Vortex Theory for Bodtes Moving tn Water 
given by 
Let p be the pressure. The Euler equation in the system S can be 
written in the form : 
1 — R —>— = = 
ie AW = = = = 9/ 5 A = 
ae ee wade CE eee et 
av 
Re => = i, 
= + @ AV_ + V(—v = 
ke R R ( a) 
<n ee ee lee 1 Ee 
- — - es ay el 
nae se a AV, Ma et oi ey 
where r is the distance from the axis a 
We suppose that F = A and put 
iS echo: is 39h Splegio =pW (4. 2) 
d s 
Ps and pg are the hydrostatic pressure and the hydrodynamic pres- 
sure respectively. Equation (4.1) becomes 
1 av a ae 1 a2 lds hist? 
eet AOR Pies oy . a ih tc tah 
ma a a Ble AOE, Deg ae J Bon co eta) 
FREE AND BOUND VORTICES 
From the Euler equation in the system S' of axes, namely : 
nie ee cine, 9 KO 
1203 
