What is Reynolds Number?

What is Reynolds Number: In simple words, It is the ratio of inertial force to the viscous force.

Units of Reynolds Number: Reynolds number is a dimensionless number hence it has no units

You may find this definition everywhere but do you know what is inertial force actually means? do you know what is viscus force? do you know Reynolds number is different for mixing in a tank than Reynolds number in a pipe flow?

There are a lot of many questions hitting your mind related to Reynolds numbers, and I can present here even more so hold tight I am taking you to through all one by one.

Reynolds number

First lets check the terms used in the definition of Reynolds number.

Terms used in defining Reynolds number

1. System: A system is nothing but a defined boundary under which we do our engineering study. In other words, a small part of any target on which we are going to apply our Mass, Energy, and Momentum transfer fundamentals. For example, a small piece of pipe through which fluid is flowing and fluid behavior is under study
2. Inertial force: The force we apply on the system or a force applied by surrounding any equipment on the system to cause some movement.
3. Viscus force: A resisting force by a fluid against the inertial force. Viscus force comes in a fluid due to the entanglement of the particles which resist the motion on the application of any external force.
   1. Viscosity: Viscosity is a property of a fluid to quantify viscus force(resisting force) that fluid can possess under the action of applied force.

Define Reynolds number

Reynolds number is defined as the ratio of inertial force to viscous force. Reynolds number helps us to define the regime in which fluid is flowing-

• Laminar
• Transition
• Turbulent

How to calculate Reynolds number (Derivation of Reynolds number)

Significance of Reynolds number

Reynolds number is very important in many aspects of engineering. It usually becomes significant when our study system involves flowing fluid. Reynolds number plays crucial role in bringing laboratory models to real life.

Predicting fluid behaviour and pattern

By applying Reynolds engineers can predict flow and pattern of a flowing fluid. A calculative value of Reynolds number can give an idea about flow regime such as laminar, transition or turbulent.

Designing and optimizing flow systems

A new flow system can be designed and optimized with the help of Reynolds number by calculating loss of energy in the form of pressure drop, friction factor etc.

Devising mixer and reactors

Reynolds number is also significant in mixing. For a mixing tank and reactor Reynolds number is inevitable for efficient mixing and high yield of a reaction.

Scale up or scale down

For a successful scale up or down of a model or prototype, dynamic similarity is required. Reynolds number is critical for dynamic similarity of a model.

Studying Boundary layer

Boundary layer study of a flowing fluid is import in fluid mechanics and Reynolds number helps in that.

Understanding Heat and Mass transport

There many experimental correlations that relies significantly on Reynold to calculate heat transfer coefficient and mass transfer coefficient.

Now the question comes why there is a need to define a flow regime?

Flow regimes in fluid mechanics

In fluid mechanics, we deal with fluid at rest in one section and fluid in motion in another part. Whenever fluid is in motion at a certain geometry/system if fluid is moving with fixed velocity and unchanged density and viscosity value, it shows a particular kind of behavior that behavior defines how energy and mass are going to transfer from one specified point to another.

Do you have a question in your mind about how Reynolds number is affecting heat and mass transfer? If Yes, Do comment below and let me know i’ll come up with more in-depth over this topic.

As far as Fluid mechanics is concerned, Study of Fluid flow is divided into 3 main regimes Laminar, Transition and Turbulent based upon behaviour of fluid particles.

Fluids’ properties such as flow velocity, density, viscosity at a defined characteristic length decides the regime in which its flow will fall. That regime predicts the fate of Heat and Mass transfer.

Laminar flow regime:

For simplicity, let’s say laminar flow has laminate layers that stick over each other. In Laminar flow, fluid particles move in the form of a layer on another layer but don’t cross each other and there is no intermixing between the two adjacent layers.

Main Features of laminar flow:

• Particles follow a stream line path in orderly manner
• Parallel movement of adjacent layers
• Stable flow, No or Negligible intermingling
• First regime to be developed when fluid just starts flowing (relatively at low speeds)
• Less efficient heat and mass transport as compared to other regimes

Examples of laminar flow:

• Relatively high viscus fluids: Flow of honey or mustard oil from a tilted box
• Water flowing through a small tube at relatively low speed

Transition flow Regime:

It is a regime where fluid possess both Laminar and turbulent flow features. Fluid layers near the wall imparts laminar flow and turbulent at a certain distance away from the wall. In short, Transition regime is a mix of laminar and turbulent flow regime.

Main features of Transition flow:

• Fluid follows ill-defined path, chaotic movement
• Unstable flow away from the edges
• In Laminar regime-no mingling, turbulent regime-complete intermingling, but In Transition Regime-Incomplete intermingling
• combination of streamline and random flow directions
• Fluid flow changes between laminar and turbulent flow

Examples of Transition flow:

• Water flowing in a pipe alternating from smooth to zig-zag motion
• Sudden disturbance in orderly flowing fluid

Turbulent flow Regime:

Turbulent flow is a regime where fluid particles doesn’t follow ordered path. Layers of fluid mix with each other randomly and that leads to complete intermingling of layers.

Main features of turbulent flow:

• Random order of particles in the flowing fluid results formation of eddies, swirls, vortices etc.
• Better intermingling between adjacent layers than other regimes
• Assumed to have complete mixing situation
• Turbulent regime considered to have efficient Heat and mass transport as compared to other regimes
• Turbulent regime generally occurs at relatively high speed and larger systems

Examples of turbulent flow:

• Relatively high-speed flowing water
• Mixing tanks

Over a period of time researchers have studied all these mechanics for different kinds of systems and shared Reynold number values for laminar, transition, and turbulent regime. I’ll tell you about very common so that you can relate it easily to your daily life.

• Water flowing through a pipe- internal flow
• Water flowing in a river- open flow

Flow regimes in pipes

When a fluid is flowing through a pipe-

Sr. No.	Flow Regime	Reynolds Number (Re)
1	Laminar	Re less than equal to 2300
2	Transition	2300<Re up to 4000
3	Turbulent	Re>4000

Types of Reynolds Number

The basic definition of the Reynolds number remains the same that is inertial force to viscous force but where you are applying it varies and leads to 3 main types of Reynolds numbers, these are-

1. Reynolds number for flowing fluid
2. Reynolds number for particle
3. Reynolds number in mixing

Reynolds number-FAQs