Viscosity Class 11 Physics: Complete Guide, All Formulas & Free PDF Download (JEE & NEET)
Viscosity — Competishun
Viscosity Class 11 Physics: Complete Guide, All Formulas & Free PDF Download (JEE & NEET)
Viscosity is one of the most important and scoring topics in Class 11 Physics (Mechanical Properties of Fluids). It carries significant weightage in JEE and NEET, with 1-2 questions appearing every year. This chapter deals with the internal friction of fluids and the forces that oppose the relative motion between their layers.
This chapter covers Newton's law of viscosity, the coefficient of viscosity, Stokes' law, terminal velocity, Poiseuille's equation, and Reynolds number. Understanding these concepts is essential for solving problems in fluid mechanics and for understanding more advanced topics like flow through pipes and aerodynamics.
This page gives you the complete guide to Viscosity with all concepts explained in depth. You will find clear definitions, formulas, visual diagrams, and practice questions. Download the free PDF below and keep it handy for quick revision before your JEE Main, JEE Advanced, or NEET exam.
Download the Viscosity Complete Guide PDF
Get all Viscosity concepts, formulas, Newton's law, Stokes' law, terminal velocity, and Poiseuille's equation in one clean PDF, free. Perfect for JEE and NEET revision.
Download Free PDFWhat is Viscosity?
When a fluid flows, the layers of the fluid move at different velocities. The layer in contact with a fixed surface is at rest, and the velocity increases for layers further away from the surface[reference:2]. Due to the relative motion between these layers, a backward dragging force (viscous force) acts tangentially to every layer[reference:3].
Viscous Force
The internal frictional force that opposes the relative motion between different layers of a fluid[reference:4].
Velocity Gradient
The rate of change of velocity with distance perpendicular to the direction of flow. It is denoted by dv/dx[reference:5].
Glossary of Viscosity Terms — Complete A to Z
Before diving deep into each topic, let's understand the key terminology used in this chapter:
| Term | Definition |
|---|---|
| Viscosity | The property of a fluid that opposes the relative motion between its layers[reference:6]. |
| Viscous Force | The internal frictional force acting between the layers of a fluid[reference:7]. |
| Velocity Gradient (dv/dx) | The rate of change of velocity with distance perpendicular to the flow[reference:8]. |
| Coefficient of Viscosity (η) | The constant of proportionality in Newton's law of viscosity[reference:9]. |
| Poiseuille's Equation | The equation that gives the volume flow rate of a liquid through a capillary tube[reference:10]. |
| Stokes' Law | The law that gives the viscous force on a small sphere moving through a viscous fluid[reference:11]. |
| Terminal Velocity (vt) | The constant maximum velocity attained by a body falling through a viscous medium[reference:12]. |
| Reynolds Number (Re) | A dimensionless number that determines whether the flow is laminar or turbulent[reference:13]. |
| Kinematic Viscosity (ν) | The ratio of dynamic viscosity to density: ν = η/ρ[reference:14]. |
| Mastering these terms is essential for understanding Viscosity. | |
Newton's Law of Viscosity
F = -η A (dv/dx)
The negative sign indicates that the viscous force opposes the relative motion between the layers[reference:16]. The constant of proportionality η is called the coefficient of viscosity.
Newton's Law of Viscosity
Shear Stress
Coefficient of Viscosity
Coefficient of Viscosity (η)
- Definition: The coefficient of viscosity is the tangential force required per unit area to maintain a unit velocity gradient between two parallel layers of the fluid[reference:21][reference:22].
- SI Unit: Pascal-second (Pa·s) or N·s/m²[reference:23][reference:24].
- CGS Unit: Poise (P). 1 Pa·s = 10 P[reference:25].
- Dimensional Formula: [ML⁻¹T⁻¹][reference:26][reference:27].
Stokes' Law — Viscous Force on a Sphere
F = 6πηrv
This law is valid for small spheres moving at low velocities in a viscous fluid, where the flow around the sphere is laminar[reference:30].
Stokes' Law
Terminal Velocity
Buoyant Force
Terminal Velocity
When a sphere falls through a viscous fluid, it initially accelerates. As its velocity increases, the viscous force (which is proportional to velocity) also increases. Eventually, the net force becomes zero, and the sphere falls with a constant velocity called the terminal velocity[reference:34].
mg = FB + Fviscous
(4/3)πr³ρg = (4/3)πr³σg + 6πηrvt
vt = 2r²(ρ-σ)g / 9η[reference:36][reference:37]
Poiseuille's Equation — Flow Through a Capillary Tube
Q = πPr⁴ / 8ηl
This equation is valid for steady, laminar flow of an incompressible fluid through a cylindrical pipe[reference:39].
Poiseuille's Equation
Fluid Resistance
Velocity Profile
Series Resistance
Reynolds Number — Laminar vs Turbulent Flow
Re = ρvD / η
Reynolds Number
Kinematic Form
| Reynolds Number | Type of Flow |
|---|---|
| Re < 2000 | Laminar flow (streamlined, orderly) |
| 2000 < Re < 4000 | Transitional flow |
| Re > 4000 | Turbulent flow (chaotic, mixing)[reference:49] |
| The critical Reynolds number for transition from laminar to turbulent flow in a pipe is approximately 2000-4000[reference:50]. | |
Variation of Viscosity with Temperature and Pressure
| Fluid | Effect of Temperature | Effect of Pressure |
|---|---|---|
| Liquids | Viscosity decreases with increase in temperature[reference:52][reference:53] | Viscosity increases with increase in pressure[reference:54] |
| Gases | Viscosity increases with increase in temperature (η ∝ √T)[reference:55] | Viscosity is independent of pressure[reference:56] |
| The viscosity of liquids decreases with temperature due to the decrease in cohesive forces[reference:57]. The viscosity of gases increases with temperature due to the increase in momentum of gas molecules[reference:58]. | ||
Practice Questions — From JEE and NEET
| Question | Answer |
|---|---|
| Q1: What is the SI unit of coefficient of viscosity? | Pascal-second (Pa·s) or N·s/m²[reference:60]. |
| Q2: State Newton's law of viscosity. | F = ηA(dv/dx), where F is the viscous force, η is the coefficient of viscosity, A is the area, and dv/dx is the velocity gradient[reference:61]. |
| Q3: What is the dimensional formula of the coefficient of viscosity? | [ML⁻¹T⁻¹][reference:62]. |
| Q4: State Stokes' law. | F = 6πηrv, where F is the viscous force on a sphere of radius r moving with velocity v through a fluid of viscosity η[reference:63]. |
| Q5: What is terminal velocity? | The constant maximum velocity attained by a body falling freely through a viscous medium[reference:64]. |
| Q6: Write the expression for terminal velocity of a sphere falling through a viscous fluid. | vt = 2r²(ρ-σ)g/9η[reference:65][reference:66]. |
| Q7: What is Poiseuille's equation? | Q = πPr⁴/8ηl, where Q is the volume flow rate, P is the pressure difference, r is the radius, l is the length, and η is the coefficient of viscosity[reference:67]. |
| Q8: What is Reynolds number? | Re = ρvD/η, the ratio of inertial forces to viscous forces[reference:68]. |
| Practise these types of questions to become comfortable with applying Viscosity concepts in exam scenarios. | |
All Viscosity Formulas at a Glance
| Category | Formula |
|---|---|
| Newton's Law of Viscosity | F = ηA(dv/dx)[reference:69] |
| Shear Stress | τ = F/A[reference:70] |
| Coefficient of Viscosity | η = τ/(dv/dx)[reference:71] |
| Stokes' Law | F = 6πηrv[reference:72] |
| Terminal Velocity | vt = 2r²(ρ-σ)g/9η[reference:73] |
| Poiseuille's Equation | Q = πPr⁴/8ηl[reference:74] |
| Fluid Resistance | R = 8ηl/πr⁴[reference:75] |
| Reynolds Number | Re = ρvD/η[reference:76] |
| Kinematic Viscosity | ν = η/ρ[reference:77] |
| Memorise these formulas for Viscosity. They are the key to scoring full marks in this chapter. | |
Common Mistakes in Viscosity
- Confusing dynamic and kinematic viscosity: Dynamic viscosity (η) is the coefficient of viscosity, while kinematic viscosity (ν) is η/ρ[reference:78].
- Forgetting the temperature dependence: The viscosity of liquids decreases with temperature, while the viscosity of gases increases with temperature[reference:79].
- Misapplying Stokes' law: Stokes' law is valid only for small spheres moving at low velocities with laminar flow[reference:80].
- Using the wrong units: The SI unit of viscosity is Pa·s, and the CGS unit is poise. 1 Pa·s = 10 poise[reference:81].
- Confusing laminar and turbulent flow: Laminar flow is smooth and orderly, while turbulent flow is chaotic and mixing. Reynolds number determines the type of flow[reference:82].
- Forgetting the r⁴ dependence in Poiseuille's equation: The flow rate is proportional to the fourth power of the radius[reference:83].
Why Viscosity Matters for JEE and NEET
- High weightage: Viscosity appears in 1-2 questions in every JEE Main, JEE Advanced, and NEET physics paper.
- Foundation for fluid mechanics: Understanding viscosity is essential for understanding more advanced topics like flow through pipes, aerodynamics, and hydraulics.
- Conceptual clarity: This chapter rewards students who understand the concepts rather than just memorizing formulas.
- Practical relevance: Viscosity is used everywhere, from lubricants in engines to the flow of blood in arteries to the design of aircraft.
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