208 DISCHARGE DIMINISHING UNIFORMLY. 



But since the discharge is the same for all portions, 



d* d* d* 



n- v = ^-T-VI = w-r-t;. = etc. 

 44 4 



d* cP 



> V *-- =V > etC ' 



Then supposing that / is constant for all the pipes, we 

 have, from (1) and (2), 



which gives the length of the equivalent uniform pipe 

 which would have the same total loss of head, for any given 

 discharge, as the pipe of varying diameter. 



COR. If the lengths of the successive portions are all 

 equal, we have l t = l z = 7 3 = etc., and (3) becomes 



111&. Pipe of Uniform Diameter with Discharge 

 Diminishing Uniformly along its Length. In the 



case of a branch main, the 



water is delivered at nearly Ay | , p ,c B 



equal distances to service i , , ^ 



pipes along the route. Let Fig 59fc 



AB be a main of diameter d 



and length L ; let Q cubic feet per second enter at A, and 



let q cubic feet per foot of its length be delivered to service 



pipes. Then at any point C, I feet from A, the discharge is 



Q = Q ql. Consider a short length dl at P. The loss 



of head in that length is 



