Discussion of “Accurate and Efficient Explicit Approximations of the Colebrook Flow Friction Equation Based on the Wright ω-Function” by Dejan Brkić and Pavel Praks, Mathematics 2019, 7, 34; doi:10.3390/math7010034

Majid Niazkar

doi:10.3390/math8050793

Abstract

Estimating the Darcy–Weisbach friction factor is crucial to various engineering applications. Although the literature has accepted the Colebrook–White formula as a standard approach for this prediction, its implicit structure brings about an active field of research seeking for alternatives more suitable in practice. This study mainly attempts to increase the precision of two explicit equations proposed by Brkić and Praks. The results obviously demonstrate that the modified relations outperformed the original ones from nine out of 10 accuracy evaluation criteria. Finally, one of the improved equations estimates closer friction factors to those obtained by the Colebrook–White formula among 18 one-step explicit equations available in the literature based on three of the considered criteria.

Highlights

Brkić and Praks [1] applied Wright ω-Function to improve the accuracy of the estimation of the Colebrook friction factor
Based on the classification introduced by Niazkar [2], their equations can be categorized as one-step relations for predicting the Darcy–Weisbach friction factor
Model 3 improves the accuracy of Model 2 based on maximum Absolute Error (maxAE), maxRE, minimum Relative Error (minRE) and maxRE+, while it decreases the precision of Model 2 according to minimum Absolute Error (minAE) and maxRE−

Summary

Introduction

Brkić and Praks [1] applied Wright ω-Function to improve the accuracy of the estimation of the Colebrook friction factor. As a result, they proposed two new explicit equations using symbolic regression software so called Eureqa. Based on the classification introduced by Niazkar [2], their equations can be categorized as one-step relations for predicting the Darcy–Weisbach friction factor. This discussion mainly aims to improve the accuracy of the proposed equations by Brkić and. The performances of the original equations and the modified ones were compared with those of other models available in the literature

Estimating Darcy–Weisbach Friction Factor

Improving the Explicit Equations Proposed by Brkić and Praks

Accuracy Evaluation Criteria

Results and Discussion

Conclusions