Darcy's Law Groundwater Flow Calculator

Darcy’s Law Darcy’s Law describes fluid flow through porous media (soil, rock, sand). Q = K × i × A Where: Q = volumetric flow rate (m³/s or m³/day) K = hydraulic conductivity (m/s or m/day) — how easily water moves through the material i = hydraulic gradient (dimensionless) = head difference / flow distance = Δh/L A = cross-sectional area perpendicular to flow (m²)

Derived by Henry Darcy (France, 1856) from experiments on sand filters for water treatment.

Hydraulic Conductivity (K) by Material Gravel: 10⁻² to 10⁰ m/s — very high permeability Coarse sand: 10⁻⁴ to 10⁻² m/s Medium sand: 10⁻⁵ to 10⁻³ m/s Fine sand / silt: 10⁻⁷ to 10⁻⁵ m/s Clay: 10⁻¹⁰ to 10⁻⁸ m/s — very low (used as aquifer barrier) Limestone karst: up to 10⁻¹ m/s (preferential flow) Basalt: 10⁻⁷ to 10⁻² m/s (highly variable)

Hydraulic Gradient i = Δh / L = (head at upstream end − head at downstream end) / distance Typical gradient in natural aquifers: 0.001–0.01 (1–10 m drop per 1 km) Steep gradients near pumping wells or in mountain streams: 0.01–0.1

Seepage Velocity vs Darcy Velocity Darcy velocity (specific discharge): q = Q / A = K × i Seepage velocity (actual water velocity): v = q / n Where n = effective porosity (fraction, typically 0.1–0.4 for aquifers) Darcy velocity is slower because it’s averaged over the total cross-section, including solid grains.

Transmissivity T = K × b (m²/day or m²/s) Where b = saturated thickness of the aquifer (m). Transmissivity describes the aquifer’s capacity to transmit water horizontally. High T (> 100 m²/day): productive aquifer | Low T (< 1 m²/day): poor aquifer