Centrifugal pump affinity laws — delivery head vs rotational speed How does the delivery head H vary with speed N for a geometrically similar centrifugal pump operating within its normal range?

Introduction:
Pump scaling and performance prediction rely on the affinity (similarity) laws. These laws relate flow rate, head, and power to impeller rotational speed for similar pumps handling the same fluid.

Given Data / Assumptions:

• Geometrically similar pump and impeller.
• Same fluid, similar efficiency region.
• Moderate changes in N (no cavitation, adequate NPSH).

Concept / Approach:
The classic affinity laws state: Q ∝ N, H ∝ N^2, and P ∝ N^3. These come from dynamic similarity with velocity triangles scaling with peripheral speed u ∝ ND and energy head H ∝ u^2/g ∝ N^2.

Step-by-Step Solution:

Verification / Alternative check:
Manufacturer curves often show that near the best-efficiency point, small speed changes follow these proportionalities closely. Deviations occur far from similarity conditions.

Why Other Options Are Wrong:

• H ∝ N: underestimates head rise with speed.
• Inverse relations: contradict similarity theory.
• Independent of N: physically incorrect for rotodynamic machines.

Common Pitfalls:
Applying affinity laws outside their valid range; ignoring changes in efficiency and cavitation limits at significantly different speeds.

Final Answer: