Economic and hydraulic considerations in pipe sizing: Which statement is correct when comparing smaller-diameter pipes at the same flow velocity and service conditions?
Correct Answer: None of these.
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:
Assess (a): Smaller D at equal V → larger head loss, so (a) is false.Assess (b): With higher friction in smaller D for same Q, pumping cost increases, not decreases → false.Assess (c): Smaller pipes are cheaper in capital cost, not more expensive → false.Thus “None of these” is correct.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.