bf'(R) f'(l) being equal to the c of Chézy's formula. From this it follows that c is not a constant for any particular sewer or stream, but varies with both R and S. The principal cause affecting the value of c, however, is the condition as to roughness of the wetted perimeter. If we wish to obtain the velocity of flow in any sewer by this formula it is necessary to select proper values for c, R, and S. S can be readily. obtained by dividing by . The value of c and R and their relation to V will now be discussed. For most of the older formulas give constant values; but since V varies with different materials of channel-walls, whose character does not affect the values of R and S, this variation must be recognized in a variable c by means of a new factor or by a new equation. Most of the efforts looking to greater accuracy have been directed toward determining values for c and thousands of experiments have been made for this purpose. D'Arcy's value, somewhat simplified and for feet measure, is 155256)* c= 12D+ Bazin's value for cut stone and brick-work is c= I .0000133 4.354+ Eytelwein's value is c = 93.4. R The formula evolved from the records of a large number of experiments by Messrs. Ganguillet and Kutter, usually called "Kutter's formula," is now generally held to give results more nearly approximating the actual velocities than any other. This formula is, for English measure, in which n is a "coefficient of roughness" of the sides of the channel, such coefficient having been obtained by averaging many experiments. In the selection of value for n great care and judgment must be exercised, particularly for small sewers, in the calculation for which n has a greater effect than in that for large channels. The values of n are approximately: Sides and bottom of channel lined with well-planed timber. .009 With neat cement, clean glazed sewer-pipe, and very smooth iron pipe.... ΟΙΟ With 1:3 cement mortar or smooth iron pipe......... .OII With unplaned timber and ordinary iron pipe. .012 With smooth brick-work or ordinary pipe sewers....... .013 With ordinary brick-work .015 With rubble or granite-block paving.. .017 Kutter's formula is seen to provide for variations in c due not only to the character of the channel but also to changes in R and S. This formula has been used to calculate the tables Nos. II and 12, n being taken as .013 in the former and .015 in the latter. If it is desired to use another value of n the corresponding values of velocity and discharge can be obtained very approximately by multiplying the quantities given in each table by the factors given below it for that purpose. For ordinary pipe or good brick sewers n may be taken as .013, for ordinary brick or smooth stone as .015. For extra smooth work n may be taken as .011. The uncertainties necessarily existing in the estimates of the amount of sewage to be provided for and the difficulty of selecting just the proper value for n, owing to the nonuniform character of the interior surface of the sewer, make a refinement of calculations out of keeping with the data used. Moreover, in the case of vitrified clay or concrete pipe the TABLE NO. 11. VELOCITY AND DISCHARGE IN SEWERS 4 TO 36 INCHES DIAMETER. Velocity in Feet per Second; Discharge in Cubic Feet per Minute; Sewers Flowing Full. (Formula V = c VRS; c calculated by Kutter's formula, with = .013. Q = 60a V.) 5.75 30.137.99 94.10 10.04 210.3 11.94 390.8 13.73 647.0 16.24 1196.0 18.59 1971.5 I gallon per day = .00009284 cubic feet per minute. TABLE NO. 11.-Continued. VELOCITY AND DISCHARGE IN SEWERS 4 TO 36 INCHES diameter. Velocity in Feet per Second; Discharge in Cubic Feet per Minute, Sewers Flowing Full. (Formula V = c VRS; c calculated by Kutter's formula, with n = .013. Q = 60a V.) 3230 9.63 4085 6.34 830 6.79 1076 7.24 1396 8.48 2497 9.06 .008 5.67 742 6.07 962 6.47 1220 7.58 2233 8.11 2889 8.61 3653 .006 833 5.60 1057 6.57 1934 7.02 2502 7.46 3164 679 4.56 860 5.35 1576 5.72 2040 6.08 2580 782 2.84 1012 3.02 1281 |