Viscosity Formula, SI Units, and Calculation Explained for Students
Viscosity is a physical property that describes a fluid's resistance to flow or to a change in shape. It represents how much internal friction occurs between different layers of a fluid when they move relative to each other. The concept of viscosity is important not only in Physics but also in various real-life situations and industrial applications.
Detailed Explanation of Viscosity
When a fluid flows, its molecules or layers move at different speeds. The internal friction that arises due to this difference in velocity is termed viscosity. Fluids with high viscosity (like honey or oil) flow more slowly, while fluids with low viscosity (like water or air) flow more readily.
Viscosity is sometimes referred to as the "thickness" of a fluid. For example, honey feels much thicker than water because it is more viscous. This characteristic helps us distinguish different fluids and understand their behaviour in various situations.
Formula and Mathematical Representation
The mathematical expression for viscosity comes from observing the force required to move one layer of fluid over another at a certain speed. The basic formula is:
Viscosity (η) = Shearing force required (F) / (Area (A) × Velocity Gradient (dv/dx))
Or, in formula form:
η = F / (A × dv/dx)
Here,
F is the force applied parallel to the area A,
dv/dx is the rate of change of velocity with distance between the fluid layers,
η (eta) is the symbol commonly used for viscosity.
Units and Table Representation
| System | Unit | Symbol | Dimension |
|---|---|---|---|
| SI | Pascal-second | Pa·s | ML-1T-1 |
| CGS | Poise | P | g·cm-1·s-1 |
| Relation | 1 Pa·s = 10 P |
Step-by-Step Approach to Solving Viscosity Problems
- Identify what quantities are given in the problem (such as force, area, layer spacing, velocity).
- Write down the standard formula for viscosity: η = F / (A × dv/dx).
- Convert all units to the SI system for consistency (N, m2, m/s).
- Substitute the values and calculate each component step by step.
- Make sure the final answer uses the correct unit (Pa·s).
Example Problem
Suppose a force of 0.002 N moves the top of a fluid layer of area 0.02 m2 at a speed difference of 0.001 m/s. The distance between the layers is 0.002 m. What is the viscosity?
F = 0.002 N
A = 0.02 m2
dv = 0.001 m/s
dx = 0.002 m
Formula: η = F / (A × dv/dx)
First, calculate dv/dx: (0.001 m/s) / (0.002 m) = 0.5 s-1
A × dv/dx = 0.02 m2 × 0.5 s-1 = 0.01 m2s-1
η = 0.002 N / 0.01 m2s-1 = 0.2 Pa·s
Common Examples of Viscosity
| Substance | Approx. Viscosity (Pa·s) |
|---|---|
| Water | 0.001 |
| Air | 0.000018 |
| Honey | 10 |
| Engine Oil | 0.25 |
Applications of Viscosity in Daily Life
- Lubricating oil in engines controls friction and wear.
- The flow of paints, adhesives, and even everyday beverages is influenced by viscosity.
- Viscosity affects blood flow in living organisms.
Key Formulas Table for Viscosity
| Formula Name | Formula | Context of Use |
|---|---|---|
| General Viscosity (Newton's law) | η = F / (A × dv/dx) | Shear flow in fluids |
| Dynamic (Absolute) Viscosity | η (eta) | Intrinsic resistance to flow |
| Kinematic Viscosity | ν = η / ρ | Viscosity per unit density |
Further Learning and Next Steps
- For detailed study of units, refer to Unit of Viscosity.
Sample Practice Questions
- Define viscosity. Give one example of a fluid with high viscosity and one with low viscosity.
- If a force of 0.005 N is applied to a fluid layer of 0.05 m2 and creates a velocity gradient of 2 s-1, what is the viscosity?
- Why does honey flow more slowly than water?
For more detailed explanations and solved examples, explore Vedantu’s viscosity resources and related topic pages linked above. Build strong foundations with stepwise solutions and topic-specific conceptual clarity.
FAQs on Viscosity in Physics: Meaning, Types, Formulas & Real-Life Uses
1. What is viscosity in Physics?
Viscosity is a measure of a fluid's resistance to flow or deformation. It reflects the internal friction between fluid layers as they move past each other. Higher viscosity fluids (like honey) flow more slowly, while lower viscosity fluids (like water) flow easily.
2. What is the SI unit of viscosity?
The SI unit of viscosity (dynamic viscosity) is the Pascal-second (Pa·s). In the CGS system, it is measured in Poise (P). 1 Pa·s = 10 Poise.
3. What is the viscosity of water at room temperature?
At room temperature (25°C), the viscosity of water is approximately 0.00089 Pa·s (or 0.89 cP). This value is commonly used for calculations and competitive exam questions.
4. Does viscosity mean thickness?
Viscosity and thickness are related but not identical. Viscosity measures a fluid's resistance to flow, often perceived as 'thickness.' However, thickness is a qualitative description, while viscosity gives a precise, measurable value.
5. How is viscosity measured?
Viscosity is measured by observing the force required to move one layer of fluid over another at a certain speed. Standard laboratory methods include:
- Capillary tube viscometer
- Falling sphere (Stoke’s Law) method
- Rotational viscometer
6. What is the difference between dynamic and kinematic viscosity?
Dynamic viscosity (η) describes a fluid's internal friction and is measured in Pa·s.
Kinematic viscosity (ν) is the ratio of dynamic viscosity to density (ν = η/ρ) and is measured in m²/s. Kinematic viscosity shows how quickly a fluid spreads or flows under gravity.
7. What does high viscosity mean?
A fluid with high viscosity flows slowly and resists deformation (for example, honey or glycerin). This is due to strong internal friction between molecules or layers in the fluid.
8. Give examples of fluids with high and low viscosity.
High viscosity:
- Honey
- Glycerin
- Engine oil
- Water
- Air
- Alcohol
9. What is the viscosity formula?
The viscosity (η) of a fluid can be calculated by:
η = F / (A × dv/dx)
Where:
- F = Force applied (N)
- A = Area of the layer (m²)
- dv/dx = Velocity gradient (s-1)
10. What is the coefficient of viscosity?
The coefficient of viscosity (η) quantifies the internal friction per unit area per unit velocity gradient. It determines the viscous force acting between two adjacent fluid layers having unit area and moving with a unit velocity gradient.
11. State two applications of viscosity in daily life or industry.
Viscosity applications:
- Designing engine oils for cars and machinery to ensure proper lubrication
- Managing blood flow in medical diagnostics
- Controlling flow in pipelines for oil, water, and food products
12. How does temperature affect viscosity?
For most liquids, viscosity decreases as temperature increases, making them flow more easily. In contrast, gases tend to become more viscous as temperature rises. This is because higher temperatures reduce internal friction among liquid molecules.
