A Constrained Demand-Scan Algorithm for the Maximum Sustainable Yield of an Aged Institutional Water Distribution Network

Abstract

Water distribution networks at expanding African universities are frequently constrained not by design parameters but by the fixed geometry of existing, ageing infrastructure. The conventional pipe sizing problem choosing diameters that satisfy a known demand is therefore inverted: given immovable pipe diameters, lengths and materials, what is the largest daily volume the network can supply while every junction satisfies a 15 m minimum service pressure and every pipe stays below 1.80 m/s velocity. This paper formulates this capacity-frontier problem as a constrained nonlinear optimisation governed by the Hazen–Williams head-loss equation and proposes a coarse fine demand-scan algorithm to solve it on commercially available hydraulic engines. The procedure was applied to the existing water network of Modibbo Adama University, Yola (Adamawa State, Nigeria), a three-reservoir, 18-junction, 20-pipe branched system of 3,454 m total length comprising 15 cast-iron, 3 ceramic and 2 PVC sections. With aged Hazen–Williams coefficients (C = 100, 105 and 135 respectively), the algorithm converged in two scan levels to an optimum daily yield of 1,825 m³/day (21.12 L/s average; 31.68 L/s peak) using 34 calls to the hydraulic solver. At this yield the minimum junction pressure is 15.20 m and the maximum pipe velocity is 1.55 m/s, both just inside the criteria. A three-axis sensitivity analysis demonstrated that the network operates at the very edge of its hydraulic envelope: acting individually, a 5 per cent deterioration in pipe roughness, a 5 per cent growth in demand, or a 2.5 m fall in reservoir level each drives multiple junctions below the pressure criterion. Specifically, the pressure margin is exhausted by a fall in the length-weighted composite C-factor of about 5 per cent (from 104 to 99), by demand growth beyond about 1,825 m³/day, and by a reservoir draw-down of 2.5 m. The result formally quantifies the well-known supply shortfall and provides a transferable algorithm for sustainable-yield assessment of similarly aged distribution networks.