Physical Sciences

Fluid Mechanics

Intermediate

Bernoulli Equation

P + \frac{1}{2}\rho v^2 + \rho g h = \text{constant}

Along a streamline, pressure, kinetic energy, and potential energy per unit volume sum to a constant.

By Daniel Bernoulli

Physical Sciences

Bernoulli Equation

1738 · Daniel Bernoulli

Classroom Ready

89%

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Story PortalWho discovered this?Discover how Daniel Bernoulli and others shaped this equation.Visual PortalWhat does it look like?See the equation come alive in the Visual Studio.Machine PortalWhere is it used?Explore machines powered by this equation — aircraft wings.Math PortalWhat does it derive from?Trace the mathematical lineage from conservation of energy.Future PortalWhere is it going?Supersonic and compressible corrections

Launch collection — full story, visual, sound & share card

Why it matters: Explains flight, blood flow, plumbing, and weather systems.

Discoverers: Daniel Bernoulli (1738)

What does it mean?

Along a streamline, pressure, kinetic energy, and potential energy per unit volume sum to a constant.

Why should I care?

Explains flight, blood flow, plumbing, and weather systems.

Equation Compass

North — Prerequisites

West — History

Daniel Bernoulli

East — Applications

South — Derivations

Derivation

Variables & Units

Symbol	Name	Unit	Meaning
$P$	Pressure	Pa	Static pressure
$ρ$	Density	kg/m³	Fluid density
$v$	Velocity	m/s	Flow speed
$h$	Height	m	Elevation

Worked Example

Airplane wing: faster air above → lower pressure → lift.

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Sources & further reading

Search Wikipedia Search Wolfram MathWorld Open in Wolfram|Alpha Watch explainers on YouTube

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