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In the case of atmospheres, the pressure-gradient force is balanced by the gravitational force, maintaining hydrostatic equilibrium. In Earth's atmosphere, for example, air pressure decreases at altitudes above Earth's surface, thus providing a pressure-gradient force which counteracts the force of gravity on the atmosphere.
An example of a geostrophic flow in the Northern Hemisphere. A northern-hemisphere gyre in geostrophic balance.Paler water is less dense than dark water, but more dense than air; the outwards pressure gradient is balanced by the 90 degrees-right-of-flow coriolis force.
The horizontal pressure gradient is a two-dimensional vector resulting from the projection of the pressure gradient onto a local horizontal plane. Near the Earth's surface, this horizontal pressure gradient force is directed from higher toward lower pressure. Its particular orientation at any one time and place depends strongly on the weather ...
Any body of arbitrary shape which is immersed, partly or fully, in a fluid will experience the action of a net force in the opposite direction of the local pressure gradient. If this pressure gradient arises from gravity, the net force is in the vertical direction opposite that of the gravitational force. This vertical force is termed buoyancy ...
A simpler case, barotropic flow, allows for density dependence only on pressure, so that the curl of the pressure-gradient force vanishes. Baroclinity is proportional to: which is proportional to the sine of the angle between surfaces of constant pressure and surfaces of constant density.
When the pressure in one part of a physical system is reduced relative to another, the fluid or gas in the higher pressure region will exert a force relative to the region of lowered pressure, referred to as pressure-gradient force. If all gas or fluid is removed the result is a perfect vacuum in which the pressure is zero.
The pressure gradient force causes an acceleration forcing air from regions of high pressure to regions of low pressure. Mathematically, this can be written as: =. The gravitational force accelerates objects at approximately 9.8 m/s 2 directly towards the center of the Earth.
Geophysical sciences such as meteorology often prefer to express the horizontal pressure gradient force as the gradient of geopotential along a constant-pressure surface, because then it has the properties of a conservative force. For example, the primitive equations that weather forecast models solve use hydrostatic pressure as a vertical ...