FLOW FROM SMALL ORIFICES 



103 



Immediately after passing the orifice, its potential energy is zero, so 

 that if we can determine its pressure energy, its kinetic energy and there- 

 fore its velocity may be inferred. Now on passing the orifice the jet is 

 exposed to atmospheric pressure, and if the pressure is the same through- 

 out its pressure energy is zero. If the jet is parallel this condition is 

 satisfied, 1 but so long as its boundary is curved the centrifugal action of 

 the outer layers necessitates an increase in pressure along the radius of 

 curvature towards the centre of the jet. It follows that in the plane of 

 the orifice, and up to the vena contracta, 

 the pressure in the interior of the jet is 

 greater than that of the atmosphere. 



The distribution of pressure and of 

 velocity across a horizontal diameter in 

 the plane of the orifice is substantially 

 as shown in Fig. 53. With free lateral 

 contraction, the velocity at the centre 

 of the jet varies from "62 to *64 \/2 g 1i, 

 while with lateral contractions sup- 

 pressed this velocity is about '69 V2 g h 

 (Bazin). 



At the vena contracta, however, the 

 pressure across the jet is uniform and atmospheric, 1 the pressure energy 

 at the orifice having been converted into kinetic energy, with a consequent 

 increase in velocity from orifice to vena contracta. 



The pressure energy at the vena contracta then is zero, the potential 



v 2 

 energy is zero, while the kinetic energy is ^ ft. Ibs. per Ib. 



* 9 



Denoting the surface by the suffix d), and the vena contracta by the 

 suffix (o), we have 



FIG. 53. 



where p t = p = ; = ; n = 



_ 



r = V 2 g zi = V 2 g h ft. per sec. 

 i.e., theoretically the velocity of efflux at the vena contracta is the same as 



1 Even in a parallel jet the pressure in the interior will be greater than atmospheric 

 because of the surface tension. The magnitude of this excess pressure, in feet of water, is 



2 T 

 given by k' = -7-777, where T is the surface tension in Ibs. per foot and d is the diameter in feet. 



