PIPE FLOW 



263 



etc. I + ^-. 



The last two terms may be written as 

 ^ t { 2 (vi 2 + r 2 2 -f etc. ) 2 (r x t- 2 -f t- 2 ?- 3 -f 

 F 2 ( fL ) I 



-f etc.) 



4/L 

 D 



& 



from which, when 

 determined. 



etc. 



, 6?2, ^3, etc., are known, the value of D may be 

 ART. 76. BRANCH MAINS. 



Where a large main is divided into a number of branches, d lt d 2 , d 3 , etc., 

 of different lengths and dis- 

 charging into reservoirs against 

 different heads, the flow along 

 each of these branches may 

 be determined as follows. Let 

 Fig. 114A represent the arrange- 

 ment diagrammatically, the 

 reservoir A supplying the pipe 

 ft, which in turn supplies the 

 reservoirs B, C, and D through 

 pipes b, c, and d. Let Z A , Z B , 

 Z G , Z D represent the heights 

 above some common datum, 

 of the free surfaces in the respective reservoirs, and let Zj represent 

 the height of the junction J. Let v a , v b , v c , etc., represent the velocities 

 in the various pipes, and let A a , A b , A c , etc., represent their areas. 



Then 



7 . - 7 _i_ ^ _i_ !^ 2 _i_ 77 j wnere A^fj represents the 

 A ~ ^ J W 2 q "*" A J * loss of head from A to J. 



FIG. 114 A. 





Similarly 



W """ 2 g 



Pjf 

 W 





W 



Z + ~ 



(2) 

 (3) 



(4) 



