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

Abstract

The study aim is to propose a mathematical model to be used to investigate the flow in an open rectangular channel with a lateral inflow channel. An incompressible flow of a Newtonian fluid through a man-made open rectangular channel is considered. The study has considered the effects of angle as it varies from zero to ninety degrees and variation of 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. Increase in the flow velocity leads to increase in the discharge. The equations governing the flow are the continuity and momentum equations. The resulting partial differential equations are coupled and nonlinear and cannot be solved analytically. Therefore, an approximate solution of these partial differential equations is determined numerically using the finite difference method. Matlab software has been used to write a code that has been used to compute and solve the problem. Solutions are represented by making use of graphs and tables. At zero degrees angle of the lateral inflow channel, the results compare to earlier research done by Kwanza et al (2007) and Thiong’o (2011). It is also found out that an increase in the cross-sectional 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. The study shows that angles of between 30o and 50o exhibits higher optimum values of velocities in the main open channel compared to other angles of the lateral inflow channel.