# Pressure-gradient force

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Pressure-gradient force

The pressure gradient force is not actually a 'force' but the acceleration of air due to pressure difference (a force per unit mass). It is usually responsible for accelerating a parcel of air from a high atmospheric pressure region to a low pressure region, resulting in wind. In meteorology, pressure gradient force refers to the horizontal movement of air according to the equation:

$frac\left\{F_x\right\}\left\{m\right\}=-frac\left\{1\right\}\left\{ ho\right\}frac\left\{dp\right\}\left\{dx\right\}$
$frac\left\{F_y\right\}\left\{m\right\}=-frac\left\{1\right\}\left\{ ho\right\}frac\left\{dp\right\}\left\{dy\right\}$
$frac\left\{F_z\right\}\left\{m\right\}=-frac\left\{1\right\}\left\{ ho\right\}frac\left\{dp\right\}\left\{dz\right\}$

The term $F/m$ is equal to the acceleration $dv/dt$ because this is an expression of Newton's law $F=ma$. $dp/dx$ is the component of the pressure gradient along the x-axis. $ho$ is the mass density and $\left(1/ ho\right)$ shows that as the mass density increases, the acceleration due to the pressure gradient becomes smaller.

The pressure gradient force acts at right angles to isobars in the direction from high to low pressure. The greater the pressure difference over a given horizontal distance, the greater the force and hence the stronger the wind.

The pressure gradient force, however, is not the only force that acts on a moving parcel of air &mdash; if it were, then low and high pressure regions would eventually disappear. Other forces acting on a horizontally moving parcel of air include; surface friction, coriolis force, centrifugal force. In large-scale atmospheric flows, the coriolis force generally balances the pressure gradient force, producing winds blowing largely along the isobars; however, near the surface the friction term is also important, generally giving a resulting net wind direction diagonal to the isobars (with a component blowing towards the low pressure center).

References

* Roland B. Stull (2000) "Meteorology for Scientists and Engineers", Second Edition, Ed. Brooks/Cole, ISBN 0-534-37214-7.

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