Bessho 



If the Kutta-Joukowski condition [6,7,8] is satisfied at the 

 trailing edge, we have the reciprocity relation 



\ \ pw dx dy = \ \ pw dx dy (1.1) 



s •^ ^ s 



by (A. 8) and (A. 24), where p is the pressure, w is the vertical 

 velocity component, and tildas denote reverse flow quantities. The 

 Integration is over the wetted portion of the ship hull S, 



Let ^(x,y) be the free surface elevation. The variation of 

 the integral 



^" J J ^^P " ^^^^ " P"^^ '^'^ "^^ ^^'^^ 



S 

 due to variations of p and p takes the form 



61 



= y y [ 6p(;^ - w) - 5p(;^ + w)] dx dy. (1 . 3) 



Since the variations 6p and 5p are arbitrary, the pressure which 

 extremizes the integral I is equivalent to the solution of the boundary 

 value problem (A. 25) and (A. 26); that is, the problem for the pertur- 

 bation potential <t> with the conditions 



(1.4) 



C^ = W = -'$2 



on the free surface. The stationary value of I is the drag; namely, 



[I] =yy P„^. dxdy, (1.5) 



X 



S 



where pg denotes the correct solution. [6,24,26] Thus, the bound- 

 ary value problem is converted to a variational problem, the solution 

 of which is suggested by various methods of approximation. [ 6] 



If we introduce the error integral, 



E*=yy (p - p^)(^ - ^J dxdy, (1.6) 



we s ee from (1.1), (1.4), and (1.5) that 



548 



