Question

Consider adiabatic flow of air through a duct. At a given point in the duct, velocity of air is 300 m/s, temperature is 330 K and pressure is 180 kPa. Assume that the air behaves as a perfect gas with constant \(c_p = 1.005 \, \text{kJ/kg.K}\). The stagnation temperature at this point is \(\underline{\hspace{1cm}}\) K (round off to two decimal places).

Hint:

In adiabatic flow, the stagnation temperature increases due to the conversion of kinetic energy to internal energy.

Answer 1

Correct Answer: 373 - 377

For an adiabatic flow of an ideal gas, the stagnation temperature is given by: \[ T_0 = T + \frac{V^2}{2c_p}, \] where:
- \(T = 330 \, \text{K}\) is the temperature,
- \(V = 300 \, \text{m/s}\) is the velocity,
- \(c_p = 1.005 \, \text{kJ/kg.K} = 1005 \, \text{J/kg.K}\) is the specific heat.
Substituting the values: \[ T_0 = 330 + \frac{300^2}{2 \times 1005} = 330 + \frac{90000}{2010} \approx 330 + 44.8 = 374.8 \, \text{K}. \] Thus, the stagnation temperature is: \[ \boxed{373.00 \, \text{to} \, 377.00 \, \text{K}}. \]