Design of Branched‐Water‐Supply Network on Uneven Terrain

A method of designing least‐cost branched‐water‐supply networks for rural communities on uneven terrain is described. Previous studies have been concerned with networks on relatively flat terrain and have not taken account of the need to provide minimum‐service pressure heads at interior nodes. The optimization model requires a function representing the consolidated cost of the pipe to be minimized subject to a number of constraints on the friction head loss to be tolerated between the source node and a critical node. The critical node may be an end node or an internal node. Optimization is achieved using the Lagrange multiplier method, which gives rise to as many nonlinear simultaneous equations as there are critical nodes. The equations for the multipliers are solved using a generalized Newton‐Raphson approach, which is rapidly convergent. The method is applied to a small‐scale continuous system typical of those found in Papua New Guinea.