Everything about Hydrostatic Equilibrium totally explained
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.
Mathematical consideration
For a volume of a fluid which isn't in motion or is in a state of constant 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.
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.
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,
»
Thus, hydrostatic balance can be regarded as a particularly simple equilibrium solution of the Navier-Stokes equations.
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.
Astrophysics
Hydrostatic equilibrium is the reason stars don't implode, or explode. In
astrophysics, in any given layer of a
star, there's 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 Earth's atmospheric pressure plus the elastic material supply 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.
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.
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.
It is also important for the
intracluster medium, where it restricts the amount of gas that can be present in the core of a
cluster of galaxies.
Planetary geology
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 adopted 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 (and likewise the larger
satellites, like the
Moon and
Io) have rough surfaces and so are not in perfect equilibrium, this definition evidently has some flexibility, but as of yet a specific means of quantifying an object's shape by this standard hasn't been announced. The amount of leeway accorded the definition could affect the classification of the asteroid
Vesta, which appears to have solidified while in hydrostatic equilibrium but to have subsequently been significantly deformed by a large impact.
Atmospherics
Hydrostatic equilibrium can explain why the
Earth's atmosphere doesn't 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.
Further Information
Get more info on 'Hydrostatic Equilibrium'.
|
External Link Exchanges
Do you know how hard it is to get a link from a large encyclopaedia? Well we're different and will prove it. To get a link from us just add the following HTML to your site on a relevant page:
<a href="http://hydrostatic_equilibrium.totallyexplained.com">Hydrostatic equilibrium Totally Explained</a>
Then simply click through this link from your web page. Our crawlers will verify your link, extract the title of your web page and instantly add a link back to it. If you like you can remove the words Totally Explained and embed the link in article text.
As long as your link remains in place, we'll keep our link to you right here. Please play fair - our crawlers are watching. Your site must be closely related to this one's topic. Any kind of spamming, dubious practises or removing the link will result in your link from us being dropped and, potentially, your whole site being banned. |
