Critical pressure-deficient operating conditions frequently occur in water distribution networks. Head driven analysis (HDA) of water distribution networks allows for the pressure-dependent nature of nodal flows and, therefore, yields the actual nodal flows and heads for both normal and subnormal pressure conditions. Hence, HDA simulation models are more practical than demand driven analysis models that assume that all demands are satisfied in full even under pressure-deficient conditions. This paper describes an approach in which a new pressure-dependent demand function that has no discontinuities has been incorporated in the Gradient Method. The procedure has been tested extensively and demonstrated to be capable of effectively simulating both normal and pressure-deficient operating conditions. The algorithm's convergence is smooth and rapid thanks to a line search and backtracking procedure that ensures progress towards the solution in each iteration. The results presented herein would appear to confirm that the proposed method is robust and efficient. Results for a real network are also included.

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