Bernoulli's Principle

What is it?

Bernoulli’s principle says that along a stream of moving fluid, where the fluid moves faster, its pressure is lower, and where it slows down, its pressure rises.^[1]

The full version, Bernoulli’s equation, links three quantities along a streamline (pressure, speed and height) and says their combined total stays constant:^[1]

p + ½ρv² + ρgh = constant

Here p is the pressure, ρ (rho) the fluid’s density, v its speed, g the acceleration due to gravity and h the height. The equation is really a statement of conservation of energy for a flowing fluid.^[1]

When does it apply?

The simple form describes an idealised fluid: one that can’t be compressed, has no internal friction, and flows steadily.^[1] Real flows are more complicated, and the full details of how an object makes lift involve conserving mass, momentum and energy all at once.^[2]

Where you see it

• Measuring speed. A Pitot tube compares pressures in a flow to work out how fast the fluid is moving.^[1]
• Entrainment. A fast jet of fluid has low pressure, so it pulls surrounding material along with it, as in atomizers and Bunsen burners.^[1]
• Wings. As the air’s speed changes around a wing, its pressure changes too, and the pressures added up over the wing give lift.^[2]

Bernoulli or Newton?

People often argue about whether lift comes from “Bernoulli” (pressure differences) or “Newton” (the wing turns air downward, so the air pushes the wing up). Both are correct when applied properly. They are two descriptions of the same flow, and adding up either the pressures or the change in the air’s motion gives the same force. The arguments usually come from oversimplified versions, such as the incorrect “equal transit time” explanation.^[2]