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

$=$

$7$

$.$

$3$

$4$

$$cm

Diameter of core

$=$

$3$

$.$

$9$

$7$

$2$

$$cm

Effective area

$=$

$1$

$2$

$.$

$3$

$8$

$$cm

$^$

$2$

Viscosity of the fluid

$=$

$0$

$.$

$6$

$5$

$$cp

Q

$1$

$=$

$0$

$.$

$5$

$$ml

$/$

hr and Q

$2$

$=$

$1$

$$ml

$/$

hr

For Q

$1$

$($

the input pressure

$($

p

$1$

$)$

$$is

$2$

$,$

$5$

$,$

$7$

$,$

$9$

$,$

$$and

$1$

$3$

$$psi$,$ and the outlet pressure

$($

p

$2$

$)$

$$is atmospheric pressure

$)$

For Q

$2$

$($

the input pressure is

$1$

$6$

$,$

$1$

$7$

$,$

$1$

$8$

$,$

$2$

$0$

$,$

$2$

$5$

$,$

$4$

$0$

$,$

$$and

$6$

$5$

$$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.