252 



HYDRAULICS AND ITS APPLICATIONS 



much in the bend itself as in the portion of straight pipe immediately 

 following, where the equalisation of velocfr'es in the stream of water 

 gives rise to eddy production. Using cast-iron pipes of 3" and 4" diameter, 

 the loss in the bend itself was found to be almost identical with (some- 

 times less than) the loss in a corresponding length of straight pipe. 

 From this point of .view it is probable that the loss occurring with a 

 bend of uniform curvature will be largely independent of the angle 

 through which the bend is taken, and that a bend of say 45 will cause 

 little less resistance than one of 90. Also, as is confirmed by experi- 

 ment, the resistance caused by a reflex bend will be much greater than 



FIG. in. 



that caused by two similar bends having continuous curvature in one 

 direction. 



The first experiments of any note on the resistance of bends are due 

 to Wcisbach, who from experiments on pipes of 1J inches diameter, 

 deduced the formula 



h B = loss of head due to bend = F ^ x 



<9 

 180 



feet, 



is 



where is the angle through which the bend is carried. 



For circular pipes, F has the value '131 + 1'847 (T^) 2 where r i 



the radius of the pipe, and R the radius of the bend. 



(Sf \ J- 

 5~B V 2 where S 



is the length of side of a section parallel to the radius of curvature of the 

 bend. 



These experiments were, however, not numerous and were only carried 



