Bernoulli in Action

Bernoulli's equation is energy conservation written for a flowing fluid: p + (1/2) rho v² + rho g h stays constant along a streamline. If the height h barely changes, then speeding up the fluid must drop its pressure, and slowing it down must raise its pressure. That single trade-off explains a surprising range of everyday events, because fluids almost always speed up when they get squeezed into a narrower space and slow down when the space widens.

A Venturi meter uses a pipe that narrows then widens again. Mass conservation (the continuity equation, A1 v1 = A2 v2) forces the fluid to speed up in the narrow throat. Bernoulli's equation then says that faster throat must be at lower pressure than the wide section before it. Measure that pressure drop, and you can solve directly for the throat speed: v = √(2 (delta p) / rho). The same logic explains two ships moving parallel and close together: the water squeezed into the narrow gap between their hulls speeds up, its pressure drops, and the higher pressure on the outer sides of both ships pushes them toward each other. A roof lifts for the same reason: fast wind over the outside drops the pressure there below the pressure of the still air trapped inside, and that pressure difference pushes the roof up and off.

This topic is Bernoulli's equation turned into a toolkit: wherever you can argue that a fluid's speed changes without much change in height, you can argue about its pressure. It connects directly to continuity, which supplies the speed change, and to the pressure-depth and buoyancy ideas earlier in the unit, which handle the height term when it does matter.