VELOCITY OF EFFLUX. 139 



that is, the velocities of efflux are as the square roots 

 of the depths. 



COR. 3. The quantity of liquid run out in any time is 

 equal to a cylinder, or prism, whose base is the area of the 

 orifice, and whose altitude is the space described in that 

 time by the velocity acquired in falling through the height 

 of the liquid. 



COR. 4. If any pressure be exerted on the surface of the 

 liquid, the velocity of efflux will be increased. 



Let h be the depth of the orifice below the surface of the 

 liquid, h l the height of the column of liquid which would 

 exert the same pressure as that which is applied at the 

 surface; then the velocity of efflux will be due to the 

 vertical height h + A x ; hence we have from (2) 



v = V2 ff (h + Aj). (4) 



If 7^ be taken equal to the height of a column of water 

 equal to the pressure of the atmosphere (=34 feet), (4) 

 becomes 



v = Vfy (h + 34). (5) 



which is the velocity of efflux ivhen a liquid is pro- 

 jected into a vacuum; the orifice being at a depth h, 

 below the surface of the liquid. 



If Tc be the area of the orifice, then the quantity of liquid 

 Q which flows through the orifice in the unit of time is 



Q = kv = k ^/fyh. (6) 



COR. 5. If a parabola, with a parameter = 2g, be 

 described with its axis vertical, and vertex in the upper 

 surface of the liquid, the velocity of efflux through any 

 small orifices in the side, would be represented by the cor- 

 responding ordinates. 



