Question

In a centrifugal compressor, the eye tip diameter is 10 cm. For a shaft rotational speed of 490 rotations per second, the tangential speed at the inducer tip is \_\_\_ m/s (rounded off to one decimal place).

Hint:

To find the tangential speed at the inducer tip in a centrifugal compressor, use the formula \( V_t = \pi \cdot D \cdot N \), where \( D \) is the diameter and \( N \) is the rotational speed.

Answer 1

To calculate the tangential speed at the inducer tip, we use the following formula: \[ V_t = \pi \cdot D \cdot N \] Where:
\( V_t \) is the tangential speed at the inducer tip,
\( D \) is the diameter at the inducer tip (10 cm or 0.1 m),
\( N \) is the rotational speed in revolutions per second (490 revolutions per second).
Substituting the values into the formula: \[ V_t = \pi \cdot 0.1 \cdot 490 \] \[ V_t \approx 3.1416 \cdot 0.1 \cdot 490 \approx 153.94 \, {m/s} \] When rounded to one decimal place, the tangential speed at the inducer tip is approximately 151.0 m/s.