A pressure vessel containing nitrogen at $300^{\circ} \mathrm{F}$ has a relief valve installed on top of the vessel. The valve is set to open at a set pressure of 125 psig and exhausts its contents at atmosphericpressure. The valve has a nozzle that has a smoothly rounded entrance and is $1.5 \mathrm{in}$. in diameter and $4 \mathrm{in}$. long, which limits the flow through the valve when it is open.

(a) If the flow resistance in the piping between the tank and the valve, and from the valve to the atmospheric discharge, is neglected, determine the mass flow rate through the valve when it opens (in $\left.\mathrm{lb}_{\mathrm{m}} / \mathrm{s}\right)$.

(b) In reality, there is a $3 \mathrm{ft}$ length of a 3 in. pipe between the tank and the valve, and a $6 \mathrm{ft}$ length of a 4 in. pipe downstream of the valve discharge. What is the effect of including this piping on the calculated flow rate?

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