Vortex Theory for Bodtes Moving tin Water 
S' is chosen as to coincide with S ata certaintime t,. As 
to is arbitrary, it is possible to express the fluid motion in term of 
the hull geometry. 
The theory of chapter V.A, applies at any time t. The fluid 
velocity ay is defined in the whole space. We have : 
reg, e+ 40, 9 FV (on) af MED , 
V(M', t) = me mes 
Aor SCONCE isa 29) 
= V,,(M', t) if MED. . (6. 1) 
=~ 
In this formula ae is the velocity of the incident flow. We have : 
= mee 
ve = ve, on x and inside an ; (6. 2) 
pe z(t) 
VM', i= cur! =~ (PY) apy fF fff ae (P") 
un) Mie D. 
py i 
with V'(M',t) 0 if M! ee nee =O ems oa (6. 3) 
‘Oh 
a 
z 
— 
- 
glo 
a 
Q 
4 
3 
®(M', t) = ee — _— ad (P'). (6. 4) 
= 
(1) For the sake of simplicity, it will be assumed in this Section and 
also in Section VII either that there exists only one free vortex 
sheet: 
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