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
Summary
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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