Manifestations of Bernoulli's Theorem
Simple Explanation
Bernoulli's principle — faster flow means lower pressure — shows up in many familiar situations: an airplane wing's lift, a perfume atomizer's spray, and the Venturi meter used to measure flow speed.
Why Do We Need It?
Recognizing the same underlying principle across such different-looking devices and phenomena is what makes Bernoulli's equation genuinely powerful — one idea explains flight, spray bottles, and industrial flow meters alike.
See It
A wing cross-section with an arrow above it labelled faster air, lower pressure, and an arrow below it labelled slower air, higher pressure, together producing an upward lift force
Formula
Pressure Difference and Lift from Bernoulli's Equation
ΔP = ½ρ(v₁² − v₂²); F_lift = ΔP × A
When fluid moves faster over one surface than another at the same height, Bernoulli's equation predicts a pressure difference between the two sides — pushing toward the faster-moving, lower-pressure side.
- ΔP
- — pressure difference between the two sides, in pascals (Pa)
- v₁, v₂
- — flow speeds on the two sides, in metres per second (m/s)
- F_lift
- — net force from the pressure difference, in newtons (N)
- A
- — surface area the pressure difference acts over, in square metres (m²)
When to use it: Whenever explaining or calculating the force created by a speed difference across two sides of a surface — such as lift on a wing or the pull of an atomizer.
Worked Example
Find the lift force on a wing
Air (ρ=1.2 kg/m³) flows over the top of a wing at 250 m/s and under it at 200 m/s. The wing has area 20 m². Find the lift force.
Why Does This Work?
A wing's curved upper surface forces air to travel faster over the top than underneath. By Bernoulli's equation, that faster-moving air has lower pressure — and the resulting pressure difference between the higher-pressure bottom and lower-pressure top pushes the wing upward.
Real-Life Example
A perfume atomizer
Squeezing the bulb of a perfume atomizer blows air rapidly across the top of a narrow tube dipped into the perfume.
The fast-moving air creates a region of low pressure at the top of the tube — the higher pressure in the perfume bottle below then pushes the liquid up the tube, where it is caught by the airstream and sprayed.
Practice
Air (ρ=1.2 kg/m³) flows over the top of a wing at 100 m/s and under it at 80 m/s. The wing has area 10 m². Find the lift force.
HardCommon mistake
Thinking air takes longer over the curved top so it must be slower — the opposite is true: the top air is forced to move FASTER to keep pace, which is exactly why the pressure there is lower.
Quick Review
- Faster flow ⟹ lower pressure (Bernoulli).
- Wing lift, atomizers, and Venturi meters all use this same principle.
- ΔP=½ρ(v₁²−v₂²), and force = ΔP × area.