A storage tank contains ethylene at $80^{\circ} \mathrm{F}$ and has a relief valve that is set to open at a pressure of $250 \mathrm{psig}$. The valve must be sized to relieve the gas at a rate of $85 \mathrm{lb}_{\mathrm{m}} / \mathrm{s}$ when it opens. The valve has a discharge coefficient (the ratio of the actual mass flux to the theoretical mass flux) of 0.975 .

(Note: This problem can be solved more accurately using the methods given in Chapter 11).

(a) What should be the diameter of the nozzle in the valve? What horsepower would be required to compress the gas from $1 \mathrm{~atm}$ to the maximum tank pressure at a rate equal to the flow rate through the valve, for

(b) A single-stage compressor.

(c) A two-stage compressor with intercooling. Assume a $100 %$ efficiency for the compressor.