Abstract

The Colebrook-White equation is often used for calculation of the friction factor in turbulent regimes; it has succeeded in attracting a great deal of attention from researchers. The Colebrook–White equation is a complex equation where the computation of the friction factor is not direct, and there is a need for trial-error methods or graphical solutions; on the other hand, several researchers have attempted to alter the Colebrook-White equation by explicit formulas with the hope of achieving zero-percent (0%) maximum deviation, among them Dejan Brkić and Pavel Praks. The goal of this paper is to discuss the results proposed by the authors in their paper:” Accurate and Efficient Explicit Approximations of the Colebrook Flow Friction Equation Based on the Wright ω-Function” and to propose more accurate formulas.

Highlights

  • In the discussed paper, Dejan Brkić and Pavel Praks [1] presented a new formula, where they claim that the error recorded is about 0.0096% for the entire range of the relative roughness, and the Reynolds number is given by the following ranges: 0 ≤ (ε/D ) ≤ 0.05 and 4000 ≤ Re ≤ 108 .The discussion in this paper adds a number of comments about the results of the authors and proposes exact formulas.2

  • Using Equation (6) instead of Equation (A1) gives a more accurate solution, the maximum deviation for the entire range of Moody diagrams (0 ≤ (ε/D ) ≤ 0.05 and 4000 ≤ Re ≤ 108 ) was: 0.147% which is very close to Vatankhah AR (2014) [6] accuracy: p = 0.8686 B + c where: 4992 ∗

  • The results were very accepted for the Equations (2 or A1), (3 or A2) and (4 or A3), the maximum deviation recorded for the rest was not accurate

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Summary

Introduction

Dejan Brkić and Pavel Praks [1] presented a new formula, where they claim that the error recorded is about 0.0096% for the entire range of the relative roughness, and the Reynolds number is given by the following ranges: 0 ≤ (ε/D ) ≤ 0.05 and 4000 ≤ Re ≤ 108 .The discussion in this paper adds a number of comments about the results of the authors and proposes exact formulas.2. Dejan Brkić and Pavel Praks [1] presented a new formula, where they claim that the error recorded is about 0.0096% for the entire range of the relative roughness, and the Reynolds number is given by the following ranges: 0 ≤ (ε/D ) ≤ 0.05 and 4000 ≤ Re ≤ 108. The discussion in this paper adds a number of comments about the results of the authors and proposes exact formulas. The Colebrook-White equation is an empirical formula; it is given by Equation (1) [2]: " ε/D 2.51 f = −2 log + p Re f !#−2 (1)

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