$8\mathrm{.}24.$ A well at a distance d from an impermeable boundary pumps at a flow rate Q$.$ The head and any point $($x$,$ y$)$ is given by the following equation:

h$($x$,$y$)=$Q$2\backslash$pi T$[$ln$($r$1$r$2)]+$C$,$

where C is a constant, r$1$ is the straight$-$line distance from the well to the point $($x$,$ y$),$ and r$2$ is the distance from the image well to the point $($x$,$ y$).$ The y$-$axis lies along the impermeable boundary. Use Darcy$$s law to show that the flow across the boundary $($y$-$axis$)$ is indeed zero.

$8\mathrm{.}25.$ A fully penetrating well pumps from a confined aquifer of thickness $20$ m and K$=10$m$/$day$.$ The radius of the well is $0\mathrm{.}25$ m and the recorded pump rate in the well is $100$m$3/$day at steady state. Assume that the radius of influence of the well is $1250$ m$.$ Compute the drawdown at the well if it is located $100$ m from an impermeable boundary $($see Problem $8\mathrm{.}24).$