### 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

*Quarterly Journal of Mechanics and Applied Mathematics*,

*10*(3), 302-311. https://doi.org/10.1093/qjmam/10.3.302