Reliability and Statistical Assessment of Methods for Pipe Network Analysis

Abstract

One of the most common important steps in water resources engineering is pipe network analysis. The key methods for this analysis are linear theory, Hardy Cross and Newton-Raphson. In this paper, a report on the evaluation and reliability of these methods using statistical methods (total error, coefficient of determination and model of selection criterion) is presented with particular attention paid to the accuracy, validity, and good fitness of each the methods. Two problems were used to demonstrate the methods. Flow rates, head losses, and Reynolds numbers were calculated using the three pipe network analysis methods. Flow rates were used for the statistical evaluation. The study show that total errors were 30.66, 41.37, and 25.38 for linear theory, Hardy Cross, and Newton-Raphson methods, respectively, and accuracy, validity, and good fitness of these methods are in order of Newton-Raphson (0.90) > linear theory (0.83) > Hardy Cross (0.82) on the basis of their coefficient of determination values and Newton-Raphson (2.38) > linear theory (1.78) > Hardy Cross (1.68) on the basis of their model of selection criterion values. Reliability (%) were 2.56, 6.22, and −3.36 for Newton-Raphson, Linear theory, and Hardy Cross, respectively. The values of coefficient of correlation were 0.842, 0.928, and 0.932 for Hardy Cross, linear theory, and Newton-Raphson, respectively. It was concluded that Newton-Raphson should be first in pipe network analysis.