The Applicability of Darcy's Law1,3
1968
Swartzendruber, D. (Dale)
Deviations from Darcian proportionality between flow velocity v and hydraulic gradient i are considered in terms of a gradient-dependent hydraulic conductivity K(i) = v/i. Published greater-than-proportional data for saturated flow indicate measured variations in K(i) of 2- to 4-fold, with a potentiality for 5- to 15-fold variations inferred from fitted non-Darcian flow equations. Non-Darcian effects for two-dimensional radial flow are also analyzed. The hydraulic head distribution is shifted from the Darcian-derived logarithmic pattern toward the characteristic linear distribution for one-dimensional flow, and the amount of the shift is velocity dependent. This implies that the flow net for two-dimensional non-Darcian flow would generally change with flow velocity, and that the high-gradient flow regions would be more permeable than for Darcian flow. For a particular unsaturated soil, the soil-water diffusivity D appears to be a gradient-dependent quantity D(θ,ω), where θ is the soil-water content, and ω is the water-content gradient. A maximum 8-fold variation in D at given low water contents is associated with a 40% discrepancy between experimental water-absorption rates and those calculated from proportional flow theory. Similarly, a 115% discrepancy is found for the vertically downward rate of infiltration into a mixture of quartz sand and ground silica, but the deviating behavior can be precisely accommodated with a non-Darcian infiltration equation derived by a simplified analysis. Various implications of non-proportional effects are discussed and enumerated briefly.
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