---
title: "Confined and unconfined aquifers"
subject: "Soil Mechanics"
chapter: 6
key: "semester_4/soil_mechanics:confined-unconfined-aquifers-k"
source: https://www.bctengineer.com/q/semester_4/soil_mechanics/confined-unconfined-aquifers-k
site: BCT Engineering
---

# Confined and unconfined aquifers

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

- Asked in: 2076 Baisakh, 3 marks
- Video: [Unconfined Aquifers vs. Confined Aquifers](https://www.youtube.com/watch?v=wx0w-Az5JOY) — Dane Andersen
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/soil_mechanics/confined-unconfined-aquifers-k
- Whole chapter: https://www.bctengineer.com/md/semester_4/soil_mechanics/chapter-6

## Question

What are confined and unconfined aquifers? Write down the equations for finding the coefficient of permeability in these aquifers.

## Short answer

A confined aquifer is a pressurized layer between impervious strata; an unconfined aquifer has a free water table. From a steady-state pumping test with two observation wells: confined, k = (q ln(r2/r1))/(2π b (h2-h1)); unconfined, k = (q ln(r2/r1))/(π (h2^2 - h1^2)).

## Answer

**Confined aquifer (artesian):** a water-bearing layer of thickness $b$ lying between two impervious layers. The water in it is under pressure, so the piezometric level stands above the top of the aquifer.

**Unconfined aquifer (water table aquifer):** a pervious layer with a free water table as its upper boundary, resting on an impervious layer. Water is at atmospheric pressure at the table.

```text
  Confined                 Unconfined
  ~~~~ piezometric         ~~~~ water table
  ==== impervious          ....
  aquifer  b               aquifer
  ==== impervious          ==== impervious
```

#### Equations from a pumping test

Let a well discharge $q$ at steady state, with two observation wells at radial distances $r_1$ and $r_2$ having water levels (heads above the impervious base) $h_1$ and $h_2$.

**Confined aquifer:**

$$
k = \frac{q\,\ln(r_2/r_1)}{2\pi\,b\,(h_2 - h_1)} = \frac{2.303\,q\,\log_{10}(r_2/r_1)}{2\pi\,b\,(h_2 - h_1)}
$$

**Unconfined aquifer:**

$$
k = \frac{q\,\ln(r_2/r_1)}{\pi\,(h_2^2 - h_1^2)} = \frac{2.303\,q\,\log_{10}(r_2/r_1)}{\pi\,(h_2^2 - h_1^2)}
$$

## Check yourself

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

1. A confined aquifer is:
   A. A pervious layer with a free water table as its top
   B. A water-bearing layer between two impervious layers, water under pressure
   C. A layer above a clay lens only
   D. A dry sand layer
   Answer: B. Confined (artesian) water is under pressure, piezometric level above the aquifer top. (Key point: Confined aquifer)

2. In an unconfined aquifer the upper boundary is:
   A. An impervious layer
   B. A free water table at atmospheric pressure
   C. The piezometric surface above the ground
   D. A confining clay
   Answer: B. It rests on an impervious layer with a free water table at the top. (Key point: Unconfined aquifer)

3. For a confined aquifer, k is:
   A. q ln(r2/r1) / (pi (h2^2 - h1^2))
   B. q ln(r2/r1) / (2 pi b (h2 - h1))
   C. q (h2 - h1) / (2 pi b ln(r2/r1))
   D. q ln(r2/r1) / (2 pi (h2^2 - h1^2))
   Answer: B. Confined: k = q ln(r2/r1)/(2 pi b (h2 - h1)). (Key point: Confined formula)

4. For an unconfined aquifer, k is:
   A. q ln(r2/r1) / (pi (h2^2 - h1^2))
   B. q ln(r2/r1) / (2 pi b (h2 - h1))
   C. q ln(r2/r1) / (pi b (h2 - h1))
   D. q (r2 - r1) / (pi (h2 - h1))
   Answer: A. The saturated thickness varies, giving h^2 terms: k = q ln(r2/r1)/(pi (h2^2 - h1^2)). (Key point: Unconfined formula)

## Related in Soil Mechanics

- [Confined and unconfined flow](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aconfined-unconfined-seepage-flow) — Soil Mechanics, chapter 7
- [Darcy's law; tests for permeability](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Adarcy-law-tests-for-k) — Soil Mechanics, chapter 6
- [Lab and field permeability tests](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Apermeability-test-names) — Soil Mechanics, chapter 6
- [Permeability method for clay](https://www.bctengineer.com/question.md?key=semester_4%2Fsoil_mechanics%3Aclay-permeability-lab-method) — Soil Mechanics, chapter 6

## Related in other subjects

- [Confined versus unconfined aquifer](https://www.bctengineer.com/question.md?key=semester_4%2Fengineering_geology_ii%3Aconfined-unconfined-aquifer) — Engineering Geology II, chapter 3, asked 4×
- [Confined versus unconfined aquifer](https://www.bctengineer.com/question.md?key=semester_3%2Fengineering_geology_i%3Aconfined-versus-unconfined-aquifer) — Engineering Geology I, chapter 6, asked 2×
- [Permeability and transmissibility from pumping test](https://www.bctengineer.com/question.md?key=semester_5%2Fengineering_hydrology%3Awell-pumping-test-unconfined-30cm) — Engineering Hydrology, chapter 1
- [Mass and energy equations for CV; nozzle, condenser](https://www.bctengineer.com/question.md?key=semester_2%2Ffundamental_of_thermodynamics_and_heat_transfer%3Amass-energy-cv-nozzle-condenser) — Fundamental of Thermodynamics & Heat Transfer, chapter 4