### 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 U_{2}/U_{1} 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 μ_{2} ρ_{2}/(μ_{1}ρ_{1}) at one value of U_{2}/U_{1}. Lock (2) has published an exact solution with a numerical result for μ_{2}ρ_{2}/(μ_{1}ρ_{1}) = 1, U_{2}/U_{1} = 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 language | English |
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Pages (from-to) | 302-311 |

Number of pages | 10 |

Journal | Quarterly Journal of Mechanics and Applied Mathematics |

Volume | 10 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Dec 1957 |

Externally published | Yes |

### Cite this

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**Laminar boundary layers at the interface of co-current parallel streams.** / Potter, O. E.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

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

AU - Potter, O. E.

PY - 1957/12/1

Y1 - 1957/12/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=0041360973&partnerID=8YFLogxK

U2 - 10.1093/qjmam/10.3.302

DO - 10.1093/qjmam/10.3.302

M3 - Article

VL - 10

SP - 302

EP - 311

JO - Quarterly Journal of Mechanics and Applied Mathematics

JF - Quarterly Journal of Mechanics and Applied Mathematics

SN - 0033-5614

IS - 3

ER -