Home / Topics / Fluids & Elasticity
Reynolds number
Advanced
Predicts the onset of turbulence.
Re = ρvd/ηRe = ρvd/η compares inertial and viscous forces. Below ~2000 in a pipe the flow is laminar, above ~4000 turbulent.
Water at 1 m/s in a 2 cm pipe: Re ≈ 20,000.
Depends on the geometry, so critical values vary.
In more detail
The Reynolds number, Re = ρvL/η, compares inertial and viscous forces in a flow. Low values indicate smooth laminar flow, and high values indicate turbulent flow.
Real-world uses
- Engineers design pipes and aircraft by checking the Reynolds number.
- Scaling wind tunnel tests to full-size vehicles uses matching Reynolds numbers.
- Engineers designing pipes and aircraft use the Reynolds number to predict whether the flow will be smooth or turbulent.
Open the interactive lesson, with simulation and quiz →
Frequently asked questions
What is a typical transition value in pipes?
About 2000 for the onset of turbulence in smooth pipes.
Is it dimensionless?
Yes, all its units cancel, so it is the same for scaled flows.
What is a typical value at which flow becomes turbulent?
In pipes it is around 2000 to 4000, though the exact value depends on the geometry and disturbances.
Related topics in Fluids & Elasticity
Poiseuille's equation · Stokes' law · Terminal velocity in fluids · Surface tension · Surface energy · Excess pressure in drops and bubbles