If a fan motor runs at 1800 RPM with a 3 inch pulley and drives a fan with a 9 inch pulley, what is the fan speed?

To determine the fan speed in this scenario, it's important to understand the relationship between the motor RPM, the pulley sizes, and how they correlate to the output speed of the fan. The speed at which the fan spins is inversely proportional to the sizes of the pulleys.

The formula for calculating the fan speed is:

[ \text{Fan Speed} = \left( \frac{\text{Motor Speed} \times \text{Motor Pulley Diameter}}{\text{Fan Pulley Diameter}} \right) ]

In this case, you have a motor speed of 1800 RPM, a motor pulley diameter of 3 inches, and a fan pulley diameter of 9 inches. Plugging these values into the formula yields:

[ \text{Fan Speed} = \left( \frac{1800 \times 3}{9} \right) ]

Calculating the above:

1. 1800 RPM multiplied by 3 inches equals 5400.

2. Divide 5400 by 9 inches results in 600 RPM.

Thus, the fan speed is determined to be 600 RPM, making this the correct answer. Understanding this principle allows one to analyze the performance of fans in systems where pulley sizes differ