Сұйықтар мен қысым күштерінің тепе-теңдігі

State of balance between external forces on a fluid and internal pressure gradient

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 physics of Earth, the pressure gradient force prevents gravity from collapsing the planetary atmosphere into a thin, dense shell, whereas gravity prevents the pressure gradient force from diffusing the atmosphere into outer space. In general, it is what causes objects in space to be spherical. Hydrostatic equilibrium is the distinguishing criterion between dwarf planets and small solar system bodies, and features in astrophysics and planetary geology. Said qualification of equilibrium indicates that the shape of the object is symmetrically rounded, mostly due to rotation, into an ellipsoid, where any irregular surface features are consequent to a relatively thin solid crust. In addition to the Sun, there are a dozen or so equilibrium objects confirmed to exist in the Solar System.

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. This equilibrium is strictly applicable when an ideal fluid is in steady horizontal laminar flow, and when any fluid is at rest or in vertical motion at constant speed. It can also be a satisfactory approximation when flow speeds are low enough that acceleration is negligible.

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, one defining characteristic of planets and dwarf planets is that they are objects that have sufficient gravity to overcome their own rigidity and assume hydrostatic equilibrium. Such a body will often have the differentiated interior and geology of a world (a planemo), though near hydrostatic or formerly hydrostatic bodies such as the proto planet 4 Vesta may also be differentiated and some hydrostatic bodies (notably Callisto) have not thoroughly differentiated since their formation. Often the equilibrium shape is an oblate spheroid, as is the case with Earth. However, in the cases of moons in synchronous orbit, nearly unidirectional tidal forces create a scalene ellipsoid. Also, the purported dwarf planet is scalene due to its rapid rotation, though it may not currently be in equilibrium. Icy objects were previously believed to need less mass to attain hydrostatic equilibrium than rocky objects. The smallest object that appears to have an equilibrium shape is the icy moon Mimas at 396 km, whereas the largest icy object known to have an obviously non equilibrium shape is the icy moon Proteus at 420 km, and the largest rocky bodies in an obviously non equilibrium shape are the asteroids Pallas and Vesta at about 520 km. However, Mimas is not actually in hydrostatic equilibrium for its current rotation. The smallest body confirmed to be in hydrostatic equilibrium is the dwarf planet Ceres, which is icy, at 945 km, whereas the largest known body to have a noticeable deviation from hydrostatic equilibrium is Iapetus being made of mostly permeable ice and almost no rock. At 1,469 km Iapetus is neither spherical nor ellipsoid. Instead, it is rather in a strange walnut like shape due to its unique equatorial ridge. Some icy bodies may be in equilibrium at least partly due to a subsurface ocean, which is not the definition of equilibrium used by the IAU (gravity overcoming internal rigid body forces). Even larger bodies deviate from hydrostatic equilibrium, although they are ellipsoidal: examples are Earth's Moon at 3,474 km (mostly rock), and the planet Mercury at 4,880 km (mostly metal). In 2024, Kiss et al. found that has an ellipsoidal shape incompatible with hydrostatic equilibrium for its current spin. They hypothesised that Quaoar originally had a rapid rotation and was in hydrostatic equilibrium, but that its shape became "frozen in" and did not change as it spun down due to tidal forces from its moon Weywot. If so, this would resemble the situation of Iapetus, which is too oblate for its current spin. Iapetus is generally still considered a planetary mass moon nonetheless, though not always. Solid bodies have irregular surfaces, but local irregularities may be consistent with global equilibrium. For example, the massive base of the tallest mountain on Earth, Mauna Kea, has deformed and depressed the level of the surrounding crust, so that the overall distribution of mass approaches equilibrium.

In the atmosphere, the pressure of the air decreases with increasing altitude. This pressure difference causes an upward force called the pressure gradient force. The force of gravity balances this out, keeping the atmosphere bound to Earth and maintaining pressure differences with altitude.