Questions: Transition to Turbulence and Reynolds Number

Question 1

Water (ρ = 1000 kg/m³, μ = 0.001 Pa·s) flows in a 5 cm diameter pipe at 0.03 m/s. What is the Reynolds number and what flow regime is expected?

Model answer: Re = ρVD/μ = 1000 × 0.03 × 0.05 / 0.001 = 1500. This is below 2,300, so the flow is laminar.

With Re = 1500, viscous forces dominate and the flow is well within the laminar regime. The Hagen-Poiseuille equation is valid here. To achieve turbulent flow in this pipe, velocity would need to exceed about 0.046 m/s (Re ≈ 2,300).

Question 2

Explain why the critical Reynolds number for pipe flow transition is not a single precise value.

Model answer: The critical Re depends on the level of disturbances in the flow. A smooth, quiet inlet can sustain laminar flow well above Re = 2,300; a rough or disturbed inlet triggers transition at lower Re. The range 2,300–4,000 is transitional, and the exact value is sensitive to pipe roughness, inlet geometry, vibration, and flow history.

Turbulent transition is a stability problem, not a simple threshold. Disturbances that grow faster than viscosity can damp them will trigger turbulence. In practice, engineers use Re = 2,300 (lower bound) and 4,000 (upper bound) as conservative design limits.