206 



BENDS. 



111. Bends. When the pipes have curved bends, the 

 resistance is much less than in elbows. If a pipe ACB is 

 curved, it also, in consequence of the 

 centrifugal force, causes the stream to 

 separate itself from the concave surface, 

 and to form a partial contraction. If 

 the bend terminates at BD, the cross- 

 section of the stream at its outlet is 

 smaller than that of the pipe. But if 

 the bend is terminated by a long straight 

 pipe BF, an eddy is formed at D, and beyond this the pipe 

 is again filled, so that the velocity of efflux v is less than the 

 velocity at D. 



If c is the coefficient of contraction, the velocity v' of the 

 contracted stream is 



*=1> 



and hence the loss of head in passing from D to F b 



y _ A _ 1 \ 2 ^ 2 



= \c /2a 



(1) 



This is Weisbach's method, but the coefficient of contrac- 

 tion for bends is not very satisfactorily ascertained, 



If r = the radius of the pipe = MH = HC, and p = 

 the radius of curvature = HO, then Weisbach's formula 

 for the coefficient of resistance at a bend in a pipe of circu- 

 lar section is 



|3 = 0.131 + 1-847 (-)*; 



and for bends with rectangular cross-sections, 



|3 = 0.124 + 3.104 (- 



(3) 



