Lecture Notes: Pressure in Liquids and Buoyancy

Introduction

• Topics Covered:
  • Calculating pressure in liquids
  • Variation of pressure with depth
  • Determinants of floating or sinking

Pressure in Liquids

• Sources of Pressure:
  • Pressure is mainly due to water molecules colliding with an object.
  • A smaller component is due to the weight of the water above the object.
• Factors Affecting Pressure:
  • Depth: Pressure increases as an object goes deeper due to the increased weight of water above it.
  • Density of the Liquid: Higher density means more mass per unit volume, increasing the pressure.
  • Gravitational Field Strength: Greater gravitational strength increases the weight and thus pressure.

Equation for Pressure in a Liquid

• Formula:
  • Pressure (Pascals) = Depth x Density x Gravitational Field Strength
• Example Calculation:
  • Given: A diver moves from 20m to 90m depth, water density = 1000 kg/m³, gravitational field strength = 9.8 m/s².
  • Pressure at 20m: 20 x 1000 x 9.8 = 196,000 Pascals
  • Pressure at 90m: 90 x 1000 x 9.8 = 882,000 Pascals
  • Pressure Difference: 882,000 - 196,000 = 686,000 Pascals
  • Alternate Calculation: Directly calculate using depth difference (70m) x 1000 x 9.8 = 686,000 Pascals

Buoyancy and Floating/Sinking

• Concept of Upthrust:
  • Surrounding water molecules exert forces on submerged objects from all directions.
  • Greater force from bottom due to greater depth causes an upward resultant force called upthrust.
• Archimedes' Principle:
  • The upthrust on an object submerged in a fluid is equal to the weight of the fluid displaced by the object.
• Floating vs Sinking:
  • Determined by comparison between upthrust and weight.
  • If weight > upthrust, object sinks.
  • If upthrust > weight, object floats.
  • This is directly related to the density of the object relative to the fluid's density. If the object is less dense than the fluid, it will float; if it's more dense, it will sink.
• Role of Density:
  • Objects denser than the liquid (e.g., rocks) will sink.
  • Objects less dense than the liquid (e.g., apples) will float.

Conclusion

• Summary of key points on liquid pressure and buoyancy, including Archimedes' Principle.
• Encouragement to review and apply these concepts in practical scenarios.