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GATE 2026 AE – Question 46

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

The figure below shows the velocity triangles at the inlet and outlet of the rotor of a low hub-to-tip ratio axial compressor at the mid-span of the blade. The absolute and relative velocities of the flow are denoted by C and W, respectively. The subscripts 1 and 2 refer to the locations before and after the rotor, respectively. The blade velocity is denoted by U. Select the CORRECT statement(s) for this device.

Two velocity triangles on a common base: the blade speed U = 100 m/s. Both have the same height of 80 m/s (the axial velocity). The inlet triangle has an absolute tangential component of 15 m/s, and the outlet triangle has an absolute tangential component of 75 m/s (a difference of 60 m/s). All values are in m/s.
  1. The axial velocity is constant across the rotor
  2. The flow coefficient is 0.6
  3. The blade loading coefficient is 0.6
  4. If the acoustic velocity at the rotor inlet is 350 m/s, then the inlet relative Mach number is 0.333

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Show answer and explanation

Correct answer: (A) The axial velocity is constant across the rotor; (C) The blade loading coefficient is 0.6; (D) If the acoustic velocity at the rotor inlet is 350 m/s, then the inlet relative Mach number is 0.333

Explanation

Both triangles have the same height, 80 m/s, so the axial velocity is constant (A). The flow coefficient is $\phi = \frac{C_a}{U} = 0.8$, not 0.6 (B false). The blade loading coefficient is $\psi = \frac{\Delta C_\theta}{U} = \frac{75 - 15}{100} = 0.6$ (C). At the inlet $W_1 = \sqrt{85^2 + 80^2} = 116.7$ m/s, so $M_{rel} = \frac{116.7}{350} = 0.333$ (D).