This study is focused on the prediction of pumping performance in MHD flow. To reach it, an analytic model based on the steady state, incompressible and fully developed laminar flow theory will be provided to analyze the flow characteristic with different scalar dimensions in duct channel. By converting the Lorentz forces which is interacted by electric current and magnetic flux into hydrostatic pressure gradient in the moment equations, the governing equations can be transformed into Poisson equation which makes the analytic solution possible. Furthermore, the concept of flow circuit which is similar to the thermal network in conduction problem will be also proposed in this study. When compared with experimental results, an excellent agreement was kept among the individual behavior and an easier way to solve the problem could be formulated through the set up of flow circuit.

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