Ogt lute 
For the thin bodies being considered, we shall suppose that 
the body boundary condition can be expressed 
ee ae ~ Ub on y= = O.,) for 2.> - ie 
The following 2-D potential function satisfies this body boundary 
condition 
dé b (x, 5) los (y +e : 
x) 
In fact, if we let v and w respectively denote the corresponding 
velocity components in the y and z directions, we find easily that 
-H(x) 
For y= +0, this can be evaluated through use of the Plemelj formula 
0 
=F - .t U df bx(x, ¢ ) 
(v 3 ee Ub (x, z) + on aes 
-H(x) 
Thus, 
7 (capee (ite pecsee Ub (x, yj 
as required, 
The above potential function satisfies the partial differential 
equation and the body boundary condition. To that potential, we can 
add the potential for any other source distribution which induces no 
net normal velocity component on y=0, -H(x) <z <0 . We choose 
to write $(x,y,z) in the following fashion 
1492 
