Please use this identifier to cite or link to this item: https://hdl.handle.net/2440/80958
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Type: Conference paper
Title: Comparing the Q-equations and Todini-Pilati formulation for solving the water distribution system equations
Author: Simpson, A.
Citation: Water Distribution Systems Analysis 2010, Proceedings of the 12th Annual Conference, WDSA 2010, Tucson, Arizona, United States, 12 -15 Sep 2010 / Kevin E. Lansey, Christopher Y. Choi, Avi Ostfeld and Ian L. Pepper (eds.): pp. 37-54
Publisher: American Society of Civil Engineers (ASCE)
Issue Date: 2010
ISBN: 9780784412039
Conference Name: Water Distribution Systems Analysis (12th : 2010 : Tucson, Arizona, USA)
Editor: Lansey,, K.
Choi, C.
Ostfeld, A.
Pepper, I.
Statement of
Responsibility: 
Angus R. Simpson
Abstract: This paper compares the solution of the network equations based on two methods. In the first method considered, the Q-equations are solved. The only unknowns in the Q-equations are the flows in each of the pipes or links. The Q-equations are formulated by taking the continuity equations at each supply node. In addition, energy equations for the head losses around primary closed loops and required independent paths between fixed head nodes in the network are written in terms of the flows in each pipe contained within the loop or path. The second method considered here is the Todini and Pilati solution method. This approach deals with all unknown flows and heads simultaneously. The governing equations are the continuity equations and the head loss equations for each individual pipe in the network written in terms of the unknown heads at the ends of the pipe and the unknown flow in the pipe. A smart two-step algorithm was developed by Todini and Pilati (1988) to first solve for the heads and then to solve for the flows sequentially in an iterative process. A simple case study involving two reservoirs, two pipes and one junction is used to illustrate the sequence of iterates for both the Q-equations and the Todini-Pilati method. It turns out that the sequence of iterates for the flows in both methods is identical. Comparison of the results for the case study leads to some interesting insights.
Rights: © 2010 American Society of Civil Engineers
DOI: 10.1061/41203(425)6
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Civil and Environmental Engineering publications

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