Propulsive efficiency of a turbojet (ideal expression) If V1 is the jet (exhaust) velocity and V0 is the flight (vehicle) speed, choose the correct ideal expression for the propulsive efficiency of a turbojet.

Introduction / Context:
Propulsive efficiency measures how effectively a propulsion system converts jet kinetic energy into useful thrust power for flight. For an ideal turbojet with a single exhaust stream, the efficiency depends on the mismatch between jet velocity and flight speed.

Given Data / Assumptions:

• Steady, one-dimensional jet with mass flow assumed constant.
• Ideal relationships (no losses, single exhaust stream).
• Vehicle speed V0 and jet speed V1 are colinear.

Concept / Approach:

Propulsive efficiency eta_p is defined as useful power (thrust * flight speed) divided by the rate of kinetic-energy increase given to the jet. Under ideal assumptions this reduces to eta_p = 2 * V0 / (V1 + V0). The closer the jet speed is to the flight speed, the higher the efficiency, which motivates high-mass-flow, low-excess-velocity designs in modern turbofans.

Step-by-Step Solution:

Verification / Alternative check:

Limit checks: if V1 → V0, eta_p → 1; if V0 → 0 (static jet), eta_p → 0. Both are physically sensible trends.

Why Other Options Are Wrong:

Other forms either invert the ratio, omit the factor of 2, or put V1 in the numerator, yielding incorrect limits (e.g., predicting high efficiency at static conditions).

Common Pitfalls:

Confusing propulsive efficiency with overall or thermal efficiency; the former concerns velocity matching, not fuel-to-jet energy conversion.

Final Answer:

2 * V0 / (V1 + V0)