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Reynolds Number and Its Significance

Within fluids, the Reynolds Number describes the ratio between internal and viscous forces.

Reynolds number and its significance

Within fluids, the Reynolds Number describes the ratio between internal and viscous forces. This ratio is impacted by a number of factors, including fluid velocity and internal motion. There is no unit for Reynolds Number, making it a dimensionless quantity in mechanics. As a result of Osborne Reynolds, the Reynolds Number gained popularity and became known as the Reynolds Number.


For viscous fluids flowing at low speeds, turbulent flow is less common, according to Osborne Reynolds. He devised the Reynolds Number (Re), a dimensionless number whose value offers an approximate idea of whether the flow would be turbulent. The formula for this is as follows:


In this formula,

µ is the velocity of fluids

Reynolds number - Re

ρ - fluid density

D – diameter of pipe

V – velocity of flow.

It is alternatively written as Re = inertial force/viscosity force.

Consequently, Re is the ratio between inertial force and viscous force.

Critical velocity

Essentially, the critical velocity is the speed at which liquid will flow laminarly or in a streamline. The flow of a liquid becomes turbulent as its velocity approaches its critical velocity. The situation is summarized as follows:

v = Kμ/ρr

In order to streamline the flow of a liquid, v should be kept as small as possible and should be increased as much as possible.


  • If the calculated Reynolds number is high, the flow through the pipe is considered to be turbulent (more than 2000).
  • In a low Reynolds number flow (less than 2000), the flow is thought of as laminar. The values are acceptable, and laminar and turbulent flows are often entrained within the same range.
  • The Reynolds number of laminar flow is less than 1100, whereas the Reynolds number of turbulent flow is larger than 2200.
  • Fluids flow in straight lines in laminar flow.
  • While turbulent flow is not smooth and contains mixing, smooth flow is.

When these two types of forces are relative to one another, the Reynolds number predicts whether a turbulent flow will be generated.

Fluid dynamics issues can be scaled by the Reynolds number, and similarities in fluid flow can be determined between two situations, such as a model plane and its full-size equivalent.

Regarding turbulent and laminar flow regimes:
  • In laminar flow, which includes fluid motion that is smooth and constant at low Reynolds numbers, there are viscous forces.
  • Turbulent flow is dominated by inertial forces at high Reynolds numbers, leading to chaotic eddies, vortices, and other flow instabilities.
Using the Reynolds number as a guide, here are six things to remember3
  • The Reynolds Number indicates the ratio between internal forces and viscous forces within a fluid.
  • Several factors contribute to this ratio, including internal movement caused by varying fluid velocities.
  • Re=ρVD/μ
  • A critical velocity is the speed at which a liquid flowing in a laminar or streamlined fashion is attained.
  • The flow is considered turbulent when the Reynolds number exceeds 2000.
  • Reynolds number less than 2000 is defined as laminar flow.
  • Although these numerical values are acceptable when lumping together laminar and turbulent flows within a range.
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Ankur Choudhary is India's first professional pharmaceutical blogger, author and founder of, a widely-read pharmaceutical blog since 2008. Sign-up for the free email updates for your daily dose of pharmaceutical tips.
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