Darcy's law is an equation that describes the flow of a fluid through a porous medium and through a Hele-Shaw cell. The law was formulated by Henry Darcy Darcy's law is an equation that describes the flow of a fluid through a porous medium and through a Hele-Shaw cell. The law was formulated by Henry Darcy based on results of experiments on the flow of water through beds of sand, forming the basis of hydrogeology, a branch of earth sciences. It is analogous to Ohm's law in electrostatics, linearly relating the volume flow rate of the fluid to the h Darcy's law is an equation that describes the flow of a fluid through a porous medium and through a Hele-Shaw cell. The law was formulated by Henry Darcy based on results of experiments on the flow of water through beds of sand, forming the basis of hydrogeology, a branch of… if there is no pressure gradient over a distance, no flow occurs (these are hydrostatic conditions), 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 flow nets, to quantify the amount of groundwater flowing under a dam. Darcy's law is only valid for slow, viscous flow; however, most groundwater flow cases fall in this category. Typically any flow with a Reynolds number less than one is clearly laminar, and it would be valid to apply Darcy's law. Experimental tests have shown that flow regimes with Reynolds numbers up to 10 may still be Darcian, as in the case of groundwater flow. The Reynolds number (a dimensionless parameter) for porous media flow is typically expressed as where ν is the kinematic viscosity of water, q is the specific discharge (not the pore velocity — with units of length per time), d is a representative grain diameter for the porous media (the standard choice is math|d30, which is the 30% passing size from a grain size analysis using sieves — with units of length). where N is the molar flux, R is the gas constant, T is the temperature, DeffK is the effective Knudsen diffusivity of the porous media. The model can also be derived from the first-principle-based binary friction model (BFM). The differential equation of transition flow in porous media based on BFM is given as

Darcy Velocity Is Not a Velocity - Haitjema - 2016 - Groundwater - Wiley Online Library Groundwater Volume 54, Issue 1 p. 1 Editorial/ Free Access # Darcy Velocity Is Not a Velocity by Henk M. Haitjema, Mary P. Anderson, by Henk M. Haitjema, Mary P. Anderson, First published: 30 November 2015 https://doi.org/10.1111/gwat.12386 view metrics Haitjema, H.M. and Anderson, M.P. (2016), Darcy Velocity Is Not a Velocity. Groundwater, 54: 1-1. https://doi.org/10.1111/gwat.12386 PDF We write Darcy's law as q = −K dh/ds. Preferences of notation aside, this is an unambiguous equation, but the terminology for “q” is ambiguous and often outright confusing, if not misleading! In groundwater hydrology “q” as defined above is variously termed: Darcy velocity, Darcy flux, groundwater flux, seepage velocity, filtration velocity, fictitious velocity, discharge velocity, and specific discharge. Does it matter? Yes, it does matter for two important reasons. To begin with, “q” is not a velocity, but a volumetric flux or specific discharge (volume of water per unit time per unit area). Moreover, an average (linear) groundwater velocity is defined as v = q/n where “n” is th