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, which is why clay is used as an 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

A worked example

A coarse sand aquifer, K = 0.001 m/s. The water table drops 5 m over a 500 m stretch, and the cross-section you care about is 100 m² (say 50 m wide by 2 m thick).

• Gradient: i = 5 / 500 = 0.01
• Darcy velocity: q = K × i = 0.001 × 0.01 = 1 × 10⁻⁵ m/s
• Flow rate: Q = q × A = 1 × 10⁻⁵ × 100 = 1 × 10⁻³ m³/s, which is 86.4 m³/day

At 25% effective porosity the water itself moves at four times the Darcy velocity, 4 × 10⁻⁵ m/s, or about 3.5 m a day. That is the number people get wrong. The Darcy velocity is a bookkeeping figure spread over the whole cross-section including solid grains; nothing in the ground actually travels at it. If you are tracking a contaminant plume, use the seepage velocity, or you will predict its arrival roughly four times too late.

Where the law stops working

Darcy’s Law assumes laminar flow, which holds while the Reynolds number stays below about 1 to 10. In clean gravel, open fractures and karst conduits, flow goes turbulent and the relationship between gradient and discharge stops being linear. The equation will still return a number in those settings. It just will not be the right one.