We have modelled an open channel flow through a porous media (River). In the model, we considered water as an incompressible fluid; the flow as steady and uniform; the system is assumed to be isothermal and the flow, also a laminar flow. We have solved the resulting equation using analytical method. By some mathematical operations, the momentum partial differential equation (PDE) was reduced to ordinary differential equation (ODE) and the resulting equations are solved analytically using the technique for solving linear equations with constant coefficients-method of variation of parameters. The analysis of the result was done and plotted on graph using MATLAB to show the effect of permeability on flow parameters such as velocity, pressure gradient and the height of the channel. Recommendations were made to control and manage the flow of rivers.
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