IMPACT OF JETS 371 



180 and to have its minimum value for the latter angle, while its value 

 may be expected to become more nearly equal to unity as the velocity of 

 impact increases. For let v\ and ?- 2 be the initial and final velocities of 

 the jet relative to the vane. Then neglecting changes of level at impact 

 and losses due to eddy formation, we have, per Ib. of the water, 



2 g ~ Z g 2 g m 



Where/ = coefficient of friction between water and vane. 

 / = length of path of contact of jet in feet. 

 m = hydraulic mean depth of stream in contact with vane 



= thickness of stream, 



and where n is less than 2 for any but very rough surfaces. For such 

 surfaces as are commonly met with forming the vanes of impulse 

 turbines, n may be taken as 1*83 and /as '005. 



Also if i'i v 2 is small, as is usually the case, v may be taken equal to 

 i'i without sensible error 



m 



actual pressure v\ r 2 cos a , 



and since the ratio 77 A . J , where a = angle 



theoretical pressure i'\ v\ cos a 



of deflection 



1 - cos a V f 1 - 



2 W I* 2 " 



this equals ~T~ ~ ( a PP rox i ma tely) 



cos a / f I \ 



= 1 -f - 5 I (approximately) 



1 cos a V 2 m t- 2 ~ n / v 



an expression which diminishes as a (Fig. 166) increases from 90 to 180, 

 and which increases, for values of a between these limits, as v increases. 



EXAMPLE. 



A 1 inch circular jet strikes the bucket of a Pelton wheel with a relative 

 velocity of 50 feet per second. The wetted surface is 20 square inches, 

 the bucket being 4 inches wide and 3 inches broad, so that the escaping 

 streams are each 3 inches wide. The length of path of contact is 

 3-33 inches = '277 feet. 

 7854 



144 , sectional area of iet 



m = - teet = r T - T - = *0109 teet 



6 width ot streams 



005 X '277 '005 X -277 



= 'Uboo 



0109 X 50 17 '" '0109 X 1-945 



B B 2 



