266 HYDRAULICS AND ITS APPLICATIONS 



tion and sizes of pipes are known, the only unknowns are the three 

 velocities v a , v b , r e , and the pressure p j. These equations may then be 

 solved and the unknown factors determined. A similar method of solu- 

 tion will apply to any case of multiple supply, with any number n of 

 sources of supply. Here we shall have n + 2 equations formed, from 

 which the (n -f- 1) velocities and the pressure at the junction may be 

 determined. 



ABT. 78. FLOW ALONG A BYE -PASS. 



If pi and p 2 Ibs. per square foot are the pressures in the main pipe at 



the entrance to and exit from the 

 bye-pass pipe or diversion (Fig. 

 116), we have, putting V and v for 

 the velocities in the large and small 



pipes respectively, 



W 



v 2 

 where K ^ represents the loss in the bye-pass at entrance and exit and 



e/ 



at any valves. 



From this we have, assuming / to have the same value in the two 

 pipes, 



If Q and q are the quantities flowing along the two pipes 



Q = V -^ ,- 



4 4 



<J- V JP- / D l l , K ' 

 " q- vffl -V L \d + K 



K'd 



L 



The proportion of the whole flow which passes along the diversion 



m Q^ ie ^nby 



q = =(Q + q). 



