# Difference Between Kinematic And Dynamic Viscosity

JEE Mains & Advanced## Introduction

Fluids play a crucial role in a wide range of industries and natural phenomena, and understanding their behavior is essential for predicting and controlling their movements. To describe a fluid's resistance to flow, we use two properties: ki nematic viscosity and dynamic viscosity. In this article, we will explore the definitions, calculations, and applications of these two fluid properties to provide a better understanding of how they differ and how they play a role in the world around us.

### Explanation of fluids and behavior

Fluids exhibit unique behaviors and properties that make them essential components in many natural and industrial processes. They can flow and adapt to their container, exert pressure on their surroundings, and change shape and volume in response to changes in temperature, pressure, and other physical variables. Understanding the properties and behavior of fluids allows us to predict, control, and manipulate their movements, making them crucial components in a wide range of applications.

### Difference between Kinematic viscosity and Dynamic viscosity

Kinematic Viscosity (ν) |
Dynamic Viscosity (η) |

Ratio of dynamic viscosity to fluid density | Ratio of shear stress to rate of strain in fluid |

Measures fluid's resistance to flow under external force | Measures fluid's internal resistance to flow and shear stress |

Square meters per second (m^2/s) | Pascal-seconds (Pa.s) |

Independent of fluid density |
Proportional to fluid density |

### Significance of the differences

The differences between kinematic viscosity and dynamic viscosity are significant because they affect the fluid's behavior in different ways. Kinematic viscosity is useful for predicting a fluid's resistance to flow under external forces and its ability to mix with other fluids, while dynamic viscosity is essential for predicting a fluid's internal resistance to flow and shear stress, which is important in applications such as fluid dynamics and heat transfer.

In industries such as lubrication, the viscosity of the lubricating fluid is critical for preventing friction and wear between moving parts. In these applications, dynamic viscosity is more useful for determining the fluid's ability to resist shear stress and flow through small spaces, while kinematic viscosity may be used to determine the fluid's ability to mix with other liquids.

Overall, understanding the differences between kinematic and dynamic viscosity is important for predicting and controlling fluid behavior in various applications, which can impact efficiency, productivity, and safety.

## Kinematic Viscosity

Kinematic viscosity (ν) is defined as the ratio of a fluid's dynamic viscosity to its density. It measures a fluid's resistance to flow under external forces, such as gravity or pressure. In other words, kinematic viscosity describes the fluid's ability to move in response to a force applied to it. The higher the kinematic viscosity, the slower the fluid will flow and the greater the resistance it will exhibit to flow.

Kinematic viscosity is an important property of fluids because it affects the fluid's ability to mix with other liquids, the fluid's stability under external forces, and its ability to transport heat and mass. For example, in applications where fluid mixing is desired, such as in paint or food production, low kinematic viscosities are desirable, as they allow for better mixing of the fluid components. In contrast, in applications where fluid stability is important, such as in oil transportation, high kinematic viscosities are preferred, as they reduce the risk of fluid separation.

### Formula for kinematic viscosity

The formula for kinematic viscosity is:

ν = η / ρ

Where:

ν = kinematic viscosity (m^2/s)

η = dynamic viscosity (Pa.s)

ρ = fluid density (kg/m^3)

This formula shows that kinematic viscosity is calculated by dividing the fluid's dynamic viscosity by its density. This provides a measure of the fluid's resistance to flow that is independent of its density, making it useful for comparing fluids of different densities.

### Unit for measurement of kinematic viscosity

The unit of measurement for kinematic viscosity is square meters per second (m^2/s). This unit is a derived unit that describes the rate of fluid flow through a unit area under a unit force. The higher the kinematic viscosity, the slower the fluid will flow and the greater the resistance it will exhibit to flow.

## Dynamic Viscosity

Dynamic viscosity (η) is a measure of a fluid's internal resistance to flow and shear stress. It describes the fluid's resistance to deformation under stress, such as when the fluid is flowing through a pipe or over a surface. The higher the dynamic viscosity, the greater the fluid's resistance to flow and shear stress.

Dynamic viscosity is an important property of fluids because it affects the fluid's behavior in applications. Such as fluid dynamics and heat transfer. For example, in fluid dynamics, the dynamic viscosity of a fluid is important. For predicting the fluid's pressure drop and flow rate through a pipe or over a surface. In heat transfer, the dynamic viscosity of a fluid affects the fluid's ability to transport heat. With higher viscosities leading to lower heat transfer rates.

### Formula for Dynamic Viscosity

** Determining Dynamic Viscosity Depends on Various Factors**: You Cannot Use a Specific Formula to Calculate Dynamic Viscosity . It Depends on Temperature, Pressure, Fluid Composition, and More.

** Measuring Shear Stress and Shear Rate:** To Determine Dynamic Viscosity, You Can Measure the Fluid's Shear Stress and Shear Rate Experimentally. The Shear Stress Represents the Force per Unit Area Applied to the Fluid, While the Shear Rate Describes the Velocity Gradient in the Fluid and Shows How Fast the Fluid is Flowing.

* Calculating Dynamic Viscosity:* You Can Calculate Dynamic Viscosity as the Ratio of the Shear Stress to the Shear Rate.

η = τ / γ

Where:

η = dynamic viscosity (Pa.s)

τ = shear stress (Pa)

γ = shear rate (s^-1)

This formula shows that the dynamic viscosity of a fluid is proportional to the shear stress and inversely proportional to the shear rate. This relationship is known as Newton's law of viscosity, which states that the shear stress in a fluid is proportional to the rate of shear strain.

### Unit of measurement for dynamic viscosity

The unit of measurement for dynamic viscosity is Pascal-seconds (Pa.s). This unit is used to describe the shear stress in a fluid, and how it changes with the rate of shear strain. The Pascal-second is a derived unit and is used to describe the resistance of a fluid to flow. A higher value of dynamic viscosity indicates that a fluid will have a greater resistance to flow and shear stress.

### Similarities between Kinematic and Dynamic Viscosity

You Use Kinematic Viscosity and Dynamic Viscosity to Describe a Fluid's Resistance to Flow and Shear Stress. Both Provide Valuable Information About a Fluid's Behavior and are Related to Each Other.

*Describing the Resistance of a Fluid to Flow*: Both kinematic viscosity and dynamic viscosity are used to describe the resistance of a fluid to flow. Kinematic viscosity provides a measure of the fluid's resistance to flow that does not depend on its density. While dynamic viscosity provides a measure of the fluid's resistance to flow and shear stress.

*Predicting and Controlling a Fluid's Behavior*: In applications such as fluid dynamics and heat transfer. Both kinematic viscosity and dynamic viscosity are used to predict and control a fluid's behavior. For example, you can use the kinematic viscosity and dynamic viscosity of a fluid to predict the fluid's pressure drop and flow rate. Through a pipe or over a surface in fluid dynamics. Or to predict the fluid's ability to transport heat in heat transfer.

### Numerical questions

**Q.1 If the shear stress of a fluid is 20 N/m² and the shear rate is 2 s-1, what is the dynamic viscosity of the fluid?**

Answer: The dynamic viscosity of the fluid would be 10 Pa·s. (20 N/m² ÷ 2 s-1 = 10 Pa·s)

**Q.2** **If the density of a fluid is 1000 kg/m³ and its kinematic viscosity is 0.001 m²/s, what is the dynamic viscosity of the fluid?**

Answer: The dynamic viscosity of the fluid would be 0.001 Pa·s. (0.001 m²/s x 1000 kg/m³ = 0.001 Pa·s)

**Q.3 What is the kinematic viscosity of a fluid if its dynamic viscosity is 0.1 Pa·s and its density is 800 kg/m³?**

Answer: The kinematic viscosity of the fluid would be 0.000125 m²/s. (0.1 Pa·s ÷ 800 kg/m³ = 0.000125 m²/s)

**Q.4 A fluid has a shear stress of 15 N/m² and a shear rate of 3 s-1. What is the dynamic viscosity of the fluid?**

Answer: The dynamic viscosity of the fluid would be 5 Pa·s. (15 N/m² ÷ 3 s-1 = 5 Pa·s)

**Q.5 The kinematic viscosity of a fluid is 0.0005 m²/s and its density is 900 kg/m³. What is the dynamic viscosity of the fluid?**

Answer: The dynamic viscosity of the fluid would be 0.45 Pa·s. (0.0005 m²/s x 900 kg/m³ = 0.45 Pa·s)

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