GATE_AE_2027_MOCK_03_Q56 GATE 2027 Aerospace Engineering All-India Master Mock 03 (Flight Dynamics, Controls & Space Trajectories) NAT · 2 Marks
Propulsion • Compressors and Turbines • Centrifugal & Axial Compressors

In a centrifugal compressor, the impeller tip radius is r_2 = 0.25 m and rotates at N = 18000 rpm. With radial blades (slip factor \sigma = 0.90), what is the whirl velocity C_{\theta 2} at the impeller tip in m/s? (Take \pi \approx 3.1416, round to nearest integer).

Answer Key:
424

Step-by-Step Verified Solution

### Solution: Tip speed U_2 = \omega * r_2 = (2 * \pi * 18000 / 60) * 0.25 = 600 * \pi * 0.25 = 150 * 3.1416 = 471.24 m/s. Whirl velocity C_{ heta 2} = \sigma * U_2 = 0.90 * 471.24 = 424.1 m/s ≈ 424 m/s. Correct: 424 (range 420 to 428).
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