144 THE TIME OF EMPTYING A CYLINDER. 



n seconds, through a given orifice, the radius r of the 

 cylinder from (4) is 



t ink Vg 



r = V 7=> ( 5 ) 



V Tr-v/SA 



and if the radius is given, its height h is 



80. The Time of Emptying a Cylinder into a 

 Vacuum. To determine the time in which a cylin- 

 drical vessel will empty itself, through an orifice in 

 the bottom, into a vacuum, when its upper surface is 

 exposed to the pressure of the atmosphere. 



Let h be the height of the vessel, h' the height of a 

 column of liquid which is equal to the weight of the 

 atmosphere ; and x the depth of the orifice below the 

 upper surface of the liquid. Then from (4) of Art. 76, the 

 velocity of discharge is Vfy (x + h'), which in (1) of 

 Art. 79 gives 



_ K r dx__ 



(x + A')* + O 



since when x = h, t = 0. 

 And making x = 0, (1) becomes 



A + A ')t_A*J (2) 



Tc 

 which is the time of emptying the vessel. 



