Glossary - D - Darcy's law

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Darcy's Law is a phenomologically derived constituative equation that describes the flow of a fluid through a porous medium (typically water through an aquifer). The law was formulated by Henry Darcy based on the results of 1855 and 1856 experiments on the flow of water through beds of sand. It, along with the conservation of mass, comprises the groundwater flow equation, which is one the basic building relationships of hydrogeology.

Darcy's Law (an expression of conservation of momentum) is analogous to Fourier's law in the field of heat conduction, Ohm's law in the field of electrical networks, or Fick's law in diffusion theory. This simple relationship relates the instantaneous discharge rate through a porous medium to the local hydraulic gradient (change in hydraulic head over a distance) and the hydraulic conductivity (k) at that point.

It shows that the total discharge, Q (units of volume per time, e.g., cm3/s) is proportional to the hydraulic conductivity, k, the cross-sectional area to flow, A, and the hydraulic gradient (the hydraulic head drop between two points a and b, divided by the distance between them, L). The negative sign is needed because water flows from high head to low head.

Darcy's law is a simple mathematical statement which neatly summarizes several familiar properties that groundwater flowing in aquifers exhibits, including:

  • if there is no hydraulic gradient (difference in hydraulic head over a distance), no flow occurs (this is hydrostatic conditions),
  • if there is a hydraulic gradient, flow will occur from high head towards low head (opposite the direction of increasing gradient - hence the negative sign in Darcy's law),
  • the greater the hydraulic gradient (through the same aquifer material), the greater the discharge, and
  • the discharge of water will be often be different — through different aquifer materials (or even through the same material, in a different direction) — even if the same hydraulic gradient exists in both cases.

A graphical illustration of the use of the steady-state groundwater flow equation (based on Darcy's law and the conservation of mass) is in the construction of flownets, to quantify the amount of groundwater flowing under a dam.

Darcy's law is only valid for slow, viscous flow; fortunately, most groundwater flow cases fall in this category.

For more detailed information - see Wikipedia