Centrifugal pump performance at constant speed: Which set of statements best describes how head, discharge, efficiency, and brake horsepower vary with discharge?

Introduction / Context:
Centrifugal pumps have characteristic head–discharge, efficiency–discharge, and power–discharge curves at constant speed. Understanding these relationships is essential for selection, control-valve sizing, and energy optimization.

Given Data / Assumptions:

• Single-stage centrifugal pump operating at constant rotational speed.
• Clear liquid, negligible viscosity effects beyond water-like behavior.
• No variable-speed drives or system interactions altering basic trends.

Concept / Approach:

The pump head–Q curve typically slopes downward; at zero flow, the shut-off head is achieved. Efficiency peaks near the “best efficiency point” (BEP), often called normal discharge for selection. Input power (and thus brake horsepower) usually rises with discharge up to near-BEP and may increase further depending on specific-speed and impeller design.

Step-by-Step Solution:

Verification / Alternative check:

Manufacturer curves consistently display these trends. System curves intersect pump curves to determine operating point; throttling shifts the operating point along the pump curve accordingly.

Why Other Options Are Wrong:

• Any single statement alone is incomplete; together they correctly describe the pump behavior, hence “all the above.”

Common Pitfalls:

• Assuming head increases with discharge at constant speed.
• Confusing shut-off head with maximum efficiency point.

Final Answer:

all the above.