Reynolds Number
Predicts laminar vs turbulent flow.
Formula
Variables
Example
Re < 2300 ⇒ laminar
How it works
The Reynolds number compares inertial forces, which try to keep a fluid moving in the same direction, with viscous forces, which resist relative motion between layers of fluid. Because it is a ratio of these competing effects, it helps predict whether a flow will stay smooth and layered or break into irregular eddies. The particular choice of length scale L depends on the geometry of the problem, such as pipe diameter, chord length, or characteristic obstacle size.
When to use it
Use this when you need to classify or compare flow regimes in pipes, around bodies, or in channels, especially before applying correlations for friction, drag, heat transfer, or mass transfer. It is also useful in scaling experiments, where matching Reynolds number helps preserve similar flow behavior between a model and a real system.
Worked example, step by step
Given: density ρ = 1000 kg/m^3, speed v = 0.40 m/s, characteristic length L = 0.050 m, viscosity μ = 1.0 × 10^-3 Pa·s Step 1: Write the formula: Re = (ρ v L) / μ Step 2: Substitute the values: Re = (1000 × 0.40 × 0.050) / (1.0 × 10^-3) Step 3: Multiply the numerator: 1000 × 0.40 × 0.050 = 20 Step 4: Divide by viscosity: Re = 20 / 0.001 = 20000 Final answer: Re = 2.0 × 10^4, indicating a flow that is likely not laminar under typical conditions.
Common mistakes to avoid
- Using the wrong characteristic length, such as radius instead of diameter for internal pipe flow
- Mixing up dynamic viscosity μ with kinematic viscosity ν and then plugging the wrong quantity into the formula
- Forgetting unit consistency, especially when density, viscosity, and length are given in mixed SI and non-SI units
Did You Know?
The Reynolds number predicts when smooth flow turns turbulent, a threshold that troubles engineers and swimmers alike.
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