Asian Research Journal of Mathematics

Flooding in affected regions poses a serious threat to both human life and economic activities. It disrupts livelihoods in multiple ways, including damage to critical infrastructure. For example, the formation of potholes, destruction and disconnection of roads, and the collapse or washing away of bridges contribute to a rise in accidents, often resulting in fatalities. Consequently, governments are forced to allocate more resources toward the repair and maintenance of transport networks, placing additional strain on public budgets. This study develops a model of fluid flow through an open channel featuring a trapezoidal cross-section and a segmented base, incorporating a lateral inflow section. Turbulence at the junction between the lateral and main channels is considered insignificant, allowing the assumption of laminar flow. The governing equations are expressed in non-dimensional form and solved using the finite difference method, with simulations carried out in MATLAB. Results indicate that enlarging the length of the lateral channel reduces discharge in the main channel, which in turn lowers the flow velocity. Correspondingly, higher surface roughness leads to greater shear stress, ultimately reducing the velocity of the flow. An increase in the angle between the two radii of the channel results to an increase in the flow velocity of the main channel. The results of this study can inform the design of drainage infrastructure in road works, urban storm-water systems, sewer networks, and dam projects in Kenya and beyond. More so, optimally dimensioned channels that maximize efficiency are highly valuable in hydro-electric power plants, where substantial volumes of fast-moving water are needed to drive turbines for power generation.