Flow in circular pipes: criterion for turbulent regime In internal flow through a straight circular pipe, the flow is classified as turbulent when the Reynolds number (based on pipe diameter) satisfies which condition?

Introduction / Context:
Classifying pipe flow as laminar, transitional, or turbulent is fundamental for choosing head-loss correlations (e.g., Darcy–Weisbach with appropriate f) and for predicting mixing and heat transfer. The Reynolds number Re encapsulates the ratio of inertial to viscous forces and serves as the key indicator.

Given Data / Assumptions:

• Straight, circular pipe of constant diameter.
• Re based on diameter: Re = (rho * V * D) / mu.
• Fully developed internal flow assumptions.

Concept / Approach:
Empirical evidence from Osborne Reynolds’ dye experiments shows three regimes: laminar (Re < about 2100), transitional (roughly 2100–3000), and turbulent (Re > about 3000). These thresholds are widely used in engineering design.

Step-by-Step Solution:

Verification / Alternative check:
Head-loss behavior: in turbulent flow, the friction factor depends weakly on Re and on relative roughness, unlike the f = 64/Re relation of laminar flow.

Why Other Options Are Wrong:

• Less than 2100 → laminar, not turbulent.
• Between 2100 and 3000 → transitional regime, not purely turbulent.
• “None of these” is incorrect because a standard threshold exists.

Common Pitfalls:
For noncircular ducts, use hydraulic diameter; near entrances or fittings the thresholds can shift due to disturbances.

Final Answer:
more than 3000