Confined and unconfined aquifers

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.

  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:

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