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Water 2018, 10(9), 1175; https://doi.org/10.3390/w10091175

Symbolic Regression-Based Genetic Approximations of the Colebrook Equation for Flow Friction

1,2,* and 1,*
1
European Commission, Joint Research Centre (JRC), Directorate C: Energy, Transport and Climate, Unit C3: Energy Security, Distribution and Markets, Via Enrico Fermi 2749, 21027 Ispra (VA), Italy
2
IT4Innovations National Supercomputing Center, VŠB—Technical University of Ostrava, 17, listopadu 2172/15, 708 00 Ostrava, Czech Republic
*
Authors to whom correspondence should be addressed.
Received: 6 August 2018 / Revised: 28 August 2018 / Accepted: 30 August 2018 / Published: 2 September 2018
(This article belongs to the Special Issue Pipeline Fluid Mechanics)
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Abstract

Widely used in hydraulics, the Colebrook equation for flow friction relates implicitly to the input parameters; the Reynolds number, Re and the relative roughness of an inner pipe surface, ε/D with an unknown output parameter; the flow friction factor, λ; λ = f (λ, Re, ε/D). In this paper, a few explicit approximations to the Colebrook equation; λ ≈ f (Re, ε/D), are generated using the ability of artificial intelligence to make inner patterns to connect input and output parameters in an explicit way not knowing their nature or the physical law that connects them, but only knowing raw numbers, {Re, ε/D}→{λ}. The fact that the used genetic programming tool does not know the structure of the Colebrook equation, which is based on computationally expensive logarithmic law, is used to obtain a better structure of the approximations, which is less demanding for calculation but also enough accurate. All generated approximations have low computational cost because they contain a limited number of logarithmic forms used for normalization of input parameters or for acceleration, but they are also sufficiently accurate. The relative error regarding the friction factor λ, in in the best case is up to 0.13% with only two logarithmic forms used. As the second logarithm can be accurately approximated by the Padé approximation, practically the same error is obtained also using only one logarithm. View Full-Text
Keywords: Colebrook equation; flow friction; turbulent flow; genetic programming; symbolic regression; explicit approximations Colebrook equation; flow friction; turbulent flow; genetic programming; symbolic regression; explicit approximations
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Praks, P.; Brkić, D. Symbolic Regression-Based Genetic Approximations of the Colebrook Equation for Flow Friction. Water 2018, 10, 1175.

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