Darcy's Law Calculator: Groundwater Flow Rate and Seepage Velocity

How It Works

1. Enter Hydraulic Conductivity (K)

   Input the permeability of the soil or rock in ft/day, cm/sec, or m/day. Use site-specific values from pump tests when available. Otherwise, select from typical values for common materials.

2. Enter Hydraulic Gradient (i)

   Input the hydraulic gradient as the dimensionless ratio of head difference to flow path length (i = delta-h / L). Measure from piezometer or monitoring well water level data.

3. Enter Cross-Sectional Area (A)

   Input the cross-sectional area perpendicular to flow in square feet or square meters. For aquifer flow, this is the aquifer thickness times the width of the flow section.

4. Review Flow Results

   See volumetric flow rate (Q), Darcy velocity (Q/A), and seepage velocity (Darcy velocity / porosity). The seepage velocity is the actual speed water moves through the pore spaces.

Built For

• Hydrogeologists estimating aquifer yield and well field production rates for water supply projects
• Geotechnical engineers sizing dewatering systems for excavations below the water table
• Environmental consultants calculating contaminant plume migration rates for remediation design
• Dam engineers estimating seepage rates through and beneath embankment structures
• Mining engineers calculating pit inflow rates for mine dewatering pump sizing
• Civil engineers estimating underseepage for levee and cofferdam design
• Landfill engineers calculating leachate migration rates through liner systems and natural soils

Features & Capabilities

Q = K x i x A Formula

Darcy's Law for laminar groundwater flow. Calculates volumetric flow rate from hydraulic conductivity, gradient, and area.

Seepage Velocity Output

Divides Darcy velocity by effective porosity to get the actual water velocity through pore spaces. This is what matters for contaminant transport travel times.

K Value Reference Table

Typical hydraulic conductivity ranges for common materials: gravel (1-1000 cm/sec), sand (0.01-1), silt (1e-5 to 1e-3), clay (1e-9 to 1e-6). Select from the table or enter your own.

Unit Conversion

K in ft/day, cm/sec, m/day, or gallons/day/ft2. Area in ft2 or m2. Flow rate in ft3/day, m3/day, gallons/min, or liters/sec.

Gradient Calculator

Enter two well water levels and distance between them to calculate hydraulic gradient. Handles both horizontal and vertical gradients.

PDF Export

Export Darcy flow analysis for hydrogeological reports, dewatering design documents, or environmental assessments.

Assumptions

• Flow is laminar (Darcy regime) with Reynolds number below approximately 1-10 for porous media.
• The aquifer or formation is homogeneous and isotropic within the modeled section.
• Hydraulic conductivity (K) is constant and does not vary with flow rate or saturation.
• Hydraulic gradient is linear between the measurement points (steady-state conditions).

Limitations

• Not valid for turbulent flow near wells, fractures, or karst conduits.
• Real aquifers are heterogeneous — K can vary by orders of magnitude over short distances.
• Does not model unsaturated zone flow, multiphase flow, or variable-density flow (saltwater).
• Literature values of K span wide ranges for each soil/rock type — site-specific testing is strongly preferred.
• Does not account for well losses, skin effect, or partial penetration near pumping wells.

References

• Darcy, H. (1856) — Les fontaines publiques de la ville de Dijon (original formulation).
• Freeze and Cherry, Groundwater — Darcy's Law derivation and applications.
• Fetter, Applied Hydrogeology — hydraulic conductivity tables and flow calculations.
• ASTM D4043/D4044 — Standard Guide for Selection of Aquifer Test Method.

Frequently Asked Questions