An axial compressor rotor has tip radius $r_{tip} = 0.40\text{ m}$ and rotates at $N = 9000\text{ rpm}$. What is the blade tip speed $U_{tip}$ in m/s? (Take $\pi \approx 3.1416$, round to nearest integer).

Answer Key:

377

### Solution: Angular velocity $\omega = \frac{2\pi N}{60} = \frac{2 \times 3.1416 \times 9000}{60} = 300 \times 3.1416 = 942.48\text{ rad/s}$. Tip speed $U_{tip} = \omega \times r_{tip} = 942.48 \times 0.40 = 376.99 \approx 377\text{ m/s}$. Correct: 377 (range 374 to 380).

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