Darcy's Law[1]​ describes, based on laboratory experiments, the characteristics of the movement of water through a porous medium.

The mathematical expression of Darcy's Law is the following:

being:.

Water, due to energy relations, circulates from highest to lowest piezometric height. As can be seen, the relationship is about the gradient of prizometric heights or hydraulic gradient and it is observed that:

so it adopts a negative value. This can be expressed:

where h is the piezometric height and z is the length traveled. Generalizing to 3 dimensions we obtain that:

K is the hydraulic conductivity (permeability) and it is a symmetric tensor diagonalizable to 3 main directions:

and you get:

The water will move in the direction where there is more permeability and this in turn will indicate the speed at which the water moves under unitary gradient conditions. In isotropic soils, the 3 main permeabilities will be identical.

-Darcy's law is valid in a saturated, continuous, homogeneous and isotropic medium and when the inertial forces are negligible (Re<1).

Darcy's law is one of the fundamental pieces of soil mechanics. Starting from Darcy's initial work, a monumental work for the time, many other researchers have analyzed and tested this law. Through these subsequent works it has been determined that it maintains its validity for most types of fluid flow in soils. For leaks of liquids at very high speeds and gases at very low speeds, Darcy's law is no longer valid.

In the case of water circulating in soils, there is overwhelming evidence to verify the validity of Darcy's Law for soils ranging from silt to medium sand. It is also perfectly applicable in clays, for steady-state flows.

For soils with greater permeability than average sand, the actual relationship between gradient and velocity must be determined experimentally for each soil and porosity studied.

Darcy's law is specifically for calculating flow rates (Q) using extracts that can be obtained from the reservoir.