322 Mr. J. L. Woodbridge on Turbines, 



For brevity make 



a 2 sin 7 2 

 n = p a cosy a —^—. — -piCosy 1} .... (19) 



. a 2 sill 7 2 



*=^?>' cos ^ (*>> 



^-V+g^V.W 7l! . . (21) 

 then -7— = will give 



-a).s 2 v / ^ 2 + 2^H=7i 2 o)^+n^H ? . . . (23) 



and this substituted in (18) will give the maximum efficiency 

 for any turbine, and in (16) will give the quantity of water 

 discharged. It would be simpler to find a> numerically for 

 any particular case before making the substitution. 



We will now use these equations to show some errors made 

 by Rankine and Weisbach. Rankine, in his ' Steam-Engine 

 and other Prime Movers,' discusses a special wheel of the 

 Fourneyron type, in which he assumes 



a 2 — a-i and y x = 90°. 



These in equation (15) give 



ri = sin7 2 Vafipf—SaPpf + fyE. . . . (25) 



This velocity is radial along the vane, and is called by 

 Eankine the " velocity of flow." The tangential component 

 of the actual velocity must, in this case, be wp^ and this, by 

 Rankine, is called the velocity of whirl (v) ; and his value of 

 v on page 196, equation (9) of the 'Steam-Engine' is not only 

 incorrect but meaningless, even for the turbine he is con- 

 sidering. 



From equation (15a) we also have 



v 2 = V<*V-2a>V + ^ H - . • • (26) 

 The expression for the efficiency becomes 



E =1tB L^ 1 * "" Wp * + Pi C ° S ya ^ V— 2o) 2 p 1 s + 2gBA . (27) 



