Economic and hydraulic considerations in pipe sizing: Which statement is correct when comparing smaller-diameter pipes at the same flow velocity and service conditions?

Introduction / Context:
Choosing pipe diameter balances capital cost against operating cost. Friction losses strongly depend on diameter, so smaller pipes tend to increase head loss and energy use at a given flow rate. Exam questions often test qualitative understanding of these trends.

Given Data / Assumptions:

• Same flow velocity or same discharge as stated.
• Comparable roughness and material.
• Pumping is required to overcome friction where relevant.

Concept / Approach:

Darcy–Weisbach shows head loss h_f ∝ (L/D) * V^2; at equal velocity, smaller D produces higher h_f. At equal discharge, V increases in a smaller pipe, further raising losses. Pumping power ∝ Q * head; therefore, smaller pipes typically raise operating cost. Capital cost generally increases with diameter, not vice versa.

Step-by-Step Solution:

Verification / Alternative check:

Manufacturer curves and lifecycle cost analyses consistently show a trade-off: larger initial cost for larger pipes but savings in pumping energy over time; the statements (a)–(c) contradict this basic principle.

Why Other Options Are Wrong:

• (a) and (b) reverse friction/power trends.
• (c) contradicts typical material/installation pricing.
• (e) cannot be true if any are false.

Common Pitfalls:

• Comparing at equal velocity vs. equal discharge without care—either way, smaller D increases losses.
• Ignoring roughness/age effects that further penalize smaller pipes.

Final Answer:

None of these.