Liquids At Rest (Hydrostatics)

Hydrostatics is the study of fluids at rest. This section focuses on how density, relative density, upthrust, and principles of buoyancy govern the behavior of objects in liquids.

1. Density (ρ)

Density is defined as the mass per unit volume of a substance. It is a fundamental property that helps identify materials.

• Formula: Density (ρ) = Mass (m) / Volume (V)
• SI Unit: Kilogram per cubic meter (kg/m³).
• Conversion: 1 g/cm³ = 1000 kg/m³.

2. Relative Density (R.D.)

Relative density (also known as specific gravity) is the ratio of the density of a substance to the density of water at 4°C. Because it is a ratio of similar quantities, it has no units.

• Formula 1: R.D. = Density of substance / Density of water
• Formula 2: R.D. = Weight of substance / Weight of an equal volume of water
• Formula 3: R.D. = Weight in air / (Weight in air - Weight in water)

3. Upthrust (Buoyancy)

Upthrust is the upward force exerted by a fluid on an object immersed in it. It is the reason objects feel lighter in water than in air.

• Upthrust (U) = Real Weight (W_air) - Apparent Weight (W_liquid)
• Factors affecting upthrust: Volume of the object submerged and the density of the liquid.

4. Archimedes' Principle

Archimedes' principle states that when an object is partially or totally immersed in a fluid, it experiences an upward force (upthrust) equal to the weight of the fluid displaced by it.

• Upthrust = Weight of fluid displaced = V × ρ_fluid × g

5. Law of Floatation

The law of floatation states that a floating object displaces its own weight of the fluid in which it floats. For a floating object, the upthrust equals the actual weight of the object.

• Floating Condition: Density of object ≤ Density of liquid.
• Formula: Weight of object = Weight of liquid displaced.

6. Applications

• Hydrometer: An instrument used to measure the relative density of liquids. It operates on the law of floatation (sinks deeper in less dense liquids).
• Ships and Submarines: Ships are hollow to increase volume and upthrust; submarines use ballast tanks to change their average density.
• Hot air balloons: They rise because the hot air inside is less dense than the cool air outside, creating enough upthrust to lift the load.