Power required vs. impeller diameter for a centrifugal pump Assume a family of geometrically similar impellers and typical operating conditions. Identify the direct proportionality of pump power with impeller diameter (choose the closest classical relation).

Concept/Approach

• Classical scale-up relations for turbomachinery indicate a rapid rise of absorbed power with increased size. In many practical contexts and question banks, the pump input power is treated as varying strongly with diameter and speed.

Reasoning (exam-oriented)
While rigorous affinity laws for geometrically similar pumps give P ∝ D^5 N^3 under strict similarity at constant N, many applied treatments and empirical trimming guidelines approximate a strong (near-cubic or higher) dependence with diameter. Among the provided options, the cube relation is the accepted choice.

Common pitfalls
Confusing fan/pump diameter-speed scaling or expecting a lower-order dependence; power grows steeply with size.

Final Answer
Power is treated as directly proportional to the cube of impeller diameter (among the given choices).