OE 



at z - 



(29) 



All other boundary conditions are the same as those described in Equations (2), 

 (4) - (6) c (18) and (20). The solutions in this case have the same forts as 

 Equations (9) and (21), with different O'reen functions. The Green functions can 

 be expressed by application of the method of Images (see Reference 5) as 



c(p,Q) -7 + 7 



(30) 



for the case of bare hull and 



G,(p,q) - Re{ln[x-x + l(z-z )] + In [x-x + i(z+z )]} (31) 



for the case of control plane. The velocity potential due to a unit vortex 

 located at (a,b) should be 



4. 2 (p) - Re{— ln[(x-a) + i(z-b)] - ~ In [(x-a) + i(z+b)]} (32) 



'2* 



2 ii 



To find the velocity potentials for the wall condition, Equations (10), (25) and 

 (26) should be replaced by Equations (30), (32) and (31), respectively. 



