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Pressure-deficient conditions are a common occurrence in water distribution systems. These situations require accurate modelling for timely decision making. However, the conventional demand-driven analysis approach to network modelling is unsuitable for operating conditions with insufficient pressure. Increasing emphasis is being placed on the need for water companies to satisfy stringent performance standards for the continuous supply of water to consumers and it is those pressuredeficient operating conditions which are critical in determining whether or not adequate supplies can be provided. It is therefore very unfortunate that the demand-driven analysis method becomes invalid for use in precisely those critical conditions. The aim of this paper is to present a new pressure-dependent demand function to help improve the simulation of pressuredeficient conditions. The proposed function has better computational properties than those in the literature and has been incorporated successfully in the governing equations for water distribution networks. In particular, the proposed function and its derivative do not have the discontinuities that often cause convergence difficulties in the solution of the constitutive equations. A robust Newton-Raphson algorithm was developed to model water distribution systems under both normal and pressure-deficient conditions in a seamless way. Examples which demonstrate the methodology are included.

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In water distribution systems (WDSs), the available flow at a demand node is dependent on the pressure at that node. When a network is lacking in pressure, not all consumer demands will be met in full. In this context, the assumption that all demands are fully satisfied regardless of the pressure in the system becomes unreasonable and represents the main limitation of the conventional demand driven analysis (DDA) approach to WDS modelling. A realistic depiction of the network performance can only be attained by considering demands to be pressure dependent. This paper presents an extension of the renowned DDA based hydraulic simulator EPANET 2 to incorporate pressure-dependent demands. This extension is termed "EPANET-PDX" (pressure-dependent extension) herein. The utilization of a continuous nodal pressure-flow function coupled with a line search and backtracking procedure greatly enhance the algorithm's convergence rate and robustness. Simulations of real life networks consisting of multiple sources, pipes, valves and pumps were successfully executed and results are presented herein. Excellent modelling performance was achieved for analysing both normal and pressure deficient conditions of the WDSs. Detailed computational efficiency results of EPANET-PDX with reference to EPANET 2 are included as well.