i$)$ Derive the expression for well discharge for a steady radial flow in an unconfied aquifer.$($ii$)$ The discharge from a fully penetrating well operating under steady state in a confined aquifer of $40$ m thickness is $2500$ Ipm. Values of drawdown at two observation wells $12$ and $120$ m away from the well are $4$ and $0\mathrm{.}4$ m respectively. Determine the hydraulic conductivity of the aquifer in m$/$day$.$