264 



i}'^{^y-m 



dS 



8x 



p^gu 



p.gu 

 dz c ^ + ^ 



P 2 



ds C 



, 2 



+ ^- I dz ?p - p^U 



dw u' , (105) 



+ p^gU 



dz c <;• + 



P 



dS f 



(103) 



F = 

 e 



P,U 



dS 



-b' 



where 





p^gu 



dz Z 



+ p^U 



do) u 



I 2 



(106) 



. 2 dx 2 



(V(J))2 + (u'2 + v'2 + w'^) 



.,8(1) , 3<f> , 3<l> 



8x 3y 3y 



(104) 



and b' represents the half width of w at the free 

 surface. If only the largest terms in oi are kept 

 in the definite integral in Eqs . (102) and (103), 

 the following approximate equations can be obtained: 



Since the following relationship is approximately 

 satisfied in a wake far from the hull: 



_ 3_ 



U 



(Ho - H) , 



(107) 



Eqs. (82), (83), (87), and (88) can be obtained from 

 (74), (77), (78), and (81) by substituting this 

 relation into (105) and (106). 



