PRELIMS

05. Pressure and Floatation

1. Pressure

• Definition: Force acting normally on unit area of a surface ( ).
• Characteristics: Scalar quantity; SI unit is pascal (Pa) or .

2. Atmospheric Pressure

• Standard Value: Pressure exerted by a 76 cm mercury column at at latitude at sea level.
  • .
  • .
• Altitude Effects: Atmospheric pressure decreases with height.

Barometer and Weather Forecast

Atmospheric pressure is measured by a Barometer.

• Sudden fall: Storm
• Slow fall: Rain
• Slow rise: Clear weather

Pressure in Liquids and Pascal's Law

• Liquid Pressure:
  • Where , , .
• Pascal's Law:
  1. In a static liquid at equilibrium, pressure is the same at all points at the same horizontal level.
  2. If external pressure is applied to an enclosed fluid, it is transmitted undiminished in every direction.
• Applications: Hydraulic lift, hydraulic press, hydraulic brake.

Pressure's Effect on Melting and Boiling Points

• Melting Point (MP):
  • Increase P, Increase MP: For substances that expand on fusion (e.g., wax).
  • Increase P, Decrease MP: For substances that contract on fusion (e.g., ice).
• Boiling Point (BP):
  • Always increases with the increase in pressure.

Buoyant Force and Archimedes Principle

• Buoyant Force (Upthrust): An upward force exerted by a liquid when a body is immersed in it.
  • Equal to the weight of liquid displaced by the body.
  • Acts at the centre of gravity of the displaced liquid (Centre of Buoyancy).
• Archimedes Principle: When a body is immersed in a liquid, there is an apparent loss in weight, which is equal to the weight of the liquid displaced by it.

Laws of Floatation

A body floats in a liquid if:

1. Relative Density: Density of the body is less than or equal to the density of the liquid.
2. Full Submersion: If densities are equal, the body floats fully submerged in neutral equilibrium.
3. Weight Balance: Weight of the floating body = Weight of the displaced liquid.
4. Alignment: The centre of gravity (CG) of the body and the CG of the displaced liquid must be on the same vertical line.

Centre of Buoyancy and Meta-centre

• Centre of Buoyancy: CG of the liquid displaced by a body.
• Meta-centre: (Not detailed in this Lucent section, but often linked in study notes for stability in floating bodies).

Relative Density / Specific Gravity

• Definition: Ratio of the density of a substance to the density of water (at ); has no units (dimensionless).
• Ice vs. Water: Ice has a lower density than liquid water (RD ), so it floats with about 90% of its volume submerged — this is why icebergs are mostly underwater.

Commonly Confused Pairs

• Thrust vs. Pressure: Thrust is the total force acting normally on a surface (vector, unit: newton); Pressure is thrust per unit area ( , scalar, unit: pascal).
• Density vs. Relative Density: Density has units ( ); Relative density is a dimensionless ratio comparing a substance's density to water's.
• Barometer vs. Manometer: A barometer measures atmospheric pressure; a manometer measures the pressure of a gas/fluid in a closed vessel.

UPSC Relevance

Pressure and Floatation are highly relevant for conceptual Prelims questions.

• Concept Traps: The different effects of pressure on the melting point of ice vs. wax, and how barometric changes predict specific weather patterns.
• Hydrostatics: The principle of undiminished pressure transmission (Pascal's Law) and how it enables heavy lifting (Hydraulic systems).
• Practical Example: The relative density of ice vs. water (why ice floats) and the density of ships (displacing enough water to equal their weight).
• Units: SI pressure unit is the pascal ( ); 1 atm ≈ 1.01 × 10⁵ Pa ≈ 760 mm Hg — conversions between atm/bar/torr are frequently tested.