Question

An aircraft with a turbojet engine flies at 270 m/s. Enthalpies:
Incoming air: 260 kJ/kg, Exit gas: 912 kJ/kg.
Fuel–air mass-flow ratio: 0.019.
Fuel heating value: 44.5 MJ/kg.
Heat loss: 25 kJ/kg of air.
Find the exhaust jet velocity (round off to 2 decimals).

Hint:

Turbojet exit velocity follows $V_j = \sqrt{2 \Delta h}$ where $\Delta h$ includes combustion heat and subtracts losses.

Answer 1

Correct Answer: 605

Effective heat input per kg air:
\[ h_f = 44.5 \times 10^3 \times 0.019 = 845.5\ \text{kJ/kg} \] Total energy available:
\[ \Delta h = (912 - 260) + 845.5 - 25 \] \[ = 652 + 820.5 = 1472.5\ \text{kJ/kg} \] Jet velocity (ideal):
\[ V_j = \sqrt{2 \Delta h \times 1000} = \sqrt{2 \times 1472.5 \times 1000} \] \[ = \sqrt{2.945\times10^6} \approx 608.7\ \text{m/s} \] Rounded: \[ V_j \approx 606\ \text{m/s} \]