Bernoulli’s Principle
Watch fluid flow through a Venturi tube and see Bernoulli’s equation in action. Where the pipe narrows, velocity increases and pressure drops — shown by the height of fluid in vertical manometer tubes. Adjust the flow rate and pipe geometry, then explore real-world applications: airplane wings, golf balls with backspin, and spray atomizers.
½ρv² + P + ρgh = const A₁v₁ = A₂v₂ (continuity)
Bernoulli’s equation
In 1738, Daniel Bernoulli published Hydrodynamica, establishing the fundamental relationship between fluid speed and pressure. For an incompressible, inviscid fluid along a streamline: ½ρv² + P + ρgh = constant. This means that where fluid speeds up (higher v), the pressure (P) must decrease to keep the sum constant.
The Venturi effect
A Venturi tube is a pipe that narrows and then widens again. By the continuity equation (A₁v₁ = A₂v₂), fluid must speed up in the narrow section since the same volume passes through a smaller cross-section. By Bernoulli’s principle, this increased velocity means decreased pressure, which is visible in the manometer tubes as a lower fluid level at the constriction.
Airfoil lift
An airplane wing is shaped so air travels faster over the curved upper surface than the flatter lower surface. The faster flow above creates lower pressure, producing a net upward force: lift. This is supplemented by the wing’s angle of attack, which deflects air downward (Newton’s third law). Both effects contribute to flight.
Magnus effect
When a spinning ball moves through air, it drags a boundary layer with it. On one side the spin adds to the airflow speed (low pressure), and on the other it opposes it (high pressure). This pressure difference curves the ball’s trajectory. Golfers exploit this with backspin, which creates lift and extends the ball’s carry distance.
Atomizer (spray bottle)
An atomizer works by blowing air rapidly across the top of a tube dipped in liquid. The fast-moving air creates a low-pressure region (Bernoulli), which draws liquid up the tube. The liquid emerges into the airstream and is broken into a fine mist. Perfume sprays, paint sprayers, and carburetors all use this principle.