(It** T-+* T" + * |-)F(x n ,y n ,z n ) 

 \ 3t T x 3x T y 3y r z 3z / 



= - {q-e 3 (y-y G ) + e 2 (z-z G )} f Xq - {?2 -e l( z-z G ) + e3(x-x G )} F yQ 

 - { J 3 -e 2 (x-x G ) + e 1 (y-y G )} f Zq + * x (F Xo -e 3 F yo+ e 2 F Zo ) 



+ WW + ^V^V^V = ° (304) 



where the dot means the differentiation with respect to t. If we write the 

 direction cosines of the outward normal as 



n, = - F /A, n = - F /A, n = - F /A (305) 



where 



2 2 

 + F + F 



y o z o 



the boundary condition on the hull surface becomes 



4 = K 



{? 1 -6 3 (y-y G )+e 2 (z-z G )} i^ + {C 2 -6 1 (z-z G )+9 3 (x-x G )} n 2 

 + {? 3 -G 2 (x-x G ) + e i (y-y G )} n 3 - ^-6^+0^) 

 - <f> (n 2 +6 3 ii -9^) - $ (n -9 2 n +0 n 2 ) = (306) 



Now we write the steady portion of the fluid velocity as 



u = U + U8<j> /3x, v = U3<f> /3y, w = U3<|> /3z (307) 



and define vectors V n = (U,0,0) and V = (u,v,w). If we employ vector 

 notations 



108 



