## Reynolds Number – Class 11 | Chapter – 10 | Physics Short Notes Series PDF for NEET & JEE

Reynolds Number: It is a dimensionless quantity that is used in fluid mechanics to describe the flow of a fluid. It is named after the British scientist Osborne Reynolds, who first described the concept in the late 19th century.

It is used to determine the type of flow that occurs in a fluid. When the Reynolds number is low (typically less than 2000), the flow is laminar, which means that the fluid flows in smooth, parallel layers. When the Reynolds number is high (typically greater than 4000), the flow is turbulent, which means that the fluid flows in a chaotic, irregular manner with vortices and eddies.

The transition between laminar and turbulent flow occurs in the range of Reynolds numbers between 2000 and 4000, depending on the specific system. The Reynolds number is an important parameter in many areas of fluid mechanics, including pipe flow, boundary layers, and heat transfer.

## Formula of Reynolds Number

The Reynolds number (Re) is calculated using the following formula:

Re = (ρvL) / μ

Where:

• ρ is the density of the fluid in kg/m³
• v is the velocity of the fluid in m/s
• L is a characteristic length scale of the system, such as the diameter of a pipe or the length of an object in the fluid, in meters
• μ is the dynamic viscosity of the fluid in Pa·s (Pascal seconds)

It is important to note that the Reynolds number is a dimensionless quantity, meaning that it has no units. This is because the units in the numerator and denominator of the equation cancel each other out. The Reynolds number is used to determine the type of flow that occurs in a fluid, with low values indicating laminar flow and high values indicating turbulent flow.

## Significance of Reynolds number

The Reynolds number is a dimensionless parameter that is used in fluid mechanics to predict the type of flow that will occur in a fluid system. The significance of the Reynolds number lies in the fact that it can be used to predict whether the flow will be laminar or turbulent, which has important implications for many practical applications.

For example, in a pipe or duct, laminar flow occurs when the Reynolds number is low, and the fluid flows smoothly in layers, with very little mixing between the layers. In contrast, turbulent flow occurs when the Reynolds number is high, and the fluid flows in a chaotic manner, with vortices and eddies that cause mixing between the layers. Turbulent flow is more efficient for mixing, but it also results in higher pressure drops and increased energy loss compared to laminar flow.

In engineering, the Reynolds number is used to design fluid systems and predict their performance under different conditions. For example, the Reynolds number can be used to determine the minimum flow rate required to avoid laminar flow in a pipe, or to predict the drag force on an object moving through a fluid.

In summary, the significance of the Reynolds number lies in its ability to predict the type of flow that will occur in a fluid system, and to inform the design and optimization of fluid systems in various practical applications.

## Critical Velocity

Critical velocity is the minimum velocity required for a fluid to transition from laminar flow to turbulent flow in a particular system. It is a function of the fluid properties (such as density and viscosity) and the geometry of the system (such as the diameter of a pipe or the shape of an object in the fluid).

In a pipe, for example, the critical velocity represents the point at which the laminar flow regime transitions to turbulent flow. The Reynolds number is often used to determine the critical velocity for a given system, with the critical Reynolds number typically falling in the range of 2000 to 4000, depending on the specific system.

When the fluid velocity is below the critical velocity, the flow is laminar, and the fluid flows in smooth, parallel layers. When the fluid velocity is above the critical velocity, the flow becomes turbulent, with chaotic, irregular motion and mixing between the layers.

The critical velocity is an important parameter in many areas of fluid mechanics and is used in the design and analysis of fluid systems, such as pipelines, chemical reactors, and heat exchangers. It is important to note that the critical velocity can be affected by changes in the fluid properties or system geometry, and may need to be reevaluated under different conditions.

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