Reynolds criteria for laminar pipe flow For internal flow inside a circular pipe, laminar flow is expected when the Reynolds number (based on diameter) satisfies which criterion?

Introduction / Context:
Flow regime identification is essential for selecting appropriate head-loss correlations and heat-transfer relations. The Reynolds number encapsulates the ratio of inertial to viscous forces and is the primary indicator for laminar versus turbulent flow in pipes.

Given Data / Assumptions:

• Flow in a straight, smooth, circular pipe.
• Reynolds number Re = ρ V D / μ.
• Entrance effects negligible; fully developed region considered.

Concept / Approach:
The classical thresholds are: laminar when Re < about 2100; transitional (critical) region roughly 2100 to 3000; and turbulent when Re > about 3000. Exact transition depends on disturbances and surface roughness, but these values are standard for engineering estimates.

Step-by-Step Solution:

Verification / Alternative check:
Experimental data (e.g., Osborne Reynolds dye-tracer experiments) corroborate these thresholds for round pipes, showing stable parabolic profiles below Re ≈ 2100.

Why Other Options Are Wrong:

• Re > 3000 corresponds to turbulent flow.
• 2100 ≤ Re ≤ 3000 is the transition band, not strictly laminar.
• “None of these” and “Re < 1000 only for oils” are incorrect generalizations.

Common Pitfalls:
Assuming the thresholds are exact for all geometries; confusing hydraulic diameter for noncircular ducts; ignoring surface roughness and perturbations in the transitional regime.

Final Answer:
Re < 2100