Murthy 



APPENDIX III 

 PRESSURE FORCES AND MOMENTS ON THE SIDE HULLS 



The force on the ACV due to the action of the pressure of 

 the fluid on the immersed side hulls is from (5. l) 



f p 



H-i 



AdS 



s 1 + s 2 



where the pressure of the water particles on and below the surface 

 of the fluid on either side of each hull is given by Bernoulli's equa- 

 tion (1- 8) with w = 



p(x,y, z;t) = - p 4> t - V4>_ +^~ ( V* ) - gz| 



x 2 



The pressure is therefore given in the moving (x,y, z)-sys- 

 tem , but the domain of integration, namely, the instantaneous posi- 

 tion of the wetted surfaces of the moving and oscillating hulls is 

 however, given in the body-fixed (x',y', z 1 ) system by the hull func- 

 tions (4-9) below the free surface z = f . 



This difficulty did not arise in the case of the cushion hull 

 since the domain of integration in that case was that part of the 

 plane z = lying within the instantaneous boundary of the cushion. 



The unit normal into the hulls is discussed in section (IV. 3) 

 and we may write 



A , A A A \ 



n dS = (H i + H j + H k ) dxdz 

 x y z 



[*/>! 3 h l A A 



a ,/a h i a h i \ai 



- J + %¥7' cose --6^ sin9 ) k j 



This applies to the hull surface S. , .In the case of the other hull 

 surfaces the above expression has to be modified slightly. The scheme 

 is set out below. 



dx'dz 1 



184 



