The velocity potential satisfies the Laplace equation 



Act) = (2) 



in the fluid region and is subject to certain boundary conditions. (Fluid 

 velocity in the x-direction is given by u = (jj^; fluid velocity in the y- 

 direction, by v = ^y) At a solid boundary, the normal velocity of the 

 fluid must equal the normal velocity of the solid boundary since fluid cannot 

 penetrate the boundary and no cavities are assumed to form in the fluid. In 

 particular, at stationary boundaries the normal velocity must vanish. At the 

 right vertical boundary of the flow domain, about 16 half-beams away from the 

 body, this condition is given by 



(()x = at X = w (3) 



Similarly, at the bottom boundary, about six half -beams below the free 

 surface, vanishing normal velocity is specified by the equation 



({>y = at y = -h (4) 



At the boundary AE directly beneath the body, where a symmetry condition is 

 specified as a wall condition, the velocity potential must satisfy the 

 equation 



(j)x = at X = (5) 



Along the body contour, the normal velocity is known from the prescribed 

 motion of the body. In fact, the normal velocity of the body at 

 (Bx(a,t), By(a,t)) is 



Vn(a,t) = nx3Bx/9t + ny3By/3t 



