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Energies 2018, 11(7), 1825; https://doi.org/10.3390/en11071825

One-Log Call Iterative Solution of the Colebrook Equation for Flow Friction Based on Padé Polynomials

1,2,* and 1,*
1
European Commission, DG 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 Ostrava, 17. listopadu 2172/15, 708 00 Ostrava, Czech Republic
*
Authors to whom correspondence should be addressed.
Received: 19 June 2018 / Revised: 5 July 2018 / Accepted: 11 July 2018 / Published: 12 July 2018
(This article belongs to the Special Issue Fluid Flow and Heat Transfer)
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Abstract

The 80 year-old empirical Colebrook function ξ, widely used as an informal standard for hydraulic resistance, relates implicitly the unknown flow friction factor λ, with the known Reynolds number Re and the known relative roughness of a pipe inner surface ε*; λ=ξ(Re,ε*,λ). It is based on logarithmic law in the form that captures the unknown flow friction factor λ in a way that it cannot be extracted analytically. As an alternative to the explicit approximations or to the iterative procedures that require at least a few evaluations of computationally expensive logarithmic function or non-integer powers, this paper offers an accurate and computationally cheap iterative algorithm based on Padé polynomials with only one log-call in total for the whole procedure (expensive log-calls are substituted with Padé polynomials in each iteration with the exception of the first). The proposed modification is computationally less demanding compared with the standard approaches of engineering practice, but does not influence the accuracy or the number of iterations required to reach the final balanced solution. View Full-Text
Keywords: Colebrook equation; Colebrook-White; flow friction; iterative procedure; logarithms; Padé polynomials; hydraulic resistances; turbulent flow; pipes; computational burden Colebrook equation; Colebrook-White; flow friction; iterative procedure; logarithms; Padé polynomials; hydraulic resistances; turbulent flow; pipes; computational burden
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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. One-Log Call Iterative Solution of the Colebrook Equation for Flow Friction Based on Padé Polynomials. Energies 2018, 11, 1825.

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