- °i (p) + h f f °i (Q) ar G(p - Q) d s q " 2k / a i (Q) ^- G(P ' Q) n * dy ' 



p ■"'o-', P 



L o 



~^2 D(x ' y) ^n~ G(P ' Q) dx ' dy ' (45) 



This is equivalent to the velocity potential 



<KP) = " If Cf(Q) G(P,Q) d S Q + j- a(Q) G(P,Q) n x dy' 



S L o 



- 4V" ff V x '' y,) G(p - Q) dx ' dy ' (46) 



where the hull surface source density is so determined that the hull sur- 

 face boundary condition is satisfied. Therefore, the only approximation 

 is the replacement of $(x,y) by $ (x,y). Numerical results show a 

 plausible agreement with measured results as shown in Figure 4. However, 

 none of these results are regarded as consistent approximations from the 

 rigorous aspect of the perturbation analysis. 



Method of Coordinate Transformation 



In the preceding section, we assumed the deviation of the flow 

 velocities around the hull from those of double body flow as a small 

 perturbation and formulated the first approximation for the wave re- 

 sistance. If we want expressions for the flow velocity or wave pattern, 

 however, the perturbation expansion of the velocity potential is needed. 



Now let us write the fluid velocity around the hull in the form 



u = u + u 1> v = v Q + v^, w = w Q + w^ (47) 



24 



