Consider supersonic $($i$.$e$.,$ M can be any value $>1)$ air flow at the entrance of a constant area duct with an internal diameter, d $=5$ cm and a constant friction factor, fav $=0\mathrm{.}002.$ What is the maximum duct length $($in metres$)$ possible so that the Mach number is sonic at the exit?

$($Assume Fanno flow within the duct and that air behaves as a perfect gas with $=1\mathrm{.}4)$