Hydrodynamic Problems Solved by Rheoelectric Analogies 



THE HYDRODYNAMIC PROBLEM 



General Equations and Boundary Conditions 



Consider the permanent and irrotational flow of an inviscid, incompressible, 

 and heavy fluid with density / past a supercavitating hydrofoil located at a depth 

 d beneath the free surface, the velocity far upstream being Vq. A set of Carte- 

 sian coordinates, x', y', and z' is chosen in such a way that the positive direc- 

 tions of the x' and z' axes are respectively those of Vq and of the upward di- 

 rection. Because the plan-form of the wings is generally symmetrical, the field 

 simulation can be limited to a quarter of the space. 



The movement is described by the perturbation velocity potential 0', 

 which must fulfill the following boundary conditions (Fig. 2): 



1. On the free surface, z 

 equilibrium condition gives 



0, the pressure p^, is constant, and thus the 



Br 



(la) 



which is a Poisson condition for 4>; where F = Vo/>/id is the Froude number, g 

 the gravity force, n the inward normal, and where = ^'/V^d, x - x'/d, and 

 n = -z/d are nondimensional magnitudes. 



u 



_^_f-2M. 



2)n\ 





^►x 





DIRECT PROBLEM 



^1 ax 



INVERSE PROBLEM 



Fig. 2 - Boundary conditions for a 

 supercavitating wing at y = c^ 



371 



