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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

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

Návaznosti

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

Rok uplatnění

2019

Kód důvěrnosti údajů

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

Název periodika

Mathematics

ISSN

2227-7390

e-ISSN

—

Svazek periodika

7

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

14

Strana od-do

—

Kód UT WoS článku

000459734200034

EID výsledku v databázi Scopus

2-s2.0-85059448011