P$3.(20$ points$)$ Water is pumped out of an artesian aquifer which is $100ft$ thick. Head at distance $r=1000ft$ is fixed and equals $120ft.$ All heads are measured relative to aquifer base, $z=0.$

Determine the theoretical maximum pumping rate of the well, $Q_{\text{m}\text{a}\text{x}}.$

Determine the distance $r$ from center of the well to the point where flow transitions from confined to unconfined for pumping rate $Q_{\text{m}\text{a}\text{x}}.$

Determine the radial flow $Q{r}_r($in $f\frac{t^2}{?}$ day$)$ and specific discharge $q{r}_r$ at transition point for $Q_{\text{m}\text{a}\text{x}}.$