Air has a velocity of 1000 km/h at a pressure of 9.81 kN/m2 in vacuum and a temperature of 47°C. Compute its stagnation properties and the local Mach number. Take atmospheric pressure = 98.1 kN/m2, R = 287 J/kg K and γ = 1.4.

Solution:

Velocity of air, $ \quad V_{0}=1000 \mathrm{~km} / \mathrm{h}=\frac{1000 \times 1000}{60 \times 60}=277.78 \mathrm{~m} / \mathrm{s} \\ $

Temperature of air, $ \quad T_{0}=47+273=320 \mathrm{~K} \\ $

Atmospheric pressure, $ \quad p_{a t m}=98.1 \mathrm{kN} / \mathrm{m}^{2} \\ $

Pressure of air (static), $ \quad p_{0}=98.1-9.81=88.29 \mathrm{kN} / \mathrm{m}^{2} …