The 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.

(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.

The 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 is 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 solutions 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 down 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 and 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.