Rational Approximation for Solving an Implicitly Given Colebrook Flow Friction Equation

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F20%3A10244887" target="_blank" >RIV/61989100:27740/20:10244887 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.3390/math8010026" target="_blank" >https://doi.org/10.3390/math8010026</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/math8010026" target="_blank" >10.3390/math8010026</a>

Result language

angličtina

Original language name

Rational Approximation for Solving an Implicitly Given Colebrook Flow Friction Equation

Original language description

The empirical logarithmic Colebrook equation for hydraulic resistance in pipes implicitly considers the unknown flow friction factor. Its explicit approximations, used to avoid iterative computations, should be accurate but also computationally efficient. We present a rational approximate procedure that completely avoids the use of transcendental functions, such as logarithm or non-integer power, which require execution of the additional number of floating-point operations in computer processor units. Instead of these, we use only rational expressions that are executed directly in the processor unit. The rational approximation was found using a combination of a Pade approximant and artificial intelligence (symbolic regression). Numerical experiments in Matlab using 2 million quasi-Monte Carlo samples indicate that the relative error of this new rational approximation does not exceed 0.866%. Moreover, these numerical experiments show that the novel rational approximation is approximately two times faster than the exact solution given by the Wright omega function.

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10100 - Mathematics

Project

Result was created during the realization of more than one project. More information in the Projects tab.

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2020

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Mathematics

ISSN

2227-7390

e-ISSN

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Volume of the periodical

8

Issue of the periodical within the volume

1

Country of publishing house

CH - SWITZERLAND

Number of pages

8

Pages from-to

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UT code for WoS article

000515730100105

EID of the result in the Scopus database

2-s2.0-85079618293