For selecting an optimum economic pipe diameter for fluid transport, the governing criterion is based on:

Introduction / Context:Pipeline sizing in process and water industries balances capital and operating expenses. A larger pipe reduces velocity and frictional head (lower pumping power) but raises capital cost; a smaller pipe does the opposite. The “economic diameter” minimizes the sum of these costs over the project horizon.

Given Data / Assumptions:

• Steady, single-phase flow in a long pipeline.
• Costs annualized to combine capital and operating burdens.
• Pump and electricity costs scale with frictional head loss and flow rate.

Concept / Approach:The optimum diameter occurs where marginal savings in pumping cost due to a small diameter increase equals the marginal increase in capital (pipe) cost. This is a total-cost minimization problem, not a single-parameter optimization in viscosity or density alone.

Step-by-Step Solution:Express total annual cost: C_total = C_capital(D) + C_pumping(D).Relate head loss to diameter (e.g., Darcy–Weisbach): h_f ∝ (L/D) * f * (v^2/2g); v ∝ 1/D^2.Operating cost ∝ power ∝ Q * ΔP ∝ Q * h_f.Find D that minimizes C_total by setting dC_total/dD = 0.

Verification / Alternative check:Empirical charts (e.g., economic velocity charts) embed the same trade-off and lead to comparable selections when local energy prices and material costs are applied.

Why Other Options Are Wrong:

• Viscosity or density alone cannot capture capital–operating trade-offs.
• Ignoring both costs defeats the purpose of “economic” sizing.
• Maximizing Reynolds number is not an economic objective.

Common Pitfalls:Using only minimum first cost; ignoring pump power and energy tariffs; neglecting time value of money in long-life pipelines.

Final Answer:Total cost (pumping/operating cost + fixed/pipe cost)