Figure 120 - Symbol relations for oblique 

 motion of a circular-arc lamina. 



At the edges of the lamina, where z = - c, q ^ oo, in general. The velocity can be made 

 finite at one edge, however, by choosing the ratio F/U so that the bracket in Equation [78i] 

 vanishes at that edge. Then dw/dz = there and the corresponding point on the initial 

 cylinder is a stagnation point. In particular, let 



U e'°- 



ir 



2n{-C-ih) 



[781] 



\ {-c-ihy 



or, since by Equation [78d,e] 



c + ih = a (cos B + i sin 8) = ae'P, 

 r = 47rot/ sin ( a + ft). 



Then, eliminating T between Equations [78i] and [781] and at the very end using 

 Equation [78m], 



[78m] 

 [78n] 



Vz' 



dw 



dz' {z-c){z-ih) 



z-ih 



,-i ia+ ft) 



Thus dv,/dz' a.nd q are now finite at s =- c, although still infinite at 3 = c. Furthermore, both 

 dw/dz' dind z' are continuous functions of s at 2 = - c, so that no discontinuity of the velocity 

 can occur there; the fluid flows smoothly away from the trailing edge along the tangent. 

 With this value of F, Equation [78j] becomes 



2 ^2 (; 

 q = [sin ( a + € ) + sin ( a + ft)h 



[7 80] 



181 



