Vortex Theory for Bodtes Moving tn Water 
hypothesis required for its validity. 
The body moves with a constant speed VE in an unbounded, 
inviscid fluid at rest at infinity. One supposes that no separation,oc- 
curs and that no vortex sheet is shed by the body. Let ()> , T ) be 
the vortex sheet which allows the fluid to adhere to the side pate of 
the hull. The vortex filaments & are closed rings on ss - They are 
orthogonal to the relative streamlines @ . Let i. be the unit vector 
tangent toa line Y inthe direction of T, and ig the unit vector 
tangent to a line € in the direction opposite to the relative velocity 
VR . A vortex filament © is defined by the curvilinear abscissa ag 
of its intersection with a line "A, o chosen once for all. The intensity 
dI of the vortex ribbon located between two vortex filaments 
ar (wg ) and oy a( o, + do.) isa constant. One has : 
dT or, A dg =e 6 ) dig: = ¥(o)) age: (8. L) 
The relative velocity is YR wh a Ve . Thus the hydro- 
dynamic force on the part (d>, , |) of the vortex distribution is 
€ 
aF iM at + AF , with 
CL pT (M) a (- V,) ad (M), 
1F. = Prawn ¥ 04) allan 
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