In atmospheric science, the pressure gradient (typically of air but more generally of any fluid) is a physical quantity that describes in which direction and at what rate the

pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country a ...

increases the most rapidly around a particular location. The pressure gradient is a dimensional quantity expressed in units of pascals per

metre The metre ( British spelling) or meter ( American spelling; see spelling differences) (from the French unit , from the Greek noun , "measure"), symbol m, is the primary unit of length in the International System of Units (SI), though its p ...

(Pa/m). Mathematically, it is the

gradient In vector calculus, the gradient of a scalar-valued differentiable function of several variables is the vector field (or vector-valued function) \nabla f whose value at a point p is the "direction and rate of fastest increase". If the gr ...

of pressure as a function of position. The negative gradient of pressure is known as the

force density In fluid mechanics, the force density is the negative gradient of pressure. It has the physical dimensions of force per unit volume. Force density is a vector field representing the flux density of the hydrostatic force within the bulk of a ...

. In petroleum geology and the petrochemical sciences pertaining to oil wells, and more specifically within hydrostatics, pressure gradients refer to the

of vertical pressure in a column of fluid within a

wellbore A borehole is a narrow shaft bored in the ground, either vertically or horizontally. A borehole may be constructed for many different purposes, including the extraction of water ( drilled water well and tube well), other liquids (such as petrole ...

and are generally expressed in pounds per square inch per foot (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 to the vertical pressure of any point within its column and the pressure gradient for any given true vertical depth.

Physical interpretation

The concept of a pressure gradient is a ''local'' characterisation of the air (more generally of the fluid under investigation). The pressure gradient is defined only at these spatial scales at which pressure (more generally

fluid dynamics In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids—liquids and gases. It has several subdisciplines, including '' aerodynamics'' (the study of air and other gases in motion) ...

) itself is defined. Within

planet A planet is a large, rounded astronomical body that is neither a star nor its remnant. The best available theory of planet formation is the nebular hypothesis, which posits that an interstellar cloud collapses out of a nebula to create a ...

ary

atmosphere An atmosphere () is a layer of gas or layers of gases that envelop a planet, and is held in place by the gravity of the planetary body. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. ...

s (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 The troposphere is the first and lowest layer of the atmosphere of the Earth, and contains 75% of the total mass of the planetary atmosphere, 99% of the total mass of water vapour and aerosols, and is where most weather phenomena occur. From ...

is typically of the order of 9 Pa/m (or 90 hPa/km). The pressure gradient often has a small but critical horizontal component, which is largely responsible for wind circulation in the atmosphere. 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 situation. At mid-

latitude In geography, latitude is a coordinate that specifies the north– south position of a point on the surface of the Earth or another celestial body. Latitude is given as an angle that ranges from –90° at the south pole to 90° at the north po ...

s, 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

Interpreting differences in air pressure between different locations is a fundamental component of many meteorological and climatological disciplines, including weather forecasting. 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.

In acoustics

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

Sound In physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the ''reception'' of such waves and their ''perception'' by ...

waves and

shock wave In physics, a shock wave (also spelled shockwave), or shock, is a type of propagating disturbance that moves faster than the local speed of sound in the medium. Like an ordinary wave, a shock wave carries energy and can propagate through a me ...

s can induce very large pressure gradients, but these are oscillatory, and often transitory disturbances.

Citations

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 Joost Alois Businger (born 29 March 1924) is a Dutch-American meteorologist. He is an emeritus professor at the University of Washington. Businger is best known for his work on atmospheric boundary layer (ABL). Career Businger was born in Haarlem, ...

(1980) ''An Introduction to Atmospheric Physics'', Second Edition, Academic Press, International Geophysics Series, Volume 25, . * John S. Wallace and Peter V. Hobbs (2006) ''Atmospheric Science: An Introductory Survey'', Second Edition, Academic Press, International Geophysics Series, .

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