In centrifugal pump design, the developed head follows the pump affinity laws. Which basic geometric/operating parameters primarily govern the head produced by a centrifugal pump?

Introduction / Context:
Centrifugal pump performance is commonly estimated using the affinity (similarity) laws. Understanding which parameters control the developed head helps in scale-up, troubleshooting, and variable-speed control in chemical and mechanical engineering applications.

Given Data / Assumptions:

• Pump type: centrifugal, geometrically similar for comparisons.
• Fluid properties and suction conditions are unchanged.
• We consider the idealized relationships from the affinity laws.

Concept / Approach:
For geometrically similar centrifugal pumps operating within similar hydraulic regimes, the affinity laws state: H ∝ N^2 and H ∝ D^2, where H is head, N is rotational speed, and D is impeller diameter. Flow rate scales as Q ∝ N and Q ∝ D^3; power scales as P ∝ N^3 and P ∝ D^5. Therefore, both speed and impeller diameter directly influence the head developed.

Step-by-Step Solution:

Verification / Alternative check:
Manufacturer pump curves plotted for different speeds show head varying with N^2. Trimmed impeller curves (reduced D) similarly show head reduction approximately with D^2, confirming the law empirically within practical ranges.

Why Other Options Are Wrong:

• Speed only: incomplete; diameter also governs head.
• Impeller diameter only: incomplete; speed also governs head.
• Neither: incorrect, as both parameters control head per similarity laws.

Common Pitfalls:
Ignoring system curve interactions; even if pump head increases with N^2, the operating point depends on the pipeline/system resistance. Also, extreme extrapolation beyond the tested range can introduce inaccuracies.

Final Answer:
both (a) and (b)