Question

During rocket testing, the characteristic velocity of a choked nozzle with stagnation temperature of 2400 K is (\(\gamma = 1.3\), \(M = 28\ \text{kg/kmol}\))

• A. 1565.65 m/s
• B. 1465.65 m/s
• C. 1365.65 m/s
• D. 1265.65 m/s

Hint:

Characteristic velocity is a key performance indicator, independent of nozzle shape.

Answer 1

The Correct Option is A

Characteristic velocity, \[ c^* = \sqrt{\frac{R T_0}{\gamma}} \cdot \left( \frac{\gamma+1}{2} \right)^{\frac{\gamma+1}{2(\gamma-1)}} \] Given: \[ R = \frac{8314}{28} = 296.93\ \text{J/kg·K},\quad T_0 = 2400\ \text{K} \] \[ c^* = \sqrt{\frac{296.93 \cdot 2400}{1.3}} \cdot \left( \frac{2.3}{2} \right)^{2.769} \approx 1565.65\ \text{m/s} \]