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Reynolds number calculator

This Reynolds number calculator gives the dimensionless number that separates smooth from turbulent flow. Example: water at 1.5 m/s in a 5 cm pipe has Re ≈ 74,700.6 – turbulent.

Example: Viscosity given as: Dynamic viscosity μ (with density) · Fluid density ρ 998 kg/m³ · Flow velocity v 1.5 m/s · Characteristic length L 0.05 m · Dynamic viscosity μ 1.002 mPa·s → Result: Re = 74,700.6 – turbulent flow (Re > 4,000). Source: Munson/Young/Okiishi, Fundamentals of Fluid Mechanics, Ch. “Viscous Flow in Pipes” (Re = ρvD/μ; laminar up to approx. 2300, turbulent from approx. 4000). Updated: .

kg/m³
Water at 20 °C: about 998 kg/m³; air: about 1.2 kg/m³.
m/s
Mean velocity of the fluid.
m
Inner diameter for a pipe, run length for a flat plate.
mPa·s
Water at 20 °C: 1.002 mPa·s. 1 mPa·s = 0.001 Pa·s.
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Result

Result
Re = 74,700.6 – turbulent flow (Re > 4,000)
All representations
QuantityValue
Reynolds number Re74,700.6
Flow regime (pipe)turbulent flow (Re > 4,000)
Kinematic viscosity ν1.00401 × 10⁻⁶ m²/s
Calculation steps
  • ν = μ / ρ = 0.001002 Pa·s / 998 kg/m³ = 1.00401 × 10⁻⁶ m²/s; Re = ρ·v·L / μ = 998 · 1.5 · 0.05 / (0.001002) = 74,700.6.
The limits 2,300 and 4,000 apply to flow in a straight, smooth pipe (L = inner diameter). Plates, spheres and wings have very different critical values.

How it is calculated

The Reynolds number Re is the ratio of inertial to viscous forces in a flow. It decides whether a fluid moves smoothly in layers (laminar) or forms eddies (turbulent), and it is the most important dimensionless number in fluid mechanics.

Formula

Re = ρ · v · L / μ, with density ρ, velocity v, characteristic length L and dynamic viscosity μ. With the kinematic viscosity ν = μ / ρ this becomes Re = v · L / ν. In a straight pipe the rule of thumb is: below 2,300 laminar, 2,300 to 4,000 transitional, above that turbulent.

Worked example

Water (ρ = 998 kg/m³, μ = 1.002 mPa·s) flows at 1.5 m/s through a pipe with 0.05 m inner diameter: Re = 998 · 1.5 · 0.05 / 0.001002 = 74,700.6. With the kinematic viscosity ν = 1.004 mm²/s, Re = 1.5 · 0.05 / (1.004 · 10⁻⁶) = 74,701.2. The two routes agree within the rounding of the fluid properties; the flow is turbulent. Air (1.2 kg/m³, 0.018 mPa·s) at 0.1 m/s in a 0.02 m pipe gives Re = 133.333.

Frequently asked questions

At what Reynolds number does flow become turbulent?

In a pipe, Re below 2,300 counts as laminar and above 4,000 as turbulent; in between is the transitional range.

What is the characteristic length?

The dimension that shapes the flow: the inner diameter for a pipe, the run length for a flat plate, the diameter for a sphere.

What is the difference between dynamic and kinematic viscosity?

Kinematic viscosity ν is dynamic viscosity μ divided by density ρ. For water: ν = 1.00401 × 10⁻⁶ m²/s.

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