Air flows steadily through a duct $7\mathrm{.}5$ cm in diameter and $20$ m long between a tank and the atmosphere. The tank pressure and temperature are $480$ kPa and $325$ K$,$ respectively, while the atmospheric pressure is $101$ kPa. If the friction factor is $0\mathrm{.}005,$ do the following:

a$.$ Determine the Mach number, pressure, and velocity at the duct inlet.

b$.$ Determine the Mach number, pressure, and temperature at the duct outlet.

c$.$ Determine the mass flow rate $[$kg$/$s$].$