HOME

TheInfoList



OR:

In
fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasma (physics), plasmas) and the forces on them. Originally applied to water (hydromechanics), it found applications in a wide range of discipl ...
, the pressure-gradient force is the
force In physics, a force is an influence that can cause an Physical object, object to change its velocity unless counterbalanced by other forces. In mechanics, force makes ideas like 'pushing' or 'pulling' mathematically precise. Because the Magnitu ...
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 eve ...
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 (mathematics), rate of change of the velocity of an object with respect to time. Acceleration is one of several components of kinematics, the study of motion. Accelerations are Euclidean vector, vector ...
according to
Newton's second law of motion Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows: # A body re ...
, 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 In physics, a fluid is a liquid, gas, or other material that may continuously motion, move and Deformation (physics), deform (''flow'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are M ...
is in an
equilibrium state Thermodynamic equilibrium is a notion of thermodynamics with axiomatic status referring to an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable ...
(i.e. there are no
net force In mechanics, the net force is the sum of all the forces acting on an object. For example, if two forces are acting upon an object in opposite directions, and one force is greater than the other, the forces can be replaced with a single force tha ...
s, and no acceleration), the system is referred to as being in
hydrostatic equilibrium In fluid mechanics, hydrostatic equilibrium, also called hydrostatic balance and 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. I ...
. In the case of
atmosphere An atmosphere () is a layer of gases that envelop an astronomical object, held in place by the gravity of the object. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A stellar atmosph ...
s, the pressure-gradient force is balanced by the
gravitational force Newton's law of universal gravitation describes gravity as a force by stating that every particle attracts every other particle in the universe with a force that is proportional to the product of their masses and inversely proportional to the sq ...
, maintaining hydrostatic equilibrium. In
Earth's atmosphere The atmosphere of Earth is composed of a layer of gas mixture that surrounds the Earth's planetary surface (both lands and oceans), known collectively as air, with variable quantities of suspended aerosols and particulates (which create weathe ...
, for example,
air pressure Atmospheric pressure, also known as air pressure or barometric pressure (after the barometer), is the pressure within the atmosphere of Earth. The Standard atmosphere (unit), standard atmosphere (symbol: atm) is a unit of pressure defined as , whi ...
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 a phenomenon that occurs when a spin (geometry), spinning Object (physics), object is moving through a fluid. A lift (force), lift force acts on the spinning object and its path may be deflected in a manner not present when ...
is an observable
phenomenon A phenomenon ( phenomena), sometimes spelled phaenomenon, is an observable Event (philosophy), event. The term came into its modern Philosophy, philosophical usage through Immanuel Kant, who contrasted it with the noumenon, which ''cannot'' be ...
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 a ...
moving through a
fluid In physics, a fluid is a liquid, gas, or other material that may continuously motion, move and Deformation (physics), deform (''flow'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are M ...
. 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 \rho, a height dz, and a surface area dA. The mass of the parcel can be expressed as, m = \rho \, dA \, dz. Using Newton's second law, F = m a, we can then examine a pressure difference dP (assumed to be only in the z-direction) to find the resulting force, F = - dP \, dA = \rho a \, dA \, dz. The acceleration resulting from the pressure gradient is then, a = -\frac \frac . 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 P as, \vec = -\frac \vec\nabla P. 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 {{climate-stub