Question $1$:

A $1\mathrm{.}5-$ ft diameter well penetrates vertically through a confined aquifer $80$ ft thick. When the well is pumped at $1500$ gpm $,$ the drawdown in a well $120$ ft away is $10$ ft and in another well $250$ ft away is $4$ ft $.$ Consider the initial piezometric level as $180$ ft above the datum. Calculate the following up to three decimal places. $($total $25$ points$)$

$($a$)$ Calculate hydraulic conductivity of the system? $(7$ points$)$

$($b$)$ Compute transmissivity of the system. $(4$ points$)$

$($c$)$ Calculate approximate head in the pumped well for steady$-$state conditions? $(10$ points$)$

$($d$)$ Calculate approximate drawdown in the well? $(4$ points$)$