Laminar and Turbulent Flow
Simple Explanation
In laminar flow, a fluid moves in smooth, parallel layers that do not mix. In turbulent flow, the fluid moves chaotically, with swirling eddies and mixing between layers. Whether a flow is laminar or turbulent is predicted by a dimensionless number called the Reynolds number (Re).
Why Do We Need It?
Whether a flow is laminar or turbulent completely changes how it behaves — turbulent flow causes far more resistance and mixing, which matters enormously in designing pipes, aircraft, and blood vessels alike.
Formula
Reynolds Number
Re = ρvd / η
A dimensionless number that predicts whether a fluid's flow will be smooth (laminar) or chaotic (turbulent) — comparing the fluid's inertia to its internal friction (viscosity).
- Re
- — Reynolds number (dimensionless — no units)
- ρ
- — fluid density, in kilograms per cubic metre (kg/m³)
- v
- — flow speed, in metres per second (m/s)
- d
- — characteristic diameter of the flow (e.g. pipe diameter), in metres (m)
- η
- — dynamic viscosity of the fluid, in pascal-seconds (Pa·s)
When to use it: Whenever predicting or classifying whether a flow is laminar (Re below about 2000) or turbulent (Re above about 4000).
Worked Example
Classify a flow using the Reynolds number
Water (ρ=1000 kg/m³, η=0.001 Pa·s) flows through a pipe of diameter 0.02 m at 0.5 m/s. Classify the flow.
Why Does This Work?
The Reynolds number compares the fluid's inertia (which tends to keep it moving in a disorderly way once disturbed) to its viscosity (which tends to smooth out and damp disturbances) — when inertia dominates (high Re), disturbances grow into turbulence; when viscosity dominates (low Re), disturbances die out and the flow stays smooth.
Real-Life Example
Smoke rising from a candle
Smoke from a candle rises smoothly in a thin column near the flame, then suddenly breaks into swirling, chaotic patterns higher up.
The smooth column is laminar flow (low Reynolds number, near the source); as the smoke speeds up and spreads, the Reynolds number rises past the threshold and the flow becomes turbulent.
Practice
Water (ρ=1000 kg/m³, η=0.001 Pa·s) flows through a pipe of diameter 0.01 m at 0.1 m/s. Find the Reynolds number.
MediumCommon mistake
Assuming turbulent flow is simply "fast" flow — it is really about the Reynolds number, which combines speed with density, viscosity, and pipe size; a slow flow in a very wide pipe of low-viscosity fluid can still be turbulent.
Quick Review
- Laminar: smooth, parallel layers. Turbulent: chaotic, mixing eddies.
- Re = ρvd/η — dimensionless, predicts which regime applies.
- Re below ~2000: laminar. Re above ~4000: turbulent. Between: transitional.