Consider the capture stream tube of an aircraft engine cruising at Mach 0.8 at an altitude of $10 \mathrm{~km}$. The capture mass flow rate is $250 \mathrm{~kg} / \mathrm{s}$. At station 1 , which is in the freestream, the static pressure and temperature are $26.5 \mathrm{kPa}$ and $223 \mathrm{~K}$, respectively. At station 2, which is downstream of station 1, the cross-sectional area is $3 \mathrm{~m}^{2}$. Further downstream at station 3, the Mach number is 0.4. Determine (a) the cross-sectional area at station 1 (usually called the capture area), (b) the Mach number at station 2, (c) the static pressure and temperature at stations 2 and 3, and (d) the cross-sectional at station 3.