Accurate and efficient explicit approximations of the colebrook flow friction equation based on the wright ω-function

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F19%3A10240873" target="_blank" >RIV/61989100:27740/19:10240873 - isvavai.cz</a>

Result on the web

<a href="https://www.mdpi.com/2227-7390/7/1/34" target="_blank" >https://www.mdpi.com/2227-7390/7/1/34</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/math7010034" target="_blank" >10.3390/math7010034</a>

Result language

angličtina

Original language name

Accurate and efficient explicit approximations of the colebrook flow friction equation based on the wright ω-function

Original language description

The Colebrook equation is a popular model for estimating friction loss coefficients in water and gas pipes. The model is implicit in the unknown flow friction factor, f. To date, the captured flow friction factor, f, can be extracted from the logarithmic form analytically only in the term of the Lambert w-function. The purpose of this study is to find an accurate and computationally efficient solution based on the shifted Lambert w-function also known as the Wright ω-function. The Wright ω-function is more suitable because it overcomes the problem with the overflow error by switching the fast growing term, y = w(ex), of the Lambert w-function to series expansions that further can be easily evaluated in computers without causing overflow run-time errors. Although the Colebrook equation transformed through the Lambert w-function is identical to the original expression in terms of accuracy, a further evaluation of the Lambert W-function can be only approximate. Very accurate explicit approximations of the Colebrook equation that contain only one or two logarithms are shown. The final result is an accurate explicit approximation of the Colebrook equation with a relative error of no more than 0.0096%. The presented approximations are in a form suitable for everyday engineering use, and are both accurate and computationally efficient. (C) 2018 by the authors.

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

10102 - Applied mathematics

Project

<a href="/en/project/LQ1602" target="_blank" >LQ1602: IT4Innovations excellence in science</a><br>

Continuities

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

Publication year

2019

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

7

Issue of the periodical within the volume

1

Country of publishing house

CH - SWITZERLAND

Number of pages

14

Pages from-to

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UT code for WoS article

000459734200034

EID of the result in the Scopus database

2-s2.0-85059448011