Working Paper Review Version 1 This version is not peer-reviewed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

How to cite: Praks, P.; Brkić, D. Review of New Flow Friction Equations: Constructing Colebrook’s Explicit Correlations Accurately. Preprints 2020, 2020050243 Praks, P.; Brkić, D. Review of New Flow Friction Equations: Constructing Colebrook’s Explicit Correlations Accurately. Preprints 2020, 2020050243

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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