Darcy's Law Calculator

About the Darcy's Law Calculator

Darcy's law is the fundamental equation governing groundwater flow through porous media. Published by Henry Darcy in 1856 based on experiments with sand filters, it states that the volumetric flow rate Q through a saturated porous medium is proportional to the hydraulic conductivity K, the hydraulic gradient i, and the cross-sectional area A: Q = K × i × A.

The Darcy velocity (specific discharge) q = K × i gives the apparent flow rate per unit area, treating the soil as a continuum. But water actually moves faster through the narrow pore channels — the real seepage velocity is v = q / n, where n is the effective porosity. This distinction is critical for contaminant transport, remediation design, and travel-time estimates.

This calculator covers the complete Darcy's law chain: from head difference and path length to gradient, Darcy velocity, seepage velocity, total flow, and travel time. Soil presets span clean gravel to clay, covering ten orders of magnitude in K. Five scenario presets model typical field situations: confined aquifers, unconfined sands, dam underseepage, clay barriers, and dewatering trenches.

When This Page Helps

Darcy's law is the starting point for nearly all groundwater analyses — from contaminant plume travel times to dewatering volumes. This calculator handles the full equation with unit conversions, soil presets, and field scenarios.

How to Use the Inputs

1. Select a soil type from the dropdown or enter a custom hydraulic conductivity K.
2. Enter the upstream and downstream total heads (elevation + pressure head).
3. Enter the flow path length between the two measurement points.
4. Enter the cross-sectional area perpendicular to flow.
5. Enter the effective porosity for seepage velocity and travel-time calculations.
6. Click a scenario preset to load a typical field case.
7. Read Darcy velocity, seepage velocity, total flow, and travel time from the outputs.

Example Calculation

Tips & Best Practices

• Three observation wells define a gradient triangle — the minimum to characterize direction and magnitude.
• In layered soils, the equivalent horizontal K is the weighted arithmetic mean; the equivalent vertical K is the weighted harmonic mean.
• For contaminant transport, multiply seepage velocity by the retardation factor R to get the contaminant front velocity.
• Pumping tests give transmissivity T = K × b directly, which is more useful than K alone for well design.
• If your travel-time estimate matters (e.g., for a wellhead protection zone), use conservative K values and verify with tracer tests.

When To Use This Calculator

Calculate groundwater flow using Darcy's law Q = KiA. Compute Darcy velocity, seepage velocity, travel time, and total flow for any soil type. Use it when you need a repeatable calculation in the physics / fluid category and want the setup, result, and supporting values kept together. This is especially helpful when small input changes, unit choices, or rounding decisions can change the final number.

How To Check The Result

Start by confirming that the inputs match the formula shown on the page. Then compare the main output with the worked example and any secondary values shown by the calculator. If the result will be used in another calculation, keep extra precision until the final step and record the assumptions beside the number.

Practical Notes

Treat the result as a calculation aid rather than a substitute for context. For schoolwork, include the formula and substitution steps. For planning, technical, financial, or health-related decisions, verify important numbers against primary records, current rules, or a qualified professional before acting on them.

Frequently Asked Questions

• When does Darcy's law not apply?

  Darcy's law assumes laminar flow (Re < 1–10 based on grain size). It breaks down in very coarse media (large gravels, karst) where flow becomes turbulent, and in very tight media (intact granite) where non-Darcy effects dominate.

• What is the difference between total head and piezometric head?

  In groundwater, total head h = z + p/(ρg) + v²/(2g). The velocity term is negligible for slow seepage, so total head ≈ piezometric head = elevation + pressure head. That is what piezometers measure.

• How do I compute the gradient from well data?

  Measure water levels (head) in at least three wells. Fit a plane to the three head values and their coordinates. The gradient magnitude and direction follow from the plane slope.

• What porosity should I use?

  Use effective porosity: the fraction of interconnected pore space that participates in flow. For clean sands it is 0.25–0.35; for clays it can be < 0.05 even though total porosity is 40–60%.

• Is seepage velocity the same as groundwater velocity?

  Approximately, yes — seepage velocity v = q/n is the average velocity of water through the pore network. However, pore-scale velocity varies widely; some paths are faster, causing mechanical dispersion.

• How does temperature affect the result?

  K depends on viscosity (K = kρg/μ). Water viscosity drops ~50% from 5°C to 25°C, so K roughly doubles. Use temperature-adjusted K or convert to intrinsic permeability k for precise work.