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dc.contributor.authorPraks, Pavel
dc.contributor.authorBrkić, Dejan
dc.date.accessioned2018-11-27T09:54:50Z
dc.date.available2018-11-27T09:54:50Z
dc.date.issued2018
dc.identifier.citationWater. 2018, vol. 10, issue 9, art. no. 1175.cs
dc.identifier.issn2073-4441
dc.identifier.urihttp://hdl.handle.net/10084/133228
dc.description.abstractWidely used in hydraulics, the Colebrook equation for flow friction relates implicitly to the input parameters; the Reynolds number, Re and the relative roughness of an inner pipe surface, epsilon/D with an unknown output parameter; the flow friction factor, ; = f (, Re, epsilon/D). In this paper, a few explicit approximations to the Colebrook equation; approximate to f (Re, epsilon/D), are generated using the ability of artificial intelligence to make inner patterns to connect input and output parameters in an explicit way not knowing their nature or the physical law that connects them, but only knowing raw numbers, {Re, epsilon/D}{}. The fact that the used genetic programming tool does not know the structure of the Colebrook equation, which is based on computationally expensive logarithmic law, is used to obtain a better structure of the approximations, which is less demanding for calculation but also enough accurate. All generated approximations have low computational cost because they contain a limited number of logarithmic forms used for normalization of input parameters or for acceleration, but they are also sufficiently accurate. The relative error regarding the friction factor , in in the best case is up to 0.13% with only two logarithmic forms used. As the second logarithm can be accurately approximated by the Pade approximation, practically the same error is obtained also using only one logarithm.cs
dc.format.extent4507546 bytes
dc.format.mimetypeapplication/pdf
dc.language.isoencs
dc.publisherMDPIcs
dc.relation.ispartofseriesWatercs
dc.relation.urihttp://doi.org/10.3390/w10091175.cs
dc.rights© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.cs
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/cs
dc.subjectColebrook equationcs
dc.subjectflow frictioncs
dc.subjectturbulent flowcs
dc.subjectgenetic programmingcs
dc.subjectsymbolic regressioncs
dc.subjectexplicit approximationscs
dc.titleSymbolic regression-based genetic approximations of the Colebrook equation for flow frictioncs
dc.typearticlecs
dc.identifier.doi10.3390/w10091175
dc.rights.accessopenAccesscs
dc.type.versionpublishedVersioncs
dc.type.statusPeer-reviewedcs
dc.description.sourceWeb of Sciencecs
dc.description.volume10cs
dc.description.issue9cs
dc.description.firstpageart. no. 1175cs
dc.identifier.wos000448821900067


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© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.
Except where otherwise noted, this item's license is described as © 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license.