Darrozes 
The arbitrary function d,(s) may be determined only after the resolu- 
tion of the whole problem, the location of P depending upon the Kutta- 
Joukowski condition at the trailing edge. The matching condition is 
fulfilled up till O(€3). 
The following term in the behaviour of the velocity potential at infini- 
ty, given by the matching conditions is : 
o Stee lee 
- Pegi a! pcos 9 + Ee” Loge 2 Ho Hie? 
bse = 
2 
Jag| 2 
3 (e) ~ 2) =A ra) 
3 Log Ot - pcos@ + —— 99 cos —— 
The expansion of $ is then: @ = x(s) +¢¢(s) +e@,te Loge #,+ o(€3) 
ae being a solution of the problem (41), written with the variables 
¥Y and Z 
Azz %, = 0 
= =—2 
¥r= = lo/ Zags jagpmeyo2 is a streamline (41) 
T 
This solution is obtained as before : 
1 5 
4 ~ V2] a5| + iff, 
2 2 
h hi diti h that f, = d =./7— which 
The matching conditions show tha B; fe) an V2 tad! laal whic 
is identically fulfilled. 
We can conclude by writting the composite expansion uniformly valid 
in the vicinity of the round leading edge. There is a shifting correc- 
tion analogous to that found by M. Van Dyke in the 2-dimensional 
case [8 
$= x(s) - Y sin&(s) + nants, Y,Z) + Jel YZ) 
| 4 (42) 
+Rfe ‘ies (1 + e Log €) + sual feats i ee . 
=~Y+iZ 
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