A Darcy's law$-$abiding column test was conducted in laboratory to determine the hydraulic conductivity of a soil. The test was made at a temperature of $15\mathrm{.}5$ degrees celcius in a cylindrical column, who's lenght is $20$cm and who's circular area is $0\mathrm{.}001$ m $2.$ A difference of hydraulic charge $0\mathrm{.}25$m from one extremity of the cylinder to the other one. The volume of water flowing through the cylinder column on a $5$ minutes time period is equal to $75*10^-6$ m$^3.$

a$)$ Calculate the hydraulical conductivity in m$/$s$,$ as well as the permeability in m$^2$ of the soil sample.