class 11 notes

Class 11 Physics Notes Chapter 2 (Chapter 2) – Physics Part-II Book

Philoid

Philoid

— 8 min read

Physics Part-II
Alright class, let's dive straight into Chapter 10: Mechanical Properties of Fluids from your NCERT Class 11 Physics Part-II book. This chapter is quite important for various government exams as it deals with fundamental principles governing the behaviour of liquids and gases at rest and in motion. Pay close attention to the definitions, laws, formulas, and their applications.

Chapter 10: Mechanical Properties of Fluids - Detailed Notes

1. Introduction to Fluids

  • Fluids: Substances that can flow. This includes liquids and gases. Unlike solids, fluids do not have a definite shape and take the shape of their container.
  • Key Difference from Solids: Fluids cannot sustain shearing stress. When a tangential force is applied, they deform continuously (flow). Solids deform initially but reach an equilibrium shape.
  • Fluid Mechanics: Study of fluids at rest (Fluid Statics) and in motion (Fluid Dynamics).

2. Pressure

  • Definition: The normal force exerted by a fluid per unit area of the surface in contact.
    • Formula: P = F / A (where F is the normal force, A is the area)
  • Unit: SI unit is Pascal (Pa). 1 Pa = 1 N/m². Other common units: atmosphere (atm), bar, torr.
    • 1 atm = 1.013 × 10⁵ Pa ≈ 101.3 kPa
    • 1 bar = 10⁵ Pa
    • 1 torr = 1 mm of Hg ≈ 133 Pa
  • Scalar Quantity: Pressure acts perpendicular to any surface in the fluid, regardless of the surface's orientation. It has magnitude but no specific direction.
  • Density (ρ): Mass per unit volume (ρ = m/V). SI unit: kg/m³. Dimension: [ML⁻³]. Liquids are largely incompressible (density is constant), while gases are highly compressible.
  • Pressure in a Fluid at Rest (Hydrostatic Pressure): The pressure at a certain depth 'h' below the surface of a liquid of density 'ρ' at rest is given by:
    • Formula: P = hρg (This is the gauge pressure, relative to the surface pressure)
    • 'g' is the acceleration due to gravity.
  • Total (Absolute) Pressure: If the surface is exposed to atmospheric pressure (Pa), the total pressure at depth 'h' is:
    • Formula: P_absolute = P_a + hρg
  • Gauge Pressure: The difference between the absolute pressure and atmospheric pressure (P_gauge = P_absolute - P_a = hρg).
  • Pascal's Law: Pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and the walls of the containing vessel.
    • Applications: Hydraulic Lift (F₂/A₂ = F₁/A₁), Hydraulic Brakes. These devices use fluids to multiply force.
  • Atmospheric Pressure: Pressure exerted by the Earth's atmosphere. Measured using a barometer. Standard atmospheric pressure at sea level supports a column of mercury 76 cm (or 760 mm) high.

3. Fluid Dynamics - Flow of Fluids

  • Steady Flow (Streamline Flow): Fluid velocity at any given point remains constant over time. Path followed by fluid particles is called a streamline. Streamlines do not cross each other.
  • Unsteady Flow: Fluid velocity at a point changes with time.
  • Turbulent Flow: Irregular, chaotic flow with eddies and vortices. Occurs at high velocities or past obstacles.
  • Laminar Flow: Smooth, orderly flow where fluid layers slide past each other without mixing. Often synonymous with streamline flow at lower velocities.
  • Ideal Fluid: An imaginary fluid with zero viscosity and is incompressible. Used to simplify analysis.
  • Equation of Continuity: For an incompressible fluid in steady flow through a pipe of varying cross-section, the volume flow rate (or mass flow rate) is constant.
    • Based on: Conservation of Mass.
    • Formula: A₁v₁ = A₂v₂ or Av = Constant (where A is the cross-sectional area, v is the fluid velocity).
    • Meaning: Where the pipe narrows, the fluid speed increases, and vice versa.

4. Bernoulli's Principle

  • Statement: For the streamline flow of an ideal (incompressible, non-viscous) fluid, the sum of pressure energy per unit volume, kinetic energy per unit volume, and potential energy per unit volume remains constant along a streamline.
    • Based on: Conservation of Energy for flowing fluids.
    • Equation: P + ½ρv² + ρgh = Constant
      • P: Static pressure
      • ½ρv²: Dynamic pressure (Kinetic energy per unit volume)
      • ρgh: Hydrostatic pressure head (Potential energy per unit volume)
  • Assumptions: Fluid is ideal (non-viscous, incompressible), flow is steady (streamline), flow is irrotational.
  • Applications:
    • Venturi-meter: Measures flow speed of incompressible fluids. Uses the principle that pressure decreases where velocity increases in a constricted tube.
    • Atomizers/Sprayers: High-speed air blown over a tube creates low pressure, drawing liquid up.
    • Aerofoil Lift (Airplane Wing): Wing shape makes air travel faster over the top surface than the bottom. This creates lower pressure on top, resulting in an upward lift force.
    • Magnus Effect: Lift force on a spinning ball (e.g., curveball in baseball, swing in cricket) due to pressure difference caused by varying air speeds around the spinning surface.

5. Viscosity

  • Definition: The property of a fluid by virtue of which it opposes relative motion between its different layers. It's essentially internal friction in fluids.
  • Cause: Cohesive forces between fluid molecules. Stronger in liquids than gases. Decreases with temperature for liquids, increases for gases.
  • Coefficient of Viscosity (η): A measure of a fluid's resistance to flow.
    • Formula (Newton's Law of Viscosity): F = -ηA (dv/dx)
      • F: Viscous force between layers
      • η: Coefficient of viscosity
      • A: Area of the layers in contact
      • dv/dx: Velocity gradient (rate of change of velocity with distance perpendicular to flow)
  • Unit: SI unit is Pascal-second (Pa·s) or Poiseuille (Pl). CGS unit is poise (1 poise = 0.1 Pa·s).
  • Dimension: [ML⁻¹T⁻¹].
  • Stoke's Law: The viscous drag force (F) experienced by a small sphere of radius 'r' moving with a velocity 'v' through a fluid of viscosity 'η'.
    • Formula: F = 6πηrv
    • Conditions: Flow must be laminar, fluid must be homogeneous and infinite in extent, sphere must be smooth and rigid.
  • Terminal Velocity (vt): The constant maximum velocity attained by a body falling through a viscous fluid when the net force (Weight - Buoyant Force - Viscous Drag) becomes zero.
    • Formula (for a sphere): vt = [2r²(ρ - σ)g] / 9η
      • r: radius of the sphere
      • ρ: density of the sphere's material
      • σ: density of the fluid
      • η: coefficient of viscosity of the fluid
      • g: acceleration due to gravity
  • Reynolds Number (Re): A dimensionless number that predicts the flow pattern (laminar or turbulent).
    • Formula: Re = ρvd / η
      • ρ: density of the fluid
      • v: characteristic velocity of the fluid
      • d: characteristic linear dimension (e.g., diameter of the pipe)
      • η: dynamic viscosity of the fluid
    • Significance:
      • Re < 1000 (approx): Flow is typically laminar/streamline.
      • Re > 2000 (approx): Flow is typically turbulent.
      • 1000 < Re < 2000: Flow is unstable, may transition between laminar and turbulent.

6. Surface Tension

  • Definition: The property of the surface of a liquid that allows it to resist an external force, due to the cohesive nature of its molecules. The liquid surface behaves like a stretched elastic membrane.
  • Cause: Net inward cohesive force on molecules at the surface compared to molecules in the bulk.
  • Surface Tension (S or T): Defined as the force per unit length acting perpendicular to an imaginary line drawn on the liquid surface.
    • Formula: S = F / L
  • Unit: N/m or J/m².
  • Dimension: [MT⁻²].
  • Surface Energy: The potential energy per unit area of the surface film. Numerically equal to surface tension.
    • Formula: S = W / ΔA (Work done to increase the surface area by ΔA).
  • Angle of Contact (θ): The angle between the tangent to the liquid surface at the point of contact and the solid surface inside the liquid.
    • Acute angle (θ < 90°): Liquid wets the solid (e.g., water and clean glass). Adhesive forces > Cohesive forces. Meniscus is concave.
    • Obtuse angle (θ > 90°): Liquid does not wet the solid (e.g., mercury and glass). Cohesive forces > Adhesive forces. Meniscus is convex.
    • θ = 90°: Liquid surface is horizontal.
    • θ = 0°: Perfect wetting.
  • Excess Pressure: Pressure inside a curved liquid surface is different from the pressure outside.
    • Inside a Liquid Drop: ΔP = P_inside - P_outside = 2S / R (R = radius of drop)
    • Inside an Air Bubble in a Liquid: ΔP = 2S / R
    • Inside a Soap Bubble (has two surfaces): ΔP = 4S / R
  • Capillarity (Capillary Action): The phenomenon of rise or fall of a liquid in a narrow tube (capillary tube) dipped into the liquid.
    • Cause: Combined effect of surface tension (cohesion) and adhesion between the liquid and the tube wall.
    • Capillary Rise: Occurs when adhesive forces > cohesive forces (e.g., water in glass tube). Angle of contact is acute.
    • Capillary Fall: Occurs when cohesive forces > adhesive forces (e.g., mercury in glass tube). Angle of contact is obtuse.
    • Ascent Formula: The height 'h' to which a liquid rises (or falls) in a capillary tube of radius 'r' is given by:
      • h = (2S cosθ) / (rρg)
      • S: surface tension, θ: angle of contact, r: radius of capillary tube, ρ: density of liquid, g: acceleration due to gravity.
      • If θ > 90°, cosθ is negative, hence 'h' is negative, indicating a fall.
  • Applications of Surface Tension: Detergent action (lowers surface tension of water), formation of drops and bubbles, floating of needle on water, waterproofing.

Multiple Choice Questions (MCQs)

  1. Pascal's law states that pressure in a fluid at rest is the same at all points:
    a) If they are at the same depth.
    b) In a horizontal plane.
    c) In a vertical line.
    d) Regardless of their position.

  2. A hydraulic lift is designed to lift heavy objects using a small force. This is based on:
    a) Bernoulli's Principle
    b) Archimedes' Principle
    c) Pascal's Law
    d) Stoke's Law

  3. According to the equation of continuity (A₁v₁ = A₂v₂), when water flowing in a broader pipe enters a narrower pipe, its speed:
    a) Increases
    b) Decreases
    c) Remains the same
    d) Becomes zero

  4. Bernoulli's principle is a consequence of the conservation of:
    a) Mass
    b) Linear Momentum
    c) Energy
    d) Angular Momentum

  5. An airplane wing is designed to generate lift. This happens because the air speed is:
    a) Higher over the top surface, resulting in lower pressure on top.
    b) Lower over the top surface, resulting in higher pressure on top.
    c) Higher over the bottom surface, resulting in lower pressure at the bottom.
    d) The same on both surfaces, lift is due to engine thrust only.

  6. The SI unit of the coefficient of viscosity (η) is:
    a) N/m²
    b) J/s
    c) Pa·s
    d) N·m

  7. A small spherical ball falling through a viscous fluid attains a constant velocity called terminal velocity. At terminal velocity, the net force on the ball is:
    a) Equal to its weight
    b) Equal to the buoyant force
    c) Equal to the viscous drag
    d) Zero

  8. Surface tension of a liquid is due to:
    a) Gravitational force between molecules
    b) Electrical force between molecules
    c) Adhesive force between molecules
    d) Cohesive force between molecules

  9. The excess pressure inside a soap bubble of radius R and surface tension S is:
    a) 2S/R
    b) 4S/R
    c) S/R
    d) S/2R

  10. Water rises in a capillary tube whereas mercury falls in the same tube. This is because:
    a) The density of water is less than mercury.
    b) The surface tension of water is higher than mercury.
    c) The angle of contact is acute for water and obtuse for mercury with glass.
    d) Water is more viscous than mercury.

Answer Key:

  1. a) If they are at the same depth. (Pascal's law relates to transmission of pressure, but pressure itself varies with depth hρg). Correction: Pascal's law is about transmission. The question is slightly ambiguous. Pressure is the same at the same depth in a static fluid. Let's rephrase the intended answer based on Pascal's law application: Pressure applied to an enclosed fluid is transmitted undiminished. However, option (a) is the most common interpretation related to pressure distribution in statics. Let's stick with (a) as the likely intended answer in many contexts, although the core of Pascal's law is transmission. Self-correction: Re-reading Pascal's law - it's about the change in pressure being transmitted. Pressure itself is equal at the same depth. So (a) is correct for hydrostatic pressure relation.
  2. c) Pascal's Law
  3. a) Increases
  4. c) Energy
  5. a) Higher over the top surface, resulting in lower pressure on top.
  6. c) Pa·s
  7. d) Zero
  8. d) Cohesive force between molecules
  9. b) 4S/R
  10. c) The angle of contact is acute for water and obtuse for mercury with glass.

Make sure you understand the concepts behind each formula and application. Practice numerical problems based on these formulas as they frequently appear in exams. Good luck with your preparation!

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