https://www.scipedia.com/wd/index.php?action=history&feed=atom&title=Article_Brkic_2019aArticle Brkic 2019a - Revision history2026-04-25T21:17:00ZRevision history for this page on the wikiMediaWiki 1.27.0-wmf.10https://www.scipedia.com/wd/index.php?title=Article_Brkic_2019a&diff=163231&oldid=prevDejan.brkic: Dejan.brkic moved page Draft Brkic 491063853 to Article Brkic 2019a2020-05-16T11:57:04Z<p>Dejan.brkic moved page <a href="/public/Draft_Brkic_491063853" class="mw-redirect" title="Draft Brkic 491063853">Draft Brkic 491063853</a> to <a href="/public/Article_Brkic_2019a" title="Article Brkic 2019a">Article Brkic 2019a</a></p>
<table class="diff diff-contentalign-left" data-mw="interface">
<tr style='vertical-align: top;' lang='en'>
<td colspan='1' style="background-color: white; color:black; text-align: center;">← Older revision</td>
<td colspan='1' style="background-color: white; color:black; text-align: center;">Revision as of 11:57, 16 May 2020</td>
</tr><tr><td colspan='2' style='text-align: center;' lang='en'><div class="mw-diff-empty">(No difference)</div>
</td></tr></table>Dejan.brkichttps://www.scipedia.com/wd/index.php?title=Article_Brkic_2019a&diff=163230&oldid=prevDejan.brkic: Created page with " == Abstract == sup>The logarithmic Colebrook flow friction equation is implicitly given in respect to an unknown flow friction factor. Traditionally, an explicit approximati..."2020-05-16T11:57:03Z<p>Created page with " == Abstract == sup>The logarithmic Colebrook flow friction equation is implicitly given in respect to an unknown flow friction factor. Traditionally, an explicit approximati..."</p>
<p><b>New page</b></p><div><br />
== Abstract ==<br />
<br />
sup>The logarithmic Colebrook flow friction equation is implicitly given in respect to an unknown flow friction factor. Traditionally, an explicit approximation of the Colebrook equation requires evaluation of computationally demanding transcendental functions, such as logarithmic, exponential, non-integer power, Lambert W and WrightΩ functions. Conversely, we herein present several computationally cheap explicit approximations of the Colebrook equation that require only one logarithmic function in the initial stage, whilst for the remaining iterations the cheap Padé approximant of the first order is used instead. Moreover, symbolic regression was used for the development of a novel starting point, which significantly reduces the error of internal iterations compared with the fixed value staring point. Despite the starting point using a simple rational function, it reduces the relative error of the approximation with one internal cycle from 1.81% to 0.156% (i.e., by a factor of 11.6), whereas the relative error of the approximation with two internal cycles is reduced from 0.317% to 0.0259% (i.e., by a factor of 12.24). This error analysis uses a sample with 2 million quasi-Monte Carlo points and the Sobol sequence.<br />
<br />
== Full document ==<br />
<pdf>Media:Draft_Brkic_491063853-6646-document.pdf</pdf></div>Dejan.brkic