Centrifugal pump behavior with speed changes Statement: For a centrifugal pump of fixed geometry operating under constant head and constant discharge, the power requirement increases with rotational speed.

Introduction / Context:
Pump affinity laws relate flow, head, and power to rotational speed for a given impeller and casing. However, those relations apply when the system allows these variables to change with speed. This statement locks head and discharge as constants, so it tests whether you can separate operating point constraints from free-scaling behavior.

Given Data / Assumptions:

• Fixed pump geometry.
• Head H and discharge Q are held constant (for example by throttling and system control).
• Efficiency changes with speed are not specified.

Concept / Approach:
Hydraulic power delivered to the fluid is P_h = ρ * g * Q * H. If Q and H are both fixed, the hydraulic power requirement is constant regardless of speed. Shaft power equals P_h / η. If efficiency remains similar, input power stays approximately constant. Therefore, a generic claim that power increases solely because speed is higher is false under the stated constraints.

Step-by-Step Solution:
Given: Q = constant, H = constant.Hydraulic power P_h = ρ g Q H = constant.Shaft power P_in = P_h / η; if η does not systematically decrease, P_in does not inherently increase with speed.Hence the blanket statement is false.

Verification / Alternative check:
If the system let Q and H vary per affinity laws, then P ∝ N^3. But that is explicitly not the case here, confirming that speed alone does not dictate higher power at fixed Q and H.

Why Other Options Are Wrong:
Options tying truth to positive displacement or zero efficiency are irrelevant; the governing relation is P_h = ρ g Q H.

Common Pitfalls:
Blindly applying affinity P ∝ N^3 without verifying whether Q and H are fixed or allowed to vary.

Final Answer:
False