Groundwater Flow Simulator: Darcy's Law & Aquifer Dynamics

simulator intermediate ~10 min
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q = 0.20 m/day — Darcy velocity through the aquifer

With K = 10 m/day and gradient 0.02, the Darcy velocity is 0.20 m/day. Actual seepage velocity through pore spaces is 0.80 m/day given 25% porosity.

Formula

q = K × i (Darcy velocity, m/day)
v = K × i / n (seepage velocity, m/day)
T = K × b (transmissivity, m²/day)

Water Beneath Our Feet

Groundwater constitutes 30% of Earth's freshwater and supplies drinking water to over two billion people. It flows slowly through pore spaces and fractures in rock and sediment, driven by differences in hydraulic head. Understanding this subsurface flow is critical for well design, contaminant remediation, and sustainable water resource management.

Darcy's Law: The Foundation

In 1856, Henry Darcy discovered that flow through sand is proportional to the hydraulic gradient and a material property called hydraulic conductivity. This linear relationship, q = Ki, holds for laminar flow in most natural aquifers. The simulation visualizes flow lines and velocity vectors as you adjust conductivity and gradient, showing how water navigates through the subsurface.

Porosity and Seepage

Water does not flow through solid rock grains — only through interconnected pore spaces. Effective porosity determines what fraction of the aquifer volume is available for flow. A seemingly slow Darcy velocity of 0.1 m/day becomes a seepage velocity of 0.4 m/day in material with 25% porosity. This distinction matters enormously for predicting contaminant travel times and well capture zones.

Pumping Wells and Drawdown

When a well pumps from an aquifer, it creates a cone of depression — a radial drawdown pattern where hydraulic head decreases toward the well. The Theis equation describes transient drawdown, while steady-state solutions yield the well-known logarithmic head profile. Transmissivity and storativity control how far and fast the cone spreads, determining sustainable yield and well spacing.

FAQ

What is Darcy's law?

Darcy's law states that groundwater flow rate through porous media is proportional to hydraulic conductivity and hydraulic gradient: q = K × i. Discovered by Henry Darcy in 1856 through sand column experiments, it remains the foundation of groundwater hydrology for laminar flow conditions.

What is the difference between Darcy velocity and seepage velocity?

Darcy velocity (q = Ki) is the apparent flow rate per unit cross-sectional area. Seepage velocity (v = Ki/n) is the actual average speed of water through pore spaces. Since water only flows through pores (not solid grains), seepage velocity is always higher than Darcy velocity by a factor of 1/n.

What controls hydraulic conductivity?

Hydraulic conductivity depends on both the porous medium (grain size, sorting, packing) and the fluid (viscosity, density). Clean gravel: 100-1000 m/day; sand: 1-50 m/day; silt: 0.001-1 m/day; clay: <0.001 m/day. It is the single most important parameter in groundwater modeling.

What is transmissivity?

Transmissivity (T = Kb) is hydraulic conductivity multiplied by aquifer thickness. It represents the aquifer's ability to transmit water across its full saturated thickness. Higher transmissivity means a well can yield more water with less drawdown.

Sources

Embed

<iframe src="https://homo-deus.com/lab/hydrology/groundwater-flow/embed" width="100%" height="400" frameborder="0"></iframe>
View source on GitHub