Fast flow, low pressure
Bernoulli's principle states that in a steadily flowing fluid, regions where the fluid moves faster have lower pressure, and regions where it moves slower have higher pressure. This is a consequence of the conservation of energy in a moving fluid.
Key formula / 关键公式
The idea in words: higher fluid speed → lower pressure.
Simplified Bernoulli relation: P + ½ρv² = constant (at the same height)
where P = pressure, ρ = fluid density, v = fluid speed.
Everyday applications
- Aeroplane wing (aerofoil): air moves faster over the curved top, so lower pressure above lifts the wing.
- Bunsen burner / spray: fast air or gas flow creates low pressure that draws in another fluid.
- Curved ball flight: different air speeds on each side create a sideways pressure difference.
Worked example / 例题
Air flows over the top of a wing at 120 m s⁻² and under it at 100 m s⁻¹ (ρ = 1.2 kg m⁻³). Estimate the pressure difference using ½ρ(vtop² − vbottom²).
= ½ × 1.2 × (120² − 100²) = ½ × 1.2 × (14 400 − 10 000) = ½ × 1.2 × 4400 = 2640 Pa lower on top, giving lift.
Worked example / 例题
Two sheets of paper hang side by side. When you blow air between them, they move together. Why?
The fast-moving air between them has lower pressure, so the higher outside pressure pushes them inward.
Remember / 记住
- Faster fluid flow → lower pressure.
- Aeroplane lift comes from lower pressure above the wing.
- Bernoulli's principle follows from conservation of energy in a fluid.