THEORY OF TURBINE DESIGN 551 



cosec a (approx.), while the area of bucket vane circle = & 2 nz #2 cosec |3 

 (approx.). 



At outlet the area of bucket vane circle = 6 3 n% 3 cosec y (approx.), 

 where a, /3, and y, are the angles as calculated when neglecting the blade 

 thickness. 



Thus the outlet area is reduced in the ratio 

 2 IT r a b 3 w 2 3 6 3 cosec y 



/, (true) = /. (approx.) 1 - - } . 



For '/a to be kept the same we must then either have r 



tan y (approx.) 



, or the breadth b 3 must be increased in the same 

 1 ?i 2 3 cosec y 



2 TT r s 

 ratio. 



Similar corrections may be applied at the inlet to the buckets and the 

 outlet from the guides. 



Allowance should be made for the difference in radii between the guide 

 and wheel vane circles, and in order to keep the velocity of flow constant 

 where the water leaves the guides and enters the wheel, the breadth b of 

 the guides may be made slightly different to that of the vanes, so as 

 to keep the area through which radial flow takes place, constant. We 

 then have 



2 TT ?- 2 w 2 2 cosec /3 ) . 



- 

 2 TT ri ui ti cosec a j 



This is only approximate since the passage of the wheel vanes before 

 the guide passages tends to diminish the effective area of the latter, while 

 the effective area of the wheel at inlet is similarly diminished by the 

 presence of the guide vanes. Sufficient data are not available to fix the 

 best number of wheel vanes in any particular case; the greater the 

 number, the more perfect is the guidance given to the water, although 

 at the same time frictional losses are increased. The longer the water 

 passages the fewer the vanes necessary to give sufficient guidance. In 

 the case of a number of modern inward radial flow turbines examined 

 by the author, and of sizes ranging from 3 inches diameter to 66 inches 

 diameter, the number of vanes was given with fair accuracy by the 



relation n = k V d, where d = diameter in inches and where A; is a 

 coefficient varying from about 7*7 in the smaller to 8'4 in the larger 

 wheels and having a mean value = 8. 



