Finite Difference Analysis of Fluid Flow in a Circular Cross-Sectional Open Channel

Abstract

This study examines non-uniform and unsteady flow through a prismatic open channel of circular cross-sectional area with lateral inflow. The flow velocity and flow depth have been taken as the flow variables. The flow parameters considered in this study are the cross-sectional area, radius of the channel, lateral inflow rate per unit length of the channel, slope of the channel, depth and Manning roughness coefficient. Analysis of the fluid flow has been done by determining the effect of the flow parameters on the flow variables. The equations governing the flow are non-linear and are highly coupled. The finite difference approximation method is used to solve them and the results presented in form of graphs and tables. The study shows that an increase in the cross-sectional area leads to decrease in the flow velocity; and an increase in the radius of the channel leads to decrease in the flow velocity. In addition, an increase in the Manning roughness coefficient leads to a decrease in the flow velocity. An increase in the flow depth leads to decrease in the flow velocity while a decrease in the lateral inflow rate per unit length of the channel leads to an increase in the flow velocity. The results of this study have application in the formulation of mathematical models to aid in construction of drainage channels in areas that are susceptible to floods.