Advanced Iterative Procedures for Solving the Implicit Colebrook Equation for Fluid Flow Friction
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989100%3A27740%2F19%3A10242741" target="_blank" >RIV/61989100:27740/19:10242741 - isvavai.cz</a>
Result on the web
<a href="https://www.hindawi.com/journals/ace/2018/5451034/" target="_blank" >https://www.hindawi.com/journals/ace/2018/5451034/</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1155/2018/5451034" target="_blank" >10.1155/2018/5451034</a>
Alternative languages
Result language
angličtina
Original language name
Advanced Iterative Procedures for Solving the Implicit Colebrook Equation for Fluid Flow Friction
Original language description
The empirical Colebrook equation from 1939 is still accepted as an informal standard way to calculate the friction factor of turbulent flows (4000 < Re < 10(8)) through pipes with roughness between negligible relative roughness (epsilon/D -> 0) to very rough (up to epsilon/D = 0.05). The Colebrook equation includes the flow friction factor lambda in an implicit logarithmic form, lambda being a function of the Reynolds number Re and the relative roughness of inner pipe surface epsilon/D: lambda = f(lambda, Re, epsilon/D). To evaluate the error introduced by the many available explicit approximations to the Colebrook equation, lambda approximate to f(Re, epsilon/D), it is necessary to determinate the value of the friction factor lambda from the Colebrook equation as accurately as possible. The most accurate way to achieve that is by using some kind of the iterative method. The most used iterative approach is the simple fixed-point method, which requires up to 10 iterations to achieve a good level of accuracy. The simple fixed-point method does not require derivatives of the Colebrook function, while the most of the other presented methods in this paper do require. The methods based on the accelerated Householder's approach (3rd order, 2nd order: Halley's and Schroder's method, and 1st order: Newton-Raphson) require few iterations less, while the three-point iterative methods require only 1 to 3 iterations to achieve the same level of accuracy. The paper also discusses strategies for finding the derivatives of the Colebrook function in symbolic form, for avoiding the use of the derivatives (secant method), and for choosing an optimal starting point for the iterative procedure. The Householder approach to the Colebrook' equations expressed through the Lambert W-function is also analyzed. Finally, it is presented one approximation to the Colebrook equation with an error of no more than 0.0617%.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
20104 - Transport engineering
Result continuities
Project
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Continuities
V - Vyzkumna aktivita podporovana z jinych verejnych zdroju
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Advances in Civil Engineering
ISSN
1687-8086
e-ISSN
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Volume of the periodical
2018
Issue of the periodical within the volume
Article number 5451034
Country of publishing house
GB - UNITED KINGDOM
Number of pages
18
Pages from-to
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UT code for WoS article
000460259400001
EID of the result in the Scopus database
2-s2.0-85051786909