A commercial steel pipe pipe $(\backslash$epsi $=0\mathrm{.}046$mm$)40$ feet long and $0\mathrm{.}824-$inch internal diameter has $300$ psig source of hydrogen $(\backslash$gamma $=1\mathrm{.}41).$ It must be equipped with a relief device to ensure equipment integrity. Temperature is $298$K$.$ This exercise is for determining the minimum mass flow rate of hydrogen required to prevent pressure rise and regulator failure. The idea is to use various methods available to calculate the mass flow rate.

a$.$ Use the orifice diameter as a pipe diameter and estimate the flow from a vessel pressurized to $300\backslash$psi g$.$ Assume choked flow.

b$.$ Use rigorous calculations for adiabatic flow $($solving equations simultaneously$)$

c$.$ Use the simplified procedure for adiabatic flow $-$ Charts for Y$\_($g$)$ and points$)$

d$.$ Use the asymptotic method

e$.$ What are your observations about the results?