• Fluid- A substance than can flow and takes the shape of its container where it placed. It includes liquid and gases. It has not define its own shape.
  • Fluid have everywhere around us. Almost 2/3 surface of Earth covered by fluid(water).
  • Solid and liquid has fixed volume.
  • The volume of solid, liquid and gas depend on pressure or stress.
  • The volume of solid and liquid depend on external pressure.
  • The fluid offers that very resistance to shear stress.

PRESSURE(P)-

  • It is a force applied in per unit area on surface.
  • P = F/A
  • Its SI unit is N m-2 and it measured in pascal (Pa) on the name of French scientist Blaise Pascal(1623-1662).
  • Its dimension is [M1L-1T-2].
  • It is scalar quantity.
  • Also pressure has a common unit is atmosphere (atm) which is pressure exerted by atmosphere at sea level(1 atm = 1.013 * 105Pa).

DENSITY(ρ)-

  • It is a mass of abject in per unit volume.
  • ρ = M/V
  • Its SI unit is Kg/m3.
  • Its dimension is [M1L-3T0].
  • It is scalar quantity and always have positive value.
  • Densities of common fluids at STP are in table-
Fluidρ (Kg m-3)
Water1.00 * 103
Sea water1.03 * 103
Air1.29
Oxygen1.43
Hydrogen9.0 * 10-2
Blood 1.06 * 103
Ethyl alcohol 0.806 * 103
Interstellar space~ 10-20

LAW OF PASCAL-

  • This law as on the name of French scientist, Blaise Pascal.
  • Pascal’s Law- It states that pressure applied to a confined fluid is transmitted equally in all directions.

PRESSURE ‘S VARIATION IN DEPTH REGION-

  • Pressure depend on vertical distance(or height) h between top and bottom point of an object which submerge, mass density of fluid p, acceleration due to gravity g.
  • Pressure increases with depth in a fluid. The deeper you go, the more weight of the fluid is above, increasing the pressure.
    • P= P0​ + ρgh, where
      • P= Pressure at depth,
      • P0= Surface pressure,
      • ρ= Density of the fluid,
      • g= Gravitational acceleration and
      • h= Depth of the fluid.

ATMOSPHERIC PRESSURE-

Atmospheric Pressure

  • Definition: Pressure exerted by the weight of the air column above a unit area.
  • Value at Sea Level: Approximately 1.013×105 (1 atm).
  • Measurement:
    • Measured using a mercury barometer.
    • A glass tube filled with mercury is inverted into a mercury trough.
    • Atmospheric pressure balances the mercury column in the tube.
    • Pressure relation: Pa=ρgh, where:
      • ρ: Density of mercury.
      • g: Gravitational acceleration.
      • h: Height of mercury column (about 76 cm at sea level, equivalent to 1 atm).

Units of Pressure

  • Torr: 1 torr=133 Pa.
  • Bar: 1 bar=105 Pa.
  • Commonly used in meteorology and medical fields.

Gauge Pressure

  • Definition: Difference between the pressure of a system and atmospheric pressure.
  • Formula: Gauge Pressure=P−P a, where P is system pressure.

Open Tube Manometer

  • Measures pressure difference using a U-shaped tube filled with liquid (oil for low pressure, mercury for high pressure).
  • Key Point: Pressure at the same horizontal level in the tube is equal.

Hydraulic Machines

  • Principle: Based on Pascal’s Law—external pressure applied to a fluid is transmitted equally in all directions.
  • Applications:
    • 1. Hydraulic Lift:
      • A smaller force applied to a small piston creates a larger force on a bigger piston.
      • Formula: F2 = A2/A1 ​​* F1, where A1​ and A2​ are areas of the small and large pistons, respectively.
    • 2. Hydraulic Brakes:
      • A small force on the brake pedal generates a large braking force by transmitting pressure via brake fluid.

Streamline Flow

  • Definition: Smooth flow of fluid where the velocity of particles remains constant over time at any point.
  • Streamline: Path a fluid particle follows, tangent to the velocity of the particle at any point.
  • Equation of Continuity: Av=constant, where:
    • A: Cross-sectional area.
    • v: Velocity of fluid.
    • Implication: Narrower pipes result in faster flow; wider pipes result in slower flow.

Bernoulli’s Principle

  • Statement: For an incompressible, non-viscous fluid in steady flow:
    • P + ½ ρv2 + ρgh = constant, where
      • P: Pressure energy per unit volume.
      • ½ ​ρv2: Kinetic energy per unit volume.
      • ρgh: Potential energy per unit volume.
  • Assumptions:Fluid is incompressible and non-viscous.
    No energy is lost to friction.
  • Applications:Explains fluid acceleration in narrow pipes and pressure drop in faster-moving fluids.
    Key Insights-
  • Atmospheric pressure decreases with altitude:
    • The density of air and value of ggg decrease with height.
    • Actual atmospheric pressure can vary due to weather conditions.
  • Fluid Density:
    • Liquids: Nearly constant density (treated as incompressible).
    • Gases: Highly variable density with pressure and temperature changes.

1. Speed of Efflux (Torricelli’s Law):

  • Efflux means the outflow of fluid.
  • Torricelli’s Law: The speed of efflux (v1v_1v1​) of a liquid from an open tank is equivalent to the speed of a freely falling body:v1​= (2gh)1/2
    • where h=y2​−y1​, the height of the liquid column above the hole.
  • Derivation Highlights:
    1. Use continuity equation: v1​A1​= v2​A2​.
    2. Apply Bernoulli’s Principle: P + ½ ρv2 + ρgy = constant
    3. If the tank is large (A2>>A1), velocity at the top (v2) can be approximated as zero.
    4. For atmospheric conditions (P= Pa), the formula simplifies to v1​= (2gh)1/2
  • Applications:
    • Rocket propulsion when pressure P>>Pa​​.
    • Water flow analysis from tanks.

2. Dynamic Lift

  • Dynamic lift is the upward force acting on a moving body in a fluid due to pressure differences.
  • Key Examples:
    1. Magnus Effect:
      • Occurs for spinning objects like cricket balls.
      • A spinning ball drags air, causing higher velocity (and lower pressure) above the ball, leading to upward lift.
    2. Airplane Wings (Aerofoil Design):
      • The curved upper surface creates faster airflows than the lower side, leading to pressure differences and upward lift.
  • Formula for Lift in Aircraft Wings:
    • ΔP * A=Weight of Aircraft:
    • Example- Boeing wing lift calculated using ΔP and Bernoulli’s principle.

3. Viscosity

  • Definition: Internal friction between layers of fluid due to relative motion.
  • Coefficient of Viscosity (η):η= Shearing Stress​/Strain Rate= (F/A)​ / (v/l)
  • Units: Pascal-second (Pa*s), Poiseuille (Pl).
  • Dependence:
    • Liquids: Viscosity decreases with temperature.
    • Gases: Viscosity increases with temperature.
  • Laminar Flow: Layers slide smoothly over one another; velocity is maximum at the center of a tube and zero at the walls.

4. Stokes’ Law

  • Viscous Force on a Sphere:F= 6πηav, where a= radius, v= velocity, and η= viscosity.
  • Terminal Velocity (vt​​): When the viscous force, buoyant force, and gravitational force balance: vt​= 2a2(ρ−σ)g​/9η
    • ​where ρ= density of the sphere, σ= density of the fluid.
  • Applications:
    • Rainfall: Raindrops reach a constant terminal velocity due to air resistance.
    • Oil tanks: Determining viscosity by measuring terminal velocity.

Key Formula Summary for Problem-Solving

  1. Speed of Efflux (Torricelli’s Law):
    v1​=(2gh)1/2​
  2. Pressure Difference in Dynamic Lift:
    ΔP=ρ (v22​−v12​​)/2
  3. Viscosity:
    η= F/ A⋅v/l ​
  4. Stokes’ Law:
    F=6πηav
  5. Terminal Velocity:
    vt​= a2(ρ−σ)g / 9η2​

Tips for Competitive Exams

  1. Focus on conceptual clarity of Bernoulli’s principle and its applications.
  2. Practice numerical problems involving pressure difference, speed of efflux, and viscosity.
  3. Remember the dependence of viscosity on temperature for liquids and gases.
  4. Use real-life analogies like airplanes and spinning balls to visualize concepts.

Surface Tension and Related Concepts

Introduction to Surface Tension

  • Surface tension is a property of liquids where the surface acts like a stretched elastic sheet due to cohesive forces between molecules.
  • It explains why:
    • Oil and water don’t mix.
    • Water sticks to us but not to ducks.
    • Mercury forms droplets and doesn’t wet glass, while water spreads on glass.
    • Water rises in a thin tube, defying gravity (capillary action).

Surface Energy

  • Molecules inside a liquid are surrounded by other molecules, creating balanced forces and low energy (negative potential energy).
  • Molecules at the surface are only partially surrounded, leading to higher energy compared to molecules inside.
  • Liquids minimize surface area to reduce surface energy.
Key Points:
  • Surface energy is proportional to the area of the surface.
  • It is approximately half the heat of evaporation for a molecule to move from the bulk to the surface.
  • Surface energy contributes to phenomena like spreading or forming droplets.

Understanding Surface Tension

  • Surface tension (S) is the force per unit length acting along the interface of two substances.
  • It is equivalent to surface energy per unit area.
  • Mathematically:S= F​/2l where F is the force, and l is the length.
  • Surface tension reduces with increasing temperature, as molecular interactions weaken.

Applications and Observations

  1. Shape of Drops and Bubbles
    • Liquid drops and bubbles form spheres to minimize surface area and energy.
    • Inside a drop, the pressure (Pi​) is higher than outside (P0​) due to surface tension: Pi-P0= 2S/r
    • Bubbles have two interfaces, so: Pi-P0= 4S/r
  2. Capillary Action
    • Liquids rise or fall in narrow tubes due to surface tension.
    • The height (h) of the rise is given by: h= 2Scosθ/pga, where-
      • S is Surface tension, θ is Contact angle, ρ is Density, a is Radius of the tube.

Angle of Contact

  • Contact Angle (θ\thetaθ): The angle between the liquid surface and the solid surface at their interface.
    • Acute (θ<90∘): Liquid spreads (e.g., water on glass).
    • Obtuse (θ>90∘): Liquid forms droplets (e.g., water on wax).
  • Equation relating interfacial tensions: Sla​cosθ +Ssl =Ssa​
    • Sla​​ is Liquid-air tension.
    • Ssl​ is Solid-liquid tension.
    • ​Ssa​ is Solid-air tension.

Experimental Measurement of Surface Tension

  • Force Balance Method:
    • A plate is dipped into a liquid, and weights are added to balance the pull due to surface tension.
    • Surface tension (S) is calculated as: S = mg/2l​
    • m: Added mass, g: Gravity, l: Plate length.

Key Phenomena Explained by Surface Tension

  1. Rise of Sap in Plants: Water rises in xylem vessels due to capillary action.
  2. Soap Bubbles: Stable due to balance of internal pressure and surface tension.
  3. Wetting and Non-Wetting:
    • Wetting occurs when the liquid spreads on a solid (e.g., water on clean glass).
    • Non-wetting occurs when the liquid forms droplets (e.g., water on lotus leaves).

Formula Summary

  1. Excess Pressure in a Drop: Pi​−Po= 2S/r
  2. Capillary Rise: h= 2Scosθ/pga​
  3. Surface Tension Measurement: S= mg/sl
  4. Relation Between Interfacial Tensions:Sla​cosθ+Ssl​=Ssa​

Additional Knowledge for Competitive Exams

  • Factors Affecting Surface Tension:
    • Temperature: Surface tension decreases as temperature rises.
    • Impurities: Detergents lower surface tension, aiding cleaning.
  • Practical Applications:
    • Capillary tubes in thermometers.
    • Use of surfactants in detergents and soaps.
    • Water-proofing agents increase the contact angle to prevent wetting.

This simplified breakdown includes essential concepts, explanations, and formulas, aiding competitive exam preparation and practical understanding.

These all are the notes of chapter 1 in physics. And after some time you get important questions and NCERT solutions HERE. *#THANKS FOR VISITING, VISIT AGAIN#* 😊