Example A Class E cement core having a length of $2\mathrm{.}54cm$ and a diameter of $2\mathrm{.}865cm$ allows a water flow rate of $0\mathrm{.}0345m\frac{L}{s}$ when placed under a pressure differential of $20$ psi. A second core containing $40\%$ silica cured in a similar manner allows only $0\mathrm{.}00345m\frac{L}{s}$ of water to flow under a pressure differential of $200$ psi. Compute the permeability of the two cement samples.