Analysis and optimisation of looped water distribution networks

A three stage procedure for the analysis and least-cost design of looped wa ter distribution networks is considered in this paper. The first stage dete cts spanning trees and identifies the true global optimum for the system. T he second stage determines hydraulically feasible pipe hows for the network by the numerical solution of a set of non-linear simultaneous equations an d shows that these solutions are contained within closed convex polygonal r egions in the solution space bounded by singularities resulting from zero f lows in individual pipes. Ideal pipe diameters, consistent with the pipe ho ws and the constant velocity constraint adopted to prevent the system degen erating into a branched network, are selected and costed. It is found that the most favourable optimum is in the vicinity of a vertex in the solution space corresponding to the minimum spanning tree. In the third stage, comme rcial pipes are specified and the design finalised. Upper bound formulae fo r the number of spanning trees and hydraulically feasible solutions in a ne twork have also been proposed. The treatment of large networks by a heurist ic procedure is described which is shown to result in significant economies compared with designs obtained by non-linear programming.