Reynolds Number

This calculator enables you to easily determine the Reynolds Number, a key indicator in fluid mechanics for analyzing the flow regime.

The Reynolds Number, denoted Re, is a dimensionless number that characterizes the type of fluid flow. It is defined by the following formula:

Re = (ρ × v × L) / μ

  • `ρ` (rho): Fluid density (kg/m³)
  • v: Fluid velocity (m/s)
  • L: Characteristic length (m), often the diameter of a pipe
  • `mu` (mu): Dynamic viscosity of the fluid (Pa·s)

Using the Reynolds Number Formula

The Reynolds Number formula Re = (ρ × v × L) / μ is essential for determining the type of flow in a fluid. Depending on the value of Re, the flow can be classified as laminar or turbulent:

  • Laminar Flow: Occurs when fluid particles move in parallel layers, without significant disturbance. This flow is characterized by Re values generally less than 2000.
  • Turbulent Flow: Characterized by chaotic flows and eddies. A flow is considered turbulent if Re exceeds about 4000.

Each variable in the Reynolds Number formula plays a crucial role:

  • `rho` (rho) - Fluid Density: It influences the mass of moving fluid and therefore the inertial forces.
  • v - Fluid Velocity: The higher the velocity, the greater the inertial forces, favoring turbulent flow.
  • L - Characteristic Length: Often represented by the diameter in pipes, this measure directly affects the fluid's velocity profile.
  • `mu` (mu) - Dynamic Viscosity: It is the measure of the fluid's internal resistance to flow. Higher viscosity favors laminar flow. Dynamic viscosity is strongly dependent on the fluid's temperature.

Real-World Examples

For example, consider the flow of water in a pipe:

  • Water density: 1000 kg/m³
  • Water velocity: 0.5 m/s
  • Pipe diameter: 0.05 m
  • Water viscosity at 20°C: 0.001 Pa·s

The Reynolds Number would therefore be calculated as follows:

Re = (1000 × 0.5 × 0.05) / 0.001 = 25000

This indicates turbulent flow.


The Reynolds Number is crucial in areas such as pipe design, automotive and aeronautical mechanics, and in the sizing of ventilation systems.


What is Laminar Regime?

A laminar regime is characterized by flow in parallel layers, without disturbance. In a pipe, this usually occurs when Re < 2000.

What is Turbulent Regime?

A turbulent regime is marked by disordered flows and eddies. This often occurs when Re > 4000.

What about Reynolds Numbers between 2000 and 4000?

This range of Reynolds Numbers often represents a 'transition flow' zone between laminar and turbulent regimes. In this transitional phase, the flow can exhibit characteristics of both laminar and turbulent types, making its analysis more complex.

See also

Fluid Mechanics
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