Murthy 



the flow is tangential when viscous effects are ignored. 



Now, the fluid velocity normal to the hull surface is 



-^r— = n. V<J> 

 on 



where n is the unit normal vector drawn into the hull given by 



A A A 



a H x i + Hy j + H z k VH 



n 7H 2 + H 2 + H 2 l T "' VHl 



L x y z J 



so that 



o-4> V4>.VH v ht ax y (4 » 



dn " IVHl ' " IVHI * } 



Now, the equation of the hull surfaces is naturally given in the body 

 fixed system (x' , y' , z' ) in the form 



H (x,y, z;t) = ghj (x 1 , z' ) - (y» - b) = 



= 5h 2 (x« , z' ) + (y' -b) = 



= 5h 2 (x' , z' ) - (y 1 +b) = 



= 5h (x 1 , z' ) + (y' + b) = 



(4-9) 



We will therefore have to evaluate -^r- given by (4-8) in the 



(x 1 , y' , z' ) system the transformation of co-ordinates between the 



(x, y, z) system and the (x' , y' , z' ) system being given by (4-1). 



Considering first the surface S 



|f .-§j[ih. {....■ )-(y-b)] 



where 



x 1 = (x - x) cosG '+ ( z - h_ - z) sin9 



128 



