Bernoulli's principle

Definition

The rule that faster-moving fluid exerts lower pressure. It is the key idea behind airplane wings, curveballs, and perfume sprayers.

P+12ρv2+ρgh=constantP + \frac{1}{2}\rho v^2 + \rho g h = \text{constant}

Unit: pascals (Pa) for each term

Technical definition

For steady, incompressible, frictionless flow along a streamline, an increase in fluid speed is accompanied by a decrease in pressure: P + ½ρv² + ρgh = constant. A statement of energy conservation for flowing fluids.

Example

An airplane wing is shaped so air flows faster over the top. By Bernoulli's principle the faster air has lower pressure, and the pressure difference between the wing's underside and top creates lift.

Common confusion

Bernoulli's principle alone does not fully explain wing lift — the popular 'equal transit time' story (air must meet up at the trailing edge) is a myth. Real lift also involves the wing deflecting air downward (Newton's third law). Bernoulli describes the pressure side of the story, not the whole story.