Darcy’s Law. Xxxxx’x Law can be written in terms of infiltration rate in the following form: f = Q = −K ⎛ dh ⎞ = −Ki (1.1) A ⎜ dz ⎟ ⎝ ⎠ where f is the specific discharge or infiltration rate of water through a unit cross-section of the porous material (L/t), Q is the volumetric flow rate (L3/t), A is the cross-sectional area perpendicular to flow (L2), K is the hydraulic conductivity (L/t), dh/dz is the hydraulic gradient (L/L), and i is a “short-hand” notation for the gradient (L/L). Xxxxx’x law illustrates that the two factors that control infiltration are hydraulic conductivity and hydraulic gradient. The hydraulic conductivity, K, is a particularly challenging parameter to estimate because it varies by orders-of-magnitude, depending on the geologic media or soil type (Freeze and Cherry, 1979). Additional uncertainties are introduced in unsaturated soils, where hydraulic conductivity is a function of the water saturation or moisture content. The hydraulic head in equation 1.1 is the driving force or energy that causes water to move through the soil. This force, which is due to gravity and pressure, is composed of two components: an elevation head, z , and a pressure head, ψ: h = z + P ρg = z +ψ
