Compute groundwater discharge through a saturated porous medium with Darcy's law, Q = K·i·A. The tool also returns the Darcy flux (specific discharge) and the seepage (linear pore) velocity, which is the speed a contaminant actually travels through the aquifer.
Darcy's law is the foundational equation of groundwater hydrology — the porous-media analogue of Ohm's law. It relates the flow of water through a saturated soil or rock to the hydraulic conductivity, the hydraulic gradient driving the flow, and the cross-sectional area. This calculator returns the volumetric discharge, the Darcy flux, and the seepage velocity that controls how fast dissolved contaminants migrate.
Henry Darcy established in 1856 that flow through a saturated porous medium is Q = K·i·A. Here Q is the volumetric discharge (m³/day), K is the hydraulic conductivity (m/day), i is the dimensionless hydraulic gradient (the head drop per unit flow length, dh/dL), and A is the gross cross-sectional area perpendicular to flow (m²). Discharge is proportional to the gradient — double the head difference and you double the flow. The law is the workhorse for sizing dewatering systems, estimating well yields, and predicting contaminant transport.
Hydraulic conductivity K bundles both the medium and the fluid: K = k·ρg/μ, where k is the intrinsic permeability (units of m², a property of the porous medium alone), ρ and μ are the fluid density and viscosity, and g is gravity. K therefore changes with temperature because viscosity does. Use intrinsic permeability k when comparing media independent of fluid, and K when working a specific water-flow problem. K spans an enormous range: from 1000 m/day in clean gravel down to below 0.001 m/day in clay.
The Darcy flux (specific discharge) q = K·i = Q/A is a fictitious velocity — it treats the flow as if it filled the whole cross-section, including the solid grains. Water actually flows only through the connected pore space, so the real average pore velocity, the seepage or linear velocity, is faster: vₛ = q / nₑ, where nₑ is the effective porosity. Because nₑ is typically 0.1–0.35, the seepage velocity is roughly three to ten times the Darcy flux. For contaminant travel-time estimates always use vₛ, never q — using the Darcy flux makes a plume appear to move several times slower than it really does.
Darcy's law assumes laminar flow, a saturated medium, and a representative continuum (no individual fractures or macropores dominating). It holds for Reynolds numbers below about 1–10 based on grain size — valid for nearly all natural groundwater. It breaks down in very coarse gravel or near pumping wells where velocities become turbulent, and in unsaturated soil where K itself depends on moisture content. The effective porosity must lie between 0 and 1; a value at or above 1, or zero, is non-physical and the seepage velocity is undefined.
The Darcy flux q = K·i is the discharge per unit gross area and is a fictitious velocity assuming flow through the entire cross-section. The seepage (linear) velocity vₛ = q/nₑ accounts for the fact that water moves only through the pore space, so it is faster by the factor 1/nₑ. Contaminant travel times must use the seepage velocity.
The hydraulic gradient i is the change in hydraulic head divided by the distance over which it occurs, i = dh/dL. It is dimensionless (m/m) and represents the slope of the water table or potentiometric surface. Water flows from high head to low head, so a steeper gradient drives faster flow. Typical natural gradients range from about 0.001 to 0.05.
Intrinsic permeability k (m²) is a property of the porous medium alone. Hydraulic conductivity K (m/day) includes the fluid through K = kρg/μ, so it depends on the fluid density and viscosity and therefore on temperature. Use k to compare media independent of fluid; use K for a specific groundwater calculation.
It assumes slow, laminar, saturated flow through a continuum. It fails where flow is turbulent — very coarse gravel or the immediate vicinity of a pumping well (high Reynolds number) — and in unsaturated soils, where conductivity varies with moisture. It also cannot represent flow dominated by individual fractures or solution channels without modification.
Approximate ranges in m/day: clean gravel 100–1000, sand 1–100, silt 0.001–1, and clay below 0.001. Conductivity spans more than ten orders of magnitude across geologic materials, which is why aquifers (sand and gravel) and aquitards (silt and clay) behave so differently.