204 ELBOWS. 



therefore, the velocity of efflux is 



8.025 VT5 



v - _ = -- T=^- = 4.51, 

 A/1 + ft A/4.74 



and consequently the discharge, from (1) of Art. 106, is 

 Q = ^d*v = ^x4x4.51x!2 

 = 170 cubic inches. 



110. Elbows. When pipes are bent so as to form 

 elbows, they present resistances to the motion of water in 

 them ; and these resistances, like many other phenomena of 

 efflux, can be determined only 

 by experiment. If a pipe ACB 

 forms an elbow, the stream sep- 

 arates itself from the inner sur- 

 face of the second branch of the 

 pipe, in consequence of the cen- 

 trifugal force. If the second 

 branch is very short, termi- 



nating, for instance, at ab, the efflux will be smaller than 

 the full cross-section of the pipe. But if the second branch 

 is longer, terminating at B, 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. This diminution of 

 the velocity of efflux must be treated in the same way as 

 the resistance produced by a contraction in the pipe 

 (Art. 109). 



Hence, if a is the cross-section of the pipe, and c is the 

 coefficient of contraction, the section of the stream at D is 

 ca, and the velocity v' of the contracted stream is 



