Nuclear energy policy

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Nuclear_energy_policy 

 

Main article: Nuclear power

Eight German nuclear power reactors (Biblis A and B, Brunsbuettel, Isar 1, Kruemmel, Neckarwestheim 1, Philippsburg 1 and Unterweser) were permanently shutdown on 6 August 2011, following the Fukushima Daiichi Nuclear Disaster in Japan.

Nuclear energy policy is a national and international policy concerning some or all aspects of nuclear energy and the nuclear fuel cycle, such as uranium mining, ore concentration, conversion, enrichment for nuclear fuel, generating electricity by nuclear power, storing and reprocessing spent nuclear fuel, and disposal of radioactive waste. Nuclear energy policies often include the regulation of energy use and standards relating to the nuclear fuel cycle. Other measures include efficiency standards, safety regulations, emission standards, fiscal policies, and legislation on energy trading, transport of nuclear waste and contaminated materials, and their storage. Governments might subsidize nuclear energy and arrange international treaties and trade agreements about the import and export of nuclear technology, electricity, nuclear waste, and uranium.

Since about 2001 the term nuclear renaissance has been used to refer to a possible nuclear power industry revival, but nuclear electricity generation in 2012 was at its lowest level since 1999. Since then it had increased back to 2,653 TWh in 2021, a level last seen in 2006. The share of nuclear power in electricity production however is at a historic low and now below 10% down from a maximum of 17.5% in 1996. Following the March 2011 Fukushima I nuclear accidents, China, Germany, Switzerland, Israel, Malaysia, Thailand, United Kingdom, and the Philippines are reviewing their nuclear power programs. Indonesia and Vietnam still plan to build nuclear power plants. Thirty-one countries operate nuclear power stations, and there are a considerable number of new reactors being built in China, South Korea, India, and Russia. As of June 2011, countries such as Australia, Austria, Denmark, Greece, Ireland, Latvia, Lichtenstein, Luxembourg, Malta, Portugal, Israel, Malaysia, and Norway have no nuclear power stations and remain opposed to nuclear power.

Since nuclear energy and nuclear weapons technologies are closely related, military aspirations can act as a factor in energy policy decisions. The fear of nuclear proliferation influences some international nuclear energy policies.

The global picture

The number of nuclear power plant constructions started each year, from 1954 to 2013. Note the increase in new constructions from 2007 to 2010, before a decline following the 2011 Fukushima Daiichi nuclear disaster.

See also: Nuclear power by country

After 1986's Chernobyl disaster, public fear of nuclear power led to a virtual halt in reactor construction, and several countries decided to phase out nuclear power altogether. However, increasing energy demand was believed to require new sources of electric power, and rising fossil fuel prices coupled with concerns about greenhouse gas emissions (see Climate change mitigation) have sparked heightened interest in nuclear power and predictions of a nuclear renaissance.

In 2004, the largest producer of nuclear energy was the United States with 28% of worldwide capacity, followed by France (18%) and Japan (12%). In 2007, 31 countries operated nuclear power plants. In September 2008 the IAEA projected nuclear power to remain at a 12.4% to 14.4% share of the world's electricity production through 2030.

In 2013, almost two years after Fukushima, according to the IAEA there are 390 operating nuclear generating units throughout the world, more than 10% less than before Fukushima, and exactly the same as in Chernobyl-year 1986. Asia is expected to be the primary growth market for nuclear energy in the foreseeable future, despite continued uncertainty in the energy outlooks for Japan, South Korea, and others in the region. As of 2014, 63% of all reactors under construction globally are in Asia.

Policy issues

See also: Energy policy

Nuclear concerns

Main article: Nuclear power debate

Nuclear accidents and radioactive waste disposal are major concerns. Other concerns include nuclear proliferation, the high cost of nuclear power plants, and nuclear terrorism.

Energy security

For some countries, nuclear power affords energy independence. In the words of the French, "We have no coal, we have no oil, we have no gas, we have no choice." Japan—similarly lacking in indigenous natural resources for power supply—relied on nuclear power for 1/3 of its energy mix prior to the Fukushima nuclear disaster; since March 2011, Japan has sought to offset the loss of nuclear power with increased reliance on imported liquefied natural gas, which has led to the country's first trade deficits in decades. Therefore, the discussion of a future for nuclear energy is intertwined with a discussion of energy security and the use of energy mix, including renewable energy development.

Nuclear power has been relatively unaffected by embargoes, and uranium is mined in "reliable" countries, including Australia and Canada.

Many commentators have criticized Germany's Energiewende policy to shut down its world-class nuclear fleet after the Fukushima disaster and rely instead on renewable energy sources, which in the interim has made them heavily dependent on Russian gas. Responding to Russia's attempt to exploit this dependency by shutting off natural gas supplies, Germany is ramping up coal production, while maintaining two nuclear plants in reserve.

Nuclear energy history and trends

Olkiluoto 3 under construction in 2009. It is the first EPR design, but problems with workmanship and supervision have created costly delays which led to an inquiry by the Finnish nuclear regulator STUK. In December 2012, Areva estimated that the full cost of building the reactor will be about €8.5 billion, or almost three times the original delivery price of €3 billion.

Proponents have long made hopeful projections of the expected growth of nuclear power, but major accidents, and a well funded anti-nuclear lobby have kept costs high and growth much lower. In 1973 and 1974, the International Atomic Energy Agency predicted a worldwide installed nuclear capacity of 3,600 to 5,000 gigawatts by 2000. The IAEA's 1980 projection was for 740 to 1,075 gigawatts of installed capacity by the year 2000. Even after the 1986 Chernobyl disaster, the Nuclear Energy Agency forecasted an installed nuclear capacity of 497 to 646 gigawatts for the year 2000. The actual capacity in 2000 was 356 gigawatts. Moreover, construction costs have often been much higher, and times much longer than projected, failing to meet optimistic projections of “unlimited cheap, clean, and safe electricity.”

Since about 2001 the term nuclear renaissance has been used to refer to a possible nuclear power industry revival, driven by rising fossil fuel prices and new concerns about meeting greenhouse gas emission limits. However, nuclear electricity generation in 2012 was at its lowest level since 1999, and new reactors under construction in Finland and France, which were meant to lead a nuclear renaissance, have been delayed and are running over-budget. China has 32 new reactors under construction, and there are also a considerable number of new reactors being built in South Korea, India, and Russia. At the same time, at least 100 older and smaller reactors will "most probably be closed over the next 10-15 years". So the expanding nuclear programs in Asia are balanced by retirements of aging plants and nuclear reactor phase-outs.

In March 2011 the nuclear emergencies at Japan's Fukushima I Nuclear Power Plant and shutdowns at other nuclear facilities raised questions among some commentators over the future of the renaissance. Platts has reported that "the crisis at Japan's Fukushima nuclear plants has prompted leading energy-consuming countries to review the safety of their existing reactors and cast doubt on the speed and scale of planned expansions around the world". China, Germany, Switzerland, Israel, Malaysia, Thailand, United Kingdom, Italy and the Philippines have reviewed their nuclear power programs. Indonesia and Vietnam still plan to build nuclear power plants. Countries such as Australia, Austria, Denmark, Greece, Ireland, Latvia, Liechtenstein, Luxembourg, Portugal, Israel, Malaysia, New Zealand, and Norway remain opposed to nuclear power. Following the Fukushima I nuclear accidents, the International Energy Agency halved its estimate of additional nuclear generating capacity built by 2035.

Following the Fukushima nuclear disaster, Germany permanently shut down eight of its reactors and pledged to close the rest by 2022. In 2011 Siemens exited the nuclear power sector following the changes to German energy policy, and supported the German government's planned energy transition to renewable energy technologies. The Italians voted overwhelmingly to keep their country non-nuclear. Switzerland and Spain have banned the construction of new reactors. Japan's prime minister called for a dramatic reduction in Japan's reliance on nuclear power. Taiwan's president did the same. Mexico has sidelined construction of 10 reactors in favor of developing natural-gas-fired plants. Belgium decided to phase out its nuclear plants.

China—nuclear power's largest prospective market—suspended approvals of new reactor construction while conducting a lengthy nuclear-safety review. In 2012 a new safety plan for nuclear power was approved by State Council, and full incorporation of International Atomic Energy Agency (IAEA) safety standards became explicit. In the 13th Five-Year Plan from 2016, six to eight nuclear reactors were to be approved each year. A draft of the 14th Five-Year Plan (2021-2025) released in March 2021 showed government plans to reach 70 GWe gross of nuclear capacity by the end of 2025.

Neighboring India, another potential nuclear boom market, has encountered effective local opposition, growing national wariness about foreign nuclear reactors, and a nuclear liability controversy that threatens to prevent new reactor imports. There have been mass protests against the French-backed 9900 MW Jaitapur Nuclear Power Project in Maharashtra and the 2000 MW Koodankulam Nuclear Power Plant in Tamil Nadu. The state government of West Bengal state has also refused permission to a proposed 6000 MW facility near the town of Haripur that intended to host six Russian reactors. In March 2018, the government stated that nuclear capacity would fall well short of its 63 GWe target and that the total nuclear capacity is likely to be about 22.5 GWe by the year 2031.

Following IPCC announcements climate concerns again started to dominate world opinion. With rising oil and gas prices in 2022, many countries are reconsidering nuclear power.

In October 2021 the Japanese cabinet approved the new Plan for Electricity Generation to 2030 prepared by the Agency for Natural Resources and Energy (ANRE) and an advisory committee, following public consultation. The nuclear target for 2030 of 20-22% is unchanged from that in the 2015 plan, but renewables increase greatly to 36-38%, including geothermal and hydro. Hydrogen and ammonia are included at 1%. The plan would require the restart of another ten reactors. Prime minister Fumio Kishida in July 2022 announced that the country should consider building advanced reactors and extending operating licences beyond 60 years.

In March 2022 Belgium delayed its plans to phase out nuclear energy by a decade. The prime minister said that two reactors (Doel 4 and Tihange 3) would continue operating to 2035 to “strengthen our county’s independence from fossil fuels in a turbulent geopolitical environment.” In June Engie said it was seeking financial aid from the government for the continued operation of the two reactors. 

Climate Change and the Energy Transition

Eliminating fossil fuels is essential in solving the climate change crisis. Nuclear power has one of the lowest life-cycle greenhouse gas emissions. Historically, nuclear power has prevented 64 gigatonnes of CO₂-equivalent greenhouse-gas emissions between 1971 and 2009. With a significant amount of renewable energy installed in the 21st century, it has been speculated that tensions between nuclear and renewable national energy development strategies might reduce their effectiveness in terms of climate change mitigation. However, newer studies have refuted this idea. Both nuclear and renewable energy have shown equally effective in the prevention of greenhouse-gas emissions. An effective climate-change mitigation strategy may include both nuclear and renewable energy sources. In 2018 the IPCC provided advice to policymakers giving four illustrative model pathways to limit warming to 1.5 degrees. In each of these pathways nuclear energy generation increased between 98% and 501% over 2010 levels by 2050.

In 2021 the European Union Joint Research Centre issued the results of its study on whether nuclear power generation meets the criteria of its Green Taxonomy. The analyses did not reveal any science-based evidence that nuclear energy does more harm to human health or to the environment than other electricity production technologies already included in the EU Green Taxonomy as activities supporting climate change mitigation. As a result of this assessment, the EU Parliament voted to include nuclear energy in its Green Taxonomy.

Moreover, nuclear energy has such a low carbon footprint that it could power carbon dioxide capture and transformation, resulting in a carbon-negative process. Specifically, various organizations are working across the globe to create designs for small modular reactors, a type of nuclear fission reactor that is smaller than conventional reactors. Some of these companies include ARC Nuclear in Canada, CNEA in Denmark, Areva TA in France, Toshiba and JAERI in Japan, OKB Gidropress in Russia, and OPEN100 and X-energy in the United States.

Policies by territory

Main articles: Nuclear energy policy by country and Nuclear power by country

See also: List of nuclear reactors

Hydrostatic equilibrium

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Hydrostatic_equilibrium

Diagram of a newly formed planet in a state of 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 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.

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.

Mathematical consideration

If the highlighted volume of fluid is not accelerating, the forces on it upwards must equal the forces downwards.

For a hydrostatic fluid on Earth:

${\displaystyle dP=-\rho (P)\cdot g(h)\cdot dh}$

Derivation from force summation

Further information: Mechanical equilibrium

Newton's laws of motion state that a volume of a fluid that is not in motion or that is in a state of constant velocity must have zero net force on it. This means the sum of the forces in a given direction must be opposed by an equal sum of forces in the opposite direction. This force balance is called a hydrostatic equilibrium.

The fluid can be split into a large number of cuboid volume elements; by considering a single element, the action of the fluid can be derived.

There are three 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,

${\displaystyle F_{\text{top}}=-P_{\text{top}}\cdot A}$

Similarly, the force on the volume element from the pressure of the fluid below pushing upwards is

${\displaystyle F_{\text{bottom}}=P_{\text{bottom}}\cdot A}$

Finally, the weight of the volume element causes a force downwards. If the density is ρ, the volume is V and g the standard gravity, then:

${\displaystyle F_{\text{weight}}=-\rho \cdot g\cdot V}$

The volume of this cuboid is equal to the area of the top or bottom, times the height — the formula for finding the volume of a cube.

${\displaystyle F_{\text{weight}}=-\rho \cdot g\cdot A\cdot h}$

By balancing these forces, the total force on the fluid is

${\displaystyle \sum F=F_{\text{bottom}}+F_{\text{top}}+F_{\text{weight}}=P_{\text{bottom}}\cdot A-P_{\text{top}}\cdot A-\rho \cdot g\cdot A\cdot h}$

This sum equals zero if the fluid's velocity is constant. Dividing by A,

${\displaystyle 0=P_{\text{bottom}}-P_{\text{top}}-\rho \cdot g\cdot h}$

Or,

${\displaystyle P_{\text{top}}-P_{\text{bottom}}=-\rho \cdot g\cdot h}$

P_top − P_bottom 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.

${\displaystyle dP=-\rho \cdot g\cdot dh}$

Density changes with pressure, and gravity changes with height, so the equation would be:

${\displaystyle dP=-\rho (P)\cdot g(h)\cdot dh}$

Derivation from Navier–Stokes equations

Note finally that this last equation can be derived by solving the three-dimensional Navier–Stokes equations for the equilibrium situation where

${\displaystyle u=v=\frac{\mathrm{\partial }p}{\mathrm{\partial }x}=\frac{\mathrm{\partial }p}{\mathrm{\partial }y}=0}$

Then the only non-trivial equation is the ${\displaystyle z}$-equation, which now reads

${\displaystyle \frac{\mathrm{\partial }p}{\mathrm{\partial }z}+\rho g=0}$

Thus, hydrostatic balance can be regarded as a particularly simple equilibrium solution of the Navier–Stokes equations.

Derivation from general relativity

By plugging the energy–momentum tensor for a perfect fluid

${\displaystyle T^{\mu \nu }=(\rho c^{-2}+P)u^{\mu }{u}^{\nu }+P{g}^{\mu \nu }}$

into the Einstein field equations

${\displaystyle R_{\mu \nu }=\frac{8\pi G}{c^4}\left(T_{\mu \nu }-\frac{1}{2}{g}_{\mu \nu }T\right)}$

and using the conservation condition

${\displaystyle {\mathrm{\nabla }}_{\mu }{T}^{\mu \nu }=0}$

one can derive the Tolman–Oppenheimer–Volkoff equation for the structure of a static, spherically symmetric relativistic star in isotropic coordinates:

${\displaystyle \frac{dP}{dr}=-\frac{GM(r)\rho (r)}{r^2}\left(1+\frac{P(r)}{\rho (r)c^2}\right)\left(1+\frac{4\pi r^{3}P(r)}{M(r)c^2}\right){\left(1-\frac{2GM(r)}{r{c}^2}\right)}^{-1}}$

In practice, Ρ and ρ are related by an equation of state of the form f(Ρ,ρ) = 0, with f specific to makeup of the star. M(r) is a foliation of spheres weighted by the mass density ρ(r), with the largest sphere having radius r:

${\displaystyle M(r)=4\pi {\int }_0^{r}d{r}^{\prime }{r}^{\prime 2}\rho (r^{\prime }).}$

Per standard procedure in taking the nonrelativistic limit, we let c→∞, so that the factor

${\displaystyle \left(1+\frac{P(r)}{\rho (r)c^2}\right)\left(1+\frac{4\pi r^{3}P(r)}{M(r)c^2}\right){\left(1-\frac{2GM(r)}{r{c}^2}\right)}^{-1}\to 1}$

Therefore, in the nonrelativistic limit the Tolman–Oppenheimer–Volkoff equation reduces to Newton's hydrostatic equilibrium:

${\displaystyle \frac{dP}{dr}=-\frac{GM(r)\rho (r)}{r^2}=-g(r)\rho (r)⟶dP=-\rho (h)g(h)dh}$

(we have made the trivial notation change h = r and have used f(Ρ,ρ) = 0 to express ρ in terms of P). A similar equation can be computed for rotating, axially symmetric stars, which in its gauge independent form reads:

${\displaystyle \frac{{\mathrm{\partial }}_{i}P}{P+\rho }-{\mathrm{\partial }}_i\ln u^t+u_t{u}^{\phi }{\mathrm{\partial }}_i\frac{u_{\phi }}{u_t}=0}$

Unlike the TOV equilibrium equation, these are two equations (for instance, if as usual when treating stars, one chooses spherical coordinates as basis coordinates ${\displaystyle (t,r,\theta ,\phi )}$, the index i runs for the coordinates r and ${\displaystyle \theta }$).

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. 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.

Astrophysics

In any given layer of a star, there is a hydrostatic equilibrium between the outward thermal pressure from below and the weight of the material above pressing inward. The isotropic gravitational field compresses the star into the most compact shape possible. A rotating star in hydrostatic equilibrium is an oblate spheroid up to a certain (critical) angular velocity. An extreme example of this phenomenon is the star Vega, which has a rotation period of 12.5 hours. Consequently, Vega is about 20% larger at the equator than at the poles. A star with an angular velocity above the critical angular velocity becomes a Jacobi (scalene) ellipsoid, and at still faster rotation it is no longer ellipsoidal but piriform or oviform, with yet other shapes beyond that, though shapes beyond scalene are not stable.

If the star has a massive nearby companion object then tidal forces come into play as well, distorting the star into a scalene shape when rotation alone would make it a spheroid. An example of this is Beta Lyrae.

Hydrostatic equilibrium is also important for the intracluster medium, where it restricts the amount of fluid that can be present in the core of a cluster of galaxies.

We can also use the principle of hydrostatic equilibrium to estimate the velocity dispersion of dark matter in clusters of galaxies. Only baryonic matter (or, rather, the collisions thereof) emits X-ray radiation. The absolute X-ray luminosity per unit volume takes the form ${\displaystyle {\mathcal{L}}_X=\mathrm{\Lambda }(T_B){\rho }_B^2}$ where ${\displaystyle T_B}$ and ${\displaystyle {\rho }_B}$ are the temperature and density of the baryonic matter, and ${\displaystyle \mathrm{\Lambda }(T)}$ is some function of temperature and fundamental constants. The baryonic density satisfies the above equation ${\displaystyle dP=-\rho gdr}$:

${\displaystyle p_B(r+dr)-p_B(r)=-dr\frac{{\rho }_B(r)G}{r^2}{\int }_0^{r}4\pi r^2{\rho }_M(r)dr.}$

The integral is a measure of the total mass of the cluster, with ${\displaystyle r}$ being the proper distance to the center of the cluster. Using the ideal gas law ${\displaystyle p_B=k{T}_B{\rho }_B/m_B}$ (${\displaystyle k}$ is Boltzmann's constant and ${\displaystyle m_B}$ is a characteristic mass of the baryonic gas particles) and rearranging, we arrive at

${\displaystyle \frac{d}{dr}\left(\frac{k{T}_B(r){\rho }_B(r)}{m_B}\right)=-\frac{{\rho }_B(r)G}{r^2}{\int }_0^{r}4\pi r^2{\rho }_M(r)dr.}$

Multiplying by ${\displaystyle r^2/{\rho }_B(r)}$ and differentiating with respect to ${\displaystyle r}$ yields

${\displaystyle \frac{d}{dr}\left[\frac{r^2}{{\rho }_B(r)}\frac{d}{dr}\left(\frac{k{T}_B(r){\rho }_B(r)}{m_B}\right)\right]=-4\pi G{r}^2{\rho }_M(r).}$

If we make the assumption that cold dark matter particles have an isotropic velocity distribution, then the same derivation applies to these particles, and their density ${\displaystyle {\rho }_D={\rho }_M-{\rho }_B}$ satisfies the non-linear differential equation

${\displaystyle \frac{d}{dr}\left[\frac{r^2}{{\rho }_D(r)}\frac{d}{dr}\left(\frac{k{T}_D(r){\rho }_D(r)}{m_D}\right)\right]=-4\pi G{r}^2{\rho }_M(r).}$

With perfect X-ray and distance data, we could calculate the baryon density at each point in the cluster and thus the dark matter density. We could then calculate the velocity dispersion ${\displaystyle {\sigma }_D^2}$ of the dark matter, which is given by

${\displaystyle {\sigma }_D^2=\frac{k{T}_D}{m_D}.}$

The central density ratio ${\displaystyle {\rho }_B(0)/{\rho }_M(0)}$ is dependent on the redshift ${\displaystyle z}$ of the cluster and is given by

${\displaystyle {\rho }_B(0)/{\rho }_M(0)\propto (1+z{)}^2{\left(\frac{\theta }{s}\right)}^{3/2}}$

where ${\displaystyle \theta }$ is the angular width of the cluster and ${\displaystyle s}$ the proper distance to the cluster. Values for the ratio range from .11 to .14 for various surveys.

Planetary geology

See also: List of gravitationally rounded objects of the Solar System

Further information: Clairaut's theorem (gravity)

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 Haumea 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).

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.

Atmospheric modeling

Further information: Atmospheric model

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.

Gemology

Gemologists use hydrostatic balances to determine the specific gravity of gemstones. A gemologist may compare the specific gravity they observe with a hydrostatic balance with a standardized catalogue of information for gemstones, helping them to narrow down the identity or type of gemstone under examination.