TIME OF EMPTYING ANT VESSEL. 143 



tity of liquid which flows through the orifice in this time 

 must equal Kdx. Hence we have 



k Vfyx dt = Kdx, 



the negative sign being taken, because x decreases as t 

 increases, 



COB. 1. If the vessel be a surface of revolution round a 

 vertical axis, K = ny*, which in (1) gives 



COB. 2. To determine the time of emptying a right 

 cylinder or prism. Here JTis constant, and (1) becomes 



Ji. / dx ~ i \ i ~ 



- = ^- 7 =x* + 

 Vx 



remembering that when t = 0, x = h. 



When x = 0, we have for the time of emptying the 

 whole cylinder, 



(4) 



k V k 



where Q denotes the quantity of liquid in the vessel. 



By comparing this result with that in (1) of Art. 78, it 

 appears that the time necessary for the entire discharge 

 of the liquid when the vessel empties itself is twice as 

 great as that which is required to discharge the same 

 quantity when the vessel is kept constantly full. 



COB. 3. If a cylinder of given altitude empty itself in 



