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Hydrostatic equilibrium occurs when compression due to gravity is balanced by a pressure gradient which creates a pressure gradient force in the opposite direction. The balance of these two forces is known as the hydrostatic balance. Gravity is a force of attraction that acts between bodies that have mass. ...
The use of water pressure - the Captain Cook Memorial Jet in Lake Burley Griffin, Canberra. ...
The pressure gradient force is the force that is usually responsible for accelerating a parcel of air from a high atmospheric pressure region to a low pressure region, resulting in wind. ...
Mathematical consideration
 If the highlighted volume of gas is not moving, the forces on it upwards must equal the forces downwards For a volume of a fluid which is not in motion, Newton's Laws state that it must have zero net force on it - the forces up must equal the forces down. This force balance is called the hydrostatic balance. Image File history File links Hydrostatic_Equilibrium. ...
Image File history File links Hydrostatic_Equilibrium. ...
Newtons laws of motion are the three scientific laws which Isaac Newton discovered concerning the behaviour of moving bodies. ...
We can split the gas into a large number of cuboid volume elements. By considering just one element, we can work out what happens to the gas as a whole. In anatomy, the cuboid bone is a bone in the foot. ...
There are 3 forces: The force downwards onto the top of the cuboid from the pressure, P, of the fluid above it is, from the definition of pressure, The use of water pressure - the Captain Cook Memorial Jet in Lake Burley Griffin, Canberra. ...
 Similarly, the force on the volume element from the pressure of the fluid below pushing upwards is  In this equation, the minus sign comes from the directon - this force supports the volume element, rather than pull it down (I'm saying positive force acts down, but this doesn't matter).
Finally, the weight of the volume element causes a force downwards. If the density is ρ, the volume is V and the acceleration due to gravity is g, then: Weight is a term of measurement referring to either an objects mass or to the gravitational force acting on the object. ...
The acceleration due to gravity denoted g (also gee) is a non-SI unit of acceleration defined as exactly 9. ...
 We can split volume into the area of the top or bottom, times the height.  By balancing these forces, the total force on the gas is  This is zero if the gas isn't moving. If we divide by A,  Or,  Ptop-Pbottom is a change in pressure, and h is the height of the volume element - a change in the distance above the ground. By saying these changes are infinitesimally small, the equation can be written in differential form. In mathematics, an infinitesimal, or infinitely small number, is a number that is smaller in absolute value than any positive real number. ...
A differential can mean one of several things: Differential (mathematics) Differential (mechanics) Differential signaling is used to carry high speed digital signals. ...
 Density changes with pressure, and gravity changes with height, so the equation would be: 
Applications
Fluids The hydrostatic equilibrium pertains to hydrostatics and the principles of equilibrium of fluids. A hydrostatic balance is a particular balance for weighing substances in water. Hydrostatic balance allows the discovery of their specific gravities. Hydrostatics, also known as fluid statics, is the study of fluids at rest. ...
A subset of the phases of matter, fluids include liquids, gases, plasmas and, to some extent, plastic solids. ...
This article needs to be cleaned up to conform to a higher standard of quality. ...
Relative density (also known as specific gravity) is a measure of the density of a material. ...
Astrophysics Hydrostatic equilibrium is the reason stars don't implode, or explode. In astrophysics, in any given layer of a star, there is a balance between the thermal pressure (outward) and the weight of the material above pressing downward (inward). This balance is called hydrostatic equilibrium. A star is like a balloon. In a balloon, the gas inside the balloon pushes outward and the elastic material supplies just enough inward compression to balance the gas pressure. In the case of a star, the star's internal gravity supplies the inward compression. The isotropic gravitational field compresses the star into the most compact shape possible: a sphere. Spiral Galaxy ESO 269-57 Astrophysics is the branch of astronomy that deals with the physics of the universe, including the physical properties (luminosity, density, temperature and chemical composition) of celestial objects such as stars, galaxies, and the interstellar medium, as well as their interactions. ...
The Pleiades, an open cluster of stars in the constellation of Taurus. ...
Balloons, like greeting cards or flowers, are given for special occasions. ...
Isotropic means independent of direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. ...
A sphere (< Greek σφαίÏα) is a perfectly symmetrical geometrical object. ...
Note however that a star becomes a sphere only in the ideal case where only its own self-gravity is involved. In real situations there are other forces at play that alter the outcome, most notably centrifugal force from a star's rotation. A rotating star becomes an oblate spheroid when in hydrostatic equilibrium. An extreme example of this is the star Vega, which has a rotation period of 12.5 hours and is about 20% fatter at the equator than at the poles because of it. Oblate also refers to a member of the Roman Catholic religious order of the Missionary Oblates of Mary Immaculate, or in some cases to a lay or religious person who has officially associated himself (or herself) with a monastic community such as the Benedictines for reasons of personal enrichment without...
Vega (α Lyr / α Lyrae / Alpha Lyrae) is a white main sequence star approximately 25. ...
If the star has a massive nearby companion object then tidal forces come into play as well, further distorting the star into an ellipsoidal shape. For an example of this see Beta Lyrae. Comet Shoemaker-Levy 9 after breaking up under the influence of Jupiters tidal forces. ...
3D rendering of an ellipsoid In mathematics, an ellipsoid is a type of quadric that is a higher dimensional analogue of an ellipse. ...
Animation showing how the light curve of a contact binary star changes as they orbit Beta Lyrae (β Lyr / β Lyrae) is a star in the constellation of Lyra. ...
The concept of hydrostatic equilibrium has also become important in determining whether an astronomical object is a planet, dwarf planet, or small solar system body. According to the definition of planet enacted by the International Astronomical Union in 2006, planets and dwarf planets are objects that have sufficient gravity to overcome their own rigidity and assume hydrostatic equilibrium. Since the terrestrial planets and dwarf planets have rough surfaces and so are not perfectly in equilibrium this definition evidently has some flexibility, but as of yet a specific means of quantifying an object's shape by this standard has not been announced. The eight planets and three dwarf planets of the Solar System. ...
Artists impression of Pluto (background) and its satellite Charon (foreground). ...
A small solar system body is a term defined in 2006 by the International Astronomical Union to describe solar system objects which are not planets or dwarf planets: [1] Therefore it refers to these objects that can be further classified based on their orbit or composition: all known minor planets...
The planet Neptune and its moon Triton, taken by Voyager 2 as it entered the outer solar system The definition of planet has proven elusive despite the term being one of the best-known astronomical words. ...
Logo of the IAU The International Astronomical Union (French: Union astronomique internationale) unites national astronomical societies from around the world. ...
A terrestrial planet or telluric planet is a planet which is primarily composed of silicate rocks. ...
Atmospherics Hydrostatic equilibrium can explain why the Earth's atmosphere does not collapse to a very thin layer on the ground. In the atmosphere, the pressure of air decreases with increasing altitude. This causes an upward force, called the pressure gradient force, which tries to smooth over pressure differences. The force of gravity, on the other hand, almost exactly balances this out, keeping the atmosphere bound to the earth and maintaining pressure differences with altitude. Without the pressure gradient force, the atmosphere would collapse to a much thinner shell around the earth, and without the force of gravity, the pressure gradient force would diffuse the atmosphere into space, leaving earth with hardly any atmosphere. Earth (IPA: , often referred to as the Earth, Terra, or Planet Earth) is the third planet in the solar system in terms of distance from the Sun, and the fifth largest. ...
The use of water pressure - the Captain Cook Memorial Jet in Lake Burley Griffin, Canberra. ...
Altitude is the elevation of an object from a known level or datum. ...
The pressure gradient force is the force that is usually responsible for accelerating a parcel of air from a high atmospheric pressure region to a low pressure region, resulting in wind. ...
See also Statics is the branch of physics concerned with physical systems in static equilibrium, that is, in a state where the relative positions of subsystems do not vary over time, or where components and structures are at rest under the action of external forces of equilibrium. ...
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