Brard 
Consequently 
Baas 2 2 
Sia My | v2 (M.) - VQ om) | (4. 11) 
Thus, when the relative motion is steady, T;(M) and VR(M) are 
colinear, and both are in the direction of the bissectrix of the angle 
(VR (Me), VR (Mi)). 
_ 
are no longer equal to each other and therefore the direction of T(M 
is no longer that of the bissectrix. 
If the relative motion is unsteady, bine (M,) | and lvR im) 
Equation (4.10) expresses the dynamical equilibrium of any 
part of a free vortex sheet. 
DEFINITION OF THE FORCE EXERTED BY THE FLOW ON AN 
ELEMENT OF THE BOUND VORTEX SHEET ADHERING TOA 
MOVING BODY 
Let us consider nowa set dE of fluid points belonging to the 
element d ‘ of the bound vortex sheet. 
We have 
V.. @ty-= 0, and —<T (aE) = 0. 
But the expression for : I (dE) does not reduce to [pa(Me) - pa(Mi)| 
0M d)>> , for, because of the adherence of the fluid t yi , a force 
= at y is exerted by the element d ys of the hull surface on dE. 
The equilibrium of dE requires: 
1208 
