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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 &lt; Re &lt; 10(8)) through pipes with roughness between negligible relative roughness (epsilon/D -&gt; 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&apos;s approach (3rd order, 2nd order: Halley&apos;s and Schroder&apos;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&apos; 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

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    20104 - Transport engineering

Result continuities

  • Project

  • 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

  • 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

  • UT code for WoS article

    000460259400001

  • EID of the result in the Scopus database

    2-s2.0-85051786909