Bernoulli's principle

Bernoulli's principle says that where a smoothly flowing fluid moves faster, its pressure is lower. Blow across the top of a strip of paper and it lifts; feel the tug as a truck rushes past on the motorway; watch a shower curtain billow inward under the running spray. It answers a surprising question: in a moving fluid, how are speed and pressure linked?

Precisely, for an ideal fluid in steady flow, along any single streamline the sum P + (1/2) rho v^2 + rho g h stays constant, where P is the pressure, rho is the density, v is the speed, g is the acceleration due to gravity, and h is the height. This is really the conservation of energy written for a flowing fluid: the three terms are the pressure energy, the kinetic energy per unit volume, and the gravitational potential energy per unit volume. If the height barely changes, then when v goes up the term (1/2) rho v^2 grows, so P must fall to keep the sum fixed, fast flow means low pressure.

Bernoulli's principle helps explain carburettors, atomiser sprays, the curve of a spinning ball, and part of the lift on a wing. But it is one of the most abused ideas in popular science, so honesty matters. It holds only for an ideal fluid along a streamline, with negligible viscosity. The familiar equal-transit-time story for aeroplane lift, that air must meet again at the trailing edge, is simply wrong; real lift is subtler and involves the wing deflecting air downward. Use Bernoulli where its assumptions genuinely hold.