Modeling Fluid Flow in an Open Rectangular Channel with Lateral Inflow Channel

Abstract

In this study, we investigate the flow in an open rectangular channel with a lateral inflow channel. The flow of an incompressible Newtonian fluid through a man-made open rectangular channel with a lateral inflow channel is investigated. We have considered the effects of angle as it varies from zero to ninety degrees, the cross-sectional area, velocity and length of the lateral inflow channel on how they affect the flow velocity in the main open rectangular channel. Since the discharge is directly proportional to the flow velocity, the increase in the flow velocity means an increase in the discharge and vice versa. The equations governing the flow are the continuity and momentum equation of motions, which are highly nonlinear and cannot be solved by an exact method. Therefore, an approximate solution of these partial differential equations is determined numerically using the finite difference method. The finite difference method is used to solve these equations because of its accuracy, consistency, stability and convergence. Matlab software is used to generate the results which are then analyzed using graphs. The findings are that, at zero degrees of the lateral rectangular channel, the results compare to earlier research done. It is also found out that an increase in the area and the length of the lateral inflow channel leads to a reduction in the velocity while an increase in the velocity of this channel leads to an increase in the velocity of the main channel. Finally, an increase in the angle of the lateral inflow channel does not necessarily lead to an increase in the velocity in the main channel. That, angles of between 300 and 500 exhibits higher values of velocities in the main open channel compared to other angles of the lateral inflow channel.