Darcy´s law
- 1. DARCY´S LAW In fluid dynamics and hydrology, Darcy's law is a phenomenological derived constitutive equation that describes the flow of a fluid through a porous medium. The law was formulated by Henry Darcy based on the results of experiments (published 1856) [ on the flow of water through beds of sand. It also forms the scientific basis of fluid permeability used in the earth sciences. Diagram showing definitions and directions for Darcy's law.
- 2. Darcy's law is a simple proportional relationship between the instantaneous discharge rate through a porous medium, the viscosity of the fluid and the pressure drop over a given distance. The total discharge, Q (units of volume per time, e.g., ft³/s or m³/s) is equal to the product of the permeability (κ units of area, e.g. m²) of the medium, the cross-sectional area ( A ) to flow, and the pressure drop ( P b − P a ), all divided by the dynamic viscosity μ (in SI units e.g. kg/(m·s) or Pa·s), and the length L the pressure drop is taking place over. The negative sign is needed because fluids flow from high pressure to low pressure. So if the change in pressure is negative (in the x -direction) then the flow will be positive (in the x -direction). Dividing both sides of the equation by the area and using more general notation leads to
- 3. where q is the filtration velocity or Darcy flux (discharge per unit area, with units of length per time, m/s) and is the pressure gradient vector. This value of the filtration velocity (Darcy flux), is not the velocity which the water traveling through the pores is experiencing The pore (interstitial) velocity ( v ) is related to the Darcy flux ( q ) by the porosity (φ). The flux is divided by porosity to account for the fact that only a fraction of the total formation volume is available for flow. The pore velocity would be the velocity a conservative tracer would experience if carried by the fluid through the formation.
- 5. 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 pressure gradient over a distance, no flow occurs (this of course, is the hydro static condition). if there is a pressure gradient, flow will occur from high pressure towards low pressure (opposite the direction of increasing gradient—hence the negative sign in Darcy's law) the greater the pressure gradient (through the same formation material), the greater the discharge rate, and the discharge rate of fluid will often be different — through different formation materials (or even through the same material, in a different direction) — even if the same pressure 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. CONCLUSIONS