a bearing on the design of the sewers such as bridges, railroad tunnels, deep cuts, culverts, etc.; and the location of possible sewer outlets and the sites for sewage disposal plants.

Fig. 24 shows a preliminary map for a section of a city, on which the necessary information has been entered. The map is made from survey notes. All streets are paved with brick. The alleys are unpaved. The entire section is built up with high-class detached residences averaging one to each lot. The lots vary from 1 to 3 feet above the elevation of the street.

43. Layout of the Separate System.—Upon completion of the preliminary map a tentative plan of the system is laid out. The lines of the sewer pipe are drawn in pencil, usually along the center line of the street or alley in such a manner that a sewer will be provided within 50 feet or less of every lot. The location of the sewers should be such as to give the most desirable combination of low cost, short house connections, proper depth for cellar drainage, and avoidance of paved streets. Some dispute arises among engineers as to the advisability of placing pipes in alleys, although there is less opposition to so placing sewers than any other utility conduit. The principal advantage in placing sewers in alleys is to avoid disturbing the pavement of the street, but if both street and alley are paved it is usually more economical to place the sewer in the street as the house connections will be shorter. On boulevards and other wide streets such as Meridian Avenue in 81Fig. 24, the sewers are placed in the parking on each side of the street, rather than to disturb the pavement and lay long house connections to the center of the street.

All pipes should be made to slope, where possible, in the direction of the natural slope of the ground. The preliminary layout of the system is shown in Fig. 24. The lowest point in the portion of the system shown is in the alley between Alabama and Tennessee Streets. The flow in all pipes is towards this point, and only one pipe drains away from any junction, except that more than one pipe may drain from a terminal manhole on a summit.

44. Location and Numbering of Manholes.—Manholes are next located on the pipes of this tentative layout. Good practice calls for the location of a manhole at every change in direction, grade, elevation, or size of pipe, except in sewers 60 inches in diameter or larger. The manholes should not be more than 300 to 500 feet apart, and preferably as close as 200 to 300 feet. In sewers too small for a man to enter the distance is fixed by the length of sewer rods which can be worked successfully. In the larger sewers the distances are sometimes made greater but inadvisedly so, since quick means of escape should be provided for workmen from a sudden rise of water in the sewer, or the effect of an asphyxiating gas. In the preliminary layout the manholes are located at pipe intersections, changes in direction, and not over 300 to 500 feet apart on long straight runs at convenient points such as opposite street intersections where other sewers may enter.

No standard system of manhole numbering has been adopted. A system which avoids confusion and is subject to unlimited extension is to number the manholes consecutively upwards from the outlet, beginning a new series of numbers prefixed by some index number or letter for each branch or lateral. This system has been followed with the manholes on Fig. 24.

82

Fig. 24.—Typical Map Used in the Design of a Separate Sewer System.

83

Fig. 25.—Typical Map Used in the Design of a Storm Sewer System.

8445. Drainage Areas.—The quantity of dry weather sewage is determined by the population rather than the topography. Lot lines and street intersections or other artificial lines marking the boundaries between districts are therefore taken as watershed lines for sanitary sewers. The quantity of sewage to be carried and the available slope are the determining factors in fixing the diameter of the sewer. Since there may be no change in diameter or slope between manholes the quantity of sewage delivered by a sewer into any manhole will determine the diameter of the sewer between it and the next manhole above. In order to determine the additional amount contributed between manholes a line is drawn around the drainage area tributary to each manhole. This line generally follows property lines and the center lines of streets or alleys, its position being such that it includes all the area draining into one manhole, and excludes all areas draining elsewhere. An entire lot is usually assumed to lie within the drainage area into which the building on the lot drains. In laying out these areas it is best to commence at the upper end of a lateral and work down to a junction. Then start again at the upper end of another lateral entering this junction, and continue thus until the map has been covered.

The areas are given the same numbers as the manholes into which they drain. The dividing lines for the drainage areas on Fig. 24 are shown as dot and dash lines, and the areas enclosed are appropriately numbered. If more than one sewer drains into the same manhole the area should be subdivided so that each subdivision encloses only the area contributing through one sewer. Such a condition is shown at manhole C2. The areas are designated by subletters or symbols corresponding to the symbol used for the sewer into which they drain. For example, the two areas contributing to manhole C2 are lettered C2_K and C2_D. The sewer from manhole C3 to C2 receives no addition, it being assumed that all the lots adjacent to it drain into the sewer on the alley. There is therefore no area C2. Likewise there is no area A1_C.

46. Quantity of Sewage.—The remaining work in the computation of the quantity of sewage is best kept in order by a tabulation. Table 19 shows the computations for the sewers discharging from the east into manhole No. 142. The computation should begin at the upper end of a lateral, continue to a junction, and then start again at the upper end of another lateral entering this junction. Each line in the table should be filled in completely from left to right before proceeding with the computations on the next line. In the illustrative solution in Table 19, computations for quantity have not been made between manholes where it was apparent that there would be an insufficient additional quantity to necessitate a change in the size of the pipe.

In making these computations the assumptions of quantity and other factors given below indicate the sort of assumptions 85which must be made, based on such studies as are given in Chapter III. The density of population was taken as 20 persons per acre, the assumption being based on the census and the character of the district. The average sanitary sewage flow was taken as 100 gallons per capita per day. The per cent which the maximum dry weather flow is of the average was taken as M = 500
P^⅕, in which P is the population in thousands. The per cent is not to exceed 500 nor to be less than 150. The rate of infiltration of ground water was assumed as 50,000 gallons per mile of pipe per day.

In the first line of Table 19, the entries in columns (1) to (6) are self-explanatory. There are no entries in columns (7) to (10), as no additional sewage is contributed between manholes 3.5 and 3.4. In column (11), 2250 persons are recorded as the number tributary to manhole No. 3.5 in the district to the north and west. These people contribute an average of 100 gallons per person per day, or a total of 0.346 second foot. This quantity is entered in column (13). The figure in column (14) is obtained from the expression M = 500
P^⅕. Column (15) is .01 of the product of columns (13) and (14). Column (16) is the product of the length of pipe between manholes 3.5 and 3.4, and the ground water unit reduced to cubic feet per second. Column (17) is the sum of column (16), and all of the ground water tributary to manhole 3.5, which is not recorded in the table. Column (18) is the sum of columns (15) and (17).

No new principle is represented in the second and third lines.

In the fourth line the first 10 columns need no further explanation. The (11th) column is the sum of the (10th) column, and the (11th) column in the third line. It represents the total number of persons tributary to manhole 3.4 on lateral No. 8. Column (13) in the fourth line is the sum of column (13) in the third line and the (12th) column in the fourth line, and the (15th) column in the fourth line is the product of the 2 preceding columns in the fourth line. Note that in no case is the figure in column (15) the sum of any previous figures in column (15). With this introduction the student should be able to check the remaining figures in the table, and should compute the quantity of sewage entering manhole No. 142 from the west, making reasonable assumptions for the tributary quantities from beyond the limits of the map.

8847. Surface Profile.—A profile of the surface of the ground along the proposed lines of the sewers should be drawn after the completion of the computations for quantity. An example of a profile is shown in Fig. 26 for the line between manholes No. 3.5 and No. 147. The vertical scale should be at least 10 times the horizontal. A horizontal scale of 1 inch to 200 feet can be used where not much detail is to be shown, but a scale of one 1 to 100 feet is more common and more satisfactory and even one inch to 10 feet has been used. The information to be given and the method of showing it are illustrated on Fig. 26. The profile should show the character of the material to be passed through and the location of underground obstacles which may be encountered. The method of obtaining this information is taken up in Chapter II. The collection of the information should be completed as far as possible previous to design, and borings and other investigations made as soon as the tentative routes for the sewers have been selected.

48. Slope and Diameter of Sewers.—After the quantity of sewage to be carried has been determined, and the profile of the ground surface has been drawn, it is possible to determine the slope and diameter of the sewer. A table such as No. 20 is made up somewhat similar to No. 19, or which may be an extension of Table 19 since the first 6 columns in both tables are the same. The elevation of the surface at the upper and lower manholes is read from the profile.

The depth of the sewer below the ground surface is first determined. Sewers should be sufficiently deep to drain cellars of ordinary depth. In residential districts cellars are seldom more than 5 feet below the ground surface. To this depth must be added the drop necessary for the grade of the house sewer. Six-inch pipe laid on a minimum grade of 1.67 per cent is a common size and slope restriction for house drains or sewers. An additional 12 inches should be allowed for the bends in the pipe and the depth of the pipe under the cellar floor. Where the elevation of the street and lots is about the same, and the street is not over 80 feet in width between property lines, a minimum depth of 8 feet to the invert of sewers, 24 inches or less in diameter is satisfactory. This is on the assumption that the axes of the house drain and the sewer intersect. For larger pipes the depth should be increased so that when the street sewer is flowing full, sewage will not back up into the cellars or for any great distance into the tributary pipes.

89

Fig. 26.—Typical Profile Used in the Design of a Separate Sewer System.

90The grade or slope at which a sewer shall be may be fixed by: the slope of the ground surface; the minimum permissible self-cleansing velocity; a combination of diameter, velocity, and quantity; or the maximum permissible velocity of flow. Sewers are laid either parallel to the ground surface where the slope is sufficient or where possible without coming too near the surface they are laid on a flatter grade to avoid unnecessary excavation. The minimum permissible slope is fixed by the minimum permissible velocity.

The velocity of flow in a sewer should be sufficient to prevent the sedimentation of sludge and light mineral matter. Such a velocity is in the neighborhood of 1 foot per second. Since sewers seldom flow full this velocity should be available under ordinary conditions of dry weather flow. The minimum velocity when full should therefore be about 2 feet per second. Under this condition, the velocity of 1 foot per second is not reached until the sewer is less than 18 per cent full. The velocity in small sewers should be made somewhat faster than in large sewers since the velocity of flow for small depths in small pipes is less than for the same proportionate depth in large pipes. The maximum permissible velocity of flow is fixed at about 10 feet per second in order to avoid excessive erosion of the invert. If the sewer is carefully laid this limit may be exceeded in sanitary sewers.

The method for determining the grade and diameter of sewers is best explained through an illustrative problem which is worked out in Table 20 for the profile shown on Fig. 26. The figures are inserted in the table from left to right in each line, one line being completed before the next one is commenced. The headings in the first 6 columns are self-explanatory. The elevations of the surface at the upper and lower manholes are read from the profile. The total flow is read from column (18) in Table 19. The slope of the ground surface is then computed, and with the quantity, slope, and coefficient of roughness, the diameter of the pipe and the velocity of flow are read from Fig. 15.

The following conditions may arise:

(1) The diameter required is less than 8 inches. Use a diameter of 8 inches as experience has shown that the use of smaller diameters is unsatisfactory.

91(2) The velocity of flow when the sewer is full is less than 2 feet per second. Increase the slope until the velocity when full is 2 feet per second.

(3) The diameter of the pipe required is not one of the commercial sizes shown in Fig. 15. Use the next largest commercial size.

(4) The slope of the ground surface is steeper than necessary to maintain the required minimum velocity and the upper end of the sewer is deeper than the required minimum depth. Place the sewer on the minimum permissible grade, or upon such a grade that its lower end will be at the minimum permissible depth.

(5) The slope of the ground surface is so steep as to make the velocity of flow greater than the maximum rate permissible. Reduce the grade by deepening the sewer at the upper manhole and using a drop manhole at this point.

It is not permissible to use a pipe larger than that called for by the above conditions. This is attempted sometimes in order to reduce the grade and thereby save excavation, under the rule of a minimum velocity of 2 feet per second when full. It is better to use the smaller pipe on the flat grade as the quantity of sewage is insufficient to fill the larger sewer and the minimum permissible velocity is more quickly reached.

Having determined the slope, the diameter, and the capacity of the pipe to be used, these values are entered in the table. The elevations of the invert of the pipe at the upper and lower manholes are next computed and entered in the table. This method is followed until all of the diameters, slopes, and elevations have been determined.

The slopes are computed from center to center of manholes, but an extra allowance of 0.01 of a foot is allowed by some designers for the increased loss in head in passing through the manhole. When it becomes necessary to increase the diameter of the sewer the top of the outgoing sewer is placed at the same elevation or below the top of the lowest incoming sewer. No extra allowance is made to compensate for loss in head in the manhole in this case. This case is illustrated in columns (14) and (15) in lines (16) and (17) of Table 20. All of the conditions listed above are illustrated in Table 20, except the condition for a velocity greater than 10 feet per second.

The first condition is met at the head of practically every lateral, and is illustrated in the second line.

92The second condition is also illustrated in the second line. The slope of the ground surface is 0.0046, which gives a velocity of only 1.8 feet per second in an 8–inch pipe. The slope is therefore increased to 0.00575, on which the full velocity is 2 feet per second.

The third condition is met in the first line. The diameter called for to carry 1.66 cubic feet per second on a slope of 0.0108 is slightly less than 10 inches. A 10–inch pipe is therefore used and its full capacity and velocity are recorded.

The fourth condition is illustrated in the fourteenth line. The cut at manhole No. 3.1 is 11.1 feet. The slope of the ground is 0.014, much steeper than is necessary to maintain the minimum velocity in a 15–inch pipe. The pipe is therefore placed on the minimum permissible slope, and excavation is saved. The student should check the figures in Table 20 and be sure that they are understood before an attempt is made to make a design independently.

49. The Sewer Profile.—The profile is next completed as shown in Fig. 26, the pipe line being drawn in as the computations are made. The cut is recorded to the nearest ⅒th of a foot at each manhole, or change in grade. It should not be given elsewhere as it invites controversy with the contractor. The cut is the difference of the elevation of the invert of the lowest pipe in the trench at the point in question, and the surface of the ground.

The stationing should be shown to the nearest ⅒th of a foot. It should commence at 0 + 00 at the outlet and increase up the sewer. The station of any point on the sewer may show the distance from it to the outlet, or a new system of stationing may be commenced at important junctions or at each junction.

Elevations of the surface of the ground should be shown to the nearest ⅒th of a foot, and the invert elevation to the nearest 1
100th of a foot.

Only the main line sewer is shown in profile in Fig. 26. The profiles of the laterals computed in Table 20, have not been shown. The approximate location of all house inlets are shown on the profile and located exactly, and are made a matter of record during construction.

50. Planning the System.—Storm sewer systems are seldom as extensive as separate or combined sewer systems, since storm sewage can be discharged into the nearest suitable point in a flowing stream or other drainage channel, whereas dry weather or combined sewage must be conducted to some point where its discharge will be inoffensive. The need of a comprehensive general plan of a storm sewer system is quite as great, however, as for a separate system. The haphazard construction of sewers at the points most needed for the moment results in the duplication of forgotten drains, expense in increasing the capacity of inadequate sewers, and difficult construction due to underground structures thoughtlessly located. A comprehensive plan permits the construction of sewers where they are needed as they are required, and enables all probable future needs to be cared for at a minimum of expense.

The same preliminary survey, map, and underground information are necessary for the design of a storm sewer system as for a separate sewer system. The map shown on Fig. 25 has been used for the design of a storm-water sewer system.

The steps in the design of a storm-water sewer system are:

1st. Note the most advantageous points to locate the inlets and lay out the system to drain these inlets. 2nd. Determine the required capacity of the sewers by a study of the run-off from the different drainage areas. 3rd. Draw the profile and compute the diameter and slope of the pipes required.

51. Location of Street Inlets.—The location of storm sewers is determined mainly by the desirable location of the street inlets. The inlets must therefore be located before the system can be planned. In general the inlets should be located so that no water will flow across a street or sidewalk, in order to reach the sewer. This requires that inlets be placed on the high corners at street intersections, in depressions between street intersections, and at sufficiently frequent intervals that the gutters may not be overloaded. City blocks are seldom so long as to necessitate the location of inlets between crossings solely on account of inadequate gutter capacity. The capacity of a gutter can be computed approximately by the application of Kutter’s formula. Inlet capacities are discussed in Chapter VI. When the area drained 94is sufficiently large to tax the capacity of the gutter or inlet, an inlet should be installed regardless of the location of the street intersections.

The street inlets are located on the map as shown in Fig. 25. The sewer lines are then located so as to make the length of pipe to pass near to all inlets a minimum. Storm sewers are seldom placed near the center of a street because of the frequent crowded condition on this line.

52. Drainage Areas.—The outline of a drainage area is drawn so that all water falling within the area outlined will enter the same inlet, and water falling on any point beyond the outline will enter some other inlet. This requires that the outline follow true drainage lines rather than the artificial land divisions used in locating the drainage lines in the design of sanitary sewers. The drainage lines are determined by pavement slopes, location of downspouts, paved or unpaved yards, grading of lawns and the many other features of the natural drainage which are altered by the building up of a city. The location of the drainage lines is fixed as the result of a study of local conditions.

The watershed or drainage lines are shown on Fig. 25 by means of dot and dash lines. A drainage line passes down the middle of each street because the crown of the street throws the water to either side and directs it to different inlets. A watershed line is drawn about 50 feet west of such streets as Kentucky St., Florida St., etc., because the downspouts from the houses on those streets discharge or will discharge into the street on which they face. The location of any watershed line within 20 feet more or less is, in most cases, a matter of judgment rather than exactness. Each area is given an identifying number or mark which is useful only in design. It usually corresponds to the inlet number.

53. Computation of Flood Flow by McMath Formula.—McMath’s Formula is used as an example of the method pursued when an empirical formula is adopted for the computation of run-off, and because of its frequent use in practice. Other formulas may be more satisfactory under favorable conditions.

Computations should be kept in order by a tabulation such as is shown in Table 21, in which the quantity of storm flow discharged from the sewer at the foot of Tennessee St., on Fig. 25, has been computed by means of the McMath Formula, using the constants suggested for St. Louis conditions, i = 2.75, and c = 0.75. The 95solutions of the formula have been made by means of Fig. 11. The column headings in the Table are explanatory of the figures as recorded. The computation should begin at the upper end of a lateral, proceed to the first junction and then return to the head of another lateral tributary to this junction. They should be continued in the same manner until all tributary areas have been covered. Special computations will be necessary for the determination of the maximum quantity of storm water entering each inlet to avoid the flooding of an inlet or gutter. These computations have not been shown as they are so easily made by the application of McMath’s Formula to each area concerned.

The determination of the average slope ratio is a matter of judgment, based on the average natural slope of the surface of the ground and an estimate of the probable future conditions.

54. Computation of Flood Flow by Rational Method.—The rational method for the computation of storm-water run-off is described in Chapter III. An example of its application to storm sewer design is given here for the district shown in Fig. 25.^[34] The computations are shown in Table 21. As in the preceding designs the table has been filled in from left to right and line by line. Computations have started at the upper end of laterals tributary to each junction. The column headed I represents the imperviousness factor in the expression Q = AIR. It is based on judgment guided by the constants given in Chapter III concerning imperviousness. The column headed “Equivalent 100 per cent I acres” is the product of the two preceding columns. It reduces all areas to the same terms so that they can be added for entry in the column headed “Total 100 per cent I acres.” It may be necessary to record the values for this column on several lines where the imperviousnesses of the tributary areas are different. This condition is illustrated in the last line of the table, for the length of sewer nearest the outlet. In the preceding lines the imperviousness recorded represents an average for all the tributary areas.

The time of concentration in minutes is assumed by judgment for the first area. For all subsequent areas it is the sum of the time of concentration for the area or areas tributary to the inlet next above and the time of flow in the sewer from the inlet next above to the inlet in question. For example, in line 2 the time 8.1 minutes is the sum of 7.0 minutes time of concentration to the inlet at the corner of State and North Carolina St., and the time of flow of 1.1 minute in the sewer on State St. from North Carolina St. to South Carolina St. Where two sewers are converging as at the corner of Varennes Road and Tennessee St. the longest time is taken. For example, the time of concentration 97down Varennes Road to Tennessee St. is shown in line 25 as 11.4 + 0.6 = 12.0 minutes. The time to the same point down Tennessee St. is shown in line 21 as 16.2 + 0.3 = 16.5 minutes. This time is therefore used in line 26.

R, the rate of rainfall in inches per hour is determined by Talbot’s formula.

Q, is in cubic feet per second and is the product of the 8th 98and 10th columns. Since the 8th column is the sum of the products of the 5th and the 6th columns for the lines representing tributary areas, then the 11th column is the product of A, I, and R.

S, is the slope on which it is assumed that the sewer will be laid. It is usually assumed as parallel to the ground surface unless the velocity for this slope becomes less than 2 feet per second. In such a case the slope is taken as one which will cause this velocity.

V, the velocity in feet per second, is computed from diagrams for the solution of Kutter’s formula. The length in feet is scaled from the map as the distance between inlets or groups of inlets, and the time is the length in feet divided by the velocity in feet per minute.

Having computed the quantity of flow to be carried in the sewer, the design is completed by drawing the profile and computing the diameters and slopes by the same method as used in the design of separate sewers.

CHAPTER VI APPURTENANCES

55. General.—The appurtenances to a sewerage system are those devices which, in addition to the pipes and conduits, are essential to or are of assistance in the operation of the system. Under this heading are included such structures and devices as: manholes, lampholes, flush-tanks, catch-basins, street inlets, regulators, siphons, junctions, outlets, grease traps, foundations and underdrains.

56. Manholes.—A manhole is an opening constructed in a sewer, of sufficient size to permit a man to gain access to the sewer. Manholes are the most common appurtenances to sewerage systems and are used to permit inspection and the removal of obstructions from the pipes. The details of the Baltimore standard manholes are shown in Fig. 27 and a manhole on a large sewer in Omaha is shown in Fig. 28. The features of these designs which should be noted are the size of the opening and working space, and the strength of the structure. Manhole openings are seldom made less than 20 inches in diameter and openings 24 inches in diameter are preferable. A man can pass through any opening that he can get his hips through provided he can bend his knees and twist his shoulders immediately on passing the hole. For this reason the manhole should widen out rapidly immediately below the opening, as shown in Fig. 27 and 38.

The walls of the manhole may be built either of brick or of concrete. Brick is more commonly used, as the forms necessary for concrete make the work more expensive unless they can be used a number of times. The walls of the manhole should be at least 8 inches thick. Greater thicknesses are used in treacherous soils and for deep manholes, or to exclude moisture. A rough expression for the thickness of the walls of a brick manhole more than 12 feet deep in ordinary firm material is t = d
2 + 2, in which t 100is the thickness in inches and d is the depth in feet. The thickness of brick walls may be changed every 5 to 10 feet or so. Concrete walls may be built thinner than brick walls.

Fig. 27.—Baltimore Standard Manhole Details.

The bottoms of brick manholes are frequently made of concrete as shown in Fig. 27. The floor slopes towards the center and is constructed so that the sewage flows in a half round or U-shaped channel of greater capacity than the tributary sewers. The sides of the channel should be high enough to prevent the overflow of sewage onto the sloping floor, which should have a pitch of about one vertical to 10 or 12 horizontal. In manholes where two or more sewers join at approximately the same level the channels in the bottom should join with smooth easy curves. Where the inlet and outlet pipes are not of the same diameter the tops of the pipes should ordinarily be placed at the same elevation to prevent back flow in the smaller pipes when the larger pipes are flowing full.

The dimensions of the manhole should not be less than 3 feet wide by 4 feet long for a height of at least 4 feet, when built in the form of an ellipse, or 4 feet in diameter when built circular. No standard method for the reduction of the diameter of the manhole near the top is observed, the rate being more or less dependent 101on the depth of the manhole. The use of sloping sides above the frost line is desirable as such a form is more resistant to heaving by frost action.

For sewers up to 48 inches in diameter the manhole is usually centered over the intersection of the pipes and has a special foundation. For larger sewers the manhole walls spring from the walls of the sewer as shown in Fig. 28.

Fig. 28.—Details of a Manhole and a Well Hole.

In the case of a decided drop in the elevation of a sewer, or of a tributary sewer appreciably higher than an outlet in any manhole, the sewage is allowed to drop vertically at the manhole, hence the name drop manhole. The Baltimore standard drop manhole is shown in Fig. 27. A well hole is an unusually deep drop manhole in which the force of the vertical drop of sewage is broken by a series of baffle plates, or by a sump at the bottom of the well hole. Fig. 28 shows a well hole at St. Paul, Minn. The use of drop manholes can be avoided in large sewers by the construction of a flight of steps or flight sewer as shown in Fig. 29, which allows the use of a steep grade and serves to break the velocity of the sewage.

The specifications of the Sanitary District of Chicago, covering the construction of manhole covers and frames are:

All castings shall be of tough, close grained, gray iron, free from blow holes, shrinkage and cold shuts, and sound, smooth, clean and free from blisters and all defects.

102All castings shall be made accurately to dimensions to be furnished and shall be planed where marked or where otherwise necessary to secure perfectly flat and true surfaces. Allowance shall be made in the patterns so that the specified thickness shall not be reduced.

All castings shall be thoroughly cleaned and painted before rusting begins and before leaving the shop with two coats of high grade asphaltum or any other varnish that the Engineer may direct. After the castings have been placed in a satisfactory manner, all foreign adhering substances shall be removed and the castings given one additional coat of asphaltum. No castings shall be accepted the weight of which shall be less than that due to its dimensions by more than 5 per cent.

Fig. 29.—Flight Sewer at Baltimore.

Eng. Record, Vol. 59, p. 161.

Fig. 30.—Baltimore Standard Manhole Frame and Cover.

The weights of frames and covers in use vary from 200 to 600 pounds, the weight of the frame being about 5 times that of the cover. The lightest weights are used where no traffic other than an occasional pedestrian will pass over the manhole. Frames and covers weighing about 400 pounds are commonly used on residential streets, whereas 600 pound frames and covers are desirable in streets on which the traffic is heavy. The frames should be so designed that the pavement will rest firmly against it and wear at the same rate as the surrounding street surface. Experience has shown that vertical sides should be used for the outside of the frame to approach this condition, and that the frame should not be less than 8 inches high. The cover should be roughened in some desirable pattern as shown in Fig. 30. Smooth covers become dangerously slippery. Where the ventilation of 103the sewers is not satisfactory the manhole covers are sometimes perforated. This is undesirable from other points of view as the rising odors and vapors are obnoxious at the surface and the entering dirt and water are detrimental to the operation of the sewer. The stealing and destruction of manhole covers and the unauthorized entering of sewers has occasionally required the locking of the covers to the frame when in place. The locks commonly used consist of a tumbler which falls into place when the manhole is closed, and which can be opened only by a special wrench or hook. Adjustable frames are sometimes used where the street grade is settling, or may be raised in order that the elevation of the top of the cover may be made to conform to that of the street surface, without reconstructing the top of the manhole. One type of adjustable cover is shown in Fig. 31. Manhole covers should be so marked that the sanitary sewer can be distinguished from the storm-water sewer, and both from the telephone conduit, etc.

Fig. 31.—Adjustable Manhole Frame and Cover.

Iron steps are set into the walls of the manhole about 15 inches apart vertically to allow entrance and exit to and from the manhole. Galvanized iron is preferable to unprotected metal as the action of rust is particularly rapid in the moist air of the sewer. 104One type of these manhole steps is shown in Fig. 27. The steps should have a firm grip in the wall as a loose step is a source of danger.

Fig. 32.—Baltimore Standard Lamphole.

57. Lampholes.—A lamphole is an opening from the surface of the ground into a sewer, large enough to permit the lowering of a lantern into the sewer. Lampholes are used in the place of manholes to permit the inspection or the flushing of sewers, and to avoid the expense of a manhole. They are located from 300 to 400 feet from the nearest manhole in such a manner that a lamp lowered in the lamp hole can be seen from the two nearest manholes.

Lampholes should be constructed of 8– to 12–inch tile or cast-iron pipe. The lower section should be a cast-iron T on a firm foundation, but if constructed of tile it should be reinforced with concrete to take up the weight of the shaft. The details of the Baltimore standard lamphole are shown in Fig. 32. Lampholes are not commonly used on sewerage systems on account of their lack of real usefulness and the troubles encountered by breaking of the pipe below the shaft.

58. Street Inlets.—A street inlet is an opening in the gutter through which storm water gains access to the sewer. The types used in different cities vary widely. Details of an inlet in successful use are shown in Fig. 33. The figure shows also a common form of connection to the sewer. A water-seal trap is sometimes used to prevent the escape of odors from the sewer. Care must be taken in design that such traps do not freeze in winter nor dry 105out in summer, although it is not always possible to prevent these contingencies.

Fig. 33.—Details of an Untrapped Street Inlet, without Catch-Basin.

The important features to be observed in the design of a street inlet are: height and length of opening, character of grating, and location. The general location of inlets is discussed in Chapter V. The clear height of opening commonly used is from 5 to 6 inches, with a clear length of 24 to 30 inches or longer. Inlets of this size have given satisfaction on paved streets with moderate slopes, where the drainage area is not greater than 10,000 to 12,000 square feet of pavement. W. W. Horner states:^[35]

The St. Louis type of inlet “old” style was a vertical opening in the curb 8 inches high and 4 feet in length with a horizontal bar making the net opening about 5 inches. It has a broad sill extending under the sidewalk. The “new” style inlet is 4½ feet long with a clear opening of 6 inches and no bar. The sill is done away with and the opening drops down directly from the curb. Tests were made of the capacity of this inlet on pavements on different slopes with sumps of depths varying from 0 to 6 inches in front of the inlet, extending out 3 feet from the gutter, and returning to the elevation of the gutter at a slope of 3 inches to the foot. The results of these tests are shown in Table 22. The capacity of the inlet is expressed as the amount of water entering just before some water begins to lap past. If a large amount of water is allowed to flow past much more water will enter the inlet thus furnishing a factor of safety for large storms. It was noted that by beginning the rise in the pavement about opposite the 106middle of the inlet the capacity of the inlet was increased from 20 to 50 per cent.

Gratings with horizontal bars will admit more water than gratings with vertical bars, but they will also admit more rubbish such as sticks, papers, leaves, etc., which serve to clog the sewers. Vertical barred gratings and gratings in the bottom of the gutter clog more quickly than other types. In the selection of the type of grating to be used a decision must be made as to whether it is more desirable to clean the sewer or catch-basin, or to flood the street as a result of clogged inlets. Where catch-basins are used or the sewers are large, horizontal bars are more satisfactory. The openings between bars should be small enough to prevent the entrance of a horse’s hoof or objects of sufficient size to clog the sewer. Four inches in the clear for vertical openings and 6 inches for horizontal openings are reasonable sizes.

The location of the inlets at the intersection of the two curb lines at a corner results in a lower first cost but on heavily traveled streets this may result in a higher maintenance cost than for other locations because of the concentration of traffic at street corners, hammering the inlet casting out of shape or position. Vehicles making short turns will tend to climb the curb and will intensify the wear upon the inlet. These objections can be overcome by the use of two inlets at each corner, set back far enough from the curb intersection to avoid interference with the cross-walks. This also makes it possible to raise the cross-walks without the use of gutters under them.

The size of the pipe from the inlet to the catch-basin or sewer should be large enough to care for all of the water which may enter 107the inlet. As the capacity of the inlet is seldom known with accuracy and the capacity of the pipe is difficult of determination, it has become customary to use a 10–inch or a 12–inch connecting pipe for each ordinary independent inlet.

59. Catch-basins.—Catch-basins are used to interrupt the velocity of sewage before entering the sewer, causing the deposition of suspended grit and sludge and the detention of floating rubbish which might enter and clog the sewer. A separate catch-basin may be used for each inlet, or to save expense, the pipes from several inlets may discharge into one catch-basin.

Fig. 34.—Catch-basin.

Outlets are not always trapped.

The types in successful use are extremely varied, but the distinguishing feature of all is an outlet located above the floor of the basin. A common form of catch-basin is shown in Fig. 34. It is constructed similar to a manhole with a diameter of about 4 or 4½ feet and a depth of retained water from 3 to 4 feet. Catch-basins of this size will care for the sewage from the inlets at the four corners of a street intersection, each draining a city block. 108In unusual situations it may be necessary to install a larger basin, but too large a catch-basin is less desirable than one which is too small, as the former stinks and the latter is useless. Traps are sometimes used to prevent the escape of odors from the sewer into the street, but odors are often created in the catch-basins themselves. Some engineers arrange the trap so that it can be opened for observation down the sewer as in Fig. 34, thus combining the advantages of a manhole with the catch-basin.

The use of catch-basins is objectionable because: they furnish a breeding place for mosquitoes and other flying insects; the septic action in them produces offensive odors; if on a combined sewer they permit the escape of offensive odors in dry weather when the water seal in the trap has evaporated; and the freezing of the water seal in the trap prevents the entrance of water to the sewer. The sole advantage lies in the prevention of the clogging of the sewers, but this may be sufficient to overbalance all of the disadvantages. In general catch-basins should be provided on paved streets which are cleaned by flushing the material into the sewers, or where the drainage is from an unimproved or macadamized street, sandy country, or into sewers in which the velocity of flow is less than 2 feet per second.

Fig. 35.—Diagrammatic Section through a Grease Trap.

60. Grease Traps.—The presence of grease in sewers results in the formation of incrustations which are difficult to remove and which cause a material loss in the capacity of the sewer. The presence of oil and gasoline has resulted in violent and destructive explosions as is described in Chapter XII. A type of grease trap used on the drains from hotels, restaurants, or other large grease producing industries is shown in Fig. 35. The trap is similar to a catch-basin except that it is too small for a man to enter, and the outlet is necessarily trapped in order to prevent the escape of grease. The details of a gasoline and oil separator approved by the New York City Fire Department are shown in Fig. 36.^[36]

109

Fig. 36.—Gasoline and Oil Separator.

61. Flush-Tanks.—These are devices to hold water used in flushing sewers. They are required only on sanitary and combined sewers. Their use tends to prevent the clogging of sewers laid on flat grades and permits flatter grades in construction than could otherwise be adopted. Flush-tanks may be operated either by hand or automatically. Automatic operation is more common than hand operation. The hand-operated tanks are similar to manholes so arranged that the inlet and outlet sewers can be plugged while the manhole or tank is being filled with water either from a hose or a special service connection. When sufficient water has been accumulated the outlet is opened and the sewer is flushed by the rush of water. A sluice gate, flap valve, or a specially fitted board is sufficient to fit over the mouth of the inlet and outlet during the filling of the tank. Such an arrangement has the advantage of being cheap, simple, and satisfactory, though somewhat crude. In some cases water is run into the tank at the same rate that it is discharged through the open outlet, maintaining a depth of 4 or 5 feet in the tank until the water passing the manhole below runs clean. The volume of water required by this method is large. Flushing water under a relatively high head is sometimes obtained by the use of tank wagons which are quickly emptied into the sewer through a canvas pipe dropped down a manhole. In all such cases if not well constructed the manhole is subject to caving due to the rush of water around the outlet. Precautions should be taken to minimize this danger by limiting the depth of water which may be accumulated. This can be done by constructing an overflow at a height of 4 or 5 feet above the bottom of the manhole, discharging into the sewer through an outside drain.

Automatic flush-tanks are constructed similar to a manhole, but special care should be taken to make them water-tight. The 110apparatus for providing the automatic discharge may operate either with or without moving parts, the latter being preferable as they require less attention and are not so liable to get out of order. An automatic flush-tank of the Miller type is shown in Fig. 37. It is a patented device manufactured by the Pacific Flush Tank Company. The small pipe at the left is a service connection to the water main. Water is allowed to flow continuously into the tank at such a rate as to fill it in the required interval between discharges. The tanks are discharged as nearly once a day as it is practicable to regulate them. The rate of flow into the tank is determined by trial and varies to some extent with the water pressure. The regulator shown in the figure is desirable as the continuous flow through the ordinary cock soon wears it away. Some waters will cause deposits to form in the small passages of the cocks or regulators, thus cutting off the flow.

Fig. 37.—Automatic Flush-Tank.

Pacific Flush Tank Co.

The tank operates as follows: when the water rising in the tank reaches the bottom of the bell, air is trapped in the bell and prevented from escaping through the main trap by the water at A. As the water continues to rise in the tank the air in the bell is compressed, the water level at A is driven down and water trickles from the siphon at C. The height of the water in the tank above the level of the water in the bell is equal at all times to the height of C above the lowering position of A. When A reaches the position of B a small amount of air is released through the short leg of the trap and a corresponding volume of water enters the bell. The head of water above the bell then becomes greater than the head of water in the short leg of the trap, which results in the discharge of all of the air in the long leg of the trap and the rapid discharge of the water in the tank through the siphon. The discharge is continued until the siphonic action is broken by the admission of air when the water level in the tank is lowered 111to the bottom of the bell. The size of the siphons is fixed by the diameter of the leg of the siphon. Table 23 shows the capacity and size of sewers for which the different sizes of siphons are recommended by the manufacturers.^[37]

When flush-tanks are placed at the upper end of laterals provision should be made for inspecting and cleaning the sewer by the construction of a separate manhole, or by combining the features of a manhole and a flush-tank in the same structure. Such a combination is shown in Fig. 38 from a design by Alexander Potter.

Except under unusual conditions flush-tanks are used only on separate sewers. They should be placed at the upper end of laterals in which the velocity of flow when full is less than 2 to 4 feet per second. The capacity of the tank or the volume of the dose is dependent on the diameter and slope of the sewer. The most effective flush is obtained by a volume of water traveling at a high velocity and completely filling the sewer. A large volume allowed to run slowly through the sewer will have but little if any flushing action. Data on the quantity of flushing water needed are given in Table 24.^[38] As the result of a series of experiments conducted by Prof. H. N. Ogden on the flushing of sewers,^[39] the conclusion was reached that the effect of a flush of about 300 gallons in an 8–inch sewer on a grade less than 1 per cent would not be effective beyond 800 to 1,000 feet, but that on steeper grades much smaller quantities of water would produce equally good results.

112

Fig. 38.—Automatic Flush-Tank and Manhole.

Miller-Potter Design. Pacific Flush Tank Co.

113Engineers do not agree upon the advisability of the use of automatic flush-tanks, some believing that they are a needless expense that can be avoided by hand flushing, and others feeling that a flush-tank should be placed at the upper end of every lateral. These diverse opinions are the result of different experiences in different cities.

62. Siphons.—There are two forms of siphons used in sewerage practice, a true siphon and an inverted siphon. A true siphon is a bent tube through which liquid will flow at a pressure less than atmospheric, first upwards and then downwards, entering and leaving at atmospheric pressure. An inverted siphon is a bent tube through which liquid will flow at a pressure greater than atmospheric first downwards and then upwards, entering and leaving at atmospheric pressure.

In sewerage practice the word siphon refers to an inverted siphon unless otherwise qualified. Siphons, both true and inverted, are used in sewerage systems to pass above or below obstacles. True siphons are seldom used as they must be kept constantly filled with liquid.^[40] Accumulated gas must be removed in order to prevent the breaking of the siphon which results in the cessation of flow. By the breaking of a true siphon is meant the stoppage of siphonic action due to the accumulation of air or gas at the peak of the siphon. Since the rate of flow of sewage fluctuates widely it is extremely difficult to control the flow so that a true siphon may be completely filled with liquid at all times.

In the design of inverted siphons care must be taken to prevent sedimentation, and to permit inspection and cleaning. Sedimentation is prevented by maintaining a velocity greater than a fixed minimum, usually taken at about 2 feet per second. This minimum is attained by providing a number of channels. The smallest channel is designed to convey the least expected flow at the minimum velocity. Each of the other channels is made as small as possible, within the limits of economy and simplicity, 114in order that the minimum velocity shall be exceeded quickly after flow has commenced in them. The last channel or channels to be filled are made somewhat larger, because the sewage conveyed in them contains less settleable matter than is contained in the more concentrated dry weather flow. The type of siphon used in New York to pass under the subway is shown in Fig. 39. Note should be taken of the clean-out manhole provided on the 14–inch pipe. The other pipes are large enough for a man to enter and clean.

Fig. 39.—Sewer Siphon under New York Subway.

Eng. News Vol. 76, p. 443.

The computations involved in the design of a siphon are illustrated in the following example, in which it is desired to construct a siphon to pass under the railway cut shown in Fig. 40. The first step is to determine the limiting diameter and slope of the smallest pipe in the siphon. One-sixth of the capacity of the 6–foot approach sewer or 19 cubic feet per second will be assumed as the minimum flow. The diameter of the pipe necessary to carry 19 cubic feet per second at a velocity of 2 feet per second is 42 inches. The hydraulic gradient should have a slope of 0.0005 if the material used has a roughness coefficient of .015. This is the minimum permissible slope of the siphon. The selection of a steeper slope will necessitate the laying of the sewer at a greater depth, and will permit the use of smaller pipes for the siphon. 115The selection of the exact slope must then be based on judgment with the minimum limitation above placed. The slope will be arbitrarily selected as 0.001, the same as that of the approach sewer. The diameter of the dry weather pipe will therefore be 36 inches, with a capacity of 18 second-feet, which is approximately the assumed dry weather flow. The velocity of flow will be 2.5 feet per second. The length of flow along the siphon is 150 feet.

Fig. 40.—Diagram for the Design of an Inverted Siphon.

The next step should be the determination of the elevation at the lower end of the 36–inch pipe. This is done by multiplying the assumed grade by the equivalent length of straight pipe, and subtracting the product from the elevation at the upper end. The length of straight pipe which will give the same loss of head as the siphon is called the equivalent pipe. It is determined as follows:

First, determine the head loss at entrance. This will vary between nothing and one velocity head, dependent on the arrangement at the entrance.^[41] The length of straight pipe which will 116give this same loss can be computed from the expression l = h
S, using for S the assumed slope of the hydraulic gradient.

Second, determine the head loss due to the bends, This is determined from the expression

in which h =

the head loss in the bend;

l =

the length of the bend;

d =

the diameter of the pipe;

v =

the average velocity of flow;

g =

the acceleration due to gravity;

f =

a factor dependent on the radius (R) of the bend and d.

The relation between f, R, and d, for 90° bends is shown as follows:^[42]

After the head loss has been determined, the equivalent length of straight pipe is determined as above.

Third. The equivalent length of pipe will be the sum of the actual length of pipe and the equivalent lengths as found above.

In the problem in hand the head lost at the entrance will be assumed as one-third of a velocity head, or 0.0324 foot. With the assumed slope of 0.001 this is equivalent to 32 feet of pipe. The radius of the bend is about 20 feet and the length for a 45° central angle is about 16 feet. The head loss for this angle will probably be a little more than one-half that for a 90° angle. The expression will therefore be taken as about 0.2V²
2g and for two bends is equivalent to about 40 feet of pipe. The equivalent length of pipe is therefore 150 + 32 + 40 = 222 feet. The elevation at the lower end should therefore be: the elevation at the upper end, 92.07 − 222 × .001 = 91.85.

The diameters of the remaining pipes in the siphon are determined so that the sewage in the approach sewer is backed up as little as is consistent with good judgment before each pipe comes into action. This is done satisfactorily by a method of 117cut and try. Let it be assumed that the siphon will be composed of three pipes: the dry weather pipe taking 18 second-feet, the second pipe taking 28 second-feet, and the third pipe taking the remaining 70 second-feet. The diameters of the two larger pipes on the assumed slope of 0.001 will therefore be 42 inches and 60 inches respectively. Other combinations might be used which would be equally satisfactory. There are many methods by which the sewage can be diverted into the different channels of the siphon. For example, the openings into the different pipes may be placed at the same elevation, and the sewage allowed to enter them in turn through automatically or hand-controlled gates, or in another method of control the openings may be placed at such elevations that when the capacity of one pipe has been exceeded the sewage will flow into the next largest pipe as shown in Fig. 40. The outlets from the different pipes are ordinarily placed at the same elevation, thus leaving each pipe standing full of sewage. Stop planks should be provided at the outlet in order that the pipes may be pumped out for cleaning. The objection to this arrangement is that the larger pipes may operate at a velocity less than 2 feet per second, and they will be standing full of sewage which might become septic. However, as they will take nothing but the storm flow near the top of the sewer no difficulty should be encountered from sedimentation in them, and all are large enough for a man to enter for inspection or cleaning.

Fig. 41.—Coffin Sewer Regulator.

63. Regulators.—Regulators are commonly used to divert the direction of flow of sewage in order to prevent the overcharging of a sewer or to regulate the flow to a treatment plant. Sewer regulators are of two types, those with moving parts and those without moving parts. An example of the moving part type is shown in Fig. 41. In this type as the sewage rises the float closes the gate to the inlet sewer, thus preventing the entrance of sewage under head from the larger sewer. There are many variations in the details of float controlled regulators, but the principle of operation is similar in all. These regulators can be adjusted to fix the maximum rate of flow to a relief channel or sewage treatment plant, or during times of storm to cut off the outlet to the dry weather channel. Another form of the moving part type is shown in Fig. 42.^[43] It has been used extensively by the Milwaukee 118Sewerage Commission. In its operation the dry weather flow is diverted by the dam into the intercepter. It passes under the movable gate on its way to the treatment plant. As the flow increases the dam is overtopped and flood waters are discharged down the storm channel. The movable gate is hung on a pivot placed below center. As the water rises in the intercepter, the pressure against the upper portion of the gate becomes greater than that against the lower portion, and the gate closes. An opening is left at the bottom to allow an amount of sewage equal to the dry weather flow to escape beneath the gate to prevent clogging or sedimentation in the intercepter channel.

Objections to all moving part regulators are their need of attention and liability to become clogged.

Fig. 42.—Moving Part Regulator without Float.

119

Fig. 43.—Leaping Weir at Danville, Illinois.

Fig. 44.—Overflow Weir at San Francisco.

Eng. News, Vol. 73, p. 307.

120

Fig. 45.—Overflow Weir in Action.

Shadow of steel knife edge which forms the lip of the weir can be seen through the falling sewage.

The overflow weir and the leaping weir have no moving parts and are used for the regulation of the flow in sewers. A leaping weir is formed by a gap in the invert of a sewer through which the dry weather flow will fall and over which a portion or all of the storm flow will leap. One form of leaping weir is shown in Fig. 43. An overflow weir is formed by an opening in the side of a sewer high enough to permit the discharge of excess flow into a relief channel. A weir at San Francisco is shown in Fig. 44. A series of tests were run on leaping weirs and overflow weirs in the hydraulic laboratory of the University of Illinois. The type of leaping weir tested was formed by the smooth spigot end of a standard vitrified sewer pipe. The overflow weirs were formed by a steel knife edge in the side of the pipe parallel to its axis as shown in Fig. 45. Tests were made in 18–inch and 24–inch pipes on various slopes from 0.018 to 0.005, for both leaping weirs and overflow weirs. The overflow weirs were varied in length from 16 inches to 42 inches and were placed at various heights from 25 per cent to 50 per cent of the diameter above the invert of the sewer. As the result of the observations the following formulas were developed. For the leaping weir the expressions for the coordinates of the curve of the surfaces of the falling stream, are:

For the outside surface x = 0.53V^⅔ + y

For the inside surface x = 0.30V + y^¾

in which x and y are the coordinates. The origin is in the upper surface of the stream vertically above the end of the invert of the pipe. The ordinate y is measured vertically downwards. V is the velocity of approach in feet per second. These expressions are applicable to any diameter of sewer up to 10 or 15 feet. They should not be used for depths of flow greater than about 14 inches; nor for slopes of more than 25 per 1,000; nor for velocities less than 1 foot per second nor more than 10 feet per second. The expression for the ordinate of the inside curve is not good for less 121than 6 inches nor more than 5 feet. The expression for the ordinate of the outside curve is limited to values between the origin and 5 feet below it.

The expression for the length of an overflow weir of the type shown in Fig. 45, necessary to discharge a given quantity, is in the form,

in which l =

the length of the weir in feet;

V =

the velocity of approach in feet per second;

d =

the diameter of the pipe in feet;

h₁ =

the head of water on the upper end of the weir;

h₂ =

the head of water on the lower end of the weir.

In the design of an overflow weir by this formula the height of the weir above the invert of the sewer and the flow over the weir should be determined arbitrarily. The height should be subtracted from the computed depth of water above the weir to determine the value of h₁. The difference between the flow over the weir and the flow above the weir will represent the rate of flow in the sewer below the weir. The value of h₂ can then be computed as the difference in the depth of flow below the weir and the height of the weir above the invert. The value of V is computed from Kutter’s formula. The length of the weir is determined by substituting these values in the formula.

64. Junctions.—At the junction of two or more sewers the elevation of the inverts should be such that the normal flow lines are at the same elevation in all sewers. The sewers should approach the junction on a steep grade to prevent sewage backing up in one when the other is flowing full. The velocity of flow at the junction should not be decreased and turbulence should be avoided in order to prevent sedimentation and loss of head. The junction should be effected on smooth easy curves with radii at least five times the diameter of the sewer where possible. Curves with short radii cause backing up of sewage thus reducing the capacity of the sewers.

The terms bellmouth or trumpet arch are sometimes applied to the junction of sewers large enough to be entered by a man. In small sewers the Y branches and special junctions are manufactured so that the center lines of the pipes intersect, and the 122junctions of mains and laterals are made in manholes. In the construction of a bellmouth the arch is carried over all the sewers. A manhole should be constructed at these junctions as clogging frequently occurs there, due to swirling and back eddies which cannot be avoided.

65. Outlets.—The outlets to a sewerage system discharging into a swiftly running stream must be protected against wash and floating debris. In a stream or other body of water subject to wide variations in elevation the backing up of the sewage during high water should be avoided. Where tidal flats or low ground about the outlet may be alternately submerged and uncovered the discharge should always be into swiftly running water. In quiescent bodies of water such as lakes and harbors, and in rivers where the dilution is low, and in many other cases, the sewer outlet should be submerged.

Fig. 46.—Tide Gate.

Outlets are protected against wash and the impact of debris by the construction of deep foundations and heavy protecting walls. Although the construction of an outlet in a slow current or a back eddy would avoid danger from wash and debris, the discharge of the sewage into the most rapid current possible aids in the prevention of a local nuisance. A row of batter piles on the upstream or exposed side of the sewer is desirable, or it may be necessary to construct a break-water to prevent the wash of the current from dislodging the pipe. These break-waters are low dams of wood or broken stone, more or less loosely thrown together. The backing up of water into the sewer can be prevented by constructing the sewer above the outlet on a steep grade. Where this is not possible the use of tide gates will be helpful. A tide gate, one form of which is shown in Fig. 46, is a special form of check valve placed on the end of the sewer.

123

Fig. 47.—Sewer Outlet on a Trestle.

Eng. News, Vol. 49, p. 9.

Sewer outlets are sometimes constructed on long trestles in order to reach deep or running water. Such a trestle is shown in Fig. 47. In Boston the outlet sewers are submerged under the harbor and discharge through outlets well out in the tidal currents. The sewage is discharged under pressure and the pumps are operated at some of the stations only at such times as the tidal currents will carry the sewage away from the harbor. It is not always necessary in a combined sewerage system to carry the storm flow to a distant submerged outlet. A double outlet can be constructed as shown in Fig. 48 in which the dry weather flow is carried to the channel in a submerged sewer and the storm 124flow is discharged on the bank.^[44] Cast-iron pipe should be used for submerged outlets as the sewer is subject to disturbance by the currents, anchors, ice, and other causes.

Fig. 48.—Dry Weather and Storm Sewer Outlet at Minneapolis, Minnesota.

Eng. Record, Vol. 63, p. 383.

66. Foundations.—Sewers constructed in firm dry soil require no special foundation to distribute the weight over the supporting medium. In soft materials the lower half of the sewer ring may be spread as shown in Fig. 22, and in rock the pressures on sewer pipes are evenly distributed by a cushion of sand. In wet ground such as quicksand, mud, swamp land, etc., a foundation must be constructed if the water cannot be drained off.

The permissible intensities of pressure on foundations in various classes of material allowed by the building codes in different cities are given in Table 25. These figures are based on the assumption that the material is restrained laterally, which is generally the condition in sewer construction. In the softer materials it becomes necessary to spread the foundations not only to reduce the intensity of pressure, but also to care for the thrust of the sewer arch. The arch thrust may be found by one of the methods of arch analysis, and the haunches spread to care for this, or the sewer invert may be transversally reinforced to assist in caring for this action. Some sewer sections in hard and soft material are shown in Fig. 22 and 23.

On soft foundations such as swamps or for outfalls on the muck bottom of rivers the sewer may be carried on a platform. For small sewers 2–inch planks, 2 to 4 feet longer than the diameter of the pipe are laid across the trench, and the sewer rests directly upon them. For large sewers imposing a heavy concentrated load, a pile foundation should be constructed. The foundation may consist of piles alone, pile bents, or a wooden platform supported on pile bents. The load which can be carried by a pile is determined with accuracy only by driving a test pile and placing a load on it. Where piles do not penetrate to a firm stratum the load they will support can be determined by any one of the various formulas, either theoretical or empirical, which have been devised. Probably the best known of these formulas are the so-called Engineering News formulas one of which is:

in which P =126

the safe load on the pile in pounds. The factor of safety is 6;

W =

the weight of the hammer in pounds;

h =

the fall of the hammer in feet;

S =

the penetration of the pile in inches at the last driving blow. The blow is assumed to be driven on sound wood without rebound of the hammer.

Reference should be made to engineering handbooks for other forms of pile formulas. The accuracy of all of these formulas is not of a high degree.

The piles are driven at about 2 to 4 feet centers, to a depth of from 8 to 20 feet, unless hard bottom is struck at a lesser depth. The butt diameter of the piles used for the smallest sewers is about 6 to 8 inches. If bents are used, 2 or 3 piles are driven in a row across the line of the sewer and are capped with a timber. For brick, block, pipe, and some concrete sewers, a wooden platform must be constructed between the pile bents for the support of the sewer.

67. Underdrains.—The construction of special foundations can sometimes be avoided by laying drains under the sewers, thus removing the water held in the soil. The laying of the underdrains facilitates the construction of the sewer and reduces the amount of ground water entering the sewer. The underdrains usually consist of 6– or 8–inch vitrified tile laid with open joints from 1 to 2 feet below the bottom of the sewer as shown in Fig. 1. If the sewers are large, parallel lines of drains may be laid beneath them. An observation hole should be constructed from the bottom of the manhole to each underdrain. This hole usually consists of a 6– or 8–inch pipe, embedded in concrete, connected to the drain and open at the top. It is too small to permit effective cleaning of the underdrains, which are usually neglected after construction, and which as a result clog and cease to function. Since the principal period of usefulness of the drains is during construction, their stoppage after the work is completed is not serious. The hollow tile used in vitrified block sewers serve as underdrains after construction, but are of little or no assistance to the draining of the trench during construction.

CHAPTER VII PUMPS AND PUMPING STATIONS

68. Need.—In the design of a sewerage system it is occasionally necessary to concentrate the sewage of a low-lying district at some convenient point from which it must be lifted by pumps. In the construction of sewers in flat topography the grade required to cause proper velocity of sewage flow necessitates deep excavation. It is sometimes less expensive to raise the sewage by pumping than to continue the construction of the sewers with deep excavation.

In the operation of a sewage-treatment plant a certain amount of head is necessary. If the sewage is delivered to the plant at a depth too great to make possible the utilization of gravity for the required head, pumps must be installed to lift the sewage. In the construction of large office buildings, business blocks, etc., the sub-basements are frequently constructed below the sewer level. The sewage and other drainage from the low portion of the building must therefore be removed by pumping. Because pumps are often an essential part of a sewerage system, their details should be understood by the engineer who must write the specifications under which they are purchased and installed.

69. Reliability.—If the only outlet from a sewerage system is through a pumping station, the inability of the pumps to handle all of the sewage delivered to them may so back up the sewage as to flood streets and basements, endangering lives and health and destroying property. Such an occurrence should be guarded against by providing sufficient pumping capacity and machinery of the greatest reliability.

70. Equipment.—The equipment of a sewage pumping station, in addition to pumping machinery, may include a grit chamber, a screen, and a receiving well. The grit chamber and screen are necessary to protect the pumps from wear and clogging. Grit chambers are not necessary in sewage devoid of gritty matter, 128such as the average domestic sewage, unless reciprocating pumps are used. Sufficient gritty matter is found in average domestic sewage to have an undesirable effect on reciprocating pumps. Receiving wells are used in small pumping stations where the capacity of the pumps is greater than the average rate of sewage flow. The pumps are then operated intermittently, the pumps standing idle during the time that the receiving well is filling.

Except for a few types of pumps of which the valve openings are unsuitable, any machine capable of pumping water is capable of pumping sewage which has been properly screened. The principles of sewage pumps are then similar to principles of water pumps. The conditions under which these principles are applied differ but slightly in the character of the liquid, and a smaller range of discharge pressures. Pumps with large passages, discharging under low heads are more commonly found among sewage pumps.

Fig. 49.—Calumet Sewage Pumping Station, Chicago, Illinois.

71. The Building.—The pumping station should, if possible, be of pleasing design and should be surrounded by attractive grounds. The Calumet Sewage Pumping Station in Chicago is shown in Fig. 49. Its architecture is pleasing particularly in contrast with its location and immediate surroundings. Such structures tend to remove the popular prejudice from sewerage and to arouse interest in sewerage questions. Service to the 129public is of value. It can be rendered more easily by arousing public interest and cooperation by the erection of attractive structures, than by feeding popular prejudice by the construction of miserable eyesores.

72. Capacity of Pumps.—The capacity of the pumping equipment should be sufficient to care for the maximum quantity of sewage delivered to it, with the largest pumping unit shut down, and the provision of such additional capacity as, in the opinion of the designer, will provide the necessary factor of safety.

Pumps can usually be operated under more or less overload. Power pumps and centrifugal pumps driven by constant speed electric motors have no overload capacity. A power pump or a centrifugal pump may be overloaded up to the maximum horse-power of any variable speed motor or steam engine driving it, provided the pump has been designed to permit it. Direct-acting steam pumps which are designed for proper piston speed and valve action at normal loads, can carry a 50 per cent overload for short periods, although the strain on the pump is great. They will carry a 20 to 25 per cent overload for about eight hours with less vibration and strain. The use of pumps capable of working at an appreciable overload is somewhat of an additional factor of safety, but the overload factor should not be taken into consideration in determining the capacity of the pumping equipment.

The load on a pumping station consists of the quantity of sewage to be pumped and the height it must be lifted. Variations in the quantity are discussed in Chapter III. The head against which the pumps must operate fluctuates with the level in the tributary sewer or pump well, and in the discharge conduit. For a free discharge or discharge into a short force main the greater the rate of sewage flow the smaller the lift, as the depth of flow in the tributary sewer increases more rapidly than that in the discharge conduit. If the discharge is into a large body of water or under other conditions where the discharge head is approximately constant, the fluctuations in total head should not exceed the diameter of the tributary sewer. Such fluctuations are of minor importance in the operation of direct-acting steam pumps, but may be of great importance in the operation of centrifugal pumps, as is brought out in Art. 78.

73. Capacity of Receiving Well.—The use of receiving wells is restricted to small installations which require, in addition to 130the standby unit, only one pump, the capacity of which is equal to the maximum rate of sewage flow. When the receiving well has been pumped dry the pump stops, allowing the well to fill again. Although the use of a large receiving well, or an equalizing reservoir, for a large pumping station would permit the operation of the pumps under more economical conditions, the storage of sewage for the length of time required would not be feasible. The sewage would probably become septic, creating odors and corroding the pumps. The extra cost of the reservoir might not compensate for the saving in the capacity and operation of the pumps.

The capacity of the receiving well should be so designed that the pump when operating will be working at its maximum capacity, and the period of rest during conditions of average rate of flow should be in the neighborhood of 15 to 20 minutes. For example, assume an average rate of flow of 2 cubic feet per second, with a maximum rate of double this amount. The pump should have a capacity of 4 cubic feet per second, and if the receiving well is to be filled in 15 minutes by the average rate of sewage flow its capacity should be 15 × 5 × 60 × 7.5 or 14,000 gallons. Under these circumstances the pump will operate 15 minutes and rest 15 minutes, during average conditions of flow.

74. Types of Pumping Machinery.—The two principal types of pumping machines for lifting sewage are centrifugal pumps and reciprocating pumps. A centrifugal pump is, in general, any pump which raises a liquid by the centrifugal force created by a wheel, called the impeller, revolving in a tight casing, as shown in Fig. 50. A reciprocating pump is one in which there is a periodic reversal of motion of the parts of the pump.

Centrifugal pumps are sometimes classified as volute pumps and turbine pumps. A volute pump is a centrifugal pump with a spiral casing into which the water is discharged from the impeller with the same velocity at all points around the circumference, as shown in Fig. 51. A turbine pump is a centrifugal pump in which the water is discharged from the impeller through guide passages into a collecting chamber, in such a manner as to prevent loss of energy in changing from kinetic head to pressure head. A turbine pump is shown in section in Fig. 51. Centrifugal pumps are sometimes classified as single stage and multi-stage. A centrifugal pump from which the water is discharged at the pressure 131created by a single impeller is called a single-stage pump. If the water in the pump is discharged from one impeller into the suction of another impeller the pump is known as a multi-stage pump. The number of impellers operating at different pressures determines the number of stages of the pump. A three-stage pump is shown in Fig. 52.

Fig. 50.—Section through de Laval Single-Stage, Double Suction Centrifugal Pump.

375

Lubricating ring.

380

Oil hole cap.

383

Oil drain tube.

404

Shaft sleeve lock nut.

440

Driving coupling.

441

Driven coupling.

443

Coupling check nut.

450

Coupling bolt.

451

Coupling bolt nut.

452

Coupling rubber.

453

Coupling rubber steel tube.

500

Pump case.

550

Bearing bracket cap.

551

Bearing.

552

Shaft.

553

Shaft sleeve, right hand thread.

PW

Impeller.

554

Shaft sleeve, left hand thread.

555

Shaft stop collar, inner.

555–1

Shaft stop collar, outer.

556

Guide ring.

560

Packing gland.

563

Bearing.

567R

Impeller protecting ring, right hand thread.

567L

Impeller protecting ring, left hand thread.

583

Pump case protecting ring.

567

Labyrinth packing.

583

Labyrinth packing.

600

Pump case cover.

692

Impeller key.

815

Bearing bracket, outer.

815–1

Bearing bracket, inner.

132

Fig. 51.—Types of Centrifugal Pumps.

Fig. 52.—Section of a Multi-Stage Centrifugal Pump.

Courtesy DeLaval Steam Turbine Co.

Reciprocating pumps are generally driven by steam and are either direct-acting, or of the crank-and-fly-wheel type. Power pumps are reciprocating machines which may be driven by any form of motor, to which they are connected by belt, chain or shaft. A Deming triplex power pump is shown in Fig. 53. Power pumps can be used only where the character of the sewage will not clog the valves nor corrode the pump. A direct-acting steam pump is one in which the steam and water cylinders are in the same straight line and the steam is used at full boiler pressure throughout the full length of the stroke. The crank-and-fly-wheel type of pumping engine permits the use of steam expansively during a part of the stroke, the energy stored in the flywheel carrying the machine through the remainder of the stroke. Reciprocating pumps are sometimes classified as plunger pumps and piston pumps. In the action of a plunger pump the water is expelled from the water cylinder, by the action of a plunger 133which only partly fills the water cylinder, as shown in Figs. 54 and 55. In a piston pump the water is expelled from the water cylinder by the action of a piston which completely fills the water cylinder, as shown in Fig. 63, which illustrates a direct-acting piston pump.

Fig. 53.—Triplex Power Pump.

Courtesy, The Deming Co.

Plungers are better than pistons for pumping sewage as the wear between the pistons and the inside face of the cylinder soon reduces the efficiency of the pump. Outside packed plungers are better than the inside packed type because the packing can be taken up without stopping the pump and the leakage from the pump is visible at all times. Outside packed pumps are more expensive in first cost, but are easier to maintain and have a longer life than piston pumps.

Fig. 54.—Water End of Inside Center-Packed Plunger Pump.

In selecting a pump to perform certain work the size of the water cylinder and the speed of the travel of the piston should be investigated to insure proper capacity. The average linear travel of the piston for slow speed pumps is estimated at about 100 feet per minute, dependent on the length of stroke and the valve area. For short strokes and small valve areas the speed may be as low as 40 feet per minute, and for long stroke fire pumps with large valves the piston can be operated at a speed of 200 feet per minute.^[45] Vertical, triple-expansion, crank-and-fly-wheel, outside packed plunger pumps with flap valves can be operated at speeds of 200 feet per minute when lifting sewage, and when equipped 134with mechanically operated valves and lifting water they can be run at speeds of 400 to 500 feet per minute. The speed of travel multiplied by the volume of piston or plunger displacement, with proper allowance for slippage, will give the capacity of the pump. The slippage allowance may be from 3 to 8 per cent for the best pumps, and for pumps in poor conditions it may be a high as 30 to 40 per cent.

Fig. 55—Water End of Outside Center-Packed Plunger Pump.

Courtesy Allis-Chalmers Co.

There are two types of ejector pumps used for lifting sewage. One of these depends on the vacuum created by the velocity of a stream of water or steam passing through a small nozzle. The operation of this pump is described in Art. 139 and it is illustrated in Fig. 97. The other type of ejector pump is known as the compressed-air ejector. It is operated by means of compressed air which is turned into a receptacle containing sewage. The details of this type are explained in Art. 83 and are illustrated in Fig. 68.

13575. Sizes and Description of Pumps.—The size of a centrifugal pump is expressed as the diameter of the discharge pipe in inches. It has nothing to do with the head for which the pump is suited. On the assumption of a velocity of flow of 10 feet per second through the discharge pipe the capacity of the pump can be approximated.

The size of a reciprocating pump involves the expression of the diameters of the steam cylinders, the water cylinder, and the length of the stroke in inches, in the order named, beginning with the steam cylinder with the highest pressure. A complete description of a steam pumping engine might be; compound, duplex, horizontal, condensing, crank-and-fly-wheel, outside-center-packed, 12″ × 24″ × 18″ × 24″ pump. The word compound means that there are a high-pressure and a low-pressure steam cylinder; the word duplex means that there are two of each of these cylinders; the word horizontal means that the axes of these cylinders are in a horizontal plane; the word condensing means that the steam is discharged from the low-pressure cylinders into a condenser; the name crank-and-fly-wheel is self-explanatory; the name outside-center-packed means that the water cylinder is divided into two portions between which the plunger is exposed to the atmosphere, and that the packing rings are on the outside of the two portions of the cylinder as shown in Fig. 55; the figures shown mean that the high-pressure steam cylinder is 12 inches in diameter, the low-pressure 24 inches in diameter, the water cylinder is 18 inches in diameter, and the stroke of the pump is 24 inches.

76. Definitions of Duty and Efficiency.—The duty of a pump is the number of foot-pounds of work done by the pump per million B.T.U., per thousand pounds of steam, or per hundred pounds of coal, consumed in performing the work. These units are only approximately equal as 100 pounds of coal or 1,000 pounds of steam do not always contain the same number of B.T.U. and may only approximately equal 1,000,000 B.T.U.

Since 1,000,000 B.T.U. are equal to 778,000,000 foot-pounds of work, a pump with a duty of 778,000,000 will have an efficiency of 100 per cent. The efficiency of a pump is therefore its duty based on B.T.U. divided by 778,000,000. The efficiencies or duties of various types of pumps are given in Table 26.^[46]

77. Details of Centrifugal Pumps.—A section of a centrifugal pump with the names of the parts marked thereon is shown in Fig. 50. Among the important parts which require the attention of the purchaser are: the impeller (PW), the impeller packing rings (567 R & L), the bearings (551, 563), the thrust bearings (555–1), the shaft (552), and the shaft coupling (440).

The impeller should be of bronze, gun metal, or other alloy, because there is no rusting or roughening of the surface, and the efficiency does not fall with age. Normal fresh sewage is not corrosive, but septic sewage and sludge are usually so corrosive that iron parts cannot be used with success in contact with them. The impeller should be machined and polished to reduce the friction with the liquid. Impellers are made either closed or open, i.e., either with or without plates on the sides connecting the blades to avoid the friction of the liquid against the side of the casing. The closed type of impeller is shown in Fig. 50. Closed impellers are slightly more expensive, but generally give better service and higher efficiencies than the open type. Single impeller pumps should have an inlet on each side of the impeller to aid in balancing the machine, unless the plane of the impeller is to be horizontal when operating. Multi-impeller pumps usually have single inlet openings for each impeller. Vibration in the pump is sometimes caused by an unbalanced impeller. The moving parts may be balanced at one speed and unbalanced at another. To determine if the moving parts are balanced the pump should be run free at different speeds and the amount of vibration observed. If the impeller is removed from the pump its balance when at rest can be studied by resting it on horizontal knife edges. If there is a tendency to rotate in any direction from any position the impeller is not perfectly balanced.

137Packing rings are used to prevent the escape of water from the discharge chamber back into the suction chamber. These rings should be made of the same material as the impeller. Labyrinth type rings, as shown in Fig. 50, are sometimes used as the long tortuous passages are efficient in preventing leakage.

The bearings must be carefully made because of the high speed of the pump. They are usually made of cast iron with babbitt lining. They should be placed on the ends of the shaft on the outside of the pump casing, as shown in Fig. 50, and should be split horizontally so as to be easily renewed. Exterior bearings are oil lubricated by means of ring or chain oilers with deep oil wells. Where interior bearings are necessary, because of the length of the shaft, they should be made of hard brass and should be water lubricated.

Fig. 56.—Marine Type Thrust Bearing.

Courtesy, DeLaval Steam Turbine Co.

Thrust bearings or thrust balancing devices are used to take up the end thrust which occurs in even the best designed pumps. To overcome this pumps are designed with double suction, opposed impellers, or two pumps with their impellers opposed may be placed on the same shaft. Due to inequalities in wear, workmanship or other conditions, end thrust will occur and must be cared for. Various types of thrust bearings are in successful use, such as: the piston, ball, roller or marine types. The marine type thrust bearing is shown in Fig. 56. The piston type of hydraulic balancing device is shown in Fig. 57. In the figure A represents the impeller, and B a piston fixed to the shaft and revolving with it. There is a passage for water through the openings (1), (2), and (3) leading from the impeller chamber to the atmosphere or to the suction of the pump. If the impeller tends to move to the right opening (1) is closed resulting in pressure on 138the right of the impeller forcing it to the left. If the impeller moves to the left (1) is opened thus transmitting pressure to the piston B forcing the impeller to the right. The flange C is not essential, but is advantageous in pumps handling gritty matter. As the channel (2) wears larger the pressure against the piston decreases allowing it to move to the left. This partially closes (3) building up the pressure again.

Fig. 57.—Piston Type of Thrust Balancing Device.

Flexible shaft couplings should be used if the shaft of the driving motor and the pump are in the same line, as direct alignment is difficult to obtain or to maintain. Where connected to steam turbines, reduction gearing and rigid couplings are usually used on sewage pumps to obtain slow speed and permit large passages. Flexible couplings are of various types, one of which is shown in Fig. 50. A rigid coupling would be formed by bolting the flanges firmly together. Shaft couplings are usually not necessary where the pump is driven by belt connection to the engine or motor, or where the pump and pulley rest on only two bearings.

The stuffing box shown in Fig. 50 is packed loosely with two layers of hemp between which is a lantern gland, in order to permit a small amount of leakage. A drip box is placed below this gland to catch the leakage and return it to the pump. The leakage is permitted as it aids in lubrication and the tightening of the gland will cause binding of the shaft. The gland on the suction side of the pump should be connected by a small pipe to the discharge chamber in order to keep a constant supply of water for lubrication and to prevent the entrance of air to the suction end of the pump.

78. Centrifugal Pump Characteristics.—The capacity of a centrifugal pump is fixed by the size and type of its impeller and by the speed of revolution. Roughly, the capacity of a pump, for maximum efficiency, varies directly as the speed of revolution, the discharge pressure varies as the square of the speed, and the power varies as the cube of the speed. These relations are found not to hold exactly in tests because of internal hydraulic friction in the pump.

139The characteristic curves for a centrifugal pump, or the so-called pump characteristics, are represented graphically by the relation between quantity and efficiency, quantity and power necessary to drive, and quantity and head, all at the same speed. The quantities are plotted as abscissas in every case. The curve whose ordinates are head and whose abscissas are quantities is known as “the characteristic.” The curve showing the relation between quantities and speeds is sometimes included among the characteristics. Characteristics of pumps with different styles of impellers are shown in Fig. 58. Fig. 59 shows the characteristics of a pump run at different speeds, the efficiencies at these speeds when pumping at different rates, and the maximum efficiency at different speeds. It is to be noted that the information given in this figure is more extensive than that in Fig. 58. The operating conditions under any head, rate of discharge, and speed are given. The curves of constant speed are parallel, and their distances apart vary as the square of the speed. The line of maximum efficiency is approximately a parabola.

Fig. 58.—Characteristics of Centrifugal Pumps with Different Styles of Impellers at Constant Speed.

A study of the characteristics of any particular pump should be made with a view to its selection for the load and conditions under which it is to be used. Among the important things to be considered in the selection of a centrifugal pump for the expected conditions of load are: the capacity required, the maximum and minimum total head to be pumped against, the maximum variations in suction and discharge heads, and the nature of the drive. For example, the pump, whose characteristics are shown in Fig. 14059, should be operated at about 800 revolutions per minute. Under total heads between 40 and 50 feet, the discharge for the best efficiency will vary between 600 and 670 gallons per minute.

Fig. 59.—Efficiency and Characteristic Curves of a Centrifugal Pump at Different Speeds.

Fig. 60.—Efficiencies of Centrifugal Pumps.

The efficiencies of centrifugal pumps increase with their capacities as is shown approximately in Fig. 60.

79. Setting of Centrifugal Pumps.—In setting a centrifugal pump, care should be taken to provide a firm foundation to hold the shafts of the pump and the electric motor or the reduction gearing in good alignment, or to prevent the pump from being displaced by the pull of a belt. It is desirable that the foundation be level. Centrifugal pumps should be set submerged for small pumping stations automatically controlled. Sludge pumps must be set submerged as otherwise they will not prime successfully. Provision should be 141made by which the pump can be lifted from the sewage, or sludge, for inspection and repair. In many cases the pump can be made self-priming by setting it in a dry, water-tight vault below the low level of sewage flow. Where possible it is desirable not to set the pump submerged as it will receive better care when easily accessible.

Fig. 61.—Centrifugal Pump in Manhole at Duluth, Minn.

Eng. Contracting, Vol. 43, 1915, p. 310.

The suction pipe should be free from vertical bends where air might collect and should be straight for at least 18 to 24 inches from the pump casing. An elbow on the suction pipe, attached directly to the casing of the pump gives a lower efficiency than a suction pipe with a short straight run. Centrifugal pumps will operate with as high a suction lift as reciprocating pumps, but at the start they must be primed and some provision must be made for priming them. The suction pipe should be equipped with foot valves to hold the priming, or some method may be provided for exhausting the air from the suction pipe. The foot valves should be so installed as to form no appreciable obstruction to the flow of water. They should have an area of opening at least 50 per cent greater than the cross-section of the suction pipe. A strainer on the suction pipe is undesirable as it becomes clogged and is usually in an inaccessible position for cleaning. A screen should be placed at the entrance to the suction well to prevent the entrance of objects that are likely to clog the pump. A gate-valve and a check-valve should be provided on the discharge pipe, the former to assist in controlling the rate of discharge and the latter to prevent back flow into the pump when it is not operating.

Centrifugal pumps are well adapted to service in either large or small units. An installation in a manhole at Park Point, Duluth, is shown in Fig. 61. This station is controlled by an automatic electric device which is operated by a float in the suction 142pit. Such automatic control is an added advantage of the use of electrically driven centrifugal pumps. The Calumet Pumping Station in Chicago, shown in Fig. 49, has a capacity of approximately 1,000 cubic feet per second. The simplicity of the layout of this station is shown in Fig. 62.

Fig. 62.—Interior Arrangement of the Calumet Sewage Pumping Station, Chicago.

Eng. News-Record, Vol. 85, 1920, p. 872.

80. Steam Pumps and Pumping Engines.—The direct-acting steam pump, one type of which is shown in Fig. 63, is adapted to pumping sewage the character of which will not corrode or clog the valves. In this form of pump it is necessary to utilize the steam at full pressure throughout the entire length of the stroke, which results in high steam consumption. A flywheel permits the use of steam expansively during a part of the stroke, thus increasing the economy of operation. Other devices used for the same purpose are known as compensators. They are not in general use.

Steam engines are classified in many different ways, for example; according to the type of valve gear, as, plain slide valve, Corliss, Lentz, etc.; or according to the number of steam expansions, 143as, simple, compound, triple-expansion, etc.; or according to the efficiency of the machine as low duty or high duty; or as

Fig. 63.—Section of Duplex Piston Steam Pump.

Courtesy, The John H. McGowan Co.

2

Steam cylinder and housing combined.

8

Steam piston head.

9

Steam piston follower.

10

Steam piston inside ring.

11

Steam piston outside ring (2).

12

Steam cylinder head.

14

Steam chest.

16

Steam chest cover.

17

Steam slide valve.

18

Steam valve rod.

20

Steam valve rod, pin and nut.

22

Steam valve rod, collar and set screw.

23

Steam valve rod, stuffing box.

24

Steam valve rod, stuffing box, nut and gland.

38

Piston rod.

47

Piston rod stuffing box.

48

Piston rod, stuffing box, nut and gland.

49

Valve gear stand.

51

Long valve crank and shaft.

52

Short valve crank and shaft.

115

Pump body.

127

Brass liner.

129

Water piston head.

130

Water piston follower.

137

Cylinder head.

139

Valve plate.

140

Cap.

152

Suction flange.

161

Discharge flange.

162

Valve seat, suction or discharge.

163

Valve, suction or discharge.

164

Suction valve spring.

167

Discharge valve spring.

168

Valve plate, suction or discharge.

169

Valve stem, suction or discharge.

55

Crank pin.

56

Valve rod link.

61

Long rocker arm.

62

Short rocker arm.

63

Rocker arm wiper.

69

Cross head.

condensing or non-condensing, etc. Throttling engines or automatic engines refer to the method of control of the steam by the governor. In throttling engines the governor controls the amount 144of opening of the throttle valve, in automatic engines the governor controls the position of the cut-off.

The simple slide valve, low-duty, non-condensing, throttling engine, is the lowest in first cost and the most expensive in the consumption of fuel. The triple-expansion Corliss, or the non-releasing Corliss, high-duty pumping engine is the most expensive in first cost but consumes less steam for the power delivered than any other form of reciprocating engine. For pumps of very small capacity the cost of fuel is not so important an item as the first cost of the machine. For this reason and because of the lower cost of attendance low-duty pumps are more frequently found in small pumping stations.

Fig. 64.—Diagram Showing Rates of Steam Consumption for Different Size Units under Different Loads.

146The steam consumption per indicated horse-power, better known as the water rate of the engine, for various types of engines at full and at part load is shown in Fig. 64. The steam consumption of other types at full load is shown in Table 27. The indicated horse-power (I.H.P.) of a steam engine is the product of the mean effective pressure (M.E.P.), the area of the steam pistons, the length of the stroke, and the number of strokes per unit of time. A common form of this expression is,