80 



HYDKAULICS AND ITS APPLICATIONS 



p _ _ 



~ 



But from (2)^= c -fj 



W 



= l _ feet f 



,. 



(3) 



_ } 



IF 2 </ ( a; 2 j 



This applies to flow through a converging channel having parallel 

 upper and lower boundaries and to the case of (inward) radial flow 

 towards a centre. The result gives the fall in pressure between two 

 points radially distant x and XQ from the origin, and may be applied to 

 flow in an inward flow radial turbine. Since with outward flow between 

 diverging boundaries the motion is unsteady, Bernoulli's equation ceases 

 to hold, so that the formula is inapplicable to the case of a radial 

 (outward flow) turbine. 1 



In the case of flow through a circular converging pipe or nozzle, 

 A = k x\ 



v = 



and assuming z constant, 



, 

 we have 



AB before 





W 2g{ 1 x*} 201 1 ~ A' 2 )' 



It follows that if a pipe of area A suffer a contraction of section to a, 

 and if p A and p a are the corresponding pressures and V A the velocity at 

 entrance to the pipe 



~W~ a= 20 



=v 



(PA -Pa) 





This enables the velocity of flow and the discharge to be obtained from 

 a measurement of PA ^ P(l , the difference of pressures in feet of water at 



1 Steady motion is, however, possible with radial outward flow without solid boundaries. 

 This is shown when two equal and steady vertical jets impinge directly on each other. Here 

 a circular disc of water with radial outward flow and having perfectly steady stream-line 

 motion, as may be shown by the introduction of colour bands, is produced. 



