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  • Improving the Dupuit-Forchheimer groundwater free surface approximation

    Author(s)
    Knight, John
    Griffith University Author(s)
    Knight, John
    Year published
    2005
    Metadata
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    Abstract
    For steady two-dimensional free surface flow over a horizontal impervious base, the Dupuit-Forchheimer theory assumes that the vertical component of velocity is zero, even for non-zero accretion rate at the free surface.-This is improved by assuming that the vertical velocity component is zero at the base, and is proportional to height above the base. This requires the piezometric head to depend linearly on the square of the height, and the two parameters in this relation can be fitted to the two boundary conditions at the free surface, to give an expression for the free surface slope in terms of accretion, free surface ...
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    For steady two-dimensional free surface flow over a horizontal impervious base, the Dupuit-Forchheimer theory assumes that the vertical component of velocity is zero, even for non-zero accretion rate at the free surface.-This is improved by assuming that the vertical velocity component is zero at the base, and is proportional to height above the base. This requires the piezometric head to depend linearly on the square of the height, and the two parameters in this relation can be fitted to the two boundary conditions at the free surface, to give an expression for the free surface slope in terms of accretion, free surface height, and the pressure integral. For problems in which the pressure integral is known explicitly, this first order of ordinary differential equation for the free surface height can be solved numerically. The solutions are more accurate than the Dupuit-Forchheimer expressions for the free surface, and much easier to calculate than numerical solutions to the full two-dimensional problem. Four examples are given, leading to some simple analytical approximations for quantities of interest.
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    Journal Title
    Advances in Water Resources
    Volume
    28
    DOI
    https://doi.org/10.1016/j.advwatres.2005.04.014
    Subject
    Applied Mathematics
    Civil Engineering
    Environmental Engineering
    Publication URI
    http://hdl.handle.net/10072/4301
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    • Journal articles

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