Mathematical Modelling of Water Distribution Networks in Urban Centres of Plateau State

This study develops mathematical models for the analysis and optimisation of water distribution networks in selected urban centres of Plateau State, North Central Nigeria, where inadequate pipe network infrastructure and high rates of non-revenue water losses pose serious public health and operational challenges to the Plateau State Water Board. The study adopts the Hardy-Cross method of pipe network analysis, supplemented by linear theory and Newton-Raphson iterative techniques, to determine equilibrium flow distributions and pressure heads in looped pipe networks. Network topology data, pipe diameters, lengths, and roughness coefficients are obtained from engineering drawings and field measurements conducted at distribution networks serving three residential neighbourhoods in Jos metropolis, covering a combined service area of approximately 45,000 households. Hazen-Williams friction coefficients appropriate to the pipe materials in use are incorporated into the hydraulic calculations. Network models are constructed and solved iteratively, with convergence achieved when head loss imbalances at each loop fall below a prescribed tolerance. Pressure deficiency zones are identified and mapped, and the effectiveness of proposed network reinforcement measures including pipe upsizing and the addition of secondary feed mains is evaluated. Results indicate that 28 percent of network nodes experience pressure heads below the minimum service threshold of 10 metres during peak demand hours. The proposed interventions are shown to reduce pressure-deficient nodes to below 5 percent. Keywords: water distribution networks, Hardy-Cross method, pipe network analysis, non-revenue water, Plateau State