Which term describes the relationship between brake horsepower and speed according to the pump affinity laws?

The correct term describing the relationship between brake horsepower and speed according to the pump affinity laws is when the brake horsepower varies with the cube of the speed. This stems from the fundamental principles of pump performance and how they are affected by changes in pump speed.

When the speed of the pump increases, both the flow rate and the head (or pressure) produced by the pump also increase. According to the pump affinity laws, the power required by a pump, which is expressed in terms of brake horsepower, is related to the flow and head. Specifically, the relationship states that if you increase the speed of the pump, the brake horsepower necessary to drive the pump increases with the cube of that speed.

Mathematically, this is expressed as:

Power (BHP) ∝ Speed³

This means that if you double the speed of the pump, the brake horsepower will increase by a factor of eight (2³). This relationship is crucial for understanding how pump systems must be sized and selected to operate efficiently at various speeds, which is essential in engineering design and applications.

All other choices do not accurately reflect the relationship established by the affinity laws. For instance, stating that brake horsepower varies directly with the speed oversimplifies the actual relationship and ignores