In
atmospheric science
Atmospheric science is the study of the Atmosphere of Earth, Earth's atmosphere and its various inner-working physical processes. Meteorology includes atmospheric chemistry and atmospheric physics with a major focus on weather forecasting. Climat ...
, the pressure gradient (typically of
air
The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing for ...
but more generally of any
fluid
In physics, a fluid is a liquid, gas, or other material that continuously deforms (''flows'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are substances which cannot resist any shear ...
) 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 and e ...
increases the most rapidly around a particular location. The pressure gradient is a dimensional quantity expressed in units of
pascals
The pascal (symbol: Pa) is the unit of pressure in the International System of Units (SI), and is also used to quantify internal pressure, stress, Young's modulus, and ultimate tensile strength. The unit, named after Blaise Pascal, is defined as ...
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 pref ...
(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 gradi ...
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
Petroleum geology is the study of origin, occurrence, movement, accumulation, and exploration of hydrocarbon fuels. It refers to the specific set of geological disciplines that are applied to the search for hydrocarbons (oil exploration).
Sedime ...
and the petrochemical sciences pertaining to
oil well
An oil well is a drillhole boring in Earth that is designed to bring petroleum oil hydrocarbons to the surface. Usually some natural gas is released as associated petroleum gas along with the oil. A well that is designed to produce only gas may ...
s, and more specifically within
hydrostatics
Fluid statics or hydrostatics is the branch of fluid mechanics that studies the condition of the equilibrium of a floating body and submerged body " fluids at hydrostatic equilibrium and the pressure in a fluid, or exerted by a fluid, on an imm ...
, pressure gradients refer to 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 gradi ...
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
The pound per square inch or, more accurately, pound-force per square inch (symbol: lbf/in2; abbreviation: psi) is a unit of pressure or of stress based on avoirdupois units. It is the pressure resulting from a force of one pound-force applied to ...
per
foot
The foot ( : feet) is an anatomical structure found in many vertebrates. It is the terminal portion of a limb which bears weight and allows locomotion. In many animals with feet, the foot is a separate organ at the terminal part of the leg made ...
(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
True vertical depth'is the measurement of a straight line perpendicularly downwards from a horizontal plane.
In the petroleum industry, true vertical depth, abbreviated as TVD, is the measurement from the surface to the bottom of the borehole ...
.
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) an ...
) 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 you ...
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. A s ...
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 Vertical pressure variation is the variation in pressure as a function of elevation. Depending on the fluid in question and the context being referred to, it may also vary significantly in dimensions perpendicular to elevation as well, and these var ...
). The value of the strength (or
norm
Naturally occurring radioactive materials (NORM) and technologically enhanced naturally occurring radioactive materials (TENORM) consist of materials, usually industrial wastes or by-products enriched with radioactive elements found in the envir ...
) 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
Wind is the natural movement of air or other gases relative to a planet's surface. Winds occur on a range of scales, from thunderstorm flows lasting tens of minutes, to local breezes generated by heating of land surfaces and lasting a few hou ...
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
Earth is the third planet from the Sun and the only astronomical object known to harbor life. While large volumes of water can be found throughout the Solar System, only Earth sustains liquid surface water. About 71% of 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 pol ...
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
Meteorology is a branch of the atmospheric sciences (which include atmospheric chemistry and physics) with a major focus on weather forecasting. The study of meteorology dates back millennia, though significant progress in meteorology did not ...
and
climatological
Climatology (from Greek , ''klima'', "place, zone"; and , '' -logia'') or climate science is the scientific study of Earth's climate, typically defined as weather conditions averaged over a period of at least 30 years. This modern field of stud ...
disciplines, including
weather forecasting
Weather forecasting is the application of science and technology forecasting, to predict the conditions of the Earth's atmosphere, atmosphere for a given location and time. People have attempted to predict the weather informally for millennia a ...
. 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
In fluid mechanics, the pressure-gradient force is the force that results when there is a difference in pressure across a surface. In general, a pressure is a force per unit area, across a surface. A difference in pressure across a surface th ...
points from high towards low pressure zones. It is thus oriented in the opposite direction from the pressure gradient itself.
In acoustics
In
acoustics
Acoustics is a branch of physics that deals with the study of mechanical waves in gases, liquids, and solids including topics such as vibration, sound, ultrasound and infrasound. A scientist who works in the field of acoustics is an acoustician ...
, the pressure gradient is proportional to the sound particle acceleration according to
Euler's equation
200px, Leonhard Euler (1707–1783)
In mathematics and physics, many topics are named in honor of Swiss mathematician Leonhard Euler (1707–1783), who made many important discoveries and innovations. Many of these items named after Euler include ...
.
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 the ...
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 med ...
s can induce very large pressure gradients, but these are oscillatory, and often transitory disturbances.
See also
*
Adverse pressure gradient
In fluid dynamics, an adverse pressure gradient is a pressure gradient in which the static pressure increases in the direction of the flow. Mathematically this is expressed as for a flow in the positive -direction.
This is important for boundar ...
*
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 ...
*
Isobar
*
Geopotential height
Geopotential height or geopotential altitude is a vertical coordinate referenced to Earth's mean sea level, an adjustment to geometric height (altitude above mean sea level) that accounts for the variation of gravity with latitude and altitude. Thu ...
*
Geostrophic wind
In atmospheric science, geostrophic flow () is the theoretical wind that would result from an exact balance between the Coriolis force and the pressure gradient force. This condition is called '' geostrophic equilibrium'' or ''geostrophic balanc ...
*
Primitive equations
The primitive equations are a set of nonlinear partial differential equations that are used to approximate global atmospheric flow and are used in most atmospheric models. They consist of three main sets of balance equations:
# A ''continuity equ ...
*
Temperature gradient
A temperature gradient is a physical quantity that describes in which direction and at what rate the temperature changes the most rapidly around a particular location. The temperature gradient is a dimensional quantity expressed in units of degree ...
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 (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, .
External links
IPCC Third Assessment Report
{{Authority control
Atmospheric dynamics
Pressure
Spatial gradient