A $10cm$ long cylindrical core sample was subjected to a laboratory linear flow test under a

pressure differential of $3\mathrm{.}4$atm using a fluid viscosity of $2\mathrm{.}5cp.$ The diameter of the core is $4$

$cm.$ A flow rate of $0\mathrm{.}35c\frac{m^3}{s}$ was obtained. Calculate the permeability of the core.