GATE 2025 AE – Question 65
A single-stage axial compressor, with a 50 % degree of reaction, runs at a mean blade speed of 250 m/s. The overall pressure ratio developed is 1.3. Inlet pressure and temperature are 1 bar and 300 K, respectively. Axial velocity is 200 m/s. Specific heat at constant pressure, $C_p$ = 1005 J/kg/K and specific heat ratio, $\gamma$ = 1.4. The rotor blade angle at the outlet is ___ degrees (rounded off to two decimal places).
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Correct answer: 21.00 to 22.00
Explanation
The stage work (isentropic) is $\Delta h_0 = C_pT_{01}\left(\pi^{(\gamma-1)/\gamma} - 1\right) = 1005 \times 300 \times (1.3^{0.2857} - 1) = 23469$ J/kg. This equals $U\Delta C_\theta$, so $\Delta C_\theta = 93.88$ m/s. For 50% reaction the velocity triangles are symmetrical ($C_{\theta 1} = W_{\theta 2}$ and $C_{\theta 2} = W_{\theta 1}$), and $W_{\theta 2} + C_{\theta 2} = U$. With $C_{\theta 2} - C_{\theta 1} = 93.88$ this gives $W_{\theta 2} = \frac{250 - 93.88}{2} = 78.06$ m/s. The rotor outlet blade angle from the axial direction is $\beta_2 = \tan^{-1}\frac{78.06}{200} = 21.32^\circ$.
Official GATE 2025 answer key: https://gate2026.iitg.ac.in/doc/download/2025_Key/AE_Keys.pdf