GATE 2022 AE – Question 35
A turbine stator delivers gas at 500 m/s and 70° to the turbine axis. Rotor blade speed is 250 m/s. Its leading-edge relative-flow blade angle β (one decimal place degrees) is ________.
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Correct answer: 51.84 to 52.36
Explanation
Resolve the gas velocity leaving the stator (nozzle), $V=500$ m/s at $\alpha=70^\circ$ to the axis, into components:
- **Tangential (whirl):** $V_w=500\sin70^\circ=469.85$ m/s.
- **Axial:** $V_a=500\cos70^\circ=171.01$ m/s.
**Relative velocity at the rotor inlet.** The blade moves with speed $U=250$ m/s in the tangential direction, so the relative tangential velocity is
$$V_{w,rel}=469.85-250=219.85\text{ m/s},$$
while the axial component is unchanged (171.01 m/s).
**Relative flow angle** (from the axial direction), which is also the leading-edge blade angle for shock-free entry:
$$\beta=\tan^{-1}\frac{V_{w,rel}}{V_a}=\tan^{-1}\frac{219.85}{171.01}=\tan^{-1}(1.2856)=\mathbf{52.1^\circ}.$$