Laminar boundary layers at the interface of co-current parallel streams

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Abstract

The approximate solution of Keulegan (1) for the steady flow of a stream of viscous incompressible fluid over another at rest is extended to the case where both fluids are moving co-current but at different velocities. This solution utilizes a sextic polynomial for the velocity distribution in the boundary layers. The solutions depend only on the ratio U2/U1 of the velocities of the two streams and on the product of the corresponding viscosity and density ratios. Numerical results are given for seven values of μ2 ρ2/(μ1ρ1) at one value of U2/U1. Lock (2) has published an exact solution with a numerical result for μ2ρ2/(μ1ρ1) = 1, U2/U1 = 0.501 and the sextic polynomial solution is evaluated for this case also. Comparison indicates that in general the sextic polynomial is more accurate than the quartic polynomial but that the advantage is not great.

Original languageEnglish
Pages (from-to)302-311
Number of pages10
JournalQuarterly Journal of Mechanics and Applied Mathematics
Volume10
Issue number3
DOIs
Publication statusPublished - 1 Dec 1957
Externally publishedYes

Cite this

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abstract = "The approximate solution of Keulegan (1) for the steady flow of a stream of viscous incompressible fluid over another at rest is extended to the case where both fluids are moving co-current but at different velocities. This solution utilizes a sextic polynomial for the velocity distribution in the boundary layers. The solutions depend only on the ratio U2/U1 of the velocities of the two streams and on the product of the corresponding viscosity and density ratios. Numerical results are given for seven values of μ2 ρ2/(μ1ρ1) at one value of U2/U1. Lock (2) has published an exact solution with a numerical result for μ2ρ2/(μ1ρ1) = 1, U2/U1 = 0.501 and the sextic polynomial solution is evaluated for this case also. Comparison indicates that in general the sextic polynomial is more accurate than the quartic polynomial but that the advantage is not great.",
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Laminar boundary layers at the interface of co-current parallel streams. / Potter, O. E.

In: Quarterly Journal of Mechanics and Applied Mathematics, Vol. 10, No. 3, 01.12.1957, p. 302-311.

Research output: Contribution to journalArticleResearchpeer-review

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T1 - Laminar boundary layers at the interface of co-current parallel streams

AU - Potter, O. E.

PY - 1957/12/1

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AB - The approximate solution of Keulegan (1) for the steady flow of a stream of viscous incompressible fluid over another at rest is extended to the case where both fluids are moving co-current but at different velocities. This solution utilizes a sextic polynomial for the velocity distribution in the boundary layers. The solutions depend only on the ratio U2/U1 of the velocities of the two streams and on the product of the corresponding viscosity and density ratios. Numerical results are given for seven values of μ2 ρ2/(μ1ρ1) at one value of U2/U1. Lock (2) has published an exact solution with a numerical result for μ2ρ2/(μ1ρ1) = 1, U2/U1 = 0.501 and the sextic polynomial solution is evaluated for this case also. Comparison indicates that in general the sextic polynomial is more accurate than the quartic polynomial but that the advantage is not great.

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