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A note on the equation of ground‐water flow

A note on the equation of ground‐water flow Since the paper by DeWiest (1966) the correct form of the storage coefficient has been discussed. However, Cooper (1966) pointed out an inaccuracy in DeWiest's derivation and found an expression for the storage coefficient equal to the one originally given by Jacob (195O). Using an approach slightly different from Cooper's and not restricting the compression of the soil to be vertical only, we have derived a governing equation 1 equivalent to Cooper's (1966) equation 20, thus joining the supporters of Jacob's form of the storage coefficient. For the present investigation the starting point is (1) −∇·ρqr=ρ2g(nβ+α)(Dh/Dt−w8) where qr is the velocity relative to the soil grains of a barotropic fluid (2) qr=−K∇h=−kρgμ∇h (Darcy's Law)h=1g∫popdpρ(p)+z The time derivative is taken following the soil grains, which have the absolute velocity (3) V8=(us, vs, ws)D/DT=∂/∂t+(V8·∇) and based on the assumption of linearly elastic materials (4) dρ=ρβ dp (fluid)dn=(1−n)α dp (soil) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Water Resources Research Wiley

A note on the equation of ground‐water flow

Madsen, Ole S.
Water Resources Research , Volume 5 (5) – Oct 1, 1969
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References (3)

Publisher
Wiley
Copyright
Copyright © 1969 by the American Geophysical Union.
ISSN
0043-1397
eISSN
1944-7973
DOI
10.1029/WR005i005p01157
Publisher site
See Article on Publisher Site

Abstract

Since the paper by DeWiest (1966) the correct form of the storage coefficient has been discussed. However, Cooper (1966) pointed out an inaccuracy in DeWiest's derivation and found an expression for the storage coefficient equal to the one originally given by Jacob (195O). Using an approach slightly different from Cooper's and not restricting the compression of the soil to be vertical only, we have derived a governing equation 1 equivalent to Cooper's (1966) equation 20, thus joining the supporters of Jacob's form of the storage coefficient. For the present investigation the starting point is (1) −∇·ρqr=ρ2g(nβ+α)(Dh/Dt−w8) where qr is the velocity relative to the soil grains of a barotropic fluid (2) qr=−K∇h=−kρgμ∇h (Darcy's Law)h=1g∫popdpρ(p)+z The time derivative is taken following the soil grains, which have the absolute velocity (3) V8=(us, vs, ws)D/DT=∂/∂t+(V8·∇) and based on the assumption of linearly elastic materials (4) dρ=ρβ dp (fluid)dn=(1−n)α dp (soil)

Journal

Water Resources Research – Wiley

Published: Oct 1, 1969

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