The Reynolds Number is a critical quantity to understand when studying fluid flow patterns. It is a parameter with no dimensions that are widely used in fluid mechanics. A flowing fluid’s Reynolds Number is defined as the ratio of inertia force to viscous force, and it quantifies the relative importance of these two types of forces for given flow conditions.
Reynolds Numbers are used to depicting laminar, transitional (intermittently turbulent), and fully turbulent pipe flows, as well as to determine the conditions that cause these types of flow.
| Formula | Reynolds number = (density * tube diameter * flow speed) / viscosity (average flow velocity multiplied by tube diameter multiplied by fluid mass density divided by absolute viscosity) |
| Laminar flow | less than about 2,000 |
| Turbulent flow | greater than 2,000 |
Table of Contents
Reynold Number Formula
For flow in a circular tube of diameter D at an average velocity V , the Reynolds number Re is defined as follows.
Re = (D x V x ρ)/μ = (D x V )/v
Re = ρ V2 ÷ μ (V/D) (multiplying both sides by the average velocity “V”)
Re = DVρ/μ (in terms of pipe diameter)
Where:
- Re is Reynold’s number
- µ is the dynamic viscosity of the fluid (Ns/m2, lbm/s ft)
- ρ is the density of the fluid ((kg/m3, lbm/ft3))
- The ratio ν/ρ is termed the kinematic viscosity
The denominator in this form represents a characteristic shear stress in the flow because it is the product of the fluid’s viscosity and a characteristic velocity gradient obtained by dividing the average velocity by the diameter of the tube. In contrast, the numerator describes inertial stress; remember that the higher the density, the more massive a material is, and mass is a measure of inertia. Therefore, we can consider the Reynolds number to be the ratio of two characteristic stresses in the flow.
Re = Inertial stress/Viscous stress
Since stress is defined as force per unit area. Therefore, the physical significance of the Reynolds number can also be expressed as follows.
Re= Inertial force/ Viscous force
The above formula shows that at low Reynolds numbers, the viscous force is relatively stronger, and disturbances in the flow are dampened by viscosity. As a result, it is difficult for disturbances to grow and persist. However, at relatively high Reynolds numbers, the damping of disturbances by viscosity is less effective, and inertia is more important, allowing disturbances to persist. This is the primary reason why the Reynolds number is used to determine whether the flow is laminar or turbulent.
Significance Reynold numbers in daily life
- The Reynolds number indicates whether the flow is laminar or turbulent.
- Reynolds number is used to predict flow and develop numerical or experimental strategies for observing flow behaviour.
- At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers flows tend to be turbulent.
- The flow through the pipe is said to be turbulent if the calculated Reynolds number is greater than 2000. The flow is said to be laminar if the Reynolds number is less than 2000.
- Reynolds number is an important factor in purified water distribution systems because it helps to maintain the necessary flow to prevent biofilm formation. Purified water is widely used in the pharmaceutical industry, laboratories, laser cutting, and automotive applications.
- In a wind tunnel, the Reynolds number allows for the analysis of a scale model when laminarity or turbulence is assumed. The Reynolds number in the wind tunnel and the actual atmospheric condition should be the same to ensure scaling accuracy.
Daily Life Examples of Reynold Numbers
Reynold Numbers are widely used in engineering to predict the behavior of fluid flow in various applications, including:
- Blood Flow in the Human Body: The Reynolds number helps to predict the flow behaviour of blood in blood vessels, which is critical for understanding blood flow dynamics and cardiovascular health.
- Airflow over an Airplane Wing: The Reynolds number is used to determine the boundary layer behaviour of air over an aeroplane wing, which is critical for optimizing aerodynamic performance and reducing drag.
- Flow in Pipes: The Reynolds number is used to predict the flow patterns and pressure drops in pipes, which is important for the design of pipelines and flow control systems.
- Flow in Automotive Engines: The Reynolds number is used to predict the flow behaviour of fluids, such as coolant and lubricating oil, in automotive engines, which is critical for optimizing engine performance and reducing wear and tear.
- Flow in HVAC Systems: The Reynolds number is used to predict the flow behaviour of air and refrigerants in heating, ventilation, and air conditioning (HVAC) systems, which is critical for optimizing energy efficiency and reducing costs.
These are just a few examples of how the Reynolds number is used in our daily lives to improve the design and performance of various systems and technologies.
Summary
Reynolds number is a dimensionless quantity that provides a measure of the relative importance of inertial and viscous forces in fluid flow
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