Flow Measurement · Glossary

What is Reynolds Number?

Symbol: RedimensionlessFlow Measurement

Reynolds number is the ratio of inertial to viscous forces in a flowing fluid. It shows whether pipe flow is laminar or turbulent.

Reynolds Number Explained

Reynolds number combines velocity, pipe size, density and viscosity into one number. Low values mean viscous forces dominate and the flow is smooth and layered. High values mean inertia dominates and the flow is turbulent.

Flow meters are specified over a Reynolds number range. Orifice discharge coefficients, vortex shedding and the velocity profile all depend on it, so check Re at minimum flow and highest viscosity.

Reynolds Number Formula

Re = ρ v D ÷ μ = v D ÷ ν

ρ	density (kg/m³)
v	average velocity (m/s)
D	pipe internal diameter (m)
μ	dynamic viscosity (Pa·s)
ν	kinematic viscosity (m²/s)

Example: Water at 20 °C (ν = 1.004 × 10⁻⁶ m²/s) at 2 m/s in a 100 mm pipe: Re = 2 × 0.1 ÷ 1.004 × 10⁻⁶ ≈ 199,000, which is turbulent.

Reynolds Number: Typical Values

Laminar	Re below about 2000 to 2300
Transition	about 2300 to 4000
Turbulent	Re above about 4000

Calculators for Reynolds Number

CalculatorReynolds Number CalculatorFree online calculator with formula and worked example.CalculatorFriction Factor CalculatorFree online calculator with formula and worked example.CalculatorVortex Flow Meter CalculatorFree online calculator with formula and worked example.

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Frequently Asked Questions

What is Reynolds Number?

Reynolds number is the ratio of inertial to viscous forces in a flowing fluid. It shows whether pipe flow is laminar or turbulent.

Why does Reynolds number matter for flow meters?

Meter coefficients change with Re. Vortex meters stop working at low Re, and DP meter discharge coefficients shift, so the meter must be used within its Re range.

Is Reynolds number different for gases?

The formula is the same. Gases have low viscosity, so gas flows are usually strongly turbulent.

Learn more on the blog

Types of flow meters

A practical guide on instrumentationblog.in with more detail on reynolds number and how it is applied on real plants.

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