Which parameter varies with the cube of the impeller diameter in a centrifugal pump?

In a centrifugal pump, the power needed to drive the pump varies with the cube of the impeller diameter. This relationship stems from the physics of fluid dynamics and pump design. Specifically, as the diameter of the impeller increases, not only does the flow area increase, leading to a greater volume of fluid being moved, but the velocity with which that fluid is discharged also increases significantly.

The formula for hydraulic power in a pump considers both the flow rate and the head (or pressure) produced by the pump. If you increase the impeller diameter, the flow rate increases, resulting in a cubic relationship with respect to power requirements because power is proportional to flow and head. Since head is related to the square of velocity and velocity is proportional to the impeller diameter, when you take both of these factors into account, power becomes a function of the cube of the diameter.

Consequently, as the impeller diameter triples, the power required to achieve the same pumping performance increases by a factor of approximately twenty-seven (3 cubed). This is why the power needed to drive the pump is a critical design consideration when selecting or adjusting impeller size in centrifugal pumps. Understanding this relationship is essential in power engineering, especially for efficient pump operation and system design