Problem $4-$Flame Consulting designed an experiment where helium is extracted from a storage tank and flows through a $150$ mm diameter pipe that is $90$ m long. The inlet conditions for the pipe $($location $1$ in the diagram$)$ are as follows: inlet temperature of $285$ K ; absolute pressure of $165$ kPa ; and inlet velocity of $\backslash (125\backslash$mathrm$\{$~m$\}/\backslash$mathrm$\{$sec$\}\backslash ).$ The consulting company determined the average friction factor in the pipe $($ f $)$ is $0\mathrm{.}004.$ Helium's specific heat ratio $(\backslash ($ k $\backslash ))$ is $1\mathrm{.}667.$

Determine the mass flow rate through the pipe and if the pipe exit is choked $($including justification$).$ Additionally outline how Sparky could determine the friction force acting on the duct $($do not solve the problem just outline the solution process$).$ This is a compressible flow problem. Only use equations and tables from the textbook to solve this problem. Note the figures in the textbook and textbook appendices are based on air, not helium, and are not valid. Evaluate the gas constant at $\backslash (20^\{\backslash$circ$\}\backslash$mathrm$\{$C$\}\backslash ).$ It may help to create a free$-$body diagram, but that is not required.