What typically happens to the power needed to drive a centrifugal pump when the impeller speed is doubled?

When the impeller speed of a centrifugal pump is doubled, the power required to drive the pump typically increases eightfold. This relationship is derived from the affinity laws that govern the performance of centrifugal pumps.

The affinity laws state that if you change the speed of a pump, the flow rate, head, and power consumption will change proportionally to the speed of the pump. Specifically, when the speed of the pump is increased, both the flow rate and the head increase with the first power of the speed. However, the power required to drive the pump increases with the third power of the change in speed.

Mathematically, if the speed of the pump is doubled (2 × original speed), the power will increase according to the formula:

Power ∝ (Speed)^3

Therefore, if the speed is doubled, the power required becomes:

Power = k × (2 × speed)^3 = k × 8 × (speed)^3

This results in the power requirement increasing by a factor of eight. Understanding this principle is crucial for managing pump systems effectively, as it has significant implications for energy consumption and mechanical design in engineering applications.