The economically optimum pipe diameter for a given fluid service is chosen primarily on what basis?

Introduction / Context:
In pipeline design, selecting pipe size impacts both capital and operating costs. A small diameter reduces material cost but increases frictional losses and hence pumping cost; a larger diameter does the opposite. The optimum diameter is an economic trade-off, not a purely hydraulic or purely mechanical decision.

Given Data / Assumptions:

• Steady, incompressible flow in a long pipeline.
• Pump efficiency and energy price are known or estimated.
• Pipe cost increases with diameter and material thickness.

Concept / Approach:
The annualized total cost = annualized capital cost of the pipeline + annual pumping (energy) cost. Frictional head loss is inversely related to approximately D^5 (via Darcy–Weisbach and continuity), so pumping power falls rapidly with diameter, while capital cost increases roughly with D and length. Minimizing the sum yields the economic diameter (e.g., using the well-known optimization known as the economic pipe diameter method).

Step-by-Step Solution:
Define C_total(D) = C_capital(D) + C_operating(D).C_operating decreases as diameter increases due to lower friction losses.C_capital increases with diameter because of material and installation costs.Choose the diameter D that minimizes C_total(D).

Verification / Alternative check:
Perform sensitivity analysis by evaluating total cost for a few candidate diameters; the minimum identifies the optimum. This aligns with classical plant design practices.

Why Other Options Are Wrong:
Viscosity or density alone: These parameters influence head loss but do not by themselves define economic optimum without considering cost trade-offs.None of these: Incorrect because total cost is the accepted criterion.

Common Pitfalls:

• Overemphasis on hydraulic efficiency without capital cost consideration.
• Ignoring energy pricing and pump efficiency in operating cost calculations.
• Neglecting installation factors (buried vs aboveground) that affect capital cost.

Final Answer:
total cost considerations (pumping cost plus fixed cost of the pipe).