= {x-£(p)}i + {r-p cos (<t>+6 k -0)}j - {p sin (<|>-6 -6)}k (15) 



where Z is the number of blades 



d£ = {tan 6i+ cos (<J)+6 k -9)j+ sin (<j)+6 -9)k}dp (16) 



which is a line element along the intersections of the 9 = (J) plane and the reference 



surface. 6 is the angle between d£ and the x = constant plane or tan 6 = dx/dr = 9A 



r 



+ Z, (r) . The axial, tangential, and radial components, u , u„ , and u are written as 

 follows 



1 



\ ' i 



d(}>dp 



u m (x,r,0) = 1- J J m (p,40 y\ (x-£) H 



r H 9 L k=1 



1 



u m (x,r,9) = - ^ J J n(p,ti ^^ sin (* +6 k - e ) H d * d P 



: H 9 L k=1 



u m (x,r,0) = -^ J J m(p,(} ) )^ r \ {r-p cos (<))-« fc -e)} H d<t>dp (17) 



^H 9 L k=1 



1 T 



u^(x,r,9) = - -tj. J j G (p,(J>)^y^3 {r sin (^-9)} H d<j)dp 



: H 9 L k=1 



Ijjt f j G s ( P ,(i>) y^3 {p2_pr c ° s ( * +6 k _e)} h d(j)dp (i8) 



a TT^ B (cont.) 



■H ~L k=1 



