Muvthy 



We will now turn our attention to the moment on the ACV due 

 to the action of the pressure of the water particles on the hulls given 

 by (5.2) 



M, 



H 



■•// 



►A, 



p (r 1 x n) dS 



Y^Z 



and as r 1 may be written in terms of the components along the 



AAA 



1 , j , k axis. 



r 1 = (x' cos 6 + y' sin0) i + y' j + (z 1 cos0 - x' sin0) k 



and 



£dS 



,^ h l £ h l „\A-A 



5 (3-77 cosfl + -r — - sin0) 1 + j + d 



dx' 



we have 



(r' x n) dS 



/d n l 



\TJ co 



* sintf) k dx'dz' 



sd 



(z 1 cos0 - x 1 sin0) > i 



(„, h -v h \ 



ax' X az'/ 



! 



+ <J+(x'cos0 + z' sin0) - 5y' 



/ah 



V^x- 



cos + — sin 



, )t } 



dx'dz' 



the upper and lower signs referring to the hull surfaces S and 

 S with h replacing h. in the case of S__|_ and S, 



The integration is now performed on the outer sides of the 

 longitudinal planes of the hulls and combining S« , and S 2 toge- 



ther as before, the integration may be confined to S 1 with the 



integrands added together. 



The combined i-moment on the two hull surfaces is there- 



fore 



% py ' ("It co 



s» 



a h i 



sin0] dx'dz' 



2 02 



