An Evaluation of Frictional Factors in Pipe Network Analysis Using Statistical Methods

Pipe network analysis is an essential ingredient in the design and distribution networks of potable and recycled water. The Hardy Cross method of successive approximations and the Darcy-Weisbach method of estimating the friction losses in pipes are the two methods commonly employed in the pipe network analysis. The accuracy of these methods depends on the frictional factor, which can be determined using various formulations such as Colebrook-White, Moody, Newton-Raphson, Barr, Wood, Haaland, and Swamee and Jain formulations, but little is known of the accuracy of these formulations. In this paper as a follow-up on a previous study by one of the authors, a report is presented on the accuracy, analysis of validity, and goodness of fit of some of these formulations using statistical methods. A three-loop diagram was adopted from the literature, and pipe network analysis was carried out using the Linear Theory method. Results of the study revealed that Colebrook-White gave the least error, the highest coefficient of determination, and best Model of Selection Criterion followed by Moody, Swamee and Jain, Barr, Haaland, and Wood. The correlation coefficients of the formulations were 1.0, 1.0, 1.0, 0.9999, 0.9997, and 0.9991 for Colebrook-White, Swamee and Jain, Moody, Barr, Haaland, and Wood, respectively. It was then concluded that the Colebrook-White, Swamee and Jain, and Moody method are the best options because they gave the highest coefficient of determination and best Model of Selection Criterion; but in the absence of computer and computer packages such as Microsoft Excel, Moody is the best because of its explicit case and its availability as a chart.