Vortex Theory for Bodtes Moving tn Water 
Conversely, the equation 
y 
oe = EB (M.) =P mt | i, 42 (M) (4. 13) 
ees 
shows that the fluid sets adjacent to dE exert the force aX, on 
the set dE. 
V. THE STRUCTURE OF THE VORTEX SHEETS GENERATED BY 
A MOVING BODY 
Two cases will be studied in the present Section. 
(i) One free vortex sheet only is shed by the body, 
(ii) Two vortex sheets are shed by the body. 
In the first case the fluid motion is irrotational everywhere 
outside the body, except through the free vortex sheet pa . In the 
second case, if the fluid motion is unsteady, vorticity is necessarily 
distributed in a certain volume downstream from the body. 
A - STEADY MOTION IN THE CASE OF A UNIQUE FREE VORTEX 
SHEET 
_ 
We can define on ba such a vortex -I’ that each of the two 
vortex distributions . 
Gi = 28 5)+(2,2) 6.1) 
Dr = (eS) (LTS .2) 
be complete and that they sum up to the total vortex distribution 
M = i 
rms 24) 135 y 2) 9), 0a) 
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