Lesson 1 · 16 min
Fluids
Pressure, buoyancy, and Bernoulli — why pipes neck down and wings remember they are fluids.
Pressure is isotropic
A fluid at rest pushes equally in all directions. Hydrostatic pressure grows with depth: P = P₀ + ρgh. That is why a dam is thick at the base, why a submarine has a collapse depth, and why your ears pop in an elevator of water (a pool).
Buoyancy is the pressure difference between bottom and top of a submerged body. Archimedes: F_b = ρ_fluid V_displaced g. A ship floats because it displaces its own weight in water, not because steel is light.
Bernoulli along a streamline, steady, incompressible, inviscid. Continuity: A₁v₁ = A₂v₂.
Worked example
Hose nozzle
- Given: Supply speed 1.2 m/s in a 25 mm hose
- Given: nozzle 10 mm
- Given: same height
Find: Exit speed, and ΔP from Bernoulli
- Continuity: v₂ = v₁ (A₁/A₂) = 1.2 × (25/10)² = 1.2 × 6.25 = 7.5 m/s
- Bernoulli: ΔP = ½ρ(v₂² − v₁²) = 0.5 × 1000 × (56.25 − 1.44)
7.5 m/s at the jet; supply must be ~27 kPa above exit (plus losses).
Check
Water (incompressible) flows from a wide pipe into a narrow one at the same height. In the narrow section