Steady and unsteady flow of water and air through soils – permeability of saturated and unsaturated soils

In the middle years of the nineteenth century, Darcy showed, by means of experiment, that the steady state rate of flow of liquid (water) is proportional to the gradient of pressure head in the direction of flow, i.e., the loss of pressure head per unit of distance in the direction of flow. Darcy’s law can be written as:

v = −ki, or k = −v/i (5.1) where v is the velocity of flow with dimensions [m/s]

k is called the coefficient of permeability

The negative sign shows that the pressure or pressure head decreases in the direction of flow. The pressure head is the pressure [N/m2] divided by the unit weight of water [N/m3], i.e., [N/m2 ·m3/N=m], hence

i, the gradient of the pressure head has a unit of [m/m], i.e., it is dimensionless.