Working Paper Review Version 1 This version is not peer-reviewed

Review of New Flow Friction Equations: Constructing Colebrook’s Explicit Correlations Accurately

Version 1 : Received: 13 May 2020 / Approved: 14 May 2020 / Online: 14 May 2020 (15:15:38 CEST)

A peer-reviewed article of this Preprint also exists.

Pavel Praks and Dejan Brkić (2020): Review of new flow friction equations: Constructing Colebrook’s explicit correlations accurately. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería (RIMNI) /International Journal of Numerical Methods for Calculation and Design in Engineering/ 36(3). https://doi.org/10.23967/j.rimni.2020.09.001, ISSN 1886-158X (online version) - ISSN 0213-1315 (printed version) Pavel Praks and Dejan Brkić (2020): Review of new flow friction equations: Constructing Colebrook’s explicit correlations accurately. Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería (RIMNI) /International Journal of Numerical Methods for Calculation and Design in Engineering/ 36(3). https://doi.org/10.23967/j.rimni.2020.09.001, ISSN 1886-158X (online version) - ISSN 0213-1315 (printed version)

Journal reference: Revista Internacional de Métodos Numéricos para Cálculo y Diseño en Ingeniería 2020, 36
DOI: 10.23967/j.rimni.2020.09.001

Abstract

Using only a limited number of computationally expensive functions, we show a way how to construct accurate and computationally efficient approximations of the Colebrook equation for flow friction. The presented approximations are based on the asymptotic series expansion of the Wright ω-function and symbolic regression. The results are verified with 8 million of Quasi-Monte Carlo points covering the domain of interest for engineers. In comparison with the built-in “wrightOmega” feature of Matlab R2016a, the herein introduced related approximations of the Wright ω-function significantly accelerate the computation. With only two logarithms and several basic arithmetic operations used, the presented approximations are not only computationally efficient but also extremely accurate. The maximal relative error of the most promising approximation which is given in the form suitable for engineers’ use is limited to 0.0012%, while for a little bit more complex variant is limited to 0.000024%.

Subject Areas

Colebrook equation; Hydraulic flow friction; Wright ω-function; explicit approximations; symbolic regression; computational intelligence

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