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GATE 2024 AE – Question 40

Propulsion · Turbomachinery: Axial compressors, work and compression, degree of reaction, multi-staging · 2 marks · Multiple choice

A multistage axial compressor, with overall isentropic efficiency of 0.83, is used to compress air at a stagnation temperature of 300 K through a pressure ratio of 10:1. Each stage of the compressor is similar, and the stagnation temperature rise across each compressor stage is 20 K. Assume $C_p$ = 1005 J/kg K and $\gamma$ = 1.4 for air. How many stages are there in the compressor?

  1. 17
  2. 13
  3. 19
  4. 11

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Correct answer: (A) 17

Explanation

The ideal temperature rise is $300\left(10^{0.2857} - 1\right) = 300 \times 0.9307 = 279.2$ K. The actual overall rise is $\frac{279.2}{0.83} = 336.4$ K. With 20 K per stage there are $\frac{336.4}{20} = 16.8$, which is 17 stages.