370 HYDRAULICS AND ITS APPLICATIONS 



Then the initial momentum per sec. in ) _ W A r 2 

 direction of jet J y 



Final momentum per sec. in this direction = - - . cos a 

 .'. Change of momentum per sec. = ) W A v 2 ^ 



, . ,*. ,. ,. f = - - (1 COS a) Ibs. 



pressure on suriace in this direction ) // 



This is a maximum when cos a is a minimum, i.e., when a = 180, as 

 in the case in a hemispherical cup. 



2 W A v 2 .. 

 Here the pressure - - Ibs. 



AET. 105. ACTUAL FORCE or IMPACT. 



In practice, with flat or recurved vanes, the pressure actually obtained 

 is always slightly less than that given by the above formulae. With 

 normal incidence on a flat plane, as previously explained, the discharging 

 stream is always slightly inclined to the plane and possesses some 

 undestroyed momentum in that direction. This, too, however large the 

 plane (within practical limits). If the plane is too small so that the 

 direction of the whole mass of water has not been completely changed 

 before discharge, a further loss will occur." To obviate this the diameter 

 of plate should be not less than three times the diameter of the jet. 



In the case of a curved vane or of a plane with oblique impact, any 

 change in the velocity of discharge affects the change of momentum and 

 hence the force of impact. In every case the final velocity is reduced by 

 surface friction and generally also by loss of energy due to eddy formation 

 in the mass of dead water at the point of impact of an unsteady jet. This 

 latter loss is obviated when the jet strikes the plane tangentially and also 

 when the jet has stream line motion. The total effect depends largely on 

 the size and form of the vanes. Where these are arranged to deflect the 

 jet through less than 90 C the actual should exceed the theoretical pressure, 

 since these losses reduce the final momentum and thus increase the change 

 of momentum. Where the jet is deflected through more than 90 the 

 actual pressure is less than the theoretical, while with normal incidence 

 the velocity of discharge only affects the force of impact in that the effect 

 of surface tension in affecting the angle of discharge, is more marked as 

 this velocity diminishes. This latter effect is, of course, common to every 

 form of vane, but becomes of less importance as the angle of deflection 

 increases or decreases from 90. 



On the whole, the ratio of actual to theoretical pressure may be 

 expected to become less as the angle of deflection is increased from 90 to 



