Darcy's law states that there is a linear relationship between flow velocity (v) and hydraulic gradient (i) for any given saturated soil under steady laminar flow conditions.

If the rate of flow is q (volume/time) through cross-sectional area (A) of the soil mass, Darcy's Law can be expressed as

v = q/A = k.i

where k = permeability of the soil
i = Dh/L
Dh = difference in total heads
L = length of the soil mass

The flow velocity (v) is also called the Darcian velocity or the superficial velocity. It is different from the actual velocity inside the soil pores, which is known as the seepage velocity, v_S. At the particulate level, the water follows a tortuous path through the pores. Seepage velocity is always greater than the superficial velocity, and it is expressed as:



where A_V = Area of voids on a cross section normal to the direction of flow
n = porosity of the soil