A Mathematical Model of Fluid Flow in an Open Trapezoidal Channel with Lateral Inflow Channel

Abstract

In this paper, an incompressible fluid flow in an open trapezoidal channel with one lateral inflow channel is investigated. The flow parameters that are investigated include the cross-sectional area, angle, length and velocity of the lateral inflow channel. The flow variables in the main trapezoidal channel include the depth and velocity of the fluid. These flow parameters in the lateral inflow trapezoidal channel are investigated on how varying each parameter independently affects the flow velocity in the main trapezoidal channel. The continuity and momentum equations are equations that govern this flow. Since these two equations are highly nonlinear, the finite difference method is used to approximate the solutions. The results are then presented by velocity profiles graphs and discussed. It is noted that a decrease in the cross-sectional area leads to an increase in the flow velocity and an increase in the length of the lateral inflow channel leads to a decrease in the flow velocity. It is also noted that an increase in the velocity of the lateral inflow channel leads to an increase in the flow velocity and an angle of between thirty and fifty degrees increased the flow velocity compared to other angles in the lateral inflow channel.