GATE 2021 AE – Question 57
An axial turbine has rotor relative inlet and exit angles 21° and 55°, degree of reaction 0.4, blade speed 340 m/s, flow area 0.08 m² and density 0.9 kg/m³. Mass flow is ___ kg/s.
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Correct answer: 18.0 to 19.5
Explanation
**Degree of reaction of an axial turbine** in terms of the flow angles and the axial velocity $V_a$ (constant through the stage):
$$R=\frac{V_a}{2U}\left(\tan\beta_3-\tan\beta_2\right),$$
where $\beta_2=21^\circ$ and $\beta_3=55^\circ$ are the relative flow angles at the rotor inlet and exit.
**Axial velocity.** With $R=0.4$ and $U=340$ m/s:
$$V_a=\frac{2UR}{\tan55^\circ-\tan21^\circ}=\frac{2\times340\times0.4}{1.4281-0.3839}=\frac{272}{1.0442}=260.5\text{ m/s}.$$
**Mass flow rate:**
$$\dot m=\rho\,A\,V_a=0.9\times0.08\times260.5=\mathbf{18.75\ kg/s}.$$
Official GATE 2021 answer key: https://gate2026.iitg.ac.in/doc/download/Answer_keys2021/ae_2021.pdf