Enrichment · STEM Explorations · Fluids

Smooth layers or
swirling eddies:
one number decides.

Choose the fluid and type the pipe size and flow speed. The calculator gives the Reynolds number, the kind of flow it means and the speeds where the flow changes.

Find the Reynolds numberWhat you get

The Reynolds number calculator

The worked example is a made-up 15 mm water pipe feeding a classroom sink at 1.2 m/s. Nothing you type leaves this browser.

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What you get

Enrichment · STEM ExplorationsFree

What you finish with
The Reynolds number, the flow regime, the laminar and turbulent velocity limits for the pipe, and a table across speeds. It prints as a summary and downloads as a spreadsheet.
Who it is for
Physics and engineering students, biology students studying blood and air flow, and science fair students.
Format
Browser calculator for a phone, tablet or computer, by touch or keyboard. Prints a summary; downloads a spreadsheet (.csv); export and import a file.
Access
Free. No account, no sign-in and nothing to install. Everything you type stays in this browser; nothing is sent to Caveat.
Where it lives
The STEM Explorations space in Caveat Enrichment.
Support
Questions, a correction or a request: team@caveatacademic.com.

How to use it

  1. Choose the fluid, or Other and type its kinematic viscosity.
  2. Type the pipe's inside diameter and the flow velocity.
  3. Read the Reynolds number and regime.
  4. Use the table to see where the flow changes.
  5. Print the summary for a lab report.

Find the Reynolds number

How the number is worked out

Inertia over viscosity.

The worked example: a classroom sink supplyVelocity × diameter1.2 × 0.015= 0.018 m²/s÷ viscosity1.004 × 10⁻⁶water at 20°C, m²/sRe17,928no unitsAbove 4,000Turbulentlaminar below 0.154 m/sThe worked example: a classroom sink supplyVelocity × diameter1.2 × 0.015= 0.018 m²/s÷ viscosity1.004 × 10⁻⁶water at 20°C, m²/sRe17,928no unitsAbove 4,000Turbulentlaminar below 0.154 m/s
The Reynolds number compares the push of the moving fluid with the drag of its viscosity. Big numbers mean the flow breaks into eddies.

The formula

The Reynolds number Re = v × D ÷ ν, with velocity v in m/s, inside diameter D in m and kinematic viscosity ν in m²/s. It has no units. In a round pipe, flow is usually laminar below about 2,300, turbulent above about 4,000 and can switch between in the transition range.

Viscosity and temperature

Warm water is thinner than cold water, so the same pipe and speed give a higher Reynolds number in a hot line. Air's kinematic viscosity is about fifteen times water's. Very smooth, still setups can stay laminar above 2,300, so the thresholds are guides, not walls.

Sources

  1. Reynolds, O. (1883). An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous. Philosophical Transactions of the Royal Society 174, 935 to 982.
  2. National Institute of Standards and Technology. NIST Chemistry WebBook: thermophysical properties of water and air (webbook.nist.gov).
  3. NASA Glenn Research Center. Reynolds number, Beginner's Guide to Aeronautics (grc.nasa.gov).
  4. OpenStax. College Physics 2e, section 12.5: the onset of turbulence (openstax.org).

The worked example is made up. Your figures stay in this browser. Support: team@caveatacademic.com.