ELBOWS. 205 



and hence the loss of head in passing from D to B is 



The coefficient of contraction c, and therefore the cor- 

 responding coefficient of resistance ft, depends upon the 

 angle of deviation BCE. From experiments with a pipe 1 

 inches in diameter, Weisbach found the coefficient of re- 

 sistance to be 



ft = 0.9457 sin* f + 2.047 sin 4 , (2) 



lil li 



by which he computed a series of coefficients of resistance 

 for different angles of deviation.* From (2) it follows that 

 the kinetic energy of water in pipes is considerably dimin- 

 ished by elbows. If the elbow is right-angled, we have, 

 from (2), |3 = 0.9846, which in (1) gives 



A t =0.9846 I ; 



hence, at a right-angled elbow, very nearly the whole head 

 due to the velocity is lost. 



Sen. If to one elbow ACB another elbow is joined, the 

 second one turning the stream to the same side as the first 

 one, there is no further contraction of the stream, and 

 therefore, for efflux with full cross-section, ft is no larger 

 than for a single elbow. But if the second elbow turns the 

 stream to the opposite side, the contraction is a double one, 

 and the coefficient of resistance is consequently twice as 

 great as for a single elbow. 



* Kncy. Brit., Vol. XII., p. 487. 



