Equations 1-11, 1-73, and 2-74 are the bases for establishing the condi- 

 tions for similarity between the distorted model and the prototype. These 

 equations will serve to represent (identically) the quantities of the 

 model and prototype, provided that K' has the same value in model and 

 prototype and the input at the entrance of the model is the same as that 

 in the prototype. More specifically, at corresponding times 



^m - \ (2-75) 



and at corresponding locations 



Xm = Xp, Y^ = Yp; (2-76) 



then. 





U'n, = U'p 



and 







V'n. = V'p 



provided that 







K'n. = K'p 



C2- 



■77) 



(2- 



-78) 



(2- 



■79) 



(2- 



■80) 



and, at the input line or at the entrance of the model given by 

 f(Xi,Yi) = 



From equation 2-80, and using equation 2-71 which defines K', 



(Lc) (de)l/2 



Denoting the scale of horizontal lengths by (^)r ^rid the scale distor- 

 tion by DF, i.e. , 



M = (M,H (2-83) 



Wm = (^)y'^"'^'(Tc) (2-85) 



44 



and 



to obtain 



