84 SEWER DESIGN 



where c has the values just given, and r is taken at values of 

 1.79 to 2.86 inches per hour. 



In 1887 Robert E. McMath of St. Louis published in the 

 Transactions of the Am. Soc. C.E.* a paper on the necessary 

 size of sewers to discharge the run-off from the excessive rains 

 of St. Louis, and deduced a formula which by actual experience 

 was so framed as to answer every purpose for that city. It 

 was derived by observing, during periods of excessive'rains, the 

 sewers which were overcharged, and plotting them as points 

 on a diagram whose abscissae were the areas drained in acres, 

 and whose ordinates were the calculated capacities of the sewers, 

 computed by Kutter's formula. By drawing a curve that should 

 pass above these points of surcharge and below or among the 

 other plotted points taken from sewers of known capacity, 

 the constants and coefficients for the curve were used as those 

 to represent the run-off to be expected. The equation of the 

 curve taken was. 



Q being the quantity of water reaching the sewer in cubic feet 

 per second, and A the area drained. In symbols it would be 



> 



where c' is the proportion of the rainfall reaching the sewers, 

 after making the proper allowance for evaporation, absorption, 

 and retention. The value taken at St. Louis, probably for the 

 built-up part of the city, was 0.75. The symbol r stands for 

 the number of cubic feet of water falling on an acre per second, 

 or practically the rainfall in inches per hour. It was assumed 

 by Mr. McMath to be 2.75 inches per hour, s is taken as the 

 mean surface-slope in feet per thousand, and in the diagram 

 is made 15. The form of the Burkli-Ziegler formula was taken, 

 and if S be changed to s, whence 5 equals 10005, so that c = 

 c'/iooo, it will be comparable with the others. Mr. McMath 



* Vol. XVI, p. 179- 



