262 HYDRAULICS AND ITS APPLICATIONS 



Thus the time of filling a reservoir A% from a second reservoir A\, whose 

 level remains constant, i.e., A\ = oo is given by 



TT d 2 



AET. 75. EQUIVALENT DIAMETEB OF AN UNIFORM MAIN. 



The diameter of an uniform pipe which will give the same discharge as 

 that of a pipe of variable diameter when laid between the same points 

 and under the same conditions as to head, may be determined by equating 

 the resistances of the two pipes. 



If 'i, ^a> fo, etc., be the length of portions of the pipe having diameters 

 di t d%, d 3 , etc., and velocities of flow, vi, v%, v a , and if L, D, and V refer 

 to the uniform pipe, we have for the same flow 



+ W + W tc .l (1) 



z g m 2 g \ mi m^ 



-(+++*'} 



The discharge Q in cubic feet per second is given by 



7TJD 2 T/ 77 di* Tld<? 



- - V -4^ ' Vl= ~f~ '' ? ' 2 ' 6tC " 



4 Q 4 O 4O 



.'. V = : vi = : v a = x, etc. 



7T 



So that equation (2) becomes 



.'. D = 



This neglects losses due to the changes of section between the lengths 

 /i, /2, etc., and will only be true when the pipe is so long, and the number 

 of changes of section so small or so gradual as to render this loss sensibly 

 negligible. 



With a pipe which has a large number of sudden enlargements in the 

 direction of flow, we get 



V* ,/LV* _ J_ [ W , kvf , W + ete I 

 2<7^ 2pm '- >lg \ ro, m a m, ' J 



