Two-Point Linearization Method for the Analysis of Pipe Networks
Publication: Journal of Hydraulic Engineering
Volume 134, Issue 8
Abstract
This note proposes a new method for snapshot analysis of water distribution systems based on the commonly used gradient method. The proposed method uses a secant (intersecting the head-loss function in two points) instead of a tangent to approximate the pipe head-loss function. A theoretical model is developed for the flow range in which the secant approximates the head-loss function without exceeding a given allowable error. This scheme allows a tradeoff to be made between the allowable error and the number of iterations required to achieve convergence. The proposed method is applied to an example network to illustrate its application and benefits. It is argued that the number of iterations required to find a solution can be reduced significantly in both snapshot and extended-period simulations.
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References
Farmani, R., Savic, D. A., and Walters, G. A. (2005). “Evolutionary multiobjective optimization in water distribution network design.” Eng. Optimiz., 37(2), 167–183.
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Todini, E., and Pilati, S. (1988). “A gradient method for the analysis of pipe networks.” Computer applications in water supply, B. Coulbeck and C. H. Orr, eds., Wiley, London, 1–20.
Univ. of Exeter Centre for Water Systems (UOECWS). (2005). “Benchmark networks for design and optimization of water distribution networks.” ⟨http://www.projects.ex.ac.uk/cws/index.php?benchmarks⟩ (Dec. 30, 2005 ).
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© 2008 ASCE.
History
Received: Dec 30, 2005
Accepted: Sep 4, 2007
Published online: Aug 1, 2008
Published in print: Aug 2008
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