The GATE Grind

GATE 2023 AE – Question 22

Propulsion · Aerothermodynamics of aircraft engines: thrust, efficiency, range and the Brayton cycle · 1 mark · Multiple choice

An aircraft cruises at $V_a$ and has engine-relative exhaust speed $V_j$. If $V_j/V_a=2$, what is propulsive efficiency?

  1. 0.50
  2. 1.00
  3. 0.33
  4. 0.67

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Correct answer: (D) 0.67

Explanation

**Propulsive (Froude) efficiency** of a jet engine, with the aircraft speed $V_a$ and jet speed $V_j$ relative to the aircraft:
$$\eta_p=\frac{\text{thrust power}}{\text{power given to the flow}}=\frac{2}{1+V_j/V_a}.$$

**Numbers.** $V_j/V_a=2$:
$$\eta_p=\frac{2}{1+2}=\frac23=\mathbf{0.67}.$$