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In the steady state, one current balance for the differential circuit element is given by where i A -i +i,. =0 (10) g1y+Ay g1y t1y t'y t'y p -6 te (11) H*Ay Upon substitution of i [y into equation 10, and taking the limit of equation 10 as Ay approaches 0, dy y pt-5e (12) t'y Kirchoff's law for the voltage balance around the closed loop abed gives In the limit as Ay approaches 0, dv. i dyy 6•H g ijy (14) I 7t^y - I Vt'y+Ay -g i,a=0 (13) g y+Ay d2v -p di g.. gj ,2 6•H dy1y dy1y g and combining this equation with equation 12 gives (15) (16) d2v, dy gte 6 •p •6 This differential equation defines the voltage drop in the electrolyte at any distance along the width, and may be related to the current density in the elec trolyte by the following equation. p •Ay The two differential equations (equations 12 and 14) may be combined by taking the second differential of equation 14, and substituting equation 12 into it. Differ entiating equation 14, 31-11PDF Image | Development of the Zinc-Chlorine Battery for Utility
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