SMALL ORIFICES 



109 



possible the centre of the jet. Draw a smooth curve through the points, 

 and draw the horizontal OX through (Fig. 56). Taking any point on 

 the curve we get, if v is the velocity of efflux, measuring horizontal 

 distances from the vena contracta, 



x = v t ; y = - // 



But 



If the issuing jet make an angle a with the horizontal, then, the origin 

 of co-ordinates being taken at the vena contracta, 



1 



x = v'cos a . t; y = g t - 



a 



sin a t. 

 Since v sin a t = x tan a, on substituting for t 2 we get : 



y + x tan a = 



- 5 



2 v 2 cos 2 a 



v= ^(y+ 



sec a 



Then (7 t . = v -f- \/ % g h. 

 1, 2/1, are measured, we get 



tan a)* 

 If a is not known, if a second pair of values 



2 (2/1 + *i tan a)' 

 and from these two equations a may be calculated. 



A second method of determining the coefficient of velocity is to allow a 

 jet of water to escape from 

 an orifice in the vertical side 

 of a tank supported on knife 

 edges (Fig. 57), the level of 

 the water in the tank being 

 maintained constant by the 

 influx of a vertical stream. 

 The position of a pointer 

 fixed to the tank is noticed 

 before the orifice is opened, 

 and when the jet is allowed 

 to escape, this pointer is 



brought back to the same mark by means of the weight W, placed at a 

 leverage x. 



