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Reynolds Number Calculator

This calculator determines Reynolds number, which is the ratio of the inertia forces to the friction forces in flow. Reynolds number is used to determine the transition from laminar flow to turbulent flow in pipes.
To help solve Reynold's Number, two extra calculators are provided for conversion purposes.

Calculation

Reynolds Number Calculator

Inputs


ρ
:1,000kg/m3​



u
:1.00m/s​



L
:1.00m​



μ
:1.00Pa s​

Output


Re
:1000​


Laminar:


Transitional:


Turbulent:


The equation for Reynolds number is given by:

Re=ρ × u × Lμ\large {Re =\dfrac {\rho \ \times\ u \ \times\ L}{\mu}}
Where:
  1. 
    
    is the density of the fluid
    
    
  2. 
    
    is the mean velocity of flow
    
    
  3. 
    
    is the characteristic linear length, such as the diameter of a pipe or the chord length of an airfoil
    
    
  4. 
    
    is the dynamic viscosity, which is a fluid property that describes the fluid's resistance to flow
    
    . A higher
    
    means the fluid will flow more slowly for a given applied force.
  5. 
    
    is Reynolds number (dimensionless)


Characteristic Length of a Non-circular Tube

If your tube is non-circular, use this calculator below to convert your tube into a characteristic length which is an input in Reynolds number calculator.
Inputs


Cross-sectional area
:1.50m2​



Wetted perimeter
:3.00m​

Output


Hydraulic diameter, Dh
:2.00m​

The equation for the hydraulic diameter is given by:

Dh=4×cross-sectional areawetted perimeterD_h= \dfrac{4\times \text{cross-sectional area}}{\text{wetted perimeter}}
Where:
  1. Cross-sectional area, is the area of a non-circular tube
  2. Wetted perimeter is the perimeter of a non-circular tube for closed channels, while on open channels it is the perimeter of the surface that comes in contact with the fluid.
  3. 
    
    is the hydraulic diameter, which can be used as your characteristic length in the Reynolds number equation


Kinematic Velocity to Dynamic Viscosity Convertor

Use the convertor below to determine the dynamic viscosity, which is an input in Reynolds number calculator.


Kinematic viscosity, v
:1.0e-6m2/s​



Density, ρ (1)
:1,000kg/m3​



Dynamic viscosity, μ (1)
:0.00Pa s​


μ=ρν​\mu= \dfrac{ρ}{\nu}​

Explanation

What is Reynolds Number?

Reynold's number, denoted by

, is a dimensionless number that describes the flow of a fluid. In aerospace engineering, aircraft design can be based on Reynolds number.

💡Who was Osborne Reynolds?

Laminar vs Turbulent Flow

Reynold's number can be defined as the ratio of internal forces to the viscous forces within a fluid experiencing relative internal movement due to different fluid velocities.

Re=inertial forcesviscous force=fluid and flow propertiesfluid propertiesRe=\dfrac{inertial \: forces}{viscous \: force} = \dfrac{fluid \: and \: flow \: properties}{fluid \: properties}
For most practical purposes concerning pipes, if the Reynolds number is:
  1. 
    
    the flow is considered laminar. However, for flat plates the flow is considered laminar if the Reynolds number is below 2000.
  2. 
    
    the flow is considered transitional
  3. 
    
    the flow is considered turbulent

Find out more about laminar vs turbulent flow in the toggle below.

💡Laminar vs Turbulent Flow

Assumptions of Reynolds Number Equation

The Reynolds number of fluid is calculated using the following equation;

Re=ρ × v × Lu\large {Re =\dfrac {\rho \ \times\ v \ \times\ L}{u}}
While the equation is convenient, several assumptions and limitations are observed, such as:
  1. the fluid is a Newtonian fluid
  2. compressibility is disregarded
  3. surface roughness is disregarded
Also, an adjustment is required to the characteristic length

if the fluid flows in a non-circular tube or open channel, wherein the new parameter is used and is called the wetted perimeter.

Related Resources

  1. Reynolds Number Calculator (for motion of a viscous fluid)
  2. Bernoulli Mass Flow Rate Calculator
  3. Froude Number Calculator: Open Channel Flow
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