In an Petroleum engineering laboratory, an experiment is underway to calculate the effective permeability of a sandstone core sample. The obtained parameters are as follows:

Length of core $=7\mathrm{.}34$ cm

Diameter of core $=3\mathrm{.}972$ cm

Effective area $=12\mathrm{.}38$ cm$^2$

Viscosity of the fluid $=0\mathrm{.}65$ cp

Q$1=0\mathrm{.}5$ ml$/$hr and Q$2=1$ ml$/$hr

For Q$1($the input pressure $($p$1)$ is $2,5,7,9,$ and $13$ psi, and the outlet pressure $($p$2)$ is atmospheric pressure$)$

For Q$2($the input pressure is $16,17,18,20,25,40,$ and $65$ psi, and the outlet pressure $($p$2)$ is atmospheric pressure$)$

Using the Darcy equation, calculate the effective permeability and provide necessary interpretation and analysis. If specific graphs or curves are required, explain how they should be plotted.