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)
Water Resources Research – Wiley
Published: Oct 1, 1969
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