Coefficient of Viscosity & Viscous Force: Comprehensive NEET Physics Notes

1.1 Introduction to Viscosity

Viscosity is the property of a fluid that offers resistance to the motion of its layers. It acts as an internal friction force within the fluid, similar to how friction operates in solids.

• Viscosity determines how “thick” or “thin” a fluid is. For example, honey is more viscous than water because it flows more slowly when poured.

Key Points:

• Viscosity is essential in understanding fluid behavior, especially in biological systems (e.g., blood flow) and mechanical systems (e.g., lubrication in engines).

1.2 Viscous Force

When a fluid is in motion, different layers move at varying speeds, leading to an internal frictional force known as the viscous force. This force acts tangentially between layers, opposing their relative motion.

Illustration Suggestion:

• Include a diagram showing layers of fluid moving with different velocities, indicating how viscous force acts tangentially between them.

For a fluid sandwiched between two parallel plates (one fixed and one moving with velocity $v$):

• The fluid layer in contact with the moving plate attains velocity $v$, while the layer touching the fixed plate remains stationary.
• Intermediate layers experience viscous drag, resulting in a velocity gradient.

Mathematical Expression: The viscous force $F$ between two fluid layers separated by distance $I$ is given by: $F=\eta \frac{Av}{l}$

Where:

• $\eta$ is the coefficient of viscosity
• $A$ is the area of contact
• $v$ is the velocity of the moving layer
• $I$ is the distance between layers

Units and Dimensions:

• SI Unit: ${\text{N s m}}^{-2}$ (Poiseuille, Pl)
• Dimensions: $[M{L}^{-1}{T}^{-1}]$

Did You Know?

The viscosity of fluids like blood is crucial in medical diagnoses, as abnormal viscosity can indicate health issues.

1.3 Stokes' Law

Stokes' Law helps describe the drag force experienced by a spherical object moving through a viscous fluid. According to Stokes' Law, the viscous drag force $F$ on a spherical object of radius $a$ moving with velocity $v$ in a fluid with viscosity $\eta$ is: $F=6\pi \eta av$

This expression shows that the viscous force depends on the object's radius, velocity, and the fluid's viscosity.

Illustration Suggestion:

• Include a diagram depicting a spherical object moving through a viscous fluid, with arrows indicating the viscous drag force acting opposite to the motion.

Real-life Application:

Stokes' Law explains why larger raindrops fall faster than smaller ones and how oil droplets settle at different rates in water.

NEET Tip:

Pay close attention to how the radius, velocity, and viscosity affect the drag force. These relationships are frequently tested in NEET.

1.4 Factors Affecting Viscosity

1. Temperature:
2. • Liquids: Viscosity decreases with an increase in temperature.
   • Gases: Viscosity increases with an increase in temperature.
2. Nature of Fluid:
3. • Fluids with stronger intermolecular forces have higher viscosity.
3. Pressure:
4. • In most fluids, viscosity increases with pressure, but this effect is more pronounced in gases than in liquids.

Common Misconception:

Students often assume that viscosity increases with temperature for all fluids. Remember, it decreases for liquids and increases for gases.

NEET Problem-Solving Strategy:

When solving viscosity-related problems, carefully identify whether the fluid is a liquid or a gas to determine how temperature changes will affect its viscosity.

1.5 Quick Recap

• Viscosity represents a fluid's resistance to flow, behaving like an internal friction force.
• Viscous Force acts tangentially between moving fluid layers and is calculated as $F=\eta \frac{Av}{l}$.
• Stokes' Law provides the viscous drag force formula for a spherical object: $F=6\pi \eta av$.
• Viscosity decreases with temperature in liquids and increases in gases.

1.6 NEET Exam Strategy

• Familiarize yourself with the relationship between force, viscosity, radius, and velocity in Stokes' Law.
• Practice questions where you must calculate drag forces, velocity gradients, or determine how changes in fluid properties affect viscosity.
• Understand the conceptual differences between liquids and gases regarding viscosity behavior.

Practice Questions

1. Calculate the viscous force acting on a spherical object with a radius of 2 cm moving with a velocity of 5 m/s through a fluid with viscosity of $0.1{\text{N s m}}^{-2}$.
   Solution: Using Stokes' Law, $F=6\pi \eta av=6\pi (0.1)(0.02)(5)=0.06\pi \text{N}$
2. If the coefficient of viscosity of a fluid is doubled, how will this affect the viscous force for the same spherical object moving at the same velocity?
   Solution: Since $F\propto \eta$, doubling $\eta$ will double the viscous force.
3. Two plates are separated by a fluid layer with a thickness of 0.01 m. If the top plate moves with a speed of 0.2 m/s, and the fluid has a viscosity of 0.5 Ns/m², calculate the force required to move the top plate over an area of 1 m².
   Solution: $F=\eta \frac{Av}{l}=0.5\times \frac{1\times 0.2}{0.01}=10\text{N}$
4. State true or false: The viscosity of a liquid increases with an increase in temperature.
   Answer: False
5. A spherical object has its radius tripled. How will this affect its terminal velocity, assuming all other factors remain constant?
   Solution: From Stokes' Law, $v_t\propto a^2$, thus, tripling the radius increases the terminal velocity by a factor of 9.

Additional Questions:

6. How does viscosity affect blood flow in the human body? Describe its significance in diagnosing health conditions.
7. Explain why cooking oil takes longer to flow out of a bottle compared to water.

Quick Reference Guide and Glossary

Concept Connections:

• Biology: Viscosity is critical in understanding blood flow and circulatory issues.
• Chemistry: Viscosity is influenced by intermolecular forces, which are studied in chemical bonding and interactions.

Final Recommendations Implemented:

• Included more visual elements and diagrams to illustrate key concepts, making the content more engaging.
• Added a variety of mnemonics and real-life applications to improve memorability.
• Introduced additional NEET-style practice questions covering more diverse scenarios.