What Is Reynolds Number And What Does It Imply?

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Reynolds number is a dimensionless quantity that states whether the flow of a fluid on a surface is laminar or turbulent in nature.

The world of science is full of numbers. There are different parameters used to define specific processes or entities, which has made the flow of information quite simple. The universally accepted norms and units have played a vital role in the advancements that mankind has made. Different teams of scientists working at different laboratories around the world can efficiently share their research because the scientific terms mean the same thing everywhere.

One such parameter that is widely used in the field of science is the Reynolds number. First introduced by George Stokes in 1851, the concept of the Reynolds number was named after innovator Osborne Reynolds, who popularized the idea in the late 19th century. Today it is one of the first things taught to someone pursuing an education in the field of science and engineering. So… what is this special Reynolds number?

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What Is Reynolds Number?

Whenever an object moves in any kind of environment, it changes the conditions of the surroundings and is therefore subject to a force generated as a result of this change. Consider for example a swimmer moving across a water stream; as he makes his way through the water, he displaces the water molecules from their position and the water molecules, in turn, try to re-acquire their initial position by exerting a force (or resistance) against the swimmer’s motion. When such objects flow across any such fluid, the resistance to their flow and thus their flow patterns are predicted by a dimensionless quantity called the Reynolds Number. The concept is applicable in the movement of every object across any environment except for a vacuum, which has no molecules of its own. The Reynolds number in a senser is used to predict the aerodynamics and flow patterns of a fluid.

Also Read: What Are The Navier-Stokes Equations?

Understanding Reynolds Number More Scientifically

Inertial Force

The scientific definition of Reynolds number states that it is a ratio between the inertia force on the moving object to the viscous or friction force. Let’s try to understand what these forces do.  When you’re running at a certain speed and try to stop, it requires a certain amount of strength, as the body wants to keep running. Similarly, your body in a state of rest needs a push or some type of force to start the run in the first place, as it wants to continue to be at rest. This tendency of a body to avoid change and continue to be in its existing state of rest or motion is called inertia. The property of inertia was introduced by Newton and is one of the most fundamental and universally applicable concepts of physics.

an object at rest tends to stay at rest unless acted upon by an outside force meme

Viscous Force

Viscosity or viscous forces is a relatively new concept, as compared to inertia. It was discovered in 1829 by French physicist Jean-Louis-Marie Poiseuille while studying blood circulation in the human body. It measures the resistance that a fluid provides against its deformation. When a fluid is in motion, there is friction between its different layers that tries to stop the free movement of the fluid. This frictional force is quantified in terms of viscosity, which is often attributed as ‘thickness’, in the case of liquids. When a fluid is set in motion, there is a continuous fight between the inertial force that wants to keep it in motion and the viscous force that is trying to stop it. Reynolds number is simply an indicator of who is winning the fight.

illustration of chemistry, The viscosity of a fluid is a measure of its resistance to gradual deformation by shear stress or tensile stress - Vector(Nasky)s
The viscosity of different fluids (Photo Credit : Nasky/ Shutterstock)

If the viscous forces dominate, we have a type of flow called laminar. If the inertial forces dominate, the flow becomes turbulent.  Reynolds number tells is which of these two types of motions will prevail.

Laminar Flow

Laminar or smooth flow depicts the ideal type of flow, where the fluid moves in infinitesimal parallel layers with no disruption between those two layers. The fluid travels smoothly in regular paths, and you can predict at any point in time the location of a particular particle. The layers of fluid in such a flow are thought to slide over one another, and the viscous forces do not come into play. Consider, for example, a viscous fluid flowing smoothly through a tube or pipe. As a result of its viscosity, the fluid has zero velocity at the edges where it is in contact with the surface, while its speed increases towards the center of the cross-section of the tube. This is a perfect example of a laminar flow.

Airflow over wings is an excellent example of laminar flow
Airflow over wings is an excellent example of laminar flow (Photo Credit : StaticFlickr)

Everyday examples of laminar flow include the flow of air over an aircraft wing. The relationship between Reynolds number and laminar flow depends on the type of system present at the surface on which the fluid is flowing. For flows in a pipe, laminar flow generally occurs below Reynolds number 1800. For flows on a plate, this number rises to 0.5 million.

Turbulent Flow

Turbulent flow is quite the opposite of laminar. It involves irregular fluctuations and mixing within a fluid, which renders its path unpredictable. Such a discharge is characterized by unprecedented and chaotic changes in fluid velocity and pressure. The particles of fluid possess excess kinetic energy, which helps in overcoming the viscosity of the surface. Consider a dam as an example: when its gates are suddenly opened, the water gushes out in random order, occupying whatever space it can. This is an example of turbulent flow. The flow of rivers and wind is generally turbulent in this sense, even if the currents appear gentle.

Dam water release,The excess capacity of the dam until spring-way overflows. - Image(NaMo Stock)s
Dam Water Release- Turbulent Flow (Photo Credit : NaMo Stock/ Shutterstock)

The Reynolds number for turbulent flow again depends on the type of system in the case at hand. For flow in pipes, turbulent flow generally occurs for a Reynolds number greater than 2100. The 1800-2100 range, in this case, is called the transition region, and is a pretty complex phenomenon. For flow over plates, 0.5 million is the critical Reynolds number, and all flows occurring above that figure are turbulent in nature.

Also Read: Is It Actually Possible To Run On A Pool Of Liquid?

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References (click to expand)
  1. Reynolds Number Interactive Simulator. - www.grc.nasa.gov
  2. RS Subramanian. Reynolds Number - Clarkson University. Clarkson University
  3. FAQ-Lecture 6.pdf - Nptel. archive.nptel.ac.in
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Rajat is an undergraduate student of BTech at BITS Pilani (India). He likes all kinds of sports and has represented his college for Athletics several times. He also loves to sing and play the guitar. He enjoys watching movies and likes to read about financial management and the stock market.