Viscosity

Have you ever wondered why honey flows more slowly than water? Or why some motor oils are described as "thicker" than others? The answer for this lies in a fundamental property of fluids called viscosity.

Viscosity plays a crucial role in everything from car engines to cooking and even human circulation. But what exactly is viscosity, and why does it matter? In this article, we’ll explore the concept of viscosity, its mathematical explanation, real-world applications, and common misconceptions.

Viscosity Definition

Viscosity is a measure of a fluid’s resistance to flow. Or simply, it describes how “thick” or “thin” a liquid is. A fluid with high viscosity, like honey, resists motion, while a fluid with low viscosity, like water, flows easily.

To understand viscosity, let’s take an example of difference between stirring a cup of coffee and a jar of honey. We can observe that the coffee moves with ease, while the honey offers resistance. This resistance arises due to the internal friction between layers of the fluid as they move past each other.

Viscosity Formula

Viscosity is a measure of a fluid's resistance to deformation or flow. It quantifies the internal friction between adjacent layers of a fluid in relative motion. Below are the key formulas related to viscosity:

Newton's Law of Viscosity

The relationship between shear stress (τ) and shear rate (𝘌) for Newtonian fluids is given by:

τ = η ⋅ 𝘌

• τ = F / A is the shear stress (force per unit area),
• 𝘌 = Δv / x is the shear rate (velocity gradient),
• η is the dynamic viscosity coefficient.

Viscous Force Formula

The viscous force (F) between two fluid layers can be expressed as:

F = -η A (dv/dx)

• A is the surface area,
• dv/dx is the velocity gradient,
• η is the dynamic viscosity.

For determining viscosity using a falling sphere in a fluid:

η = (2 g a² (Δρ)) / (9 v)

• g is acceleration due to gravity,
• a is the radius of the sphere,
• Δρ is the density difference between the sphere and fluid,
• v is the terminal velocity of the sphere.

Types of Viscosity

There are several types of viscosity, each describing different aspects of a fluid's resistance to flow. Below is an overview of the main types:

1. Dynamic Viscosity (Absolute Viscosity)

Dynamic viscosity measures a fluid's internal resistance to flow when an external force is applied. It is defined as the ratio of shear stress to shear rate:

• Symbol: μ\muμ
• Unit: Pascal-seconds (Pa·s) or N·s/m²
• Example: Honey has high dynamic viscosity compared to water.

2. Kinematic Viscosity

Kinematic viscosity relates dynamic viscosity to the fluid's density. It measures the fluid's resistance to flow under gravitational forces:

• Formula: ν=μ/ρ, where μ is dynamic viscosity and ρ is density.
• Unit: m²/s
• Example: Oil industries often use kinematic viscosity for flow analysis.

Newtonian vs. Non-Newtonian Fluids

• Newtonian Fluids: These have a constant viscosity regardless of applied force (e.g., water, air), which means their flow behaviour remains constant.
• Non-Newtonian Fluids: Their viscosity changes when force is applied (e.g., ketchup, blood, cornstarch in water), which means their flow behaviour can vary under different conditions.

Applications of Viscosity

• Motor Oil & Lubrication: Engines require oil with specific viscosity to reduce friction and wear. The right viscosity ensures efficient performance and fuel economy.
• Food Industry: The viscosity of chocolate, sauces, and syrups affects their texture and how they coat food.
• Medical Applications: Blood viscosity impacts circulation and cardiovascular health. Abnormal viscosity levels can lead to medical conditions like high blood pressure.
• Aerospace & Manufacturing: Paints, inks, and coatings must have the correct viscosity for smooth application and durability.

Viscosity Examples

Example 1: Calculating the Shear Stress in a Fluid

Solutions: A fluid has a dynamic viscosity of 0.5 Pa·s, and the velocity gradient is 2 s⁻¹. Find the shear stress.

τ = η du/dy 

τ = (0.5)(2) 

τ = 1Pa

Thus, the shear stress is 1 Pascal.

Example 2: Comparing Flow Rates of Two Fluids

Solutions: Honey has a viscosity of 5 Pa·s, while water has a viscosity of 0.001 Pa·s. Which fluid flows more easily?

Since water has a much lower viscosity than honey, it offers less resistance to flow and moves more easily. Therefore, water pours quickly, while honey drips slowly.