Bernoulli's equation

:See Bernoulli differential equation for an unrelated topic in ordinary differential equations.

Related Topics:
Bernoulli differential equation - Ordinary differential equation

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In fluid dynamics, Bernoulli's equation, derived by Daniel Bernoulli, describes the behavior of a fluid moving along a streamline.

Related Topics:
Fluid dynamics - Daniel Bernoulli - Fluid - Streamline

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: {v^2 over 2}+gh+{p over ho}=mathrm{constant}

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: v = fluid velocity along the streamline

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: g = acceleration due to gravity on Earth

Related Topics:
Acceleration due to gravity - Earth

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: h = height from an arbitrary point in the direction of gravity

Related Topics:
Height - Gravity

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: p = pressure along the streamline

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: ho = fluid density

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These assumptions must be met for the equation to apply:

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• Inviscid flow − viscosity (internal friction) = 0
• Steady flow
• Incompressible flow − $ho$ = constant. (There exists a second form of Bernoulli's equation that is applicable for compressible flow, which makes use of the thermodynamic enthalpy.)
• Generally, the equation applies along a streamline. For irrotational flow, it applies throughout the entire flow field.

The decrease in pressure simultaneous with an increase in velocity, as predicted by the equation, is often called Bernoulli's principle.

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The equation is named for Daniel Bernoulli although it was first presented in the above form by Leonhard Euler.

Related Topics:
Daniel Bernoulli - Leonhard Euler

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Bernoulli's equation: Derivation ►