# Pressure gradient

In atmospheric science (meteorology, climatology and related fields), the **pressure gradient** (typically of air, more generally of any fluid) is a physical quantity that describes in which direction and at what rate the pressure increases the most rapidly around a particular location. The pressure gradient is a dimensional quantity expressed in units of pressure per unit length, or Pa/m

Mathematically, it is obtained by applying the del operator to a pressure function of position. The negative gradient of pressure is known as the force density.

In the Petroleum Geology and Petrochemical sciences pertaining to oil wells, and more specifically within Hydrostatic Pressure, pressure gradients refer to the gradient of vertical pressure in a column of fluid within a wellbore generally expressed in psi/ft. this column of fluid is subject to the compound pressure gradient of the overlying fluids. The path and geometry of the column is totally irrelevant, only the vertical depth of the column has any relevance on the vertical pressure of any point within its column and the pressure gradient for any given true vertical depth.

## Physical interpretation

Strictly speaking, the concept of pressure gradient is a *local* characterisation of the air (more generally of the fluid under investigation). The pressure gradient is defined only at those spatial scales at which pressure (more generally fluid dynamics) itself is defined.

Within planetary atmospheres (including the Earth's), the pressure gradient is a vector pointing roughly downwards, because the pressure changes most rapidly vertically, increasing downwards, see vertical pressure variation. The value of the strength (or norm) of the pressure gradient in the troposphere is typically of the order 9 Pa/m (or 90 hPa/km).

The pressure gradient often has a small but critical horizontal component, which is largely responsible for the wind circulation. The **horizontal pressure gradient** is a 2-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 situation. At mid-latitudes, the typical horizontal pressure gradient may take on values of the order of 10^{−2} Pa/m (or 10 Pa/km), although rather higher values occur within meteorological fronts.

## Weather and climate relevance

Differences in air pressure between different locations are critical in weather forecasting and climate. As indicated above, the pressure gradient constitutes one of the main forces acting on the air to make it move as wind. Note that the pressure gradient force points from high towards low pressure zones, it is thus oriented in the opposite direction from the pressure gradient itself.

Sound waves and shock waves are events that can induce very large pressure gradients, but these are often transitory disturbances.

## Pressure gradient in acoustics

In acoustics the pressure gradient is proportional to the sound particle acceleration according to Euler's equation.

## See also

- Gradient
- Force density
- Isobar
- Geopotential height
- Geostrophic wind
- Primitive equations
- Temperature gradient

## References

- Conner A. Perrine (1967)
*The nature and theory of the general circulation of atmosphere*, World Meteorological Organization, Publication No. 218, Geneva, Switzerland. - Robert G. Fleagle and Joost A. Businger (1980)
*An Introduction to Atmospheric Physics*, Second Edition, Academic Press, International Geophysics Series, Volume**25**, ISBN 0-12-260355-9. - John S. Wallace and Peter V. Hobbs (2006)
*Atmospheric Science: An Introductory Survey*, Second Edition, Academic Press, International Geophysics Series, ISBN 0-12-732951-X.