In
fluid mechanics
Fluid mechanics is the branch of physics concerned with the mechanics of fluids ( liquids, gases, and plasmas) and the forces on them.
It has applications in a wide range of disciplines, including mechanical, aerospace, civil, chemical and ...
, the pressure-gradient force is the
force that results when there is a
difference in pressure across a surface. In general, a
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 ...
is a force per unit area, across a surface. A difference in pressure across a surface then implies a difference in force, which can result in an
acceleration
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by t ...
according to
Newton's second law of motion, if there is no additional force to balance it. The resulting force is always directed from the region of higher-pressure to the region of lower-pressure. When a
fluid is in an
equilibrium state
Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermod ...
(i.e. there are no
net force Net Force may refer to:
* Net force, the overall force acting on an object
* ''NetForce'' (film), a 1999 American television film
* Tom Clancy's Net Force, a novel series
* Tom Clancy's Net Force Explorers, a young adult novel series
{{disam ...
s, and no acceleration), the system is referred to as being in
hydrostatic equilibrium
In fluid mechanics, hydrostatic equilibrium (hydrostatic balance, hydrostasy) is the condition of a fluid or plastic solid at rest, which occurs when external forces, such as gravity, are balanced by a pressure-gradient force. In the planetary ...
. In the case of
atmospheres, the pressure-gradient force is balanced by the
gravitational force
In physics, gravity () is a fundamental interaction which causes mutual attraction between all things with mass or energy. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong ...
, maintaining hydrostatic equilibrium. In
Earth's atmosphere
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 fo ...
, for example,
air pressure
Atmospheric pressure, also known as barometric pressure (after the barometer), is the pressure within the atmosphere of Earth. The standard atmosphere (symbol: atm) is a unit of pressure defined as , which is equivalent to 1013.25 millibars ...
decreases at altitudes above Earth's surface, thus providing a pressure-gradient force which counteracts the force of gravity on the atmosphere.
Magnus effect
The
Magnus effect
The Magnus effect is an observable phenomenon commonly associated with a spinning object moving through a fluid. The path of the spinning object is deflected in a manner not present when the object is not spinning. The deflection can be expl ...
is an observable
phenomenon
A phenomenon ( : phenomena) is an observable event. The term came into its modern philosophical usage through Immanuel Kant, who contrasted it with the noumenon, which ''cannot'' be directly observed. Kant was heavily influenced by Gottfried ...
that is commonly associated with a spinning
object
Object may refer to:
General meanings
* Object (philosophy), a thing, being, or concept
** Object (abstract), an object which does not exist at any particular time or place
** Physical object, an identifiable collection of matter
* Goal, an ...
moving through a
fluid. The path of the spinning object is deflected in a manner that is not present when the object is not spinning. The deflection can be explained by the difference in pressure of the fluid on opposite sides of the spinning object. The Magnus effect is dependent on the speed of rotation.
Formalism
Consider a cubic parcel of fluid with a density
, a height
, and a surface area
. The mass of the parcel can be expressed as,
. Using Newton's second law,
, we can then examine a pressure difference
(assumed to be only in the
-direction) to find the resulting force,
.
The acceleration resulting from the pressure gradient is then,
The effects of the pressure gradient are usually expressed in this way, in terms of an acceleration, instead of in terms of a force. We can express the acceleration more precisely, for a general pressure
as,
The direction of the resulting force (acceleration) is thus in the opposite direction of the most rapid increase of pressure.
References
* Roland B. Stull (2000) ''Meteorology for Scientists and Engineers'', Second Edition, Ed. Brooks/Cole, .
Fluid dynamics
Atmospheric dynamics
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