Pressure in Liquids and References

Chapter 2: Pressure

2.1 PRESSURE IN LIQUIDS

  • Understanding Pressure in Liquids:

    • A liquid in a container exerts pressure due to its weight acting on the surface of objects submerged in it.

    • Formula derivation for the pressure in a liquid:

    • Pressure (P) = Force (F) / Area (A)

    • Given that Pressure (P) = Density (ρ) * Gravity (g) * Height (h), where:

    • Density (ρ) = mass per unit volume

    • Gravity (g) = acceleration due to gravity (approximately 9.81 m/s²)

    • Height (h) = depth of the liquid column above the point of measurement.

  • Characteristics of Pressure in Liquids:

    • Pressure does not depend on:

    • Shape of the container

    • Size of the container

    • Surface area acting upon

  • Container Example:

    • If a container has base area A filled to depth h with a liquid of density ρ:

    • Volume, V = A * h

    • Mass, m = ρ * V = ρ * (A * h)

    • Weight, W = mg = ρ * A * h * g

    • Force (F) on base = W = ρ * A * h * g

    • Pressure, P = F/A = (ρ * A * h * g) / A = ρ * h * g

  • Depth Relationship:

    • Pressure in a liquid is directly proportional to depth: P ∝ h

    • Higher depth results in higher pressure, e.g., water pressure increases with depth.

  • Relating Density to Pressure:

    • The pressure at the same height in different liquids depends on the density (ρ).

    • Example: If the density of sea water is 1150 kg/m³, then pressure at 40m depth:

    • P = ρ * h * g = 1150 * 40 * 9.81 = 451260 Pa

2.2 ATMOSPHERIC PRESSURE

  • Definition: Atmospheric pressure is caused by the weight of air above a given surface.

  • Unit of Measurement:

    • Standard atmospheric pressure = 1.03 × 10⁵ Pa

    • Also defined as 760 mmHg.

  • Characteristics of Atmospheric Pressure:

    1. Decreases with altitude (density of air decreases at higher elevations).

    2. Acts equally in all directions.

    3. Independent of the surface area of an object; depends only on height above sea level.

  • Measurement:

    • Mercury Barometer: Uses a tube filled with mercury placed upside down in a mercury reservoir; the mercury height is stable at 760 mm at sea level, indicating standard atmospheric pressure.

    • Observation: The height of the mercury changes with atmospheric pressure. Increased pressure raises the mercury level; decreased pressure lowers it.

  • Applications of Atmospheric Pressure:

    • Influence on weather, hydration, and adaptability in extreme conditions.

2.3 GAS PRESSURE

  • Gas Pressure Measurement Methods:

    1. Bourdon Gauge: Curved tube that straightens under gas pressure, moving a pointer on a scale.

    2. Manometer: Measures gas pressure differences using liquid columns.

  • Pascal's Principle:

    • States that pressure applied to an enclosed fluid transmits uniformly throughout the fluid.

    • Applications in hydraulic systems where small forces can generate larger forces via pressure transmission.

2.4 ARCHIMEDE'S PRINCIPLE

  • Buoyant Force:

    • Buried force resulting from an object being submerged in a fluid, measured by the volume of fluid displaced.

    • Expresses that the upward buoyant force is equal to the weight of fluid displaced.

  • Equations:

    • Buoyant Force: FB = ρ * V * g, where V is the volume of displaced fluid.

    • Apparent loss of weight: Wapparent = W - Fb

  • Applications of Archimede's Principle:

    • Explains why ships float while small heavy objects sink; high displacement leads to larger buoyant forces.

    • Hot air balloons rise as the buoyancy of hot air exceeds their weight.

    • Submarines adjust buoyancy through ballast tanks to sink or float.

  • Hydrometer: Measures the relative density of liquids based on buoyancy.

2.5 BERNOUlli'S PRINCIPLE

  • Bernoulli's Principle: Pressure decreases as fluid speed increases.

    • Example: High-speed air flow over an aerofoil creates lift on an airplane's wings.

  • Applications:

    • Explains principles behind carburetors, Bunsen burners, and various sports dynamics.

    • Critical for understanding dynamics in aviation and underwater vehicles.

  • Real-Life Examples:

    • Effect of passing trains on pedestrians due to rapid air movement, impacting perceived pressure.

    • Water dynamics between fast-moving boats, risking collision due to pressure differences.

These notes summarize key concepts and formulas related to pressure in liquids, atmospheric pressure, gas pressure, buoyant forces, and Bernoulli's Principle, substantiated with real-world examples and applications, guiding in-depth understanding.