Question $6(20$ marks$)$

A confined sandstone aquifer is to be developed as a public water supply from a borehole that fully penetrates the aquifer with a thickness of $30$ m $.$ Test pumping of a newly drilled borehole is conducted until steady$-$state conditions are reached. At steady$-$state, the measured groundwater levels at two observation boreholes situated $100$ m and $500$ m from the pumping borehole are $58$ m and $60$ m $,$ respectively, above the top of the aquifer $($this means that $h_1=88$ m and $h_2=90m).$ During the test, the pumped borehole yielded a flow of $15$ litres per second $(1$ Litre is equal to $0\mathrm{.}001m^3).$ Using the pumping test data, calculate the transmissivity and hydraulic conductivity of the sandstone aquifer. Comment on any assumptions made in your calculation.