Malavard 



of the conducting fluid. The Fourier condition, linear relation between the po- 

 tential and its normal derivative, is frequent in heat problems and thin- jet flap 

 problems (8) or lifting- line problems (2). Considering block C of Fig. 3, the 

 Kirchhoff law permits us to write 



« 



3n 



which is comparable to 



= b 



provided that S = aM^As and V = b. 



For these three conditions, it is sometimes necessary to impose the con- 

 servation of the flow between the two sides of a slit. In this case, the electric 

 setups are similar to those of A, B, and C, but additionally they require a trans- 

 former which automatically assures this supplementary condition (blocks A', B', 

 and C of Fig. 3). 



It is evident that the precision of the analog representation of a problem de- 

 pends fundamentally on the electric transposition of the boundary conditions. To 

 describe in detail the techniques applied to make the boundary systems as accu- 

 rate as possible would go beyond the limits of this paper. Nevertheless, it is in- 

 teresting to note that, even in the most difficult cases, the elements inserted into 

 the electric circuit are passive, i.e., resistances, potentiometers, and trans- 

 formers. This process of simulation contrasts with that used elsewhere (40), 

 in which active elements, of intricate electronics, are incorporated in rheoelec- 

 tric experiments which are in themselves of great simplicity. 



TWO-DIMENSIONAL PROBLEMS 



Subcavitating Hydrofoil Near the Free Surface 



Although the study of the subcavitating hydrofoil is not chronologically the 

 first naval hydrodynamic problem to be treated at the Centre de Calcul Ana- 

 logique, we believe it is interesting to begin the review of two-dimensional prob- 

 lems with this study. 



Solution of the Direct Problem — Consider an immersed foil represented by 

 its mean line, i - ^(f), near the free surface. The hydrodynamics characteris- 

 tic of the hydrofoil are determined in solving the following boundary value prob- 

 lem: on the free surface we have the condition of Eq. (lb), on the slit LT repre- 

 senting the foil, 4^* ~ "P' - -'^, on the trailing edge, 3i//+/3n + 3i/'"/^n = o. The 

 electrical simulation of the condition in Eq. (lb) is performed by the use of nega- 

 tive resistors (40), but their use is not easy and sure. We preferred to use an 

 indirect method which allows the replacement of the Poisson condition by a 

 Dirichlet condition. It takes into account the fact that for each vortex distribution 

 connected to the lifting foil, the ordinates of the free surface, which is in fact 



376 



