Pumping energy vs. pipe diameter—trend for a given fluid and flow For a given fluid and duty, as the pipe diameter increases, how does the pumping cost typically change?

Introduction / Context:
Pumping power is a major operating cost in pipelines and process plants. Understanding how pipe diameter affects friction losses guides economic trade-offs between CAPEX (bigger pipe) and OPEX (energy).

Given Data / Assumptions:

• Steady incompressible flow of a given fluid and required volumetric flow rate.
• Same pipeline length and roughness class.
• Newtonian behavior assumed for the general rule of thumb.

Concept / Approach:
Frictional head loss in pipes scales approximately with velocity squared and inversely with diameter to the fifth power for turbulent flow at constant volumetric rate (via Darcy–Weisbach and continuity). Larger diameter reduces velocity and friction factor influence, lowering pressure drop. Hence, for the same flow, pumping power decreases as diameter increases, though the installed cost of larger pipe rises—driving an economic optimum (pumping cost down vs. pipe CAPEX up).

Step-by-Step Solution:

Verification / Alternative check:
Pipeline optimization (e.g., the “economic diameter”) problems show total annual cost curves where energy falls with diameter and capital cost rises, confirming the monotonic energy reduction.

Why Other Options Are Wrong:

• Increases: contradicts friction loss physics for fixed flow.
• Remains the same: only true if ΔP were unchanged, which it is not.
• Newtonian vs. non-Newtonian: the qualitative trend persists; the exact exponent changes but energy still drops with increased D for fixed flow.

Common Pitfalls:
Ignoring that oversized pipes may increase capital and installation costs; the optimum diameter balances CAPEX and OPEX rather than minimizing one alone.

Final Answer:
decreases.