CHAPTER IX. 



Losses in a pipe line Hydraulic gradient Losses at Valves Bends Elbows Exit Flow 

 in long pipes Time of discharge through pipe line Equivalent diameter of uniform 

 main Branch mains Multiple supply Bye-pass Distribution of water Pipe line 

 accessories Syphons Inverted Syphons Flow through nozzles Form of nozzle- 

 Maximum discharge of kinetic energy through a nozzle. 



ART. 71. PIPE LINE LOSSES. 



IN constructing a pipe line to connect two reservoirs, or to distribute 

 the discharge from any reservoir, the problem which usually presents 

 itself to the engineer is that of determining the minimum size oJ 

 pipe which, under given conditions of head loss, shall be capable ol 

 discharging a given quantity of water per minute. In the construction 

 of a supply pipe line for a power station, the problem is much the 

 same, and in every case it is first of all necessary to determine the 

 conditions involving loss of head, and the magnitude of these losses. 



Commencing at the supply end of the pipe, we have 



(1) Loss due to friction and eddy formation at the entrance to the 

 pipe. 



(2) Frictional losses in the pipe itself. 



(3) Losses at valves, sluices, etc. 



(4) Losses at all elbows, bends, or deviations from the straight. 



(5) Losses at pipe junctions. 



(6) Losses at sudden enlargements, or contractions in the area of the 

 pipe. 



(7) Loss at exit, due to the rejection of kinetic energy. 



In every case these losses are approximately proportional to the 

 square of the velocity, so that if v be the velocity we may write total loss 

 of head = iH 7 = *V. 



Where a pipe line connects two reservoirs, the difference of head 

 between their free surfaces must then equal F v*, for the pipe to run full 

 with velocity v. 



If in Fig. 110 a horizontal A B be drawn through the upper free 

 surface, and if a series of ordinates be drawn vertically downwards from 

 A B representing on the vertical scale of the drawing the total loss of 

 pressure energy per Ib. from the pipe entrance to the particular point 



