148 VELOCITY OF EFFLUX. 



Let v be the velocity of efflux ; then the quantity of 

 liquid which flows through the orifice in an element of 

 time is kvdt, and since in the same time the surface K 

 descends a distance equal to dx, we have 



Kdx = kvdt, or -=j = -- ^, (2) 



at XL 



the negative sign being taken because x decreases as t 

 increases ; 



cPx _ k dv 



'* di? ~ ~T~di' 

 which in (1) gives 



k dv _ dp + gpdx 



K dt pdx 



or, 



, , pkdv dx pk z r , ., 



dp + gpdx = -g- -^ = -^ vdv [from (2)]. 



Integrating, we have 



p + gpx = - 





remembering that when x = 0, K = k. 

 Hence, 2gx = v 2 { 1 



which is the velocity of efflux at a, depth x. 



When x = h, or the vessel is full, we have for the velocity 



- 



