Economic diameter concept for pumping mains If the selected pipe diameter is smaller than the economic (optimum) diameter for a pumping main, which of the following statements is true?

Introduction / Context:
The economic (optimum) diameter minimizes the total annual cost, which is the sum of capital cost (pipe) and operating cost (pumping energy). Deviating below this diameter reduces capital cost but increases friction losses and energy costs.

Given Data / Assumptions:

• Steady discharge in a pumped main.
• Economic analysis includes energy cost over the service life.

Concept / Approach:
Head loss in pipes varies approximately with 1/D^5 (Darcy–Weisbach with velocity terms), so smaller D sharply increases head loss and power consumption. The optimum occurs when the marginal increase in capital cost equals the marginal saving in energy.

Step-by-Step Solution:

Verification / Alternative check:
Classical formulas (e.g., power-cost-based diameter selection) show total annual cost curve convex with a minimum at the economic diameter.

Why Other Options Are Wrong:

• (a), (b), and (c) are each individually correct effects.
• Hence (d) “All of the above” is the right holistic statement; (e) is false.

Common Pitfalls:
Selecting diameter solely on material cost without lifecycle energy analysis leads to higher total cost of ownership.

Final Answer:
All of the above