RADIAL FLOW 



81 



the entrance and throat of the pipe. The Venturi meter (Art. 196) 

 depends directly on this principle for its action. 



An interesting phenomenon accompanying radial outward flow is 

 noticed if a plate on which 

 a jet is impinging normally 

 be brought gradually nearer 

 to the orifice, until a point 

 is reached where the escap- 

 ing stream touches both 

 plate and nozzle (Fig. 38). 



Let ?'i, pi, vi t ai t be the 

 radius, pressure, velocity, 

 and area of the issuing 

 stream at the exit from the 

 orifice and at the commence- 

 ment of its flow between 

 the plate and the nozzle. 



Let r , po, VQ, and a Q represent similar quantities at the point of escape 

 of the stream into the atmosphere. 



Then 



= 2 TT TI t, where t = thickness of the escaping stream. 



= 2 7T TO t. 



FIG. 38. 



p Q = atmospheric pressure. 

 Neglecting frictional and eddy losses between (1) and (0), we have 



-.a 



W 



v i ^ 2 " I u an _ i X" i ^i * i 



!l~(/~W*~2ci~~W^' 1 rg'r' a 



IF 



mv 



"W 



(1) 



Since i\ is less than r , p Q pi is positive, 

 and the pressure at (1) is less than atmospheric. 

 It follows that since the pressure between (l) 

 and (0) is everywhere less than atmospheric, 

 while that on the corresponding portion of the 

 outer face of the plate is atmospheric, there 

 will be a resultant force tending to force the 

 plate up to the orifice. 



When the distance * becomes very small, 

 the pressure over the area wi 2 approximates to the static head and the 



H.A. Q 



Fir 39 



