Questions: Laminar-Turbulent Transition and Critical Reynolds Number

Question 1

A pipe flow has Re = 3,200. An engineer needs to calculate the pressure drop per unit length. What is the best approach?

• A. Use f = 64/Re from the Hagen-Poiseuille laminar formula, since Re < 4,000
• B. Use the turbulent Moody chart friction factor, since Re > 2,300
• C. Recognize that Re = 3,200 is in the transitional region; neither the laminar nor turbulent formula is reliable, and additional information about disturbance levels is needed
• D. Average the laminar and turbulent friction factors for Re = 3,200

Answer: (C)

Re = 3,200 falls in the transitional region (roughly 2,300–4,000) where the flow can flicker between laminar and turbulent states depending on inlet conditions, pipe roughness, and vibration. Neither the laminar Hagen-Poiseuille result nor the turbulent Moody chart is reliably applicable. In practice, engineers often design to avoid this region because the friction factor — and heat transfer — are unpredictable there. The sharp answer '< 4,000 means laminar' is the dangerous misconception; transition begins around 2,300, not 4,000.

Question 2

Why does the friction factor jump so dramatically when pipe flow transitions from laminar to turbulent at the same Reynolds number?

• A. Turbulent flow has higher viscosity, which increases the wall shear stress
• B. Turbulent eddies bring high-momentum fluid from the core to the wall region, dramatically increasing wall shear stress beyond what viscous laminar flow produces
• C. Transition increases the effective pipe diameter, changing the Re calculation
• D. The pressure drop formula changes from linear to quadratic only because of the different Reynolds number used

Answer: (B)

In laminar flow, momentum transfer to the wall occurs only through viscous diffusion — a slow process that produces the smooth parabolic velocity profile and moderate wall shear. In turbulent flow, eddies actively mix high-velocity fluid from the core toward the wall, dramatically steepening the velocity gradient near the wall and greatly increasing shear stress. This is why the turbulent friction factor is 4–10× higher than the laminar value at the same Re. Viscosity itself doesn't change — the mechanism of momentum transport changes.

Question 3

Under carefully controlled laboratory conditions with very smooth pipes and disturbance-free flow, laminar flow can persist well above Re = 2,300.

• T. True
• F. False

Answer: True

Re ≈ 2,300 is a practical engineering threshold, not an absolute physical law. In the laboratory, laminar pipe flow has been maintained to Re > 100,000 by meticulously eliminating inlet disturbances, vibration, and roughness. The transition is a physical instability: at Re > 2,300, small disturbances *can* grow rather than being damped by viscosity, but only if those disturbances are present. In ordinary engineering conditions disturbances are unavoidable, making 2,300 the practical transition point — but the underlying physics is about disturbance amplification, not a hard switch.

Question 4

The transition from laminar to turbulent flow occurs instantaneously at Re = 2,300 — below this value the flow is laminar, above it turbulent.

• T. True
• F. False

Answer: False

Transition is not a sharp switch — it is a region. In pipes, flow is reliably laminar below Re ≈ 2,300 and reliably turbulent above Re ≈ 4,000, but the region between these values is transitional: flow can intermittently switch between states, and the friction factor is neither predictable nor well-described by either the laminar or turbulent formula. The precise transition point within this range depends on inlet conditions, surface roughness, and disturbance levels.

Question 5

Why does temperature have opposite effects on laminar-turbulent transition tendency for liquids versus gases?

Model answer: Temperature affects the dynamic viscosity μ, which appears in the denominator of Re = ρVD/μ. For liquids, viscosity decreases with temperature — a hotter liquid is less viscous, so Re rises at fixed velocity, making turbulence more likely as the liquid heats up. For gases, viscosity increases with temperature (due to greater molecular collision frequency), so Re falls at fixed velocity, making turbulence less likely as gas heats. The direction of the temperature effect on transition therefore depends entirely on which way viscosity moves, and liquids and gases behave oppositely.

This is a direct application of viscosity-temperature dependence to the Reynolds number formula. The intuition: viscosity is the 'resistance to turbulence' in the Re ratio. Higher viscosity (lower Re) means viscous damping is relatively stronger and laminar flow is more stable. Lower viscosity (higher Re) means inertial forces dominate and transition is more likely. Because liquids and gases have opposite viscosity-temperature relationships, their transition behaviors with heating are also opposite.