Bernoulli's principle

Bernoulli's principle is the statement, for steady incompressible inviscid flow, that along any single streamline the sum of static pressure, dynamic pressure, and hydrostatic pressure is constant: p + ½ρv² + ρgh = const. It is an energy-conservation argument for fluids: the three terms are pressure energy, kinetic energy, and gravitational potential energy per unit volume.

The practical consequence is counter-intuitive: faster-moving fluid has lower static pressure than slower-moving fluid at the same height. Blow across the top of a piece of paper and the paper lifts because the moving air has lower pressure than the still air underneath. Water through a narrowed pipe speeds up and drops in pressure — the Venturi effect. The principle contributes to airplane lift (alongside Newton's third law via downwash), to the spin of thrown baseballs, and to the suction of a perfume atomiser.

Daniel Bernoulli published the principle in 1738 in Hydrodynamica; Euler derived it rigorously from his equations of motion in 1757.