---
title: "Darcy's law; tests for permeability"
subject: "Soil Mechanics"
chapter: 6
key: "semester_4/soil_mechanics:darcy-law-tests-for-k"
source: https://www.bctengineer.com/q/semester_4/soil_mechanics/darcy-law-tests-for-k
site: BCT Engineering
---

# Darcy's law; tests for permeability

Soil Mechanics · Chapter 6: Principle of Effective Stress, Capillarity and Permeability

- Asked in: 2078 Baisakh, 2 marks
- Video: [Soil Permeability - Darcy's Law](https://www.youtube.com/watch?v=-bYptlimsdI) — Elementary Engineering
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/darcy-law-tests-for-k
- Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-6

## Question

Explain Darcy's law in regard to discharge velocity. Write down the names of different tests done to find the coefficient of permeability of the soil, both in the laboratory and field.

## Short answer

Darcy's law states discharge velocity v = k i with Q = k i A, where i = h/L, valid for laminar flow. Laboratory tests: constant head (coarse soils), falling head (fine soils), indirect methods (consolidation, Hazen). Field tests: pumping out, pumping in, packer, and tracer tests.

## Answer

**Darcy's law** states that for laminar flow through a saturated soil, the discharge velocity is directly proportional to the hydraulic gradient:

$$
v = k\,i, \qquad Q = k\,i\,A
$$

where $v = Q/A$ is the discharge velocity (the flow per unit gross area, not the actual velocity in the pores), $i = h/L$ is the hydraulic gradient and $k$ is the coefficient of permeability. The law is valid for a Reynolds number below about 1 (fine sands, silts and clays); it fails in coarse gravel (turbulent flow).

#### Tests to find k

**Laboratory**
- Constant head permeability test (for coarse-grained soils)
- Falling (variable) head permeability test (for fine-grained soils)
- Indirect: from consolidation test data, horizontal capillarity test, empirical formulae (Hazen's, $k = C D_{10}^2$)

**Field**
- Pumping out test (from wells)
- Pumping in test
- Borehole (auger hole) tests
- Packer test (for rock)
- Tracer tests

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Darcy's law v = k i is valid for:
   A. Turbulent flow in gravel
   B. Laminar flow, Reynolds number below about 1
   C. Any flow
   D. Unsaturated flow only
   Answer: B. It holds for laminar flow and fails in coarse gravel where flow is turbulent. (Key point: Darcy's law)

2. Which pair are laboratory tests for k?
   A. Pumping out and pumping in
   B. Packer and tracer
   C. Constant head and falling head
   D. Borehole and pumping out
   Answer: C. Constant head (coarse) and falling head (fine) are the main lab tests. (Key point: Lab tests)

3. Which is a field test for k?
   A. Pumping out test from wells
   B. Falling head test
   C. Constant head test
   D. Hazen's formula
   Answer: A. Pumping out/in, borehole, packer and tracer tests are field methods. (Key point: Field tests)

## Related in Soil Mechanics

- [Lab and field permeability tests](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Apermeability-test-names) — Soil Mechanics, chapter 6
- [Darcy's law with neat figure](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Adarcy-law-inclined-figure) — Soil Mechanics, chapter 6
- [Shear strength tests (lab and field)](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Ashear-strength-tests-names) — Soil Mechanics, chapter 10, asked 3×
- [Field tests for sand and clay](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Afield-tests-sand-clay) — Soil Mechanics, chapter 3
- [Average permeability of layered soil](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Alayered-soil-average-permeability) — Soil Mechanics, chapter 6
- [Index tests for soil](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aindex-tests-list) — Soil Mechanics, chapter 2, asked 2×

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