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80-494: A caldera ( / k ɔː l ˈ d ɛr ə , k æ l -/ kawl- DERR -ə, kal- ) is a large cauldron -like hollow that forms shortly after the emptying of a magma chamber in a volcanic eruption . An eruption that ejects large volumes of magma over a short period of time can cause significant detriment to the structural integrity of such a chamber, greatly diminishing its capacity to support its own roof, and any substrate or rock resting above. The ground surface then collapses into

160-435: A magnetic field , possibly to the point of behaving like a solid. The viscous forces that arise during fluid flow are distinct from the elastic forces that occur in a solid in response to shear, compression, or extension stresses. While in the latter the stress is proportional to the amount of shear deformation, in a fluid it is proportional to the rate of deformation over time. For this reason, James Clerk Maxwell used

240-407: A caldera, possibly an ash-flow caldera. The volcanic activity of Mars is concentrated in two major provinces: Tharsis and Elysium . Each province contains a series of giant shield volcanoes that are similar to what we see on Earth and likely are the result of mantle hot spots . The surfaces are dominated by lava flows, and all have one or more collapse calderas. Mars has the tallest volcano in

320-651: A cauldron is made of cast iron and is used to burn loose incense on a charcoal disc, to make black salt (used in banishing rituals), for mixing herbs, or to burn petitions (paper with words of power or wishes written on them). Cauldrons symbolize not only the Goddess but also represent the womb (because it holds something) and on an altar, it represents earth because it is a working tool. Cauldrons are often sold in New Age or "metaphysical" stores and may have various symbols of power inscribed on them. The Holy Grail of Arthurian legend

400-505: A cauldron. Also, in Irish folklore , a cauldron is purported to be where leprechauns keep their gold and treasure . In some forms of Wicca , appropriating aspects of Celtic mythology , the cauldron is associated with the goddess Cerridwen . Welsh legend also tells of cauldrons that were useful to warring armies. In the second branch of the Mabinogi in the tale of Branwen, Daughter of Llŷr ,

480-436: A constant viscosity ( non-Newtonian fluids ) cannot be described by a single number. Non-Newtonian fluids exhibit a variety of different correlations between shear stress and shear rate. One of the most common instruments for measuring kinematic viscosity is the glass capillary viscometer. In coating industries, viscosity may be measured with a cup in which the efflux time is measured. There are several sorts of cup—such as

560-399: A diameter of 290 km (180 mi). The average caldera diameter on Mars is 48 km (30 mi), smaller than Venus. Calderas on Earth are the smallest of all planetary bodies and vary from 1.6–80 km (1–50 mi) as a maximum. The Moon has an outer shell of low-density crystalline rock that is a few hundred kilometers thick, which formed due to a rapid creation. The craters of

640-502: A fluid, just as thermal conductivity characterizes heat transport, and (mass) diffusivity characterizes mass transport. This perspective is implicit in Newton's law of viscosity, τ = μ ( ∂ u / ∂ y ) {\displaystyle \tau =\mu (\partial u/\partial y)} , because the shear stress τ {\displaystyle \tau } has units equivalent to

720-464: A magma chamber whose magma is rich in silica . Silica-rich magma has a high viscosity , and therefore does not flow easily like basalt . The magma typically also contains a large amount of dissolved gases, up to 7 wt% for the most silica-rich magmas. When the magma approaches the surface of the Earth, the drop in confining pressure causes the trapped gases to rapidly bubble out of the magma, fragmenting

800-415: A momentum flux , i.e., momentum per unit time per unit area. Thus, τ {\displaystyle \tau } can be interpreted as specifying the flow of momentum in the y {\displaystyle y} direction from one fluid layer to the next. Per Newton's law of viscosity, this momentum flow occurs across a velocity gradient, and the magnitude of the corresponding momentum flux

880-583: A noticeable drop in temperature around the world. Large calderas may have even greater effects. The ecological effects of the eruption of a large caldera can be seen in the record of the Lake Toba eruption in Indonesia . At some points in geological time , rhyolitic calderas have appeared in distinct clusters. The remnants of such clusters may be found in places such as the Eocene Rum Complex of Scotland,

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960-416: A specific fluid state. To standardize comparisons among experiments and theoretical models, viscosity data is sometimes extrapolated to ideal limiting cases, such as the zero shear limit, or (for gases) the zero density limit. Transport theory provides an alternative interpretation of viscosity in terms of momentum transport: viscosity is the material property which characterizes momentum transport within

1040-649: Is 1 cP divided by 1000 kg/m^3, close to the density of water. The kinematic viscosity of water at 20 °C is about 1 cSt. The most frequently used systems of US customary, or Imperial , units are the British Gravitational (BG) and English Engineering (EE). In the BG system, dynamic viscosity has units of pound -seconds per square foot (lb·s/ft ), and in the EE system it has units of pound-force -seconds per square foot (lbf·s/ft ). The pound and pound-force are equivalent;

1120-457: Is a linear combination of the shear and bulk viscosities that describes the reaction of a solid elastic material to elongation. It is widely used for characterizing polymers. In geology , earth materials that exhibit viscous deformation at least three orders of magnitude greater than their elastic deformation are sometimes called rheids . Viscosity is measured with various types of viscometers and rheometers . Close temperature control of

1200-681: Is a borrowing of the Old Norse variant ketill "cauldron". Cauldrons can be found from the late Bronze Age period; these include vast ones with a volume of 60–70 litres (16–18  US gal ). Cauldrons have largely fallen out of use in the developed world as cooking vessels. While still used for practical purposes, a more common association in Western culture is the cauldron's use in witchcraft —a cliché popularized by various works of fiction , such as William Shakespeare 's play Macbeth . In fiction, witches often prepare their potions in

1280-462: Is a calculation derived from tests performed on drilling fluid used in oil or gas well development. These calculations and tests help engineers develop and maintain the properties of the drilling fluid to the specifications required. Nanoviscosity (viscosity sensed by nanoprobes) can be measured by fluorescence correlation spectroscopy . The SI unit of dynamic viscosity is the newton -second per square meter (N·s/m ), also frequently expressed in

1360-453: Is a measure of a fluid's dynamic resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of thickness ; for example, syrup has a higher viscosity than water . Viscosity is defined scientifically as a force multiplied by a time divided by an area. Thus its SI units are newton-seconds per square meter, or pascal-seconds. Viscosity quantifies

1440-550: Is a viscosity tensor that maps the velocity gradient tensor ∂ v k / ∂ r ℓ {\displaystyle \partial v_{k}/\partial r_{\ell }} onto the viscous stress tensor τ i j {\displaystyle \tau _{ij}} . Since the indices in this expression can vary from 1 to 3, there are 81 "viscosity coefficients" μ i j k l {\displaystyle \mu _{ijkl}} in total. However, assuming that

1520-532: Is called the rate of shear deformation or shear velocity , and is the derivative of the fluid speed in the direction parallel to the normal vector of the plates (see illustrations to the right). If the velocity does not vary linearly with y {\displaystyle y} , then the appropriate generalization is: where τ = F / A {\displaystyle \tau =F/A} , and ∂ u / ∂ y {\displaystyle \partial u/\partial y}

1600-453: Is derived from the Latin viscum (" mistletoe "). Viscum also referred to a viscous glue derived from mistletoe berries. In materials science and engineering , there is often interest in understanding the forces or stresses involved in the deformation of a material. For instance, if the material were a simple spring, the answer would be given by Hooke's law , which says that

1680-448: Is determined by the viscosity. The analogy with heat and mass transfer can be made explicit. Just as heat flows from high temperature to low temperature and mass flows from high density to low density, momentum flows from high velocity to low velocity. These behaviors are all described by compact expressions, called constitutive relations , whose one-dimensional forms are given here: where ρ {\displaystyle \rho }

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1760-402: Is ejected, the emptied chamber is unable to support the weight of the volcanic edifice above it. A roughly circular fracture , the "ring fault", develops around the edge of the chamber. Ring fractures serve as feeders for fault intrusions which are also known as ring dikes . Secondary volcanic vents may form above the ring fracture. As the magma chamber empties, the center of the volcano within

1840-534: Is equal to the SI millipascal second (mPa·s). The SI unit of kinematic viscosity is square meter per second (m /s), whereas the CGS unit for kinematic viscosity is the stokes (St, or cm ·s = 0.0001 m ·s ), named after Sir George Gabriel Stokes . In U.S. usage, stoke is sometimes used as the singular form. The submultiple centistokes (cSt) is often used instead, 1 cSt = 1 mm ·s  = 10  m ·s . 1 cSt

1920-587: Is first recorded in Middle English as caudroun (13th century). It was borrowed from Norman caudron ( Picard caudron , French : chaudron ). It represents the phonetical evolution of Vulgar Latin *caldario for Classical Latin caldārium "hot bath", that derives from cal(i)dus "hot". The Norman-French word replaces the Old English ċetel (German (Koch)Kessel "cauldron", Dutch (kook)ketel "cauldron"), Middle English chetel . The word "kettle"

2000-552: Is heated by solid flexing due to the tidal influence of Jupiter and Io's orbital resonance with neighboring large moons Europa and Ganymede , which keep its orbit slightly eccentric . Unlike any of the planets mentioned, Io is continuously volcanically active. For example, the NASA Voyager 1 and Voyager 2 spacecraft detected nine erupting volcanoes while passing Io in 1979. Io has many calderas with diameters tens of kilometers across. Cauldron The word cauldron

2080-576: Is in terms of the standard (scalar) viscosity μ {\displaystyle \mu } and the bulk viscosity κ {\displaystyle \kappa } such that α = κ − 2 3 μ {\displaystyle \alpha =\kappa -{\tfrac {2}{3}}\mu } and β = γ = μ {\displaystyle \beta =\gamma =\mu } . In vector notation this appears as: where δ {\displaystyle \mathbf {\delta } }

2160-658: Is not a fundamental law of nature, but rather a constitutive equation (like Hooke's law , Fick's law , and Ohm's law ) which serves to define the viscosity μ {\displaystyle \mu } . Its form is motivated by experiments which show that for a wide range of fluids, μ {\displaystyle \mu } is independent of strain rate. Such fluids are called Newtonian . Gases , water , and many common liquids can be considered Newtonian in ordinary conditions and contexts. However, there are many non-Newtonian fluids that significantly deviate from this behavior. For example: Trouton 's ratio

2240-670: Is often associated with power and dominion over the land. Therefore, the ding is often used as an implicit symbolism for power. The term "inquiring of the ding" (Chinese: 问鼎; pinyin: wèn dǐng) is often used to symbolize the use of divination or for the quest for power. One example of the ding cauldron and gaining power over the traditional provinces of China is the Nine Tripod Cauldrons (whether regarded as myth or history). Archeologically intact actual cauldrons with apparent cultural symbolism include: Cauldrons known only through myth and literature include: Viscosity Viscosity

2320-526: Is relatively young (1.25 million years old) and unusually well preserved, and it remains one of the best studied examples of a resurgent caldera. The ash flow tuffs of the Valles caldera, such as the Bandelier Tuff , were among the first to be thoroughly characterized. About 74,000 years ago, this Indonesian volcano released about 2,800 cubic kilometres (670 cu mi) dense-rock equivalent of ejecta. This

2400-439: Is sometimes referred to as a "cauldron", although traditionally the grail is thought of as a hand-held cup rather than the large pot that the word "cauldron" usually is used to mean. This may have resulted from the combination of the grail legend with earlier Celtic myths of magical cauldrons. The common translation for ding is often referred to as a cauldron. In Chinese history and culture, possession of one or more ancient dings

2480-581: Is the dynamic viscosity of the fluid, often simply referred to as the viscosity . It is denoted by the Greek letter mu ( μ ). The dynamic viscosity has the dimensions ( m a s s / l e n g t h ) / t i m e {\displaystyle \mathrm {(mass/length)/time} } , therefore resulting in the SI units and the derived units : The aforementioned ratio u / y {\displaystyle u/y}

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2560-408: Is the density, J {\displaystyle \mathbf {J} } and q {\displaystyle \mathbf {q} } are the mass and heat fluxes, and D {\displaystyle D} and k t {\displaystyle k_{t}} are the mass diffusivity and thermal conductivity. The fact that mass, momentum, and energy (heat) transport are among

2640-425: Is the local shear velocity. This expression is referred to as Newton's law of viscosity . In shearing flows with planar symmetry, it is what defines μ {\displaystyle \mu } . It is a special case of the general definition of viscosity (see below), which can be expressed in coordinate-free form. Use of the Greek letter mu ( μ {\displaystyle \mu } ) for

2720-606: Is the ratio of extensional viscosity to shear viscosity . For a Newtonian fluid, the Trouton ratio is 3. Shear-thinning liquids are very commonly, but misleadingly, described as thixotropic. Viscosity may also depend on the fluid's physical state (temperature and pressure) and other, external , factors. For gases and other compressible fluids , it depends on temperature and varies very slowly with pressure. The viscosity of some fluids may depend on other factors. A magnetorheological fluid , for example, becomes thicker when subjected to

2800-554: Is the unit tensor. This equation can be thought of as a generalized form of Newton's law of viscosity. The bulk viscosity (also called volume viscosity) expresses a type of internal friction that resists the shearless compression or expansion of a fluid. Knowledge of κ {\displaystyle \kappa } is frequently not necessary in fluid dynamics problems. For example, an incompressible fluid satisfies ∇ ⋅ v = 0 {\displaystyle \nabla \cdot \mathbf {v} =0} and so

2880-466: The Pair Dadeni (Cauldron of Rebirth) is a magical cauldron in which dead warriors could be placed and then be returned to life, save that they lacked the power of speech. It was suspected that they lacked souls. These warriors could go back into battle until they were killed again. In Wicca and some other forms of neopagan or pagan belief systems, the cauldron is still used in magical practices. Most often

2960-495: The San Juan Mountains of Colorado , where the 5,000 cubic kilometres (1,200 cu mi) Fish Canyon Tuff was blasted out in eruptions about 27.8 million years ago. The caldera produced by such eruptions is typically filled in with tuff, rhyolite , and other igneous rocks . The caldera is surrounded by an outflow sheet of ash flow tuff (also called an ash flow sheet ). If magma continues to be injected into

3040-577: The Zahn cup and the Ford viscosity cup —with the usage of each type varying mainly according to the industry. Also used in coatings, a Stormer viscometer employs load-based rotation to determine viscosity. The viscosity is reported in Krebs units (KU), which are unique to Stormer viscometers. Vibrating viscometers can also be used to measure viscosity. Resonant, or vibrational viscometers work by creating shear waves within

3120-425: The density of the fluid ( ρ ). It is usually denoted by the Greek letter nu ( ν ): and has the dimensions ( l e n g t h ) 2 / t i m e {\displaystyle \mathrm {(length)^{2}/time} } , therefore resulting in the SI units and the derived units : In very general terms, the viscous stresses in a fluid are defined as those resulting from

3200-431: The shear viscosity . However, at least one author discourages the use of this terminology, noting that μ {\displaystyle \mu } can appear in non-shearing flows in addition to shearing flows. In fluid dynamics, it is sometimes more appropriate to work in terms of kinematic viscosity (sometimes also called the momentum diffusivity ), defined as the ratio of the dynamic viscosity ( μ ) over

3280-491: The BG and EE systems. Nonstandard units include the reyn (lbf·s/in ), a British unit of dynamic viscosity. In the automotive industry the viscosity index is used to describe the change of viscosity with temperature. The reciprocal of viscosity is fluidity , usually symbolized by ϕ = 1 / μ {\displaystyle \phi =1/\mu } or F = 1 / μ {\displaystyle F=1/\mu } , depending on

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3360-463: The Couette flow, a fluid is trapped between two infinitely large plates, one fixed and one in parallel motion at constant speed u {\displaystyle u} (see illustration to the right). If the speed of the top plate is low enough (to avoid turbulence), then in steady state the fluid particles move parallel to it, and their speed varies from 0 {\displaystyle 0} at

3440-416: The Earth's volcanic activity (the other 40% is attributed to hotspot volcanism). Caldera structure is similar on all of these planetary bodies, though the size varies considerably. The average caldera diameter on Venus is 68 km (42 mi). The average caldera diameter on Io is close to 40 km (25 mi), and the mode is 6 km (3.7 mi); Tvashtar Paterae is likely the largest caldera with

3520-658: The English term cauldron is also used, though in more recent work the term cauldron refers to a caldera that has been deeply eroded to expose the beds under the caldera floor. The term caldera was introduced into the geological vocabulary by the German geologist Leopold von Buch when he published his memoirs of his 1815 visit to the Canary Islands , where he first saw the Las Cañadas caldera on Tenerife , with Mount Teide dominating

3600-510: The Moon have been well preserved through time and were once thought to have been the result of extreme volcanic activity, but are currently believed to have been formed by meteorites, nearly all of which took place in the first few hundred million years after the Moon formed. Around 500 million years afterward, the Moon's mantle was able to be extensively melted due to the decay of radioactive elements. Massive basaltic eruptions took place generally at

3680-644: The San Juan Mountains of Colorado (formed during the Oligocene , Miocene , and Pliocene epochs) or the Saint Francois Mountain Range of Missouri (erupted during the Proterozoic eon). For their 1968 paper that first introduced the concept of a resurgent caldera to geology, R.L. Smith and R.A. Bailey chose the Valles caldera as their model. Although the Valles caldera is not unusually large, it

3760-718: The Solar System, Olympus Mons , which is more than three times the height of Mount Everest, with a diameter of 520 km (323 miles). The summit of the mountain has six nested calderas. Because there is no plate tectonics on Venus , heat is mainly lost by conduction through the lithosphere . This causes enormous lava flows, accounting for 80% of Venus' surface area. Many of the mountains are large shield volcanoes that range in size from 150–400 km (95–250 mi) in diameter and 2–4 km (1.2–2.5 mi) high. More than 80 of these large shield volcanoes have summit calderas averaging 60 km (37 mi) across. Io, unusually,

3840-410: The base of large impact craters. Also, eruptions may have taken place due to a magma reservoir at the base of the crust. This forms a dome, possibly the same morphology of a shield volcano where calderas universally are known to form. Although caldera-like structures are rare on the Moon, they are not completely absent. The Compton-Belkovich Volcanic Complex on the far side of the Moon is thought to be

3920-425: The bottom to u {\displaystyle u} at the top. Each layer of fluid moves faster than the one just below it, and friction between them gives rise to a force resisting their relative motion. In particular, the fluid applies on the top plate a force in the direction opposite to its motion, and an equal but opposite force on the bottom plate. An external force is therefore required in order to keep

4000-576: The caldera atop Fernandina Island collapsed in 1968 when parts of the caldera floor dropped 350 metres (1,150 ft). Since the early 1960s, it has been known that volcanism has occurred on other planets and moons in the Solar System . Through the use of crewed and uncrewed spacecraft, volcanism has been discovered on Venus , Mars , the Moon , and Io , a satellite of Jupiter . None of these worlds have plate tectonics , which contributes approximately 60% of

4080-658: The collapsed magma chamber, the center of the caldera may be uplifted in the form of a resurgent dome such as is seen at the Valles Caldera , Lake Toba , the San Juan volcanic field, Cerro Galán , Yellowstone , and many other calderas. Because a silicic caldera may erupt hundreds or even thousands of cubic kilometers of material in a single event, it can cause catastrophic environmental effects. Even small caldera-forming eruptions, such as Krakatoa in 1883 or Mount Pinatubo in 1991, may result in significant local destruction and

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4160-597: The convention used, measured in reciprocal poise (P , or cm · s · g ), sometimes called the rhe . Fluidity is seldom used in engineering practice. At one time the petroleum industry relied on measuring kinematic viscosity by means of the Saybolt viscometer , and expressing kinematic viscosity in units of Saybolt universal seconds (SUS). Other abbreviations such as SSU ( Saybolt seconds universal ) or SUV ( Saybolt universal viscosity ) are sometimes used. Kinematic viscosity in centistokes can be converted from SUS according to

4240-461: The dynamic viscosity (sometimes also called the absolute viscosity ) is common among mechanical and chemical engineers , as well as mathematicians and physicists. However, the Greek letter eta ( η {\displaystyle \eta } ) is also used by chemists, physicists, and the IUPAC . The viscosity μ {\displaystyle \mu } is sometimes also called

4320-402: The emptied or partially emptied magma chamber, leaving a large depression at the surface (from one to dozens of kilometers in diameter). Although sometimes described as a crater , the feature is actually a type of sinkhole , as it is formed through subsidence and collapse rather than an explosion or impact. Compared to the thousands of volcanic eruptions that occur over the course of a century,

4400-453: The equivalent forms pascal - second (Pa·s), kilogram per meter per second (kg·m ·s ) and poiseuille (Pl). The CGS unit is the poise (P, or g·cm ·s = 0.1 Pa·s), named after Jean Léonard Marie Poiseuille . It is commonly expressed, particularly in ASTM standards, as centipoise (cP). The centipoise is convenient because the viscosity of water at 20 °C is about 1 cP, and one centipoise

4480-409: The fluid do not depend on the distance the fluid has been sheared; rather, they depend on how quickly the shearing occurs. Viscosity is the material property which relates the viscous stresses in a material to the rate of change of a deformation (the strain rate). Although it applies to general flows, it is easy to visualize and define in a simple shearing flow, such as a planar Couette flow . In

4560-459: The fluid is essential to obtain accurate measurements, particularly in materials like lubricants, whose viscosity can double with a change of only 5 °C. A rheometer is used for fluids that cannot be defined by a single value of viscosity and therefore require more parameters to be set and measured than is the case for a viscometer. For some fluids, the viscosity is constant over a wide range of shear rates ( Newtonian fluids ). The fluids without

4640-426: The force experienced by a spring is proportional to the distance displaced from equilibrium. Stresses which can be attributed to the deformation of a material from some rest state are called elastic stresses. In other materials, stresses are present which can be attributed to the deformation rate over time . These are called viscous stresses. For instance, in a fluid such as water the stresses which arise from shearing

4720-459: The formation of a caldera is a rare event, occurring only a few times within a given window of 100 years. Only eight caldera-forming collapses are known to have occurred between 1911 and 2018, with a caldera collapse at Kīlauea , Hawaii in 2018. Volcanoes that have formed a caldera are sometimes described as "caldera volcanoes". The term caldera comes from Spanish caldera , and Latin caldaria , meaning "cooking pot". In some texts

4800-405: The friction between the layers of the fluid which are in relative motion. For a tube with a constant rate of flow, the strength of the compensating force is proportional to the fluid's viscosity. In general, viscosity depends on a fluid's state, such as its temperature, pressure, and rate of deformation. However, the dependence on some of these properties is negligible in certain cases. For example,

4880-460: The human species was reduced to approximately 5,000–10,000 people. There is no direct evidence, however, that either theory is correct, and there is no evidence for any other animal decline or extinction, even in environmentally sensitive species. There is evidence that human habitation continued in India after the eruption. Some volcanoes, such as the large shield volcanoes Kīlauea and Mauna Loa on

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4960-409: The internal frictional force between adjacent layers of fluid that are in relative motion. For instance, when a viscous fluid is forced through a tube, it flows more quickly near the tube's center line than near its walls. Experiments show that some stress (such as a pressure difference between the two ends of the tube) is needed to sustain the flow. This is because a force is required to overcome

5040-429: The island of Hawaii , form calderas in a different fashion. The magma feeding these volcanoes is basalt , which is silica poor. As a result, the magma is much less viscous than the magma of a rhyolitic volcano, and the magma chamber is drained by large lava flows rather than by explosive events. The resulting calderas are also known as subsidence calderas and can form more gradually than explosive calderas. For instance,

5120-475: The landscape, and then the Caldera de Taburiente on La Palma . A collapse is triggered by the emptying of the magma chamber beneath the volcano, sometimes as the result of a large explosive volcanic eruption (see Tambora in 1815), but also during effusive eruptions on the flanks of a volcano (see Piton de la Fournaise in 2007) or in a connected fissure system (see Bárðarbunga in 2014–2015). If enough magma

5200-529: The liquid. In this method, the sensor is submerged in the fluid and is made to resonate at a specific frequency. As the surface of the sensor shears through the liquid, energy is lost due to its viscosity. This dissipated energy is then measured and converted into a viscosity reading. A higher viscosity causes a greater loss of energy. Extensional viscosity can be measured with various rheometers that apply extensional stress . Volume viscosity can be measured with an acoustic rheometer . Apparent viscosity

5280-559: The magma to produce a mixture of volcanic ash and other tephra with the very hot gases. The mixture of ash and volcanic gases initially rises into the atmosphere as an eruption column . However, as the volume of erupted material increases, the eruption column is unable to entrain enough air to remain buoyant, and the eruption column collapses into a tephra fountain that falls back to the surface to form pyroclastic flows . Eruptions of this type can spread ash over vast areas, so that ash flow tuffs emplaced by silicic caldera eruptions are

5360-435: The most relevant processes in continuum mechanics is not a coincidence: these are among the few physical quantities that are conserved at the microscopic level in interparticle collisions. Thus, rather than being dictated by the fast and complex microscopic interaction timescale, their dynamics occurs on macroscopic timescales, as described by the various equations of transport theory and hydrodynamics. Newton's law of viscosity

5440-464: The only volcanic product with volumes rivaling those of flood basalts . For example, when Yellowstone Caldera last erupted some 650,000 years ago, it released about 1,000 km of material (as measured in dense rock equivalent (DRE)), covering a substantial part of North America in up to two metres of debris. Eruptions forming even larger calderas are known, such as the La Garita Caldera in

5520-515: The relative velocity of different fluid particles. As such, the viscous stresses must depend on spatial gradients of the flow velocity. If the velocity gradients are small, then to a first approximation the viscous stresses depend only on the first derivatives of the velocity. (For Newtonian fluids, this is also a linear dependence.) In Cartesian coordinates, the general relationship can then be written as where μ i j k ℓ {\displaystyle \mu _{ijk\ell }}

5600-460: The ring fracture begins to collapse. The collapse may occur as the result of a single cataclysmic eruption, or it may occur in stages as the result of a series of eruptions. The total area that collapses may be hundreds of square kilometers. Some calderas are known to host rich ore deposits . Metal-rich fluids can circulate through the caldera, forming hydrothermal ore deposits of metals such as lead, silver, gold, mercury, lithium, and uranium. One of

5680-555: The term fugitive elasticity for fluid viscosity. However, many liquids (including water) will briefly react like elastic solids when subjected to sudden stress. Conversely, many "solids" (even granite ) will flow like liquids, albeit very slowly, even under arbitrarily small stress. Such materials are best described as viscoelastic —that is, possessing both elasticity (reaction to deformation) and viscosity (reaction to rate of deformation). Viscoelastic solids may exhibit both shear viscosity and bulk viscosity. The extensional viscosity

5760-715: The term containing κ {\displaystyle \kappa } drops out. Moreover, κ {\displaystyle \kappa } is often assumed to be negligible for gases since it is 0 {\displaystyle 0} in a monatomic ideal gas . One situation in which κ {\displaystyle \kappa } can be important is the calculation of energy loss in sound and shock waves , described by Stokes' law of sound attenuation , since these phenomena involve rapid expansions and compressions. The defining equations for viscosity are not fundamental laws of nature, so their usefulness, as well as methods for measuring or calculating

5840-583: The top plate moving at constant speed. In many fluids, the flow velocity is observed to vary linearly from zero at the bottom to u {\displaystyle u} at the top. Moreover, the magnitude of the force, F {\displaystyle F} , acting on the top plate is found to be proportional to the speed u {\displaystyle u} and the area A {\displaystyle A} of each plate, and inversely proportional to their separation y {\displaystyle y} : The proportionality factor

5920-507: The two systems differ only in how force and mass are defined. In the BG system the pound is a basic unit from which the unit of mass (the slug ) is defined by Newton's Second Law , whereas in the EE system the units of force and mass (the pound-force and pound-mass respectively) are defined independently through the Second Law using the proportionality constant g c . Kinematic viscosity has units of square feet per second (ft /s) in both

6000-403: The viscosity depends only space- and time-dependent macroscopic fields (such as temperature and density) defining local equilibrium. Nevertheless, viscosity may still carry a non-negligible dependence on several system properties, such as temperature, pressure, and the amplitude and frequency of any external forcing. Therefore, precision measurements of viscosity are only defined with respect to

6080-609: The viscosity of a Newtonian fluid does not vary significantly with the rate of deformation. Zero viscosity (no resistance to shear stress ) is observed only at very low temperatures in superfluids ; otherwise, the second law of thermodynamics requires all fluids to have positive viscosity. A fluid that has zero viscosity (non-viscous) is called ideal or inviscid . For non-Newtonian fluid 's viscosity, there are pseudoplastic , plastic , and dilatant flows that are time-independent, and there are thixotropic and rheopectic flows that are time-dependent. The word "viscosity"

6160-571: The viscosity rank-2 tensor is isotropic reduces these 81 coefficients to three independent parameters α {\displaystyle \alpha } , β {\displaystyle \beta } , γ {\displaystyle \gamma } : and furthermore, it is assumed that no viscous forces may arise when the fluid is undergoing simple rigid-body rotation, thus β = γ {\displaystyle \beta =\gamma } , leaving only two independent parameters. The most usual decomposition

6240-500: The viscosity, must be established using separate means. A potential issue is that viscosity depends, in principle, on the full microscopic state of the fluid, which encompasses the positions and momenta of every particle in the system. Such highly detailed information is typically not available in realistic systems. However, under certain conditions most of this information can be shown to be negligible. In particular, for Newtonian fluids near equilibrium and far from boundaries (bulk state),

6320-630: The world's best-preserved mineralized calderas is the Sturgeon Lake Caldera in northwestern Ontario , Canada, which formed during the Neoarchean era about 2.7 billion years ago. In the San Juan volcanic field , ore veins were emplaced in fractures associated with several calderas, with the greatest mineralization taking place near the youngest and most silicic intrusions associated with each caldera. Explosive caldera eruptions are produced by

6400-463: Was the largest known eruption during the ongoing Quaternary period (the last 2.6 million years) and the largest known explosive eruption during the last 25 million years. In the late 1990s, anthropologist Stanley Ambrose proposed that a volcanic winter induced by this eruption reduced the human population to about 2,000–20,000 individuals, resulting in a population bottleneck . More recently, Lynn Jorde and Henry Harpending proposed that

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