Question 9.PS.72: Calculate the air temperature and pressure at the stagnation......
Calculate the air temperature and pressure at the stagnation point right in front of a meteorite entering the atmosphere (-50 °C, 50 kPa) with a velocity of 2000 m/s. Do this assuming air is incompressible at the given state and repeat for air being a compressible substance going through an adiabatic compression.
Kinetic energy: \frac{1}{2} \mathbf{V} ^2=\frac{1}{2}(2000)^2 / 1000=2000 \,kJ / kg
Ideal gas: v _{ atm }= RT / P =0.287 \times 223 / 50=1.28 \,m ^3 / kg
a) incompressible
Energy Eq.6.13: \Delta h =\frac{1}{2} \mathbf{V} ^2=2000 \,kJ / kg
If A.5 \Delta T =\Delta h / C _{ p }=1992 \,K unreasonable, too high for that C _{ p }
Use A.7:
Bernoulli (incompressible) Eq.9.17:
b) compressible
T _{ st }=1977 \,K the same energy equation.
From A.7.2: Stagnation point P_{r \,s t}=1580.3 ; \text { Free } P_{r\, o}=0.39809
\begin{aligned}P_{ st } & =P_{ o } \times \frac{ P _{ r\,st }}{ P _{ r\,o }}=50 \times \frac{1580.3}{0.39809} \\& =198485 \,k P a\end{aligned}
Notice that this is highly compressible, v is not constant.
