Fluids
Core ideas
Fluids exert pressure P = F/A; in a static fluid, pressure increases with depth: P = P₀ + ρgh. Buoyancy follows Archimedes' principle: the buoyant force equals the weight of displaced fluid, F_b = ρ_fluid·V_displaced·g. An object floats when its density is less than the fluid's, displacing a volume whose weight matches its own.
For moving fluids, the continuity equation A₁v₁ = A₂v₂ expresses conservation of mass for incompressible flow: narrower pipe means faster flow. Bernoulli's equation, P + ½ρv² + ρgh = constant, expresses energy conservation along a streamline: faster flow or higher elevation means lower pressure.
Candidates must distinguish gauge pressure from absolute pressure and apply buoyancy with correct displaced volume (submerged portion only).
Traps
- Using the object's full volume as displaced volume when it only partly floats.
- Thinking a submerged object always sinks - density comparison decides.
- Believing faster flow means higher pressure - Bernoulli says the opposite along a streamline.
- Forgetting that pressure depends on depth, not on container shape.
Rule of thumb
For floating objects, set buoyant force equal to weight: ρ_fluid·V_submerged·g = ρ_object·V_total·g. The fraction submerged equals the density ratio.
Worked example
A block of density 600 kg/m³ floats in water (1000 kg/m³). Fraction submerged = 600/1000 = 0.60, so 60% of the block is underwater. In a pipe where the area halves, the speed doubles by continuity, and Bernoulli predicts a pressure drop in the narrow section.