PROBLEM 5 (20 Points): Supersonic flow with a Mach number of 5 and static pressure of 50 \( \mathrm{kPa} \) absolute enters a constant-area frictional duct with a diameter of \( 10 \mathrm{~cm} \) and friction coefficient of 0.015 at the inlet marked ( \( i) \). At a distance of \( 2 \mathrm{~m} \) from the entrance \( (i) \), a normal shock wave (NSW) is observed in the duct. (a) What are the total length of the pipe \( (L) \) and the imposed back pressure \( \left(P_{B}\right) \), if the Mach number at the exit plane of the duct marked \( (e) \) is known to be 0.95 ? (b) Draw the locations of the various points in the duct \( (i, 1,2 \) and \( e \) ) on a \( T-s \) diagram with the aid of a Fanno line. (c) Plot the variations of both the static and stagnation pressures vs. the distance \( x \) measured from
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