Darcy’s Law of Permeability

The law of flow of water through soil was first studied by Darcy (1856)  who demonstrated experimentally that for laminer flow conditions in a saturated soil, the rate of flow or the discharge per unit lime is proportional to the hydraulic gradient.

    q  =   k i A

V = q / A = k i

where

q = discharge per unit time
A = total cross-sectional area of soil mass, perpendicular to the direction of flow
i  = hydraulic gradient
k =  Darcy’ s coefficient of permeability
v = velocity of flow, or average discharge velocity.

Flow of Water Through Soil (Permeability)

If a soil sample of length L and cross-sectional area A, is subjected to differential head of water  h1 – h2 ,the hydraulic gradient i will be equal to h1 – h2 / L and, we have

q = k (h1 – h2 / L) A

From Equation when hydraulic gradient is unity, k is equal to v. Thus, the coefficient of permeability, or simply Permeability  is defined as the average velocity of flow that will occur through the total cross-sectional area of soil under unit hydraulic gradient. The dimensions of the coefficient of permeability k  are the same as those of velocity. It is usually as cm/sec  or m/day or feet/day.