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