Problem #$5(40$ points$)$ A $1-$m diameter well penetrates vertically through a confined aquifer $30$ m thick. When the well is pumped at $113$m $^3/$ h $*$ r the drawdown in a well $15$ m away is $1\mathrm{.}8$ m; in another well $50$ m away, it is $0\mathrm{.}5$ m$.$ What is the approximate head in the pumped well for steady$-$state conditions and what is the approximate drawdown in the well? Also compute the transmissivity of the aquifer and the radius of influence of the pumping well. Take the initial piezometric level as $40$ m above the datum.