THEOKY OF TURBINE DESIGN 537 



From this it would appear that it is an advantage to make (B as large as 



( tan a ^ 

 possible. But since we have f% = u'z tan a = u% -j tan a <-, the 



I ~tan~ J 



velocity of flow for a given peripheral wheel speed diminishes as ft 

 increases, so that an increase in ft necessitates either a larger and more 

 expensive turbine or a higher peripheral speed. In the latter case fric- 

 tional losses are increased, and in view of these facts it has become usual 

 to make ft = 90 for all medium heads. For very high heads ft may 

 range from 60 to 90, and for very low heads from 90 to 135. 

 In the case where ft = 90 the hydraulic efficiency is given by 



(10a) 



3 ?'3 



Similarly, although the hydraulic efficiency decreases as a increases, yet 

 the volume passing through the turbine, and consequently its horse power, 

 also increases, the maximum power being obtained when the product of Q 

 and 17 is a maximum. It follows that the most satisfactory value of a 

 depends on the purpose for which the turbine is desired. In a high-class 

 turbine, a will be as small as mechanical considerations permit generally 

 between 10 and 15, and the turbine will gain in efficiency at the expense 

 of a higher prime cost. Where a cheap turbine is required a may have 

 any value up to about 35. 



The volume of water passing through the turbine per second is given by 

 Q = 2 TT r 2 &2/2 = 2 TT 7*2 &2 ^2 tan a cubic feet, 1 and when the turbine is 

 working under conditions of maximum efficiency this becomes 



2+ (^ 

 V b B r 3 



Q = 2 TT r a & 2 tan o\ / I . / fc, ra , \2 _ tan a 



tan ft 



so that both the velocity of the turbine for maximum efficiency and the 

 volume of water passed through the wheel vary as V H'. 



1 This assumes that the passages run full, and neglects the effect of the thickness of the 

 vanes. The latter factor may readily be allowed for, and is considered later (Art. 144). The 

 construction of the vanes may, however (p. 543), cause some contraction of the stream as 

 indicated in Fig. 257 c, in which case the actual area over which flow takes place is less than 

 that of the passages. We then get 



= It x 2 TT r 2 &2/a = '' x 2 TT r 2 ^2 w? 2 tan o cubic feet, 

 where 7t equals the coefficient of discharge of the passages. This, which includes both the 

 coefficient of velocity and of contraction, is usually taken as about -95 and must be 

 introduced in the application of these formulas to any specific example. 



