Module 7 · Lesson 7.2
Darcy's law and seepage velocity
The linear law for flow through soil, and why the water moves faster than it looks.
Why this matters
Darcy's law is the workhorse of groundwater flow: a simple linear relationship between how fast water flows and the hydraulic gradient driving it. Understanding it — and the difference between the two 'velocities' it involves — prevents a common and large error.
From first principles
Darcy velocity and the true seepage velocity
We want to show: Relate the flow rate, the apparent (Darcy) velocity and the true speed of the water.
Darcy measured the flow through the WHOLE cross-section of a sand column and found it proportional to the gradient. But water only travels through the voids — a fraction n of the area — so the real water speed is higher.
Try it
Hydraulic-head explorer
Water flows from high total head to low. Set the heads and soil, and read the Darcy flow.
- Head loss Δh
- 0.80 m
- Gradient i = Δh/L
- 1.60
- Darcy velocity v = ki
- 1.60e-5 m/s
- Seepage velocity vs = v/n
- 4.00e-5 m/s
- Flow rate q = kiA
- 1.60e-7 m³/s
The seepage velocity is 1/n = 2.5× the Darcy velocity, because water only travels through the voids.
Worked example
Flow through a sand sample
Given
- Sample length L = 0.5 m
- Head loss Δh = 0.4 m
- k = 5 × 10⁻⁴ m/s
- Porosity n = 0.35
- Cross-section A = 0.01 m²
Find
Hydraulic gradient, Darcy velocity, seepage velocity and flow rate.
Assumptions
- Steady, laminar, saturated flow — Darcy's law applies.
Practice
Water flows through a soil at a Darcy velocity of 2 × 10⁻⁵ m/s. The porosity is 0.5. What is the seepage velocity, in m/s?
Summary
- Darcy's law: q = kiA, and the Darcy velocity v = ki.
- The true seepage velocity vs = v/n is always larger, because water travels only through the voids.
- Hydraulic conductivity k spans ten orders of magnitude and must be measured, not assumed.
This is educational material. It uses simplified examples to teach principles, and must not be relied on for real design or safety-critical decisions. Module overview and checkpoint