Murthy 



$ (x, y, z;t). These are (i) the kinematic and dynamic conditions on 

 the free surface of water on all sides exterior to the immersed part 

 of the hull and (ii) the conditions on the immersed part of the hull 

 itself. The latter condition takes the form of the equality of the nor- 

 mal velocity of the fluid and that of the hull, i. e. that the flow is pu- 

 rely tangential to the hull surface when boundary layer effects are 

 ignored. This is therefore a Neumann problem. Also, when dealing 

 with an ideal amphibious hovercraft as in the previous study (1970) 

 which was assumed completely separated from the water surface at 

 all times both conditions relate to the free surface of water, one on 

 the external free surface (EFS) and the other on the internal free 

 surface (IFS) which is the vertical projection of the cushion opening 

 (i. e. of the hemline of the skirts) on the water surface directly below 

 the craft. Both these conditions relate to the pressure on the free 

 surface giving a Dirichlet problem. 



In the case of the general type of ACV now under considera- 

 tion, there will be three types of conditions : 



(i) The kinematic and dynamic conditions on the EFS 



(ii) A normal velocity condition on the immersed parts of 

 the side hulls which separate the EFS from the IFS 



(iii) A pressure condition on the IFS which forms the lower 

 boundary of the cushion. 



This is therefore a mixed boundary condition problem. 



IV. 1 Conditions on the External Free Surface (EFS) 



The kinematic free surface condition applicable to the EFS 

 and IFS has been derived in Section II in the form 



4>f+<i>f+4>f+ (a>y - V) f -wxf+r=0 (4-1) 



xxyyzz' 7 x y; t 



on z = f . On the EFS the pressure is zero and substituting p = 

 in Bernoulli's equation (1 -8) we derive 



r- ± 



1 2 



$ + (-wy - V) * -oix* + — ( V4>) 

 t x yd 



(4-2) 



also on z = T 



124 



