Analytical Formula for the Mean Velocity Profile in a Pipe Derived on the Basis of a Spatial Polynomial Vorticity Distribution

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dc.contributor.authorŠtigler, Jaroslavcs
dc.coverage.issue10cs
dc.coverage.volume13cs
dc.date.accessioned2021-09-22T14:57:29Z
dc.date.available2021-09-22T14:57:29Z
dc.date.issued2021-05-14cs
dc.description.abstractThe derivation of the mean velocity profile for a given vorticity distribution over the pipe cross-section is presented in this paper1. The velocity profile and the vorticity distribution are axisymmetric, which means that the radius is the only variable. The importance of the vortex field for the flow analysis is discussed in the paper. The polynomial function with four free parameters is chosen for the vorticity distribution. Free parameters of this function are determined using boundary conditions. There are also two free exponents in the polynomial. These exponents are determined based on the comparison of this analytical formula with experimental data. Experimental data are taken from the Princeton superpipe data which consist of 26 velocity profiles for a wide range of Reynolds numbers (Re). This analytical formula for the mean velocity profile is more precise than the previous one and it is possible to use it for the wide range of Reynolds number <31,577; 35,259,000>. This formula is easy to use, to integrate, or to derivate. The empirical formulas for the profile parameters as a function of Re are also included in this paper. All information for the mean velocity profile prediction in the mentioned Re range are in the paper. It means that it is necessary to know the average velocity v((av)), the pipe radius R, and Re to be able to predict the turbulent mean velocity profile in a pipe.en
dc.formattextcs
dc.format.extent1-27cs
dc.format.mimetypeapplication/pdfcs
dc.identifier.citationWater. 2021, vol. 13, issue 10, p. 1-27.en
dc.identifier.doi10.3390/w13101372cs
dc.identifier.issn2073-4441cs
dc.identifier.other172540cs
dc.identifier.urihttp://hdl.handle.net/11012/201645
dc.language.isoencs
dc.publisherMDPIcs
dc.relation.ispartofWatercs
dc.relation.urihttps://www.mdpi.com/2073-4441/13/10/1372cs
dc.rightsCreative Commons Attribution 4.0 Internationalcs
dc.rights.accessopenAccesscs
dc.rights.sherpahttp://www.sherpa.ac.uk/romeo/issn/2073-4441/cs
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/cs
dc.subjectfluid flow in pipeen
dc.subjectturbulent mean velocity profileen
dc.subjectvorticityen
dc.titleAnalytical Formula for the Mean Velocity Profile in a Pipe Derived on the Basis of a Spatial Polynomial Vorticity Distributionen
dc.type.driverarticleen
dc.type.statusPeer-revieweden
dc.type.versionpublishedVersionen
sync.item.dbidVAV-172540en
sync.item.dbtypeVAVen
sync.item.insts2022.02.07 12:54:57en
sync.item.modts2022.02.07 12:14:51en
thesis.grantorVysoké učení technické v Brně. Fakulta strojního inženýrství. EÚ-odbor fluidního inženýrství Viktora Kaplanacs
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EÚ-odbor fluidního inženýrství Viktora Kaplana