Vortex Theory for Bodtes Moving tn Water 
BEHAVIOR OF THE FREE PART OF A VORTEX SHEET 
Let dE be the set of fluid points belonging to an element 
d a of a vortex sheet. The sheet begins or ends on the surface oe of 
a body moving in the fluid. Its bound part is located between the in- 
terior side pae and the exterior side vee of >) and the relative 
velocity Vp of every fluid set belonging to this bound part is null. 
On the contrary if dE belongs to the free part > 2 ¢ of the vortex 
sheet, it moves with the relative velocity Vp inside the sheet. Let 
De fie Wiese denote the two sides of pat » 1 be the unit vector normal 
to f in the direction from ys fe towards yy fi » and let ¢« be the 
infinitely small thickness of the sheet. The vorticity inside the sheet 
1S) Gete=s Lieqvath 
T ho. ner Nar by Peat 
T, (M) a R (M,) Ve mi) 
Far ay dy oe € —— > € 
MEd). » MM, = ,,.—-iMM-=m,.s , 
Since there is no exchange of matter between the sheet and the adjacent 
fluid sets 
av. 
a> R 
Fale MGR) =? edd, 
+p iy FM). Vv. (M,) s EvaAwe)  Vip(M,) a pe, (4. 5) 
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