Context : A test column, based on the Darcy set up$,$ has been made in the laboratory to determine the hydraulic conductivity of a soil. The experiment was made at a temperature of $15\mathrm{.}5,$ in a cylindrical column of $20$cm of lenght and who's circular area was $0\mathrm{.}001$ m$^2.$ A difference of hydraulic charge of $0\mathrm{.}25$m is maintained between each extremities of the column and the volume of water going through the column during an interval of $5$ minutes equals $75*10^-6$ m$^3.$

Questions:

a$)$ Calculate the hydraulic conductivity $($in m$/$s$)$ and the permeability of the sample $($in m$^2).$

b$)$ If the test had been made at a temperature of $5$ degrees celcius, at which the dynamic viscosity of water is at $1\mathrm{.}52$ cP$,$ which would have been the volume of water going through the column for a period of $5$ minutes? Suppose that the volumic mass of water didn't change in relation to the viscosity.