Transition criterion in circular pipes: above which Reynolds number does laminar flow of a Newtonian fluid typically cease to exist (onset of transition)?

Introduction:
The Reynolds number quantifies the ratio of inertial to viscous forces and is the primary criterion for flow regime identification in internal flows. Correctly identifying the laminar–turbulent boundary is essential for choosing correlations for friction and heat/mass transfer.

Given Data / Assumptions:

• Circular pipe, Newtonian fluid, steady flow.
• Re = ρ v D / μ, based on pipe diameter.

Concept / Approach:
Experiments indicate laminar flow is generally maintained for Re < 2100. Between about 2100 and 4000 lies the transition region, and for Re > 4000 the flow is usually fully turbulent (subject to entrance effects and disturbances). Therefore “laminar ceases” is commonly associated with Re ≈ 2100.

Step-by-Step Solution:
Identify standard thresholds: laminar Re < 2100; transition 2100–4000; turbulent Re > 4000.Hence, laminar regime ceases to exist beyond about Re ≈ 2100.

Verification / Alternative check:
Classic experiments by Osborne Reynolds and subsequent standard texts adopt these nominal limits for smooth pipes.

Why Other Options Are Wrong:

• 4000/3000/1500/1000: do not match widely used criterion for laminar cessation in pipes.

Common Pitfalls:
Confusing entrance length or surface roughness effects with the fundamental regime thresholds; exact transition can vary, but 2100 is the conventional design cut-off.

Final Answer:
Re ≈ 2100