GATE 2024 AE – Question 58
A centrifugal compressor is designed to operate with air. At the leading edge of the tip of the inducer (eye of the impeller), the blade angle is $45^o$, and the relative Mach number is 1.0. The stagnation temperature of the incoming air is 300 K. Consider $\gamma$ = 1.4. Neglect pre-whirl and slip. The inducer tip speed is ________ m/s (rounded off to the nearest integer).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 234
Explanation
With no pre-whirl the absolute velocity is axial, $C_a$, and the relative flow follows the blade at $45^\circ$: $U = C_a\tan 45^\circ = C_a$ and $W_1 = \sqrt 2\,C_a$. The relative Mach number is 1, so $W_1 = a_1 = \sqrt{\gamma RT_1}$, with $T_1 = T_{01} - \frac{C_a^2}{2c_p}$. Then $2C_a^2 = \gamma RT_{01} - \frac{\gamma - 1}{2}C_a^2$, which gives $2.2C_a^2 = 1.4 \times 287 \times 300 = 120540$ and $C_a = 234.1$ m/s. So the tip speed is 234 m/s.