Methane is fed to a reactor at a rate of $10 \mathrm{lb}_{\mathrm{m}} / \mathrm{min}$. The methane is available in a pipeline at $20 \mathrm{psia}, 70^{\circ} \mathrm{F}$, but the pressure in the reactor fluctuates between 2 and 10 psia. To control the flow rate, you want to install an orifice plate that will choke the flow at the desired rate. What should the diameter of the orifice be?