where a constant head condition is applied at the edge of the island ($r_2$).

@dupuit1857 also derived a radial flow solution for unconfined aquifers by neglecting the vertical flow component. Following a similar approach to confined aquifers, @dupuit1857 estimated the steady-state head difference between two distances from the pumping well for unconfined aquifers as $$\label{dupuit_unconfined}
  h^{2}(r_{2}) - h^{2} (r_{1}) = \frac{Q}{\pi K} \log\left(
    \frac{r_2}{r_1}\right).$$ These two solutions are only strictly valid for finite domains; when applied to domains without a physical boundary at $r_2$, the outer radius essentially becomes a fitting parameter. The solutions are also used in radially infinite systems under pseudo-static conditions, when the shape of the water table does not change with time.

Equations and are equivalent when $b$ in is average head $\left( h(r_1)+h(r_2)\right)/2$. In developing , [@dupuit1857] used the following assumptions (now commonly called the Dupuit assumptions) in context of unconfined aquifers:

-   the aquifer bottom is a horizontal plane;

-   groundwater flow toward the pumping wells is horizontal with no vertical hydraulic gradient component;

-   the horizontal component of the hydraulic gradient is constant with depth and equal to the water table slope; and

-   there is no seepage face at the borehole.

These 