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To model the flow in FFs, it is assumed that the flow rate is analogous to the electrical current and the pressure is analogous to the electrical potential due to their same behavior in series or parallel channels or electrical circuits. In electrical circuits, the relationship between electrical current and potential is expressed as: π = π πππΌ where V, I, and Re are electrical potential, current, and resistance, respectively. The same relationship may be written for Q and ΞP as well: π₯π = π π (3.32) ππ£ where Rv is the viscous resistance for the respective porous or non-porous medium. The viscous resistances for the channels and porous medium can be obtained by manipulating Equations 3.29 and 3.31: π=ππ·h4βπ βπ =4πΆππ (3.33) 4πΆππ π π ππ·h4 βππ=π π βπ π=ππ€π (3.34) π€π π hπππ πhπππ Kirchhoffβs laws quantify how current flows through and how potential varies in an electrical circuit. They are described as the following statements: 1- In each node, the sum of the current is zero (Ξ£I=0). 2- In each loop, the sum of the potential is zero (Ξ£V=0). 2a- The potential difference between two nodes is equal to the resistance between them multiplied by the passing current. (Vij= RijIij) 37PDF Image | Analysis of Fluid Flow in Redox Flow Batteries
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