$9\mathrm{.}26.$ Air flows from a large reservoir in which the pressure and temperature are $1$ MPa and $30$ deg $*$ C respectively through a convergent$-$divergent nozzle and into a constant area duct. The ratio of the nozzle exit area to its throat area is $3\mathrm{.}0$ and the length$-$to$-$diameter ratio of the duct is $15.$ Assuming that the flow in the nozzle is isentropic$,$ that the flow in the duct is adiabatic, and that the average friction factor is $0\mathrm{.}005,$ find the back pressure for a normal shock to appear at the exit to the duct.

The answer is supposed to be: back pressure is $273\mathrm{.}7$ Kpa.