Reynolds number calculator
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Result
Calculate the Reynolds number of the flow in a pipe and find out whether it is laminar, transitional or turbulent. Enter the mean velocity or the flow rate, the pipe diameter and the fluid: water at 10, 20 or 60 °C, air at 20 °C, or your own fluid with either its kinematic viscosity or its density and dynamic viscosity. The steps show every conversion, and for laminar flow you also get the friction factor 64/Re.
Step-by-step solution
Fluid properties
Reynolds number
Flow regime in a pipe
Key formulas
- Reynolds number
- Re = V·D/ν = ρ·V·D/μ
- Flow regime
- laminar below Re ≈ 2000, turbulent above Re ≈ 4000
- Mean velocity
- V = Q/A, A = π·D²/4
How to calculate the Reynolds number
- Find the mean velocity. If you know the flow rate Q, divide it by the area of the pipe: V = Q/A = 4Q/(πD²).
- Look up the fluid properties at its temperature: the density ρ and the dynamic viscosity μ, or the kinematic viscosity ν = μ/ρ.
- Convert everything to SI units: V in m/s, D in m and ν in m²/s.
- Compute Re = ρVD/μ = VD/ν. The Reynolds number has no unit.
- Compare it with the limits for pipe flow: below about 2300 laminar, above about 4000 turbulent, and transitional in between.
Questions and answers
What does the Reynolds number mean physically?
It is the ratio of the inertial forces to the viscous forces in the flow. At a low Reynolds number viscosity damps out disturbances and the flow stays smooth and layered (laminar); at a high Reynolds number disturbances grow into turbulent eddies.
Why do some books use 2000 instead of 2300?
The transition is not sharp. It depends on the pipe inlet, the roughness and vibrations, so textbooks quote lower limits between about 2000 and 2300. In very smooth, careful experiments flow has stayed laminar far above that.
Which diameter do I use for a duct that is not round?
Use the hydraulic diameter D_h = 4A/P, where A is the flow area and P the wetted perimeter. For a square duct with side a, D_h = a.
How much does the temperature matter?
A lot for liquids. The viscosity of water falls from 1.31 mPa·s at 10 °C to 0.47 mPa·s at 60 °C, so the same flow has almost three times the Reynolds number in hot water.
What is the difference between dynamic and kinematic viscosity?
The dynamic viscosity μ, in Pa·s, measures the internal friction of a fluid; the kinematic viscosity ν = μ/ρ, in m²/s, divides it by the density. Since Re = ρVD/μ = VD/ν, you need either μ and ρ, or ν alone.
Practise it yourself
Practise Pipe friction & head loss
A calculator gives the answer. In the exam you need the method: practise it with new problems, hints and worked solutions.