# Viscosity

### Table of Contents

## Introduction to Viscosity

**Viscosity**is a fundamental property of fluids that describes the**internal friction**or**resistance**to flow when subjected to an external force.- It can also be understood as the
**thickness**or**stickiness**of a fluid.

**Historical Background**

**Ancient Civilizations**:

- Early societies observed
**differences**in the flow properties of liquids but lacked a**scientific framework**to explain them.

**Newton’s Law of Viscosity**:

- Sir Isaac Newton formulated a law describing the relationship between shear stress and shear rate in a fluid, laying the foundation for understanding viscosity.

**Mathematical Models**:

- Over time, scientists and engineers developed
**mathematical models**and**experimental methods**to quantify and predict viscosity, enhancing its practical applications.

## Understanding Viscosity

**Viscosity**:

- Viscosity is the
**measure**of a fluid’s**resistance**to shear or flow. It indicates how**thick**or**sticky**a fluid is.

**Formula**:

- The relationship between shear stress ($τ$) and shear rate ($γ˙ $) in a fluid is described by the formula: $τ=μ×γ˙ $
- Where $μ$ is the
**dynamic viscosity**of the fluid.

**Units of Viscosity in SI and CGS Systems**

**SI System**:

- The unit of viscosity in the SI (International System of Units) is the
**Pascal-second (Pa·s)**or**Newton-second per square meter (N·s/m^2)**.

**CGS System**:

- In the CGS (Centimeter-Gram-Second) system, viscosity is measured in
**Poise (P)**or**dyne-second per square centimeter (dyne·s/cm^2).**

**Newton’s Law of Viscosity**

**Newton’s Law**:

- Also known as the
**Newtonian Law of Viscosity**, it states that the shear stress ($τ$) in a fluid is directly proportional to the shear rate ($γ˙ $). - The linear relationship can be expressed as: $τ=μ×γ˙ $ Where $μ$ is the
**viscosity coefficient**or**dynamic viscosity**of the fluid.

**Newtonian Fluids**:

- Fluids that obey Newton’s Law of Viscosity are termed as
**Newtonian fluids**. Examples include water, air, and most common liquids and gases under normal conditions.

## Factors Affecting Viscosity

**Temperature and Viscosity**

**General Trend**: In most fluids, viscosity**decreases**with an**increase**in temperature.**Explanation**: As temperature rises, the kinetic energy of the fluid molecules increases, leading to weaker intermolecular forces and thus reduced viscosity.

**Examples**:

**Water**: Becomes less viscous and flows more easily as it’s heated.**Motor Oil**: Thins out and becomes less sticky when warmed up, improving engine lubrication.

**Nature of Fluid and Viscosity**

**Different Liquids and Gases**:

**Variability**: Viscosity values can vary widely among different fluids due to differences in molecular structure and composition.

**Newtonian vs. Non-Newtonian Fluids**:

**Newtonian Fluids**: Exhibit constant viscosity regardless of the applied shear stress, e.g., water and air.**Non-Newtonian Fluids**: Viscosity changes with shear rate or stress, e.g., ketchup, honey, and certain types of industrial slurries.

**Pressure and Viscosity**

**Effect of Pressure**:

**General Observation**: In gases, viscosity tends to**increase**with an**increase**in pressure.**Non-Newtonian Fluids**: In some non-Newtonian fluids like**polymers**, pressure can significantly alter viscosity, making it a crucial factor to consider in industrial processes.

**Explanation**:

**Compressibility**: Gases can be compressed, leading to closer molecular interactions and increased viscosity.**Shear-Thinning or Shear-Thickening**:**Shear-Thinning**: Viscosity decreases with increasing shear rate, typical for certain non-Newtonian fluids under pressure.**Shear-Thickening**: Viscosity increases with increasing shear rate, observed in some non-Newtonian fluids under pressure.

### Types of Fluids Based on Viscosity

**Newtonian Fluids**

**Definition**:**Newtonian fluids**are fluids that**obey**Newton’s Law of Viscosity, meaning they have a**constant viscosity**at a given temperature, regardless of the shear rate or stress applied.

**Examples**:**Water**: At standard conditions, water exhibits consistent viscosity and follows Newton’s Law.**Air**: For practical purposes and under normal conditions, air behaves as a Newtonian fluid.

**Non-Newtonian Fluids**

**Explanation**:**Non-Newtonian fluids**are fluids whose viscosity**changes**with the applied shear rate or stress. They do not follow Newton’s Law of Viscosity.

**Classification**:**Shear-Thinning Fluids**: Viscosity**decreases**with increasing shear rate. Example:**Ketchup**, where shaking or squeezing reduces its viscosity.**Shear-Thickening Fluids**: Viscosity**increases**with increasing shear rate. Example:**Cornstarch and water mixture**(sometimes called oobleck), which becomes thicker and more resistant when stirred or pressed quickly.**Bingham Plastic**: Exhibits a**yield stress**before it begins to flow. Example:**Toothpaste**, which stays in place until a certain pressure is applied.**Thixotropic Fluids**: Viscosity**decreases**over time under constant shear stress. Example:**Paint**, which becomes thinner when stirred but thickens when left undisturbed.

**Applications of Non-Newtonian Fluids**

**Daily Life**:**Food Industry**:- Non-Newtonian fluids like ketchup, mayonnaise, and yogurt exhibit shear-thinning properties, making them easier to pour or spread.

**Personal Care Products**:- Toothpaste and certain lotions demonstrate Bingham plastic behavior, maintaining shape until squeezed or dispensed.

**Industry**:**Oil Drilling**:- Drilling muds often consist of non-Newtonian fluids tailored to shear-thinning or shear-thickening properties to optimize drilling efficiency and safety.

**Manufacturing**:- Non-Newtonian fluids are used in various processes like mixing, coating, and 3D printing due to their adjustable viscosity and flow properties.

**Importance and Applications of Viscosity**

**Fluid Mechanics**:

- Viscosity is
**paramount**in understanding the behavior of fluids, influencing flow patterns, turbulence, and pressure drops in pipes and channels. - It determines the
**efficiency**of fluid machines like pumps, turbines, and propellers.

**Daily Life**:

**Examples**:- The slow flow of honey compared to water illustrates viscosity.
- The thicker consistency of motor oil and the pourability of ketchup are also examples.

**Practical Implications**:- Understanding viscosity helps in choosing the right fluids for various applications, like lubricants for machinery or paints for surfaces.

**Industrial Processes**:

**Mixing and Stirring**:- Viscosity affects the
**ease**and**efficiency**of mixing processes in industries such as food and pharmaceuticals.

- Viscosity affects the
**Pumping and Transportation**:- Proper viscosity is crucial for the
**smooth**and**efficient**pumping of liquids in chemical, petroleum, and wastewater industries.

- Proper viscosity is crucial for the
**Lubrication**:- In automotive and machinery sectors, viscosity determines the
**effectiveness**of lubricants in reducing friction and wear.

- In automotive and machinery sectors, viscosity determines the

### Conclusion on Viscosity

Viscosity, as a fundamental property of fluids in physics, serves as a cornerstone in understanding fluid behavior and dynamics. It defines a fluid’s resistance to flow or shear, effectively representing its thickness or stickiness.

**Newtonian Fluids**: These fluids, like water and air, adhere to Newton’s Law of Viscosity, maintaining a constant viscosity regardless of the applied shear stress. They are foundational in many fluid mechanics applications due to their predictable behavior.**Non-Newtonian Fluids**: In contrast, non-Newtonian fluids, which include categories like shear-thinning, shear-thickening, Bingham plastic, and thixotropic fluids, do not follow this law. Their viscosity varies based on shear rate or stress, leading to a wide range of intriguing and often useful flow behaviors.

### FAQ’s

Viscosity is a measure of a fluid’s resistance to flow. In simpler terms, it’s how thick or thin a fluid is. Honey, for example, has a high viscosity, while water has a low viscosity.

The SI unit of viscosity is pascal-second (Pa·s). It can also be expressed as newton-second per square meter (N·s/m²).

Resistance.

Viscosity is a property of all fluids, both liquids and gases. So, you’ll encounter it everywhere you find fluids – from honey in your kitchen to the oil in your car engine.

### MCQ’s

**1. What does viscosity measure?**

- a) Density
- b) Speed
- c) Resistance to flow
- d) Temperature

**Answer: c) Resistance to flow**

**2. Which of the following fluids is a Newtonian fluid?**

- a) Honey
- b) Water
- c) Ketchup
- d) Cornstarch and water mixture

**Answer: b) Water**

**3. In which system is the unit of viscosity given as Pascal-second (Pa·s)?**

- a) CGS
- b) FPS
- c) MKS
- d) SI

**Answer: d) SI**

**4. What happens to the viscosity of most fluids as temperature increases?**

- a) Increases
- b) Remains constant
- c) Decreases
- d) Fluctuates

**Answer: c) Decreases**

**5. Which type of non-Newtonian fluid becomes thinner when shaken or squeezed?**

- a) Shear-thickening
- b) Bingham plastic
- c) Shear-thinning
- d) Thixotropic

**Answer: c) Shear-thinning**

**6. What does a Bingham plastic fluid exhibit before flowing?**

- a) Constant viscosity
- b) Increasing viscosity
- c) Yield stress
- d) Decreasing viscosity

**Answer: c) Yield stress**

**7. What does the Newtonian Law of Viscosity state?**

- a) Viscosity varies with temperature.
- b) Viscosity is constant.
- c) Viscosity increases with pressure.
- d) Viscosity is independent of shear rate.

**Answer: b) Viscosity is constant.**

**8. What happens to the viscosity of gases with increasing pressure?**

- a) Increases
- b) Decreases
- c) Remains constant
- d) Becomes zero

**Answer: a) Increases**

**9. Which fluid exhibits shear-thickening behavior when stirred or pressed quickly?**

- a) Water
- b) Air
- c) Ketchup
- d) Honey

**Answer: c) Ketchup**

**10. What is the unit of viscosity in the CGS system?**

- a) Poise
- b) Pascal-second
- c) Newton-second
- d) Joule-second

**Answer: a) Poise**

**11. Which of the following is not a factor affecting viscosity?**

- a) Temperature
- b) Pressure
- c) Volume
- d) Nature of fluid

**Answer: c) Volume**

**12. What type of fluid has a viscosity that decreases over time under constant shear stress?**

- a) Newtonian fluid
- b) Shear-thickening fluid
- c) Shear-thinning fluid
- d) Thixotropic fluid

**Answer: d) Thixotropic fluid**

**13. Which fluid is often used in oil drilling due to its non-Newtonian behavior?**

- a) Water
- b) Air
- c) Bingham plastic
- d) Newtonian fluid

**Answer: c) Bingham plastic**

**14. What does the viscosity coefficient represent in the formula $τ=μ×γ˙ $?**

- a) Shear stress
- b) Shear rate
- c) Viscosity
- d) Temperature

**Answer: c) Viscosity**

**15. Which type of fluid exhibits a linear relationship between shear stress and shear rate?**

- a) Newtonian fluid
- b) Shear-thickening fluid
- c) Bingham plastic
- d) Thixotropic fluid

**Answer: a) Newtonian fluid**

**16. What does the term ‘thixotropic’ mean?**

- a) Increasing viscosity with time
- b) Decreasing viscosity with time
- c) Constant viscosity
- d) Variable temperature

**Answer: b) Decreasing viscosity with time**

**17. What is the main factor responsible for the viscosity of fluids?**

- a) Mass
- b) Pressure
- c) Molecular structure
- d) Color

**Answer: c) Molecular structure**

**18. Which fluid is used as a lubricant due to its low viscosity?**

- a) Honey
- b) Motor oil
- c) Ketchup
- d) Toothpaste

**Answer: b) Motor oil**

**19. What is the unit of viscosity in the FPS system?**

- a) Pascal-second
- b) Poise
- c) Slug-foot per second
- d) Newton-second

**Answer: c) Slug-foot per second**

**20. Which of the following fluids has a Bingham plastic behavior?**

- a) Water
- b) Honey
- c) Toothpaste
- d) Air

**Answer: c) Toothpaste**