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GATE 2023 AE – Question 21

Propulsion · Turbomachinery: Axial compressors, work and compression, degree of reaction, multi-staging · 1 mark · Multiple choice

For a stage of a 50% reaction ideal axial flow compressor (symmetrical blading), select the correct statement from the options given.

  1. The stagnation enthalpy rise across the rotor is 50% of the rise across the stage.
  2. The static enthalpy rise across the rotor is 50% of the rise across the stage.
  3. Axial velocity component of the flow at the rotor exit is 50% of that at the rotor entry.
  4. The static pressure rise across the rotor is 50% of the rise across the stator.

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Show answer and explanation

Correct answer: (B) The static enthalpy rise across the rotor is 50% of the rise across the stage.

Explanation

**Degree of reaction** of a compressor stage is the fraction of the stage's static enthalpy rise that occurs in the rotor:
$$R=\frac{\Delta h_{rotor}}{\Delta h_{stage}} .$$

For a **50% reaction** stage, $R=0.5$, which means:
- the static enthalpy rise in the rotor is **half** the stage's static enthalpy rise (option B), and
- the other half occurs in the stator.

Why the other options are wrong:
- **A.** All the stagnation enthalpy rise (the work input) occurs in the rotor, since only the rotor does work. The stator does none.
- **C.** In an ideal stage the axial velocity is constant across the rotor.
- **D.** At 50% reaction the pressure rises in the rotor and the stator are about equal, not 50% of each other.

Answer **B**.