120 HYDRAULICS AND ITS APPLICATIONS 



ART. 45. VELOCITY OF APPROACH. 



Where the surface area of a vessel is not so large as to allow of the 

 velocity of approach of the water to an orifice being neglected, if the 

 suffixes d) and ( 2 ) refer to the surface and to the vena contracta 

 respectively, we have 



Putting pi = and p% = 0, we have 



*? ~^<, 

 ____+_ 



i?i a 

 = x |- h (h = head over orifice) 



/. v<? = 2 g h + v?. 



Here Vi is the velocity of approach. 



In words, the kinetic energy at efflux is equivalent to the potential 

 energy at the surface, together with the kinetic energy due to the velocity 

 of approach. 



The statical head which would give the same velocity of efflux is now 



= h -}- h'. 

 So that the effect of the velocity of approach in increasing the outflow is 



o 



theoretically the same as that of an additional head h' where h' = ~- m 

 If -, c be the ratio of the vena contracta and surface areas, we have 



A 



... t; a a == 2 g ft + i> a 8 -^ = 2 ^* a 



1 ~"T a 

 i.e., the effective head is increased in the ratio - 



The discharge is therefore increased in the ratio 

 = - g- (approximately). 



