Hydrodynamic Problems Solved by Rheoelectric Analogies 



Some of the examples given show that to obtain the best results from the 

 rheoelectric method, it is convenient, very often, to modify the theoretical 

 statement of the problem with a view to simplifying the electrical setups of the 

 boundary conditions and still obtain a good workability. This approach may 

 suggest to some a new way of constructing theoretical models for hydrodynamic 

 problems in order to simplify the analogy. On the contrary, these models would 

 prohibitively complicate the task of the mathematicians who may try to solve 

 hydrodynamic problems by analytical or numerical methods. Rheoelectric 

 methods utilize the possibilities of both numerical analysis and computers to 

 facilitate the preparation of data and to exploit their results. Numerical and 

 computer analysis is also employed in the establishment of new hybrid analog- 

 digital methods. The solution of the thick hull problem shows clearly this 

 interconnection between numerical and analog computation. 



Many kinds of problems can be treated directly numerically, but our ex- 

 perience shows that before any extensive programming is undertaken, it is use- 

 ful to check the validity of the theoretical model by rheoelectric simulation. The 

 physical nature of the analogy often allows a good criterion for disclosing the 

 difficulties of the proposed mathematical model. ' ■ >-' :'■■• 



Finally, it should be observed that specialists in rheoelectric analogy are 

 convinced of the usefulness of large computers. The analog point of view when 

 applied to numerical solutions, often permits us to obtain conventional yet effec- 

 tive methods. ; . ,,..■-.-. -■-■ ' J . . ; .. ..- .- . „. . 



ACKNOWLEDGMENTS 



The author wishes to thank the Office of Naval Research, Department of the 

 Navy— U.S.A., who partially supported, under contract numbers 62558-2545, 

 62558-2997, 62558-1861, 62558-3645, 62558-4113, 62558-4483, and 62558-4998, 

 numerous studies described in this paper. He would like also to thank Dr. D. H. 

 Fruman of the Centre de Calcul Analogique for his most efficient assistance in 

 the preparation of this paper. 



REFERENCES 



1. Peres, J. and Malavard, L., "Sur les Analogies Electriques en Hydro- 

 dynamique," CRAS*, 18 avril 1932 



2. Malavard, L., "Application de I'Analogie Electrique a la Solution de 

 Quelques Problemes d'Hydrodynamique," Publ. Sc. et Tech. du Min. de 

 I'Air, fasc. 57, 18 decembre 1934 



3. Peres, J. and Malavard, L., "Realisations Analogiques d'Ecoulements avec 

 Lignes de Jet," CRAS, 7 Janvier 1938 



*Comptes-rendus de I'Academie des Sciences —Paris. 



411 



