Viscosity

Table of Contents

Introduction

Viscosity is a measure of a fluid’s resistance to flow. It describes the internal friction of a moving fluid. A fluid with large viscosity resists motion because its molecular makeup gives it a lot of internal friction. A fluid with low viscosity flows easily because its molecular makeup results in very little friction when it is in motion.

Definition of Viscosity

Viscosity can be formally defined as the property of a fluid that resists the force tending to cause the fluid to flow. It is often denoted by the Greek letter $\mu$ and is measured in the SI units of Pascal-seconds ( $\text{Pa} \cdot \text{s}$ ).

Newton’s Law of Viscosity

Newton’s law of viscosity gives us a quantitative way to discuss viscosity. This law states that the rate of change of velocity perpendicular to the direction of shear stress is directly proportional to the shear stress in the fluid. Mathematically, it can be represented as:

$\tau = \mu \cdot \dfrac{du}{dy}$

where:

$\tau$ is the shear stress in the fluid,
$\mu$ is the dynamic viscosity,
$\frac{du}{dy}$ is the velocity gradient perpendicular to the direction of shear.

Types of Viscosity

There are two types of viscosity: dynamic viscosity and kinematic viscosity.

Dynamic Viscosity

Dynamic viscosity, usually denoted $\mu$ , is a measure of internal resistance to shear flow. The SI unit for dynamic viscosity is the pascal-second ( $\text{Pa} \cdot \text{s}$ ).

Kinematic Viscosity

Kinematic viscosity, usually denoted $\nu$ , is the ratio of the fluid’s dynamic viscosity to its density. The SI unit for kinematic viscosity is the square meter per second (m²/s). The relationship between dynamic and kinematic viscosity is given by:

$\nu = \dfrac{\mu}{\rho}$

where:

$\nu$ is the kinematic viscosity,
$\mu$ is the dynamic viscosity,
$\rho$ is the density of the fluid.

Factors Influencing Viscosity

The viscosity of a fluid depends on several factors including temperature, pressure, and the specific chemical composition of the fluid.

Temperature

In general, the viscosity of a liquid decreases with temperature, while the viscosity of a gas increases with temperature.

Pressure

For most liquids, viscosity is largely independent of pressure. Gases, on the other hand, often see increased viscosity with increased pressure.

Importance of Viscosity

Viscosity is a critical factor in any scenario where fluid flow is involved. It plays a key role in the fields of engineering and physics, influencing the operation of machinery and natural phenomena alike. For example, in mechanical and chemical engineering, understanding viscosity is vital to the design of systems that involve the flow of fluids, such as pipelines, lubrication systems, and chemical mixing equipment.

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Introduction

Definition of Viscosity

Newton’s Law of Viscosity