Topic: Gas Dynamics
A re-entry module flies with Mach 10 at an ambient temperature of $-27^{\circ}C$ with $C_{P}=840$ $J/kg-K,$ gas constant $R=140~J/kg-K.$ What is the stagnation temperature at the tip of the nose of the re-entry module?
- A. $-23^{\circ}C$
- B. $1377^{\circ}C$
- C. $2477^{\circ}C$
- D. $-253^{\circ}C$
Explanation: This question was excluded for evaluation by ISRO. Theoretically, $\gamma = C_{p}/C_{v} = C_{p}/(C_{p}-R) = 840/(840-140) = 840/700 = 1.2$. Ambient temperature $T = -27^{\circ}C = 246~K$. Stagnation temperature $T_{0} = T(1 + \frac{\gamma-1}{2}M^{2}) = 246(1 + \frac{1.2-1}{2}10^{2}) = 246(1 + 0.1 \times 100) = 246 \times 11 = 2706~K$. In Celsius, $2706 - 273 = 2433^{\circ}C$, which does not perfectly match any option.