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# Bernoulli equation

Demonstration of the Venturi effect, where fluid flow velocity increases upon path constriction; the Venturi effect derives from the Bernoulli equation. Source: Creative Commons
This article has been reviewed by the following Topic Editor: C Michael Hogan

The Bernoulli equation, in fluid mechanics, sometimes called the Bernoulli function, gives the total energy of a fluid:

 This article is written at a definitional level only. Authors wishing to expand this entry are inivited to expand the present treatment, which additions will be peer reviewed prior to publication of any expansion.

B = gz + αp + u2

where g is gravitational acceleration, z is the vertical coordinate, α is the specific volume, p is the pressure and u is the horizontal velocity. The first two terms of this are called the Montgomery potential, and sometimes the Bernoulli equation in the geostrophic approximation. The gradient of this drives the flow in models with z, isopycnal or sigma coordinates in the vertical.

The Bernoulli formalism assumes that a fluid is incompressible and that the mass density of a fluid parcel is invariant. The formalism is named for the Swiss Dutch mathematician Daniel Bernoulli.

• Physical Oceanography Index
• Landau, L.D.; Lifshitz, E.M. (1987) Fluid Mechanics. Course of Theoretical Physics (2nd ed.). Pergamon Press. ISBN 0-7506-2767-0.
• Saunders, P. (1995) The Bernoulli function and flux of energy in the ocean. J. Geophys. Res., 100(C11), 22647-22648, doi:10.1029/95JC02614,

## Citation

Steve Baum (Lead Author);C Michael Hogan (Topic Editor) "Bernoulli equation". In: Encyclopedia of Earth. Eds. Cutler J. Cleveland (Washington, D.C.: Environmental Information Coalition, National Council for Science and the Environment). [First published in the Encyclopedia of Earth March 30, 2010; Last revised Date July 9, 2012; Retrieved May 24, 2013 <http://www.eoearth.org/article/Bernoulli_function>

## The Author

Assistant Research Scientist, Physical Section Department of Oceanography Texas A&M University   ... (Full Bio)