Definition · Plain-language
Bernoulli’s principle
Bernoulli’s principle states that, within a steadily flowing fluid, an increase in the fluid’s speed is accompanied by a decrease in its pressure.
The step most authors miss
Doing CRediT right? Don’t stop at the statement.
A CRediT statement credits you inside one paper. The recognition CRediT was built for happens when those roles are tied to you, persistently. Sign in with your ORCID — free — and claim your CRediT contributions on casrai.org, the home of the standard. They become a verified, portable part of your identity, not a line that disappears into one PDF.
Free: claim your contributions, then export a journal-ready CRediT statement, schema.org structured data, JATS XML, CSV or BibTeX — and preview your public profile. A membership publishes that profile publicly and verifies the journals you serve.
Faster flow means lower pressure
Bernoulli’s principle, derived by Daniel Bernoulli in 1738, applies to a fluid (a liquid or gas) flowing steadily. It states that as the speed of the fluid increases, its pressure decreases, and vice versa. The principle is really a statement of energy conservation for a flowing fluid: along a streamline, the sum of the pressure energy, the kinetic energy of motion and the gravitational potential energy stays constant. If the fluid speeds up, its kinetic energy rises, so — height being equal — its pressure energy must fall to keep the total unchanged. It applies to ideal, non-viscous, incompressible flow, and approximates many real flows well.
Everyday demonstrations
The principle shows up in simple experiments. Blow across the top of a sheet of paper and it lifts, because the moving air above it has lower pressure than the still air beneath. Squeeze a hose nozzle and the water speeds up where the opening narrows. A shower curtain billows inward when the water runs, as the fast-moving air and water inside lower the pressure there. Aircraft and Formula One cars use shaped surfaces to set up pressure differences, and a spinning ball curves in flight partly because it drags air faster on one side than the other.
The truth about aeroplane lift
Bernoulli’s principle is famously used to explain how wings generate lift: air moving faster over the curved upper surface has lower pressure than the slower air below, and the pressure difference pushes the wing up. This is correct as far as it goes, but it is an incomplete explanation. Real lift also depends on the wing deflecting air downward — a direct consequence of Newton’s third law — and the popular “equal transit time” story (that air must rejoin at the trailing edge) is simply wrong. Accurate accounts of lift combine Bernoulli’s principle with the downward turning of the airflow.
Key facts
At a glance
- Definition: in a steady fluid flow, higher speed accompanies lower pressure
- Basis: conservation of energy along a streamline
- Conserved sum: pressure energy + kinetic energy + potential energy
- Conditions: ideal (non-viscous, incompressible) steady flow
- Examples: paper lifting when you blow over it; flow speeding up in a narrowing pipe
- Caveat: explains part, not all, of how aircraft wings generate lift
Common misconceptions
What people often get wrong
Often heard: Bernoulli’s principle alone fully explains how aeroplanes fly.
Actually: It explains part of the lift, but real lift also relies on the wing deflecting air downward (Newton’s third law). The “equal transit time” version of the story is incorrect.
Often heard: Higher pressure always means faster-moving fluid.
Actually: The relationship is the reverse: faster flow goes with lower pressure, and slower flow with higher pressure, along a streamline.
Often heard: Bernoulli’s principle is a separate law unrelated to energy.
Actually: It is essentially conservation of energy applied to a flowing fluid; the constant total is the sum of pressure, kinetic and potential energy along a streamline.
Going deeper
