Darcy's Law Calculator — Groundwater Flow Rate
Apply Darcy's law to find the volumetric flow rate of water through a saturated porous medium. Enter hydraulic conductivity, cross-sectional area, head difference and flow path length.
m/s
m²
m
m
Volume of water flowing through the cross-section per second
- 1
Hydraulic gradient i = Δh ÷ L
0.5 ÷ 10 = 0.05 - 2
Darcy flux q = K × i
0.001 × 0.05 = 0.00005 m/s - 3
Volumetric flow rate Q = q × A
0.00005 × 1 = 0.00005000 m³/sQ equals the Darcy flux times the full cross-sectional area, including solid grains.
How does this calculator work?
Darcy's law gives the volumetric groundwater flow rate as Q = K × A × (Δh / L), where K is hydraulic conductivity, A is cross-sectional area, and Δh / L is the hydraulic gradient. The Darcy flux q = K × (Δh / L) is the specific discharge per unit area. The law holds for laminar, saturated flow — it breaks down at high velocities and in fractured media.
Formula
How this is calculated
Darcy's law describes steady-state laminar flow through a saturated porous medium. The volumetric flow rate Q (m³/s) equals the hydraulic conductivity K (m/s) multiplied by the cross-sectional area A (m²) and the hydraulic gradient i, where i = Δh / L is the ratio of the head difference to the flow path length. Larger head difference or higher conductivity both increase flow proportionally.
The Darcy flux q = K × i (also called specific discharge) is the apparent velocity averaged over the entire cross-section, including the solid grains. The true pore-water velocity is higher — equal to q divided by the porosity n — but Darcy's law itself does not require porosity as an input. The chart plots Q against hydraulic gradient across the operating range, with your current values marked.
The law assumes laminar, steady-state flow (Reynolds number below roughly 1–10 for most groundwater settings) through a homogeneous, isotropic, fully saturated medium. It breaks down in coarse gravels at high velocity, near pumping wells, and in fractured or karst rock where conduit flow dominates. Hydraulic conductivity spans many orders of magnitude — gravel ≈ 10⁻² m/s, clean sand ≈ 10⁻³, silt ≈ 10⁻⁶, clay ≈ 10⁻⁹ — and is best determined from field or lab tests for a specific site.
Frequently asked questions
Hydraulic conductivity K (m/s) describes how easily water moves through a porous medium. It combines the medium's intrinsic permeability with the fluid's viscosity and density. Gravel lets water pass quickly (K ≈ 10⁻² m/s) while clay is nearly impermeable (K ≈ 10⁻⁹ m/s). Values are best determined by field pumping tests or laboratory permeameter tests.
Darcy flux q = K × i is a superficial velocity averaged over the whole cross-section including solid grains. True pore-water (seepage) velocity is q / n where n is the porosity. Because porosity is always less than 1, actual pore-water velocity is always higher than the Darcy flux.
Darcy's law requires laminar flow. It fails in coarse gravel or near pumping wells where velocities are high enough to cause turbulent flow (Reynolds number > roughly 10), and in fractured or karst aquifers where flow is channelised through discrete fractures rather than distributed through pores.
TG we-Calculate Editorial Team. (2026). Darcy's Law Calculator — Groundwater Flow Rate [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/darcys-law-calculator
TG we-Calculate Editorial Team. "Darcy's Law Calculator — Groundwater Flow Rate." TG we-Calculate. 2026. https://we-calculate.com/calculator/darcys-law-calculator.
TG we-Calculate Editorial Team, "Darcy's Law Calculator — Groundwater Flow Rate," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/darcys-law-calculator
@misc{wecalculate_darcys_law_calculator, title = {Darcy's Law Calculator — Groundwater Flow Rate}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/darcys-law-calculator}}, year = {2026}, note = {TG we-Calculate} }
Did this calculator help you?