Soil Mechanics / Water in soil and Darcy's law
Darcy's law and seepage velocity
The linear law for flow through soil, and why the water moves faster than it looks.
Lesson review: expert verification remains open
This lesson has received a full-context editorial review and a check of its technical explanations. Selected arithmetic has been checked separately. This is not independent engineering sign-off.
Corrections checked in this pass
- Corrected the sign of hydraulic flow and the direction of arrows when heads are reversed.
Checks needed for project use
- A geotechnical reviewer must check laboratory interpretation, classification conventions and the limits of drained, undrained and one-dimensional idealisations.
- Darcy laminar saturated constant-permeability model; sample graphic length remains schematic and labelled rather than to physical scale.
These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.
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Read the lesson register and outstanding review notesWhy 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. Positive flow is left to right; negative flow is right to left. The sample sketch is not to scale.
- 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.