<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1405-7743</journal-id>
<journal-title><![CDATA[Ingeniería, investigación y tecnología]]></journal-title>
<abbrev-journal-title><![CDATA[Ing. invest. y tecnol.]]></abbrev-journal-title>
<issn>1405-7743</issn>
<publisher>
<publisher-name><![CDATA[Universidad Nacional Autónoma de México, Facultad de Ingeniería]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1405-77432020000400008</article-id>
<article-id pub-id-type="doi">10.22201/fi.25940732e.2020.21.4.036</article-id>
<title-group>
<article-title xml:lang="es"><![CDATA[Evaluación de la profundidad de recursión de la solución analítica de la ecuación de Colebrook-White en la exactitud de la predicción del factor de fricción]]></article-title>
<article-title xml:lang="en"><![CDATA[Evaluation of the recursion depth of the analytical solution of the Colebrook-White equation in the accuracy of the friction factor prediction]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Alfaro-Guerra]]></surname>
<given-names><![CDATA[Marco]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Guerra-Rojas]]></surname>
<given-names><![CDATA[Rodrigo]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Olivares-Gallardo]]></surname>
<given-names><![CDATA[Alan]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Universidad de La Serena Instituto de Investigación Multidisciplinario en Ciencia y Tecnología ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Universidad de La Serena Facultad de Ingeniería Departamento de Ingeniería en Obras Civiles]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad de La Serena Facultad de Ingeniería Departamento de Ingeniería en Obras Civiles]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Chile</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2020</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2020</year>
</pub-date>
<volume>21</volume>
<numero>4</numero>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1405-77432020000400008&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1405-77432020000400008&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1405-77432020000400008&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen: La ecuación de Colebrook, más conocida como ecuación de Colebrook-White, es valorada por su exactitud en la predicción del factor de fricción en tuberías cilíndricas en zona de flujo turbulento y por ello, es ampliamente utilizada en el cálculo de pérdidas de carga. Esta ecuación es implícita y debe resolverse utilizando métodos numéricos o mediante aproximaciones como la función W de Lambert. En 2015, Mikata y Walczak, propusieron una solución analítica exacta de la ecuación del factor de fricción que presenta una estructura recursiva, por lo que una búsqueda de la solución exacta de la ecuación de Colebrook requiere mucho tiempo y consume importantes recursos computacionales. Por esa razón, en este trabajo se muestra el nivel de exactitud en el cálculo del factor de fricción, representado por el error obtenido al implementar la solución analítica en función de la profundidad de recursión &#8220;n&#8221;, para lo que se desarrolló una macro de Excel en lenguaje VBA. La originalidad del presente trabajo corresponde a la evaluación de la exactitud en la predicción del factor de fricción, en el rango de uso práctico de la ecuación en ingeniería, considerando valores de rugosidad relativa de 10-1 a 10-6 y valores del número de Reynolds de 104 a 108, lo que genera una matriz de análisis que contiene 839.937 datos. Como resultado del análisis realizado se puede concluir que la precisión de la solución de la ecuación de Colebrook depende de la profundidad de recursión, llegando a un máximo error relativo de 5,369E-08 % para una profundidad de recursión de n=10.]]></p></abstract>
<abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: The Colebrook equation, better known as the Colebrook-White equation, is valued for its accuracy in the prediction of the friction factor in cylindrical pipes in turbulent flow zone and is therefore widely used in the calculation of load losses. This equation is implicit and must be solved using numerical methods or by approximations such as the Lambert W function. In 2015, Mikata and Walczak proposed an exact analytical solution of the friction factor equation that presents a recursive structure, so the search for the exact solution of the Colebrook equation requires a lot of time and consumes significant computational resources. For this reason, this work shows the level of accuracy in the calculation of the friction factor, represented by the error obtained when implementing the analytical solution based on the depth of recursion &#8220;n&#8221;, for which a macro of Excel in VBA language. The originality of the present work corresponds to the evaluation of the accuracy in the prediction of the friction factor, in the range of practical use of the engineering equation considering relative roughness values of 10-1 to 10-6 and Reynolds numbers values from 104 to 108, which generates an analysis matrix that contains 839,937 data. As a result of the analysis performed, it can be concluded that the precision of the solution of the Colebrook equation depends on the depth of recursion, reaching a maximum relative error of 5,369E-08 % for a recursion depth of n=10.]]></p></abstract>
<kwd-group>
<kwd lng="es"><![CDATA[Factor de fricción]]></kwd>
<kwd lng="es"><![CDATA[ecuación de Colebrook]]></kwd>
<kwd lng="es"><![CDATA[solución analítica]]></kwd>
<kwd lng="es"><![CDATA[profundidad de recursión]]></kwd>
<kwd lng="en"><![CDATA[Friction factor]]></kwd>
<kwd lng="en"><![CDATA[Colebrook equation]]></kwd>
<kwd lng="en"><![CDATA[analytical solution]]></kwd>
<kwd lng="en"><![CDATA[recursion depht]]></kwd>
</kwd-group>
</article-meta>
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