Journal article Open Access

Rational Approximation for Solving an Implicitly Given Colebrook Flow Friction Equation

Praks, Pavel; Brkić, Dejan

MARC21 XML Export

<?xml version='1.0' encoding='UTF-8'?>
<record xmlns="">
  <controlfield tag="005">20200120171818.0</controlfield>
  <controlfield tag="001">3607210</controlfield>
  <datafield tag="700" ind1=" " ind2=" ">
    <subfield code="0">(orcid)0000-0002-2502-0601</subfield>
    <subfield code="a">Brkić, Dejan</subfield>
  <datafield tag="856" ind1="4" ind2=" ">
    <subfield code="s">1169138</subfield>
    <subfield code="z">md5:6df5f1f99d96eb9bc89e7f60342167b1</subfield>
    <subfield code="u"></subfield>
  <datafield tag="542" ind1=" " ind2=" ">
    <subfield code="l">open</subfield>
  <datafield tag="260" ind1=" " ind2=" ">
    <subfield code="c">2019-12-20</subfield>
  <datafield tag="909" ind1="C" ind2="O">
    <subfield code="p">openaire</subfield>
    <subfield code="o"></subfield>
  <datafield tag="909" ind1="C" ind2="4">
    <subfield code="c">26</subfield>
    <subfield code="n">1</subfield>
    <subfield code="p">Mathematics</subfield>
    <subfield code="v">8</subfield>
  <datafield tag="100" ind1=" " ind2=" ">
    <subfield code="0">(orcid)0000-0002-3913-7800</subfield>
    <subfield code="a">Praks, Pavel</subfield>
  <datafield tag="245" ind1=" " ind2=" ">
    <subfield code="a">Rational Approximation for Solving an Implicitly Given Colebrook Flow Friction Equation</subfield>
  <datafield tag="540" ind1=" " ind2=" ">
    <subfield code="a">Free for private use; right holder retains other rights, including distribution</subfield>
  <datafield tag="650" ind1="1" ind2="7">
    <subfield code="a">cc-by</subfield>
    <subfield code="2"></subfield>
  <datafield tag="520" ind1=" " ind2=" ">
    <subfield code="a">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.</subfield>
  <datafield tag="024" ind1=" " ind2=" ">
    <subfield code="a">10.3390/math8010026</subfield>
    <subfield code="2">doi</subfield>
  <datafield tag="980" ind1=" " ind2=" ">
    <subfield code="a">publication</subfield>
    <subfield code="b">article</subfield>
Views 13
Downloads 24
Data volume 28.1 MB
Unique views 13
Unique downloads 24


Cite as