Hydrodynamic Problems Solved by Rheoelectric Analogies 



BOUNDARY CONDITION 



A- DIRICHLET 



'P-«P(*) 



. B - NEUMANN 



Bn dn 



-C -FOJRIER 



i>-a—- = b 



A- DIRICHLET- FU3W CONSERVATION 

 -p*- f '. A "P (S) 



B- NEUMANN -FLOW CONSERVATION 



M1M=M (s) 

 dn 3n 3n 



ELECTRICAL REPRESENTATION 



V s Kf 

 V Elecfnco! Porendal 



=W! 



R H_l_ 



M 

 an 





-v'=A^(s) 



TMJ 



C- FOURIER- FLOW CONSERVATION 



1^ 



R = 



- 1 

 On 



A VE b 



R = a 



Fig. 3 - The three boundary conditions and 

 their electric analogs 



Figure 3 shows the three types of boundary conditions — Dirichlet, Neumann, 

 and Fourier — and the corresponding analog setups. The Dirichlet condition, po- 

 tential given on a boundary, Eq. (5a), is easily given by the use of potentiometers 

 or of voltage dividers. The Neumann condition of the Eq. (4a) type is realized 

 using resistances of a high value !R, so that, in feeding by a unity reference po- 

 tential, the potential on the electrode is equal or inferior to 0.05. Thus is found 



3V 

 dn 



,As5^ 



-K 



dn 



where As, represents the surface of an electrode and K an analog constant. The 

 values of iR are determined byAsfR % l/a^KCdc^/dn), where a^ is the conductivity 



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