If a centrifugal pump motor is replaced with one that has 20 percent more speed, how much will the horsepower required increase?

When a centrifugal pump motor speed is increased, the power required by the pump does not increase linearly with speed. Instead, the horsepower required can vary significantly due to the cubic relationship between speed and flow rate.

In centrifugal pumps, the flow rate is proportional to the speed, while the pressure head is proportional to the square of the speed. Consequently, when you increase the speed of the motor by 20 percent, the flow rate (Q) increases by 20 percent, but the head (H) increases by the square of the speed increase. Specifically, a 20 percent increase in speed raises the head to approximately 1.2 squared, which equals 1.44—or an increase of about 44 percent in effective head.

The horsepower (HP) required is calculated using the formula:

[ \text{HP} = \frac{Q \times H}{3,960} ]

Considering the increases in both flow and head, the actual increase in horsepower required due to the 20 percent increase in speed turns out to be approximately 73 percent. This comes from the combination of the increases in flow and head, which ultimately impacts the horsepower requirement more than what might be expected from a direct percentage increase in speed alone. Thus