TITLE:
Mathematical Modeling of Open-Channel Flow Hydrodynamics: Effects of Flow Manning Roughness and Bed Roughness
AUTHORS:
Simon Mutugi Mung’ori, Mark Okongo, Alice Lunani Mulama Murwayi
KEYWORDS:
Manning’s Roughness, Finite Difference Method, Numerical Simulation, Pollution
JOURNAL NAME:
Open Journal of Fluid Dynamics,
Vol.16 No.4,
October
29,
2026
ABSTRACT: Pollution in the environment has increased drastically in recent times. Environmentalists and scientists have faced challenges in finding ways to minimize pollution and manage its effects. Water pollution has tremendously increased, which causes human aquatic activities like fishing, transportation, sea mining, and others to be unpredictable. The influx of pollutants into the flow causes significant changes in flow density, bed level, flow depth, flow velocity, and consequently bed topography. Soluble pollutants affect the density of flow and hence its velocity and other flow parameters. Insoluble pollutants have a reasonable effect on bed level, flow depth, and bed topography. This study aims to mathematically model open-channel flow hydrodynamics and assess how Manning’s roughness coefficient and bed roughness influence flow velocity, water depth, and discharge under different flow conditions. The study investigates how the roughness of an open-channel bed affects the way water flows, particularly its velocity, depth, discharge, and energy loss. The differential equations governing the flow are first expressed in dimensionless form and discretized using the finite difference method with appropriate initial and boundary conditions. Numerical values are simulated using the Python program, and results obtained from this study are represented graphically. The results indicate that flow velocity decreases with an increase in pollutants in the flow; a consistent increase in average friction slope as the Manning roughness coefficient increases; and further demonstrate that flow depth increases with increasing Manning roughness coefficient.