200 SUDDEN ENLARGEMENT OF SECTION. 



work lost by the water at the abrupt change of velocity 



W 



= C W _ V ')2IL. d\ 



fy 



If h l is the head of water corresponding to this loss of 

 work, we have, for the work lost, 



*. ir =(*-; () 



1 \ / O/y ' ^ / 



and therefore the head lost is 



(<g #')2 



ft> 1 ^ rr * C O I 



</0 



i 



Hence, the head lost at the abrupt change of velocity 

 is measured by the height due to this change of ve- 

 locity. 



Since we have v : v' :: a' : a, 



a' , 



.'. v = v ; 

 a 



substituting this in (3), we have, for the loss of head, 



(a' \ 2 

 l) 5 (5) 

 G/ f 



which is the corresponding coefficient of resistance.* 



(Sen. When the edges are rounded off so as to cause a 

 gradual passage from one pipe into the other, and the dif- 

 ference in the pipes is small, the loss of work as shown by 

 experiment is very small. 



* First found by Borda. (See Weisbach's Mechs., p. 884.) 



