How much additional horsepower is required when using a motor with 20 percent more speed?

When the speed of a motor increases, the horsepower required does not simply increase linearly, but rather, it increases with the cube of the speed ratio. This is based on the formula that states that power is proportional to the cube of the speed (Power ∝ Speed^3).

In this scenario, if a motor’s operating speed is increased by 20 percent, the new speed can be expressed as 1.2 times the original speed. To determine the additional horsepower required at this new speed, we calculate:

[

(1.2)^3 = 1.728

]

This means that the horsepower required at 20 percent more speed is approximately 1.728 times the original horsepower. Therefore, the correct answer demonstrates the significant increase in power requirement due to the cube relationship associated with speed changes. This principle is crucial in the context of mechanical and electrical engineering, especially in applications involving pumps and motors in wastewater treatment systems.