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GATE 2020 AE – Question 59

Propulsion · Turbomachinery: Centrifugal compressors and axial turbines · 2 marks · Numerical answer

The axial-turbine T–S diagram gives T₀₁ = 1050 K, T₀₂ = 823 K, p₀₁ = 7.8 bar and p₀₂ = 2.5 bar. For γ = 1.33, find stage isentropic efficiency in percent, to 2 decimals.

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Correct answer: 87 to 89

Explanation

At the same exit total pressure, ideal temperature is $T_{02s}=1050(2.5/7.8)^{(1.33-1)/1.33}\approx791.74$ K. Turbine efficiency is actual enthalpy drop divided by ideal drop: $\eta_t=(1050-823)/(1050-T_{02s})\approx0.877$. Thus approximately 87.89%, within the original 87–89% interval.

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