Open Channel Flow over a Permeable River Bed

Godwin Christopher Ezike Mbah, Cyril Ifeany Udogu

Department of Mathematics, University of Nigeria, Nsukka, Nigeria.

DOI: 10.4236/oalib.1101475                

Abstract

This paper presents results of a modeled 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 pattern is laminar. We have solved the resulting Brinkman equation using analytical method. By some mathematical operation, the momentum partial differential equation (PDE) was reduced to ordinary differential equation (ODE) and the resulting equations are solved analytically using the standard solution technique for a second order ODE. 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 height of the channel. It is found that velocity of the open channel decreases with increase in permeability. Also, increase in the height of the open channel results in increase in velocity of flow in the open channel. We also found that an increase in the permeability of an open channel resulted in decrease in pressure.

Keywords

Fluid, Flow, Permeable River Bed, Open Channel

Conflicts of Interest

The authors declare no conflicts of interest.

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