Viscosity

An easy explanation of viscosity as the internal friction in fluids that affects how easily they flow.

1. Concept Overview

Viscosity describes how easily a fluid flows. It is the internal friction between layers of the fluid when they move relative to each other. A fluid with high viscosity flows slowly, like honey or oil. A fluid with low viscosity flows easily, like water or air.

This internal friction comes from the interactions between the molecules of the fluid, and it plays an important role in fluid motion.

2. Definition

Viscosity: The internal resistance offered by a fluid to the relative motion between its layers. Mathematically, viscous force between layers is given by \( F = \eta A \dfrac{dv}{dx} \), where \( \eta \) is the coefficient of viscosity.

3. Understanding Viscous Behaviour

3.1. Fluid Layers and Internal Friction

When a fluid flows, it can be imagined as several layers sliding over each other. The layer touching a surface moves slowly, the layer far from the surface moves faster. Due to molecular interaction, these layers resist this difference in speed. This resistance is viscosity.

3.2. Velocity Gradient

In a flowing fluid, velocity changes from one layer to another. This change of velocity with distance is called the velocity gradient:

\( \dfrac{dv}{dx} \)

A larger velocity gradient produces a stronger viscous force.

3.3. Coefficient of Viscosity

The coefficient of viscosity (\(\eta\)) measures how viscous a fluid is. A larger value of \(\eta\) means the fluid resists flow more. Honey has a large \(\eta\), while water has a much smaller value.

3.4. Formula for Viscous Force

The viscous force between two fluid layers is:

\( F = \eta A \dfrac{dv}{dx} \)

Where:

  • \( F \): viscous force
  • \( A \): area of the fluid layer
  • \( \dfrac{dv}{dx} \): velocity gradient
  • \( \eta \): coefficient of viscosity

4. Laminar Flow vs Turbulent Flow

4.1. Laminar Flow

In laminar flow, fluid flows in smooth, parallel layers with no mixing between them. Viscosity plays a major role here because it controls how easily these layers slide past each other.

4.2. Turbulent Flow

In turbulent flow, the fluid motion becomes irregular with eddies and mixing. Viscosity still acts, but its effects are overshadowed by chaotic motion. Turbulence occurs at high speeds.

5. Factors Affecting Viscosity

5.1. Temperature

For liquids, viscosity decreases with increase in temperature because molecules move more freely. For gases, viscosity increases with temperature because molecular collisions become more frequent.

5.2. Nature of Fluid

Thicker fluids with strong intermolecular forces (like glycerine or honey) have high viscosity. Fluids with weaker interactions (like water, kerosene, or air) have low viscosity.

6. Applications of Viscosity

6.1. Lubrication

Oil used in machines must have suitable viscosity. Too high, and motion becomes difficult; too low, and parts wear out quickly.

6.2. Blood Flow

Viscosity affects how easily blood flows through vessels. Slight changes in viscosity have strong effects on circulation.

6.3. Raindrop Motion

When raindrops fall, air viscosity opposes their motion. This creates terminal velocity, limiting their falling speed.

7. Examples to Build Intuition

7.1. Honey vs Water

Honey flows slowly because it has high viscosity. Water flows easily because its viscosity is low. Temperature changes affect honey much more noticeably.

7.2. Stirring a Thick Liquid

It takes more effort to stir thick liquids like paint or syrup. This additional effort comes from viscous resistance within the liquid.

7.3. Sliding of Fluid Layers in a Pipe

Fluid inside a pipe moves fastest at the centre and slowest at the walls. Viscosity controls how smooth or difficult this layered motion is.