IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2019i1p26-d300499.html
   My bibliography  Save this article

Rational Approximation for Solving an Implicitly Given Colebrook Flow Friction Equation

Author

Listed:
  • Pavel Praks

    (European Commission, Joint Research Centre (JRC), 21027 Ispra, Italy
    IT4Innovations, VŠB—Technical University of Ostrava, 708 00 Ostrava, Czech Republic)

  • Dejan Brkić

    (European Commission, Joint Research Centre (JRC), 21027 Ispra, Italy
    IT4Innovations, VŠB—Technical University of Ostrava, 708 00 Ostrava, Czech Republic
    Research and Development Center “Alfatec”, 18000 Niš, Serbia)

Abstract

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 Padé 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.

Suggested Citation

  • Pavel Praks & Dejan Brkić, 2019. "Rational Approximation for Solving an Implicitly Given Colebrook Flow Friction Equation," Mathematics, MDPI, vol. 8(1), pages 1-8, December.
    • Handle: RePEc:gam:jmathe:v:8:y:2019:i:1:p:26-:d:300499
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/1/26/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/1/26/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Pavel Praks & Dejan Brkić, 2018. "One-Log Call Iterative Solution of the Colebrook Equation for Flow Friction Based on Padé Polynomials," Energies, MDPI, vol. 11(7), pages 1-12, July.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Artur J. Jaworski, 2019. "Special Issue “Fluid Flow and Heat Transfer”," Energies, MDPI, vol. 12(16), pages 1-4, August.
    2. Dejan Brkić & Pavel Praks, 2019. "Accurate and Efficient Explicit Approximations of the Colebrook Flow Friction Equation Based on the Wright ω-Function: Reply to Discussion," Mathematics, MDPI, vol. 7(5), pages 1-7, May.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2019:i:1:p:26-:d:300499. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.