Reynolds Number Calculator
Calculate the Reynolds number to determine if a fluid flow is laminar or turbulent.
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Table of Contents
Reynolds Number Formula
The Reynolds number is a dimensionless quantity used to predict flow patterns in different fluid flow situations.
Where:
- Re = Reynolds number (dimensionless)
- ρ = Fluid density (kg/m³)
- v = Flow velocity (m/s)
- L = Characteristic length (m)
- μ = Dynamic viscosity (Pa·s)
How to Calculate
To calculate the Reynolds number, follow these steps:
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1Determine the fluid density (ρ)
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2Measure the flow velocity (v)
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3Determine the characteristic length (L)
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4Find the dynamic viscosity (μ)
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5Multiply density, velocity, and length, then divide by viscosity
Flow Regimes
The Reynolds number helps determine the type of flow:
- Re < 2300: Laminar flow (smooth, orderly flow)
- 2300 ≤ Re < 4000: Transitional flow
- Re ≥ 4000: Turbulent flow (chaotic, irregular flow)
- These values are approximate and may vary depending on the specific application
- The transition between flow regimes is not abrupt but gradual
- Other factors like surface roughness can affect the transition
Practical Examples
Example 1 Water in a Pipe
Calculate the Reynolds number for water flowing through a 2 cm diameter pipe at 1 m/s.
ρ = 1000 kg/m³
v = 1 m/s
L = 0.02 m
μ = 0.001 Pa·s
Re = (1000 × 1 × 0.02) / 0.001 = 20,000
Example 2 Air Flow
Calculate the Reynolds number for air flowing over a 1 m wide plate at 5 m/s.
ρ = 1.225 kg/m³
v = 5 m/s
L = 1 m
μ = 1.81 × 10⁻⁵ Pa·s
Re = (1.225 × 5 × 1) / (1.81 × 10⁻⁵) = 338,398