SMALL ORIFICES 121 



AKT. 46. 



Time of emptying a Vessel through a small, freely discharging Orifice. 



(1) Suppose the surface area A of the vessel to be uniform and large 

 compared with the area a of the orifice. 



Let v velocity of efflux at any instant, and h the height of free 

 surface above fha vena contracta at the same instant. 

 Now assuming that v = c v +J 2 g h, we have, since 

 velocity of fall of surface __ a c 

 velocity of efflux ~ A' 



velocity of surface = - ^ = C v % 

 (t t A. 



.-. .-a-dt=-Y (2) 



Integrating between any two limits of height hi and Ji% we get the time 

 ti = t, necessary to lower the surface through the distance AI /< 2 . 



t=7T- L 4=Ul 2 -/*2 t ( 3 ) 



If C be the coefficient of discharge for the orifice the time will then be 

 given by 



EXAMPLE. 

 With Borda's mouthpiece running freely 



Time of emptying a Reservoir of varying Cross -section, by small freely 

 discharging Orifice. Here A is no longer constant but will be a function 

 of h, so that equation (1) 



_dh_Ca J-^h 



dt~ A 

 may be integrated if A is an integrable function of h. 



EXAMPLE I. 



Reservoir with uniformly varying cross -sectional Area. Let k D = area 

 of reservoir at the orifice. 



