Untformly Valtd Soluttons of Laplace Equatton 
Figure I The Body shape 
The straight lines ( L, ) and ( Lz, ),edges of the vortex sheet (2), are 
tangent to the planform at points i and j, projections of the points I 
and J belonging to the obstacle. In order to avoid separated flows, the 
rear part of ( A ) from Ito J is assumed to be a sharp edge. The body 
is smooth at any other points. The vector nis a unit outward normal. 
Written under its usual non-dimensional form, the problem to be sol- 
ved for the velocity potential @ (x,y,z, € ) is the Laplace equation : 
Ae =0 
i'.0 e =o on oe) uo. Cue) (Ty 
db ~x at infinity 
It is easily proved in any text-book, that the function @ , may be 
approximated in term of an asymptotic expansion, the first step being 
the undisturbed uniform flow $= x 
}+(x;) yp Zz; ej 4+ eb (x, y, z) tg?) (x,y,z) + ore) (2°) 
At each step, we have to find an harmonic function, vanishing at infi- 
nity, and satisfying some boundary conditions, on both sides ( + and - ) 
of planform S. 
Ag!') . fe) 
-- —« © at infinity 
1741 
