The Applicability of Darcy's Law

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.