Question

The rotor of a millimeter-scale gas turbine engine has a radius of 1 mm. It has to reach a tip, or rim speed of nearly the speed of sound for an effective compression. Assuming that the speed of sound is 340 m/s, calculate the rotor rotational inlcrs speed in revolutions per minute (rpm).

Answer 1

The rotational speed of the rotor in revolutions per minute (rpm) is approximately 287.

Step-by-step explanation:

To calculate the rotor rotational speed in revolutions per minute (rpm), we can use the formula:

Rotational speed in rpm = (Tip speed in m/s) ÷ (2π x Radius in meters x 60)

Given that the tip speed needs to be nearly the speed of sound, which is 340 m/s, and the radius is 1 mm, we can plug in these values:

Rotational speed in rpm = (340 m/s) ÷ (2π x 0.001 m x 60)

Simplifying this equation gives us the answer:

Rotational speed in rpm ≈ 287