GATE 2021 AE – Question 56

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

At design conditions, a single-stage axial compressor has rotor exit blade angle 30°, absolute inlet/exit velocities 140/240 m/s and relative inlet/exit velocities 240/140 m/s, as shown in the velocity triangle. The mean-radius blade speed is ___ m/s (two decimals).

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Correct answer: 275.73 to 278.51

Explanation

**Velocity triangle at the rotor exit.** The relative velocity leaving the rotor is $W_2=140$ m/s at a blade angle of $30^\circ$ from the axial direction. The absolute exit velocity is $V_2=240$ m/s. (The inlet triangle is the mirror image: absolute 140 m/s and relative 240 m/s.)

**Axial velocity.** From the exit triangle,
$$V_a=W_2\cos30^\circ=140\times0.8660=121.24\text{ m/s}.$$

**Absolute whirl velocity at the exit** (the absolute exit speed is 240 m/s, with the same axial component):
$$V_{\theta2}=\sqrt{240^2-121.24^2}=207.12\text{ m/s}.$$

**Blade speed** from the triangle ($U=V_\theta+W_\theta$, with $W_\theta=W_2\sin30^\circ=70$ m/s):
$$U=207.12+70=\mathbf{277.12\ m/s}.$$