Revisiting the Estimation of Colebrook Friction Factor: A Comparison between Artificial Intelligence Models and C-W based Explicit Equations

Abstract

Application of Colebrook-White (C-W) relation for calculating Darcy-Weisbach (D-W) friction factor has been widely accepted in literature. However, its implicit formation made it unsuitable in practice. The main aim of this study is to investigate the computational accuracy of friction factor calculation in pressurized flows. Based on the number of recursive steps exploited for calculating friction factor, forty C-W based explicit equations available in the literature are classified into one-step, two-step, three-step, and four-step models. In favour of improving the accuracy of such estimation, two new explicit equations are proposed. The performances of these forty two explicit equations are compared with that of artificial neural network (ANN) and genetic programming (GP) using both global and local criteria while the results of C-W formula are considered as benchmarks. The results indicate that the accuracy of the best and worst ones among these forty four models differ order of magnitudes from one another. Furthermore, the first proposed equation outperformed others based on all eleven considered criteria. Moreover, GP and ANN results are found to be comparable with the best one-step explicit equations. Finally, the results demonstrate that explicit equations with higher recursive steps do not necessarily yield to closer estimations to implicit C-W formula comparing with all of equations with lower number of steps even though the best n-step explicit formula yields to better results than the best (n-1)-step one based on the global criteria.