J l 



b(p.q) w'>iy> + i- ^m 0(x ., y ., z .) 



d Y 3x' 



dx'dy 1 



z'=0 



because of the relation of Equation (11) . Integrating by parts twice, the 

 second term with respect to x', yields 



H, 



rrv ^ a<Kx' >y ', z ') , 1 aV(x',y' >Z ') 

 dz Y 3x' 



dx'dy' 



z* = 



c(p.q) 3 ^;;T'- 2,) -*(x',yV)^g^ 



dy' 



z' = 



where L is the intersection of S and £ . If 



3x 



2 r 3z 



z=0 



(14) 



then the velocity potential can be written as 



»(P) = - 



4tt 



g(p >Q ) Jffia _ W) leg^ 



d S, 



^-J [ccp.q, W -♦«> ^ 



dy 



z' = 



" 4 ^ Y J. 



'(x',y') G(P,Q) 



dx'dy' 



z' = 



(15) 



10 



