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Reynolds Number Calculator

Predicting flow regime (Laminar/Turbulent).

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Reynolds Number

Formula first

Overview

The Reynolds number is a dimensionless quantity used to predict fluid flow patterns by calculating the ratio of inertial forces to viscous forces. It serves as the primary criterion for identifying whether a flow is laminar, where fluid moves in smooth layers, or turbulent, characterized by chaotic fluctuations in pressure and velocity.

Symbols

Variables

Re = Reynolds Number, = Density, v = Velocity, L = Char. Length, = Dyn. Viscosity

Re
Reynolds Number
Variable
Density
Velocity
m/s
Char. Length
Dyn. Viscosity
Pa s

Apply it well

When To Use

When to use: Use this equation when characterizing flow regimes in pipes, over airfoils, or around submerged objects to determine if viscosity or inertia dominates. It assumes a Newtonian fluid and requires a defined characteristic length scale specific to the geometry, such as pipe diameter or wing chord length.

Why it matters: It is essential for scaling experiments from small models to full-sized engineering designs and for calculating drag and heat transfer coefficients. Understanding the transition to turbulence helps engineers optimize energy efficiency in pumping systems and improve aerodynamic performance.

Avoid these traps

Common Mistakes

  • Using kinematic viscosity instead of μ.
  • Forgetting to use meters for length.

One free problem

Practice Problem

A fluid with a density of 1000 kg/m³ flows through a pipe with a diameter of 0.1 m at a velocity of 2.0 m/s. If the dynamic viscosity is 0.001 Pa·s, calculate the Reynolds number.

Density1000 kg/m^3
Velocity2 m/s
Char. Length0.1 m
Dyn. Viscosity0.001 Pa s

Solve for: Re

Hint: Plug the values directly into the formula: Re = (rho × v × L) / mu.

The full worked solution stays in the interactive walkthrough.

References

Sources

  1. Bird, R. Byron; Stewart, Warren E.; Lightfoot, Edwin N. (2007). Transport Phenomena (2nd ed.). John Wiley & Sons.
  2. Incropera, Frank P.; DeWitt, David P.; Bergman, Theodore L.; Lavine, Adrienne S. (2007). Fundamentals of Heat and Mass Transfer (6th ed.).
  3. Wikipedia: Reynolds number
  4. IUPAC Gold Book: Reynolds number
  5. Britannica: Reynolds number
  6. IUPAC Gold Book: Dynamic viscosity
  7. Incropera, F. P., DeWitt, D. P., Bergman, T. L., & Lavine, A. S. (2007). Fundamentals of Heat and Mass Transfer (6th ed.).
  8. Bird, R. B., Stewart, W. E., & Lightfoot, E. N. (2007). Transport Phenomena (2nd ed.). John Wiley & Sons.