532 HYDRAULICS AND ITS APPLICATIONS 



down, to which the design must conform if the turbine is to be efficient 

 and these will now be briefly indicated. 

 In the following demonstrations : 



Let to = angular velocity of the wheel in radians per second. 

 r = radius in feet at any point indicated by a suffix, 

 r = velocity of supply stream at its exit from the guide vanes, in 



feet per second. 



u = <o r = velocity of wheel at point indicated by a suffix. 

 f = velocity of flow. 

 ?r = velocity of whirl, 

 a = angle between guide vanes and direction of motion of wheel 



at entrance. 

 /3 = angle between lip of moving vanes and direction of motion of 



wheel. 

 y = angle between discharge edges of moving vanes and direction 



of motion of wheel. 

 Q = flow in cubic feet per second. 

 W = weight of 1 cubic foot of water = 62*4 Ibs. 



ART. 142. GENERAL CASE OF INWARD RADIAL FLOW TURBINE 



(FiG. 255). 



Let the suffix (a) refer to the state of affairs in the supply pipe. 



(!>) refer to the state of affairs in the discharge pipe. 



(1) refer to the state of affairs at the exit from guide 



vanes. 



(2) refer to the state of affairs at the inlet to wheel 



vanes. 



(3) refer to the state of affairs at the exit from whiwl 



vanes. 



Then a consideration of the diagram shows that if the vane angles are 

 proportioned so as to avoid shock at entrance : 



/ 2 = w 2 tan a = (; a w 2 ) tan /?,.'. -j/ 2 = w 2 ^ 1 - j^- 



/a = (% w s ) tan y ; 2 t> = / 2 cosec ft ; 3 v r = / 3 cosec y. 

 The moment of momentum of the \ 



water leaving the guide vanes per ,- = u\ 1\ ft. Ib. units, and since, 



sec. about the axis of rotation J 

 if losses at the exit from the guide vanes are neglected, Wi = w. 2 , while, 



W Q 



neglecting clearance, ?'i = i\, this becomes - ^ w% r 2 ft. Ib. units. 



a 



