Coefficient of Viscosity Formula and Dimensional Formula Derivation
The coefficient of viscosity is a fundamental property that quantifies a fluid's resistance to flow and deformation. Understanding this concept is crucial for analyzing fluid behavior in engineering applications, biological systems, and industrial processes. This article explores the coefficient of viscosity formula, dimensional analysis, units, and practical applications to provide you with comprehensive knowledge for physics studies.
What is Coefficient of Viscosity?
The coefficient of viscosity, denoted by the Greek letter η (eta), represents a material property that measures internal friction between adjacent layers of fluid when they move relative to each other. When you observe honey flowing slowly compared to water, you're witnessing the effects of different viscosity coefficients.
Viscosity arises due to intermolecular forces and momentum transfer between fluid layers. In liquids, molecules are closely packed, and viscosity primarily results from cohesive forces. For gases, viscosity stems from molecular collisions and momentum exchange. This fundamental concept helps explain phenomena ranging from fluid friction to blood circulation in living organisms.
Coefficient of Viscosity Formula
The coefficient of viscosity formula is derived from Newton's law of viscosity, which states that shear stress is proportional to the velocity gradient in flowing fluids.
Mathematical Expression:
Where:
- η = coefficient of viscosity
- F = tangential force applied (Newton)
- d = distance between fluid layers (meter)
- A = area of each layer (square meter)
- v = relative velocity between layers (meter per second)
This formula can also be expressed in terms of shear stress (τ) and velocity gradient (dv/dy):
Dimensional Formula of Coefficient of Viscosity
To derive the coefficient of viscosity dimensional formula, we analyze each quantity in the basic equation:
- Force (F) has dimensions: $[MLT^{-2}]$
- Distance (d) has dimensions: $[L]$
- Area (A) has dimensions: $[L^2]$
- Velocity (v) has dimensions: $[LT^{-1}]$
Substituting these dimensions into the coefficient of viscosity formula:
Therefore, the coefficient of viscosity dimensional formula is **[ML⁻¹T⁻¹]**.
Units of Coefficient of Viscosity
The coefficient of viscosity is expressed in different units across various measurement systems:
| System | Unit | Symbol | Conversion |
|---|---|---|---|
| SI (International) | Pascal-second | Pa·s | 1 Pa·s = 1 N·s·m⁻² |
| CGS | Poise | P | 1 P = 1 g·cm⁻¹·s⁻¹ |
| Practical CGS | Centipoise | cP | 1 cP = 0.01 P |
| Alternative SI | kg·m⁻¹·s⁻¹ | — | 1 kg·m⁻¹·s⁻¹ = 1 Pa·s |
The relationship between major units is: 1 Pa·s = 10 P = 1000 cP. For practical applications, centipoise is commonly used since water at 20°C has a viscosity of approximately 1 cP.
Coefficient of Viscosity Values for Common Fluids
Understanding typical viscosity values helps in comparing fluid behavior:
| Fluid | Temperature (°C) | Viscosity (Pa·s) | Viscosity (cP) |
|---|---|---|---|
| Air | 20 | 1.8 × 10⁻⁵ | 0.018 |
| Water | 20 | 1.0 × 10⁻³ | 1.0 |
| Water | 100 | 2.8 × 10⁻⁴ | 0.28 |
FAQs on What is Coefficient of Viscosity? Complete Guide to Formula, Units and Applications
1. What is the coefficient of viscosity?
Coefficient of viscosity is a measure of a fluid's internal resistance to flow. It quantifies how much force is required to move one layer of the fluid in relation to another.
- Represented by the Greek letter eta (η)
- SI unit is pascal second (Pa·s) or kg·m-1·s-1
- Key concept in physics and fluid mechanics
- Relevant in CBSE Class 11 Physics syllabus, particularly in the chapter Mechanical Properties of Fluids
2. What is the definition of viscosity?
Viscosity is defined as the property of a fluid that resists the force causing the fluid to flow. It determines how 'thick' or 'thin' a liquid is.
- High viscosity: Slow flow (e.g., honey)
- Low viscosity: Fast flow (e.g., water)
- Measured using coefficient of viscosity
3. State the SI unit and CGS unit of coefficient of viscosity.
The SI unit of coefficient of viscosity is pascal second (Pa·s), while the CGS unit is poise.
- 1 Pa·s = 10 poise
- SI: kg·m-1·s-1
- CGS: g·cm-1·s-1
4. On what factors does the coefficient of viscosity depend?
The coefficient of viscosity depends on several factors, mainly:
- Nature of the fluid: Gases, liquids, or solutions
- Temperature: Viscosity of liquids decreases with temperature, while that of gases increases
- Pressure: Usually negligible effect for liquids, but can affect gases
5. What are the applications of viscosity in daily life?
Viscosity plays an important role in everyday activities:
- Lubrication: Oil viscosity ensures smooth functioning of machine parts
- Cooking: Consistency of food like honey or syrups
- Blood flow: Viscosity of blood crucial for health and diagnostics
- Paints and inks: Proper viscosity required for application
6. Why does honey flow more slowly than water?
Honey flows more slowly than water because it has a higher coefficient of viscosity.
- High viscosity means greater resistance to motion
- More force needed to make honey flow compared to water
- This is why honey pours out slower than less viscous liquids
7. How is coefficient of viscosity measured experimentally?
Coefficient of viscosity can be measured using several experiments:
- Capillary tube method (Poiseuille's law) - fluid flows through a narrow tube and pressure drop is measured
- Falling sphere method - a sphere drops in the fluid and terminal velocity is noted
- Both methods relate force, velocity, and area to calculate η
8. What is Poiseuille's law?
Poiseuille's law describes the flow of a liquid through a narrow tube:
- States that the rate of flow is proportional to the pressure difference and the fourth power of the radius, and inversely proportional to the length of the tube and viscosity
- Formula: V = πPr4 / (8ηl)
9. Explain Newton’s law of viscosity.
Newton’s law of viscosity states that the shear stress between adjacent fluid layers is proportional to the velocity gradient between them:
- Expressed mathematically as τ = η (du/dy)
- Newtonian fluids obey this law (e.g., water, air)
10. What is the effect of temperature on viscosity of liquids and gases?
Temperature has opposite effects on viscosity of liquids and gases:
- In liquids: Viscosity decreases as temperature increases
- In gases: Viscosity increases as temperature increases
- This is due to changes in intermolecular forces and molecular motion
11. Why is the knowledge of viscosity important in industries?
Understanding viscosity is crucial in many industries:
- Ensures correct lubrication in machinery
- Affects quality of paints, adhesives, and food products
- Helps in transportation of fluids like oil and chemicals
- Critical in designing pipelines and reactors
12. Name some fluids that have low and high viscosity.
Examples of low and high viscosity fluids include:
- Low viscosity: Water, alcohol, air
- High viscosity: Honey, glycerin, tar
