Groundwater Flow Rate Calculator
This calculator applies Darcy's Law, the fundamental equation governing groundwater flow through porous media (Darcy, 1856). Enter hydraulic conductivity, the hydraulic gradient, cross-sectional flow area, and effective porosity to calculate specific discharge (Darcy flux) and volumetric flow rate. Darcy's Law is the basis of all groundwater modeling and aquifer analysis methods used by USGS and hydrogeological practitioners worldwide.
Darcy's Law formula
q = K x i Q = q x A v = q / n
Where q = specific discharge (Darcy flux, m/day), K = hydraulic conductivity (m/day), i = hydraulic gradient (dimensionless), Q = volumetric flow rate (m3/day), A = cross-sectional area (m2), v = seepage velocity (m/day), n = effective porosity (fraction). Source: Darcy (1856), as formalised in USGS Groundwater Techniques publications.
Typical hydraulic conductivity values
| Material | K (m/day) | Aquifer Type |
|---|---|---|
| Clean gravel | 100-1,000 | High yield |
| Coarse sand | 10-100 | Good aquifer |
| Medium sand | 1-10 | Moderate aquifer |
| Fine sand / silt | 0.001-1 | Poor aquifer |
| Clay | 0.00001-0.001 | Aquitard |
Groundwater flow rate calculator: frequently asked questions
What is Darcy's Law?
Darcy's Law describes the flow of a fluid through a porous medium. Published by Henry Darcy in 1856, the law states that the specific discharge (q) equals the hydraulic conductivity (K) multiplied by the hydraulic gradient (i): q = K x i. Volumetric flow Q = q x A, where A is the cross-sectional area.
What is hydraulic conductivity?
Hydraulic conductivity (K) is a measure of how easily water can flow through an aquifer material. It ranges from 10^-12 m/s for unfractured crystalline rock to 10^-2 m/s for clean gravel. Values are determined by laboratory tests, field pumping tests, or published soil/rock data.
What is the hydraulic gradient?
The hydraulic gradient (i) is the change in hydraulic head per unit length in the direction of flow: i = dh/dL. For example, if the water table drops 1 metre over a horizontal distance of 100 metres, i = 0.01. It is dimensionless.
What is specific discharge versus seepage velocity?
Specific discharge (q) is the Darcy flux, calculated as K x i. It is not the actual velocity of water in the pore spaces. Seepage velocity (v) is the average velocity of water through connected pores: v = q / n, where n is effective porosity. Seepage velocity is always greater than specific discharge.
When does Darcy's Law not apply?
Darcy's Law assumes laminar flow and is not valid at very high flow velocities where turbulent flow occurs (high Reynolds number). This may occur in very coarse gravels or fractured rock. The law also assumes a homogeneous, isotropic porous medium, which is an approximation for real aquifers.
Official sources
- USGS Office of Groundwater: USGS Groundwater Science.
- USGS Techniques of Water-Resources Investigations: Basic Groundwater Hydrology (Heath, 1983).
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.