PRESSURE IN A ROTATING LIQUID 



95 



A formula connecting the area of the vena contracta with that of the 

 aperture in the diaphragm, in terms of the relative area of pipe and of 

 aperture, is given by Bankine, and is 



C - a * - ' 618 



c a I rt 2 " 



V 1 - -618^ 



Thus when a = A, C c = 1. 



a is very small, C c has the limiting value *618. 



The effect of the portion of the pipe before the orifice is to produce a 

 closer approximation to parallelism of the stream lines, and in conse- 

 quence a vena contracta of larger area is obtained, with a reduced after- 

 enlargement, and hence less loss than where this constraint is absent. 



ART. 37. CHANGE OF PRESSURE ACROSS STREAM LINES. 



If water be moving with stream line motion, these stream lines being 

 curved, the pressure varies from one stream 

 tube to another. This change in pressure 

 may be determined by considering the equilib- 

 rium of an elementary column of fluid of 

 sectional area B a (Fig. 48), having its axis radial, 

 and resting with its two ends in two stream 

 tubes, whose pressures are p and (p + 8 p) 

 respectively. The centrifugal force on the 

 balanced by the difference of 

 two ends and we have, for 



is 



column 



pressure on the 

 equilibrium, 



W 



,, v 2 dp ^ 

 Br . = -j . B r 

 g r d r 



. W ^ - d P 

 r dr 



FIG. 48. 



8a 



ART. 38. VORTEX MOTION. PRESSURE IN A ROTATING LIQUID. 



Where a mass of liquid moves as a whole with vortex motion, this may 

 occur in either of two ways. 



The first is seen when a vessel containing water is rapidly rotated, or 

 when the contained water is stirred so as to make it rotate as a solid 

 body, the velocity increasing with the radius. Such a vortex is termed 

 a Forced Vortex. 



The second is seen when water flows through a hole in the bottom of 



