Darcy's Law Calculator

Calculate groundwater flow using Darcy's law Q = KiA. Compute Darcy velocity, seepage velocity, travel time, and total flow for any soil type.

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.

Why Use This Darcy's Law Calculator?

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. The note above highlights common interpretation risks for this workflow. Use this guidance when comparing outputs across similar calculators. Keep this check aligned with your reporting standard.

How to Use This Calculator

  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.

Formula

Darcy's Law: Q = K × i × A Hydraulic gradient: i = (h₁ − h₂) / L Darcy velocity: q = K × i Seepage velocity: v = q / n Travel time: t = L / v Where: • K = hydraulic conductivity (m/s) • i = hydraulic gradient (dimensionless) • A = cross-sectional area (m²) • n = effective porosity • h₁, h₂ = total head at upstream/downstream points (m) • L = flow path length (m)

Example Calculation

Result: Q = 2.5×10⁻⁴ m³/s (21.6 m³/day)

i = (120−115)/500 = 0.01. q = 5×10⁻⁴ × 0.01 = 5×10⁻⁶ m/s. Q = 5×10⁻⁶ × 50 = 2.5×10⁻⁴ m³/s. Seepage v = 5×10⁻⁶ / 0.25 = 2×10⁻⁵ m/s. Travel time = 500 / 2×10⁻⁵ ≈ 289 days.

Tips & Best Practices

Practical Guidance

Use consistent units, verify assumptions, and document conversion standards for repeatable outcomes.

Common Pitfalls

Most mistakes come from mixed standards, rounding too early, or misread labels. Recheck final values before use. ## Practical Notes

Use this for repeatability, keep assumptions explicit. ## Practical Notes

Track units and conversion paths before applying the result. ## Practical Notes

Use this note as a quick practical validation checkpoint. ## Practical Notes

Keep this guidance aligned to the calculator’s expected inputs. ## Practical Notes

Use as a sanity check against edge-case outputs. ## Practical Notes

Capture likely mistakes before publishing this value. ## Practical Notes

Document expected ranges when sharing results.

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.

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