$($Please show work and clear steps. Circle$/$box all final answers$)$ Problem $5$

Air at a pressure of $0\mathrm{.}685$ atm and temperature $37^($@$)$C enters a $60$ cm inside diameter duct at a Mach

number of $3\mathrm{.}0.$ The flow passes through a standing normal shock wave at a location L$\_(1)$ meters

$($downstream of the duct's inlet or entry$)$ where the Mach number is $2\mathrm{.}5.$ The flow exits the duct

at a location L$\_(2)$ meters $($downstream of the shock$)$ at a Mach number of $0\mathrm{.}8.$ The mean friction

coefficient bar$($f$)$ is $0\mathrm{.}005.$ Determine:

a$)$ the length L$\_(1)$ and L$\_(2),$

b$)$ The static pressure, static temperature, and the density of the air at the exit of the duct, and

c$)$ the mass flow rate through the duct.