Reynolds number

What is Reynolds Number?

  • In various fluid flow scenarios, the Reynolds number (Re) aids in the prediction of flow patterns. Laminar (sheet-like) flow typically predominates in flows with low Reynolds numbers, whereas turbulent flow typically predominates in flows with high Reynolds numbers.

History :

  • The theory was presented by George Stokes in the year 1851, but the it was named by Arnold Sommerfeld in the year 1908 after Osborne Reynolds (1842–1912), who researched, developed, and popularized its use in the year 1883.


  • It describes the relationship between inertial and viscous forces within a fluid that is experiencing relative internal motion as a result of varying fluid velocities. A boundary layer, such as the bounding surface inside a pipe, is an area where these forces affect how they behave.
  • It is the ratio of inertial forces to viscous forces.
  • It is a dimensionless number used to classify the fluids systems in which the result of viscosity is significant in controlling the velocities or the flow pattern of a fluid.
Reynolds number-Laminar Flow and Turbulent Flow
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Reynolds Number Equation:

Reynolds Number = (Inertial Force / Viscous Force)

Re = ρ * VD/ µ


  • Re = Reynolds number
  • ρ = Density of the fluid
  • V = Velocity of flow
  • D = Pipe diameter
  • μ = Viscosity of the fluid

Reynolds number units is unitless and dimensionless

Conclusion (what does reynolds number mean ?):

  • Re value is high (greater than 2000)- flow through the pipe will be turbulent.
  • Re value is low (less than 2000), flow will be laminar in pattern. 

Applications of Reynolds Number

  1. In a few fluid mechanics equations, including the Darcy-Weisbach equation, the it is crucial for calculating the friction factor.
  2. When simulating (swimming motion) the motion of aquatic species, it is used for modelling purpose.
  3. Air in the atmosphere is regarded as a fluid. So, it is possible to determine the Renumber for it. As a result, it can be used to test various surfaces’ aerodynamic characteristics in wind tunnels.
  4. In supersonic flights, when the high speed results in a localised increase in the density of the air surrounding the aircraft, it plays a crucial role in the testing of wind lift on aircraft.


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