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HSSLIVE Plus One Physics Chapter 10: Mechanical Properties of Fluids Notes

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Mechanical Properties of Fluids examines the physics of liquids and gases at rest and in motion. Students learn about pressure, buoyancy, and Pascal’s principle to understand phenomena from hydraulic systems to floating ships. This chapter introduces fluid dynamics concepts, including the continuity equation and Bernoulli’s principle, explaining everything from airplane lift to blood flow in arteries, connecting theoretical principles to practical applications in engineering and biology.

Plus One Physics Notes – Chapter 10: Mechanical Properties of Fluids

SCERT Kerala Board

Pressure in Fluids

Definition: Pressure is the force acting perpendicular to a surface per unit area.

Formula: P = F/A

  • P = pressure (N/m² or Pascal)
  • F = force (N)
  • A = area (m²)

Characteristics:

  • Pressure in a fluid acts equally in all directions
  • Pressure at a point in a fluid depends on depth, not on shape or size of container

Pascal’s Law

Statement: Pressure applied to an enclosed fluid is transmitted undiminished to every point of the fluid and to the walls of the container.

Applications:

  • Hydraulic lift
  • Hydraulic brakes
  • Hydraulic press

Mechanical Advantage of Hydraulic Systems: MA = F₂/F₁ = A₂/A₁

  • F₁, F₂ = input and output forces
  • A₁, A₂ = input and output areas

Variation of Pressure with Depth

Formula: P = P₀ + ρgh

  • P = pressure at depth h
  • P₀ = atmospheric pressure (at surface)
  • ρ = density of fluid
  • g = acceleration due to gravity
  • h = depth below the surface

Pressure difference between two points: ΔP = ρg(h₂ – h₁)

Atmospheric Pressure

Definition: The pressure exerted by the weight of air in the atmosphere.

Standard atmospheric pressure: 1 atm = 1.01 × 10⁵ Pa = 760 mm of Hg

Measurement devices:

  • Mercury barometer
  • Aneroid barometer

Gauge Pressure and Absolute Pressure

Gauge Pressure: The pressure measured relative to atmospheric pressure.

Absolute Pressure: The total pressure including atmospheric pressure.

Relationship: Absolute Pressure = Gauge Pressure + Atmospheric Pressure

Buoyancy and Archimedes’ Principle

Buoyancy: The upward force exerted by a fluid on an object partially or fully immersed in it.

Archimedes’ Principle: When a body is partially or fully immersed in a fluid, it experiences an upward force equal to the weight of the fluid displaced by it.

Buoyant Force: F_B = ρgV

  • ρ = density of fluid
  • g = acceleration due to gravity
  • V = volume of fluid displaced

Conditions for floating and sinking:

  • Object floats when: ρ_object < ρ_fluid
  • Object sinks when: ρ_object > ρ_fluid
  • Object remains suspended when: ρ_object = ρ_fluid

Surface Tension

Definition: The property of a liquid surface to behave like a stretched membrane with tendency to contract.

Formula: Surface tension (T) = Force/Length = F/L

  • SI unit: N/m or J/m²

Molecular explanation: Surface molecules experience net inward attraction, creating tension.

Applications:

  • Formation of drops and bubbles
  • Capillary action
  • Water striders walking on water
  • Cleaning action of detergents

Surface Energy

Definition: The energy required to increase the surface area of a liquid by a unit amount.

Formula: Surface Energy = Surface Tension × Change in Area = T × ΔA

Angle of Contact

Definition: The angle between the tangent to the liquid surface and the solid surface inside the liquid.

For water:

  • With glass: acute angle (< 90°)
  • With wax/oil: obtuse angle (> 90°)

Wetting and non-wetting liquids:

  • Wetting: angle of contact < 90° (e.g., water on clean glass)
  • Non-wetting: angle of contact > 90° (e.g., mercury on glass)

Capillary Rise and Depression

Formula for capillary rise/depression: h = 2T cos θ / (ρgr)

  • h = height of capillary rise/depression
  • T = surface tension
  • θ = angle of contact
  • ρ = density of liquid
  • r = radius of capillary tube

Rise occurs when: θ < 90° (e.g., water in glass tube) Depression occurs when: θ > 90° (e.g., mercury in glass tube)

Viscosity

Definition: The property of a fluid that resists the relative motion between its layers.

Cause: Momentum transfer between fluid molecules moving at different velocities.

Newton’s Law of Viscosity: F/A = η(dv/dx)

  • F/A = tangential force per unit area (shear stress)
  • η = coefficient of viscosity
  • dv/dx = velocity gradient perpendicular to layers

SI unit of viscosity: Pascal-second (Pa·s) or kg/(m·s)

Stokes’ Law: The viscous force acting on a sphere moving through a viscous fluid is: F = 6πηrv

  • η = coefficient of viscosity
  • r = radius of the sphere
  • v = velocity of the sphere

Terminal Velocity

Definition: The constant velocity attained by a body falling through a viscous fluid when the viscous force plus the buoyant force balances the weight.

Formula: v_t = 2r²g(ρ_s – ρ_f)/(9η)

  • v_t = terminal velocity
  • r = radius of the sphere
  • g = acceleration due to gravity
  • ρ_s = density of the sphere
  • ρ_f = density of the fluid
  • η = coefficient of viscosity

Bernoulli’s Principle

Statement: For an ideal fluid in steady flow, the sum of pressure energy, kinetic energy, and potential energy per unit volume remains constant throughout the flow.

Mathematical form: P + ½ρv² + ρgh = constant

  • P = pressure
  • ρ = density of fluid
  • v = fluid velocity
  • g = acceleration due to gravity
  • h = height from reference level

Applications:

  • Aircraft wing lift
  • Venturi meter
  • Atomizers and sprayers
  • Blowing off of roofs in storms

Reynolds Number

Definition: A dimensionless quantity that determines the nature of fluid flow (laminar or turbulent).

Formula: Re = ρvD/η

  • ρ = density of fluid
  • v = fluid velocity
  • D = characteristic linear dimension
  • η = coefficient of viscosity

Flow classification:

  • Re < 2000: Laminar flow
  • 2000 < Re < 4000: Transitional flow
  • Re > 4000: Turbulent flow

Practice Problems

  1. Calculate the pressure at a depth of 10 m in a swimming pool. (Density of water = 1000 kg/m³)
  2. A hydraulic lift has an input piston of area 20 cm² and output piston of area 200 cm². What force must be applied to the input piston to lift a car of mass 1500 kg?
  3. A steel ball of radius 0.5 cm falls through glycerin. Calculate its terminal velocity if the density of steel is 7800 kg/m³ and that of glycerin is 1260 kg/m³. (Viscosity of glycerin = 1.5 Pa·s)

These notes cover the essential concepts of Mechanical Properties of Fluids for Plus One Physics following the SCERT Kerala Board syllabus, presented in a simplified manner for easier understanding.

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