Vortex Theory for Bodtes Moving in Water 
(6. 9) 
Se Me pS ae ME te eM! 
Let us consider the following three particular cases: 
Casea - Vv. =0,; no free vortex is shed by the body. 
According to (6.7) and (6.9) we obviously obtain 
wim. t) = 4% v(m) u(t). (6. 10), 
Case b - Me = 0; o (t) aad | ae aes (0) = constant ; 
the fluid motion is steady with respect to the body. Hence, the support 
of the free vortex sheet is close to the surface generated by half 
straight lines starting from the curve in the direction of -V 7 (0). 
At P fixed with respect to the body and located on the generatrix 
starting from B, we have 
Bee ee 3 es (6. 10), 
M, and uw, being the values of u in the vicinity of OF on the parts 
oe ? = of > adjacent to each other along FB: To determine 
Mon bm a complementary condition is needed. Since the pressure 
p is necessarily continuous through the free vortex sheet > ¢ this 
condition expresses that p is continuous on > eS through@e : 
EA33 
