Mr. J. L. Woodbridge on Turbines. 321 



Eliminating V in (10) and (11), we have 



v l * + cc*p*-2v l co Pl cos yi = 2 9 \)-^ + ^. . (12) 



Substituting in equation (6), p<2 = l>a + g&h, we have 



Adding (12) and (13), we have 



2ft)V-«V = 2 #(IW i ) +^v 1 top 1 cos 7 1 -ty 2 . (14) 

 From (9) and (14), H being substituted for (§—h), we find 



a 9 2 sin 2 y 3 

 1 a^ sin 2 Yi 



+ A »sin» Yi (^ r 2^ + 2 y H) Vdn^, 



V a 1 2 sm 2 Y 1 a^si^Yx ri " v 



o 2 sm 72 

 v 2 = cop, -*—, — - cos y 1 



1 ri a 1 SUiy l 



+ \/coW -2"W + 2yH + "jl S S S y , » V cos 2 7, ■ • • • (15a) 



2 ^2, 



~ a 2 sin* 72 



Q = GJOj -^— - '- cos 7! 



^ ri o^siny, 



+ a,8in 7> /y/a,V-2^ , + 2^H + ^^»VcoB«7i. - (16) 

 The efficiency will be, from equation (8), 

 E = -gQg = -^[a> 2 /3l 2 --Q) 2 /) 2 2 -p 1 i' 1 cos7 1 + p 2 v 2 cos7 2 ], . . . (17) 



which, substituting the values of i\ and v 2 , gives 



-mlfoooo r a 2 sin 7 2 



oH i Pl " p2 + W I/ 2 ° 0S 72 "" a sin 7 pl C0S 7l J 



«2 sm y 2 

 .% sin 7! 



^cosYx+^V-Z^V + ^H + ^ig^-V^cos 2 ^] }. (18) 

 To find the angular velocity that will give a maximum 

 dco 



efficiency, make -r— =0, in (18). 



