372 



HYDEAULICS AND ITS APPLICATIONS 



.-. r a = ri V 1 -0053 = '967 ri. 

 . , actual pressure _ 1 '967 cos a 

 theoretical pressure ~" 1 cos a 



If a = 160 (cos a = -9397) the ratio becomes '984, a value which 

 would diminish as the velocity diminished. This demonstration has 

 neglected any loss directly due to eddy formation. The actual ratio in 

 the case of a Pelton wheel bucket, where such loss is small, would prob- 

 ably be about '95, and would be less than this in the case of a jet 

 impinging normally at the centre of a hemispherical cup. 



The following are the results of a series of experiments carried out by 

 the author on an apparatus designed by Professor Osborne Reynolds to 

 determine the ratio of actual to theoretical force of impact, under varying 

 conditions. In each case the surface to be acted upon was rigidly fixed 

 to the end of a horizontal lever, which was then accurately balanced. A 

 vertical jet was allowed to impinge from below on this surface, and the 

 flow was adjusted until the force of impact was sufficient to balance a 

 known weight resting on the lever vertically above the axis of the 

 jet, and to cause the lever to float in its equilibrium position. The 

 velocity of impact was measured by measuring the area of the discharge 

 orifice and the weight of water discharged in a given time, and by taking 

 into account the height h (small) between the orifice and the surface. 

 Thus if v = velocity of impact and V Q = velocity at orifice, we have 

 v = V i-Q 1 2 # h. 



The surfaces experimented upon consisted of three flat circular brass 

 plates of diameters respectively "54 inch, T15 inches, and 2'0 inches, 

 each JQ inch thick and having edges perpendicular to the plane of the 

 plate ; a similar flat plate of 2 inches diameter, having its rear face 

 ground down until it formed a knife edge around the discharging 

 periphery ; and a plain hemispherical cup of 1 inch diameter. The 

 diameter of the orifice was accurately '200 inch. 



The results of these experiments are tabulated below. 



(1) Flat Plate "54 in. diameter, -fg in. thick. 



