VELOCITY POTENTIAL 



HULL 



The coordinate syateta, oxyz, moves at a speed U, which la the mean forward 

 speed of the submersible along the positive ox-axle (see Figure 1). The posi- 

 tive oz-axia is always directed vertically upwards. Tne origin Is located 

 above the center of gravity of the subaersible. The oxy-plane is the plane of 

 the undisturbed free surface. 



We assures initially that the submersible and coordinate system are sta- 

 tionary and that the fluid around the submersible moves toward the negative ox- 

 axis wit*, uniforra speed U. Then, the total velocity potential for the bare hull 

 cen be expressed by 



$(x,y,z) - -Ux + $(x,y,z) 



(1) 



where $ Is disturbance velocity potential due to the submersible. The distur- 

 bance velocity potential satisfies the following conditions: 



1. Laplace equation In the fluid domain 



2 2 

 S » Q | 



2 2 



ox By 



o $ 



oz 



- 



(2) 



2. The linearized free-surface condition 



^4 ♦ k ^L „ 



(3) 



3. The body boundary condition 



OX. - U n, 

 6d l 



(4) 



