11 + ^=0, Z=0 (2-39) 



1^ + N-2K7?' = (2-40) 



where 



K=-ji^. (2-41) 



The solution of the wave problem for a particular environment would be 



<J> = 4>(X, Y, Z, N,K,r) (2-42) 

 and 



n' = T?'(X, Y, Z, N, K, t) . (2-43) 



Equations 2-42 and 2-43 are the bases for establishing the conditions 



for obtaining similarity between model and prototype. The corresponding 

 times are given by the relation 



(r)^ = (r)p (2-44) 

 and for similarity, 



(N)n, = (N)p (2-45) 



and 



(K)^ = (K)p . (2-46) 



Equation 2-45 states that similarity between model and prototype will be 

 obtained only when the linear scales are not distorted. Also, equation 

 2-46 states that for corresponding times, i.e.. 



(A-i-X 



K must have the same value in model and prototype. Thus, from equation 

 2-41 



gT2\ /gxA 



dTJ (2-47) 



which is a Froude relationship. If Lp be the linear scale of the model, 

 and since the model is not distorted in scale. 



("'l ' ^'(U t^-^^' 



39 



