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72-487: Two major goals were set for the campaign. Specifically, understand: In order to achieve Goal 1, the WCRP outlined and established Core Projects that would receive priority. The first of these was the "Global Description" project, which was meant to obtain data on the circulation of heat, fresh water and chemicals, as well as the statistics of eddies . The second project—"Southern Ocean"—placed particular emphasis on studying

144-435: 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

216-436: 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

288-527: A diel vertical migration but without more evidence on the biomass of their prey within this zone, these conclusions cannot be made only using this circumstantial evidence. The biomass in the mesopelagic zone is still understudied leading to the biomass of fish within this layer to potentially be underestimated. A more accurate measurement on this biomass may serve to benefit the commercial fishing industry providing them with additional fishing grounds within this region. Moreover, further understanding this region in

360-463: A fluid dynamics experiment involving water and dye, where he adjusted the velocities of the fluids and observed the transition from laminar to turbulent flow, characterized by the formation of eddies and vortices. Turbulent flow is defined as the flow in which the system's inertial forces are dominant over the viscous forces. This phenomenon is described by Reynolds number , a unit-less number used to determine when turbulent flow will occur. Conceptually,

432-506: 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

504-584: A model. The model is then progressed in time using new data and repeating the process. The success of these methods requires sufficient data to fully constrain the model, hence the need for a comprehensive field program. Goals for the WOCE Field Program were as follows. Major elements of the WOCE Field Program This list, though not comprehensive, outlines a sampling of the most highly cited articles and books resulting from

576-415: 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

648-416: 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

720-664: 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;

792-457: 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

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864-462: 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

936-550: 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

1008-468: Is an eddy which is an undulation that is a deviation from mean flow, but does not have the local closed streamlines of a vortex. The propensity of a fluid to swirl is used to promote good fuel/air mixing in internal combustion engines. In fluid mechanics and transport phenomena , an eddy is not a property of the fluid, but a violent swirling motion caused by the position and direction of turbulent flow. In 1883, scientist Osborne Reynolds conducted

1080-532: 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}

1152-457: 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

1224-448: 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 }

1296-540: 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

1368-411: 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 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

1440-576: 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 } }

1512-658: 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

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1584-462: 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"

1656-588: 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}

1728-408: 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

1800-425: 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

1872-611: 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

1944-554: 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

2016-413: Is vital in grasping an understanding of environmental systems. By understanding the transport of both particulate and dissolved solids in environmental flows, scientists and engineers will be able to efficiently formulate remediation strategies for pollution events. Eddy formations play a vital role in the fate and transport of solutes and particles in environmental flows such as in rivers, lakes, oceans, and

2088-933: The Antarctic Circumpolar Current and the Southern Ocean ’s interaction with the World Ocean. The third and final Core Project serving goal one was the " Gyre Dynamics Experiment." The second and third of these focuses are designed specifically to address the ocean’s role in decadal climate changes. Initial planning of the WOCE states that achievement of Goal 1 would involve "strong interaction between modeling and field activities," which are described further below. Specifically: Models in WOCE were used for both experimental design and data analysis. Models with use of data can incorporate various properties, including thermal wind balance, maintenance of

2160-553: The Kuroshio Current , and the Antarctic Circumpolar Current, amongst others. Mesoscale ocean eddies are characterized by currents that flow in a roughly circular motion around the center of the eddy. The sense of rotation of these currents may either be cyclonic or anticyclonic (such as Haida Eddies ). Oceanic eddies are also usually made of water masses that are different from those outside

2232-589: 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

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2304-522: The barotropic vorticity budget, and conservation of heat, fresh water, or mass. Measurements useful for these parameters are heat, fresh water or tracer concentration; current, surface fluxes of heat and fresh water; sea surface elevation. Both inverse modeling and data assimilation were employed during WOCE. Inverse modeling is the fitting of data using a numerical least squares or maximum likelihood fitting procedure. The data assimilation technique requires data to be compared with an initial integration of

2376-425: 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

2448-431: 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

2520-594: The Atlantic is also thought to be an ocean desert, which creates an interesting paradox due to it hosting a variety of large pelagic fish populations and apex predators . These mesoscale eddies have shown to be beneficial in further creating ecosystem-based management for food web models to better understand the utilization of these eddies by both the apex predators and their prey. Gaube et al. (2018), used “Smart” Position or Temperature Transmitting tags (SPOT) and Pop-Up Satellite Archival Transmitting tags (PSAT) to track

2592-491: 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

2664-468: 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

2736-513: The Reynolds number is the ratio between inertial forces and viscous forces. The general form for the Reynolds number flowing through a tube of radius r (or diameter d ): where v is the velocity of the fluid, ρ is its density , r is the radius of the tube, and μ is the dynamic viscosity of the fluid. A turbulent flow in a fluid is defined by the critical Reynolds number, for a closed pipe this works out to approximately In terms of

2808-429: The WOCE. Eddies In fluid dynamics , an eddy is the swirling of a fluid and the reverse current created when the fluid is in a turbulent flow regime. The moving fluid creates a space devoid of downstream-flowing fluid on the downstream side of the object. Fluid behind the obstacle flows into the void creating a swirl of fluid on each edge of the obstacle, followed by a short reverse flow of fluid behind

2880-437: The anticyclonic eddies were 57% more common and had more dives and deeper dives than the open ocean eddies and Gulf Stream cyclonic eddies. Within these anticyclonic eddies, the isotherm was displaced 50 meters downward allowing for the warmer water to penetrate deeper in the water column. This warmer water displacement may allow for the white sharks to make longer dives without the added energetic cost from thermal regulation in

2952-448: The arterial tree are typically laminar (high, directed wall stress), but branches and curvatures in the system cause turbulent flow. Turbulent flow in the arterial tree can cause a number of concerning effects, including atherosclerotic lesions, postsurgical neointimal hyperplasia, in-stent restenosis, vein bypass graft failure, transplant vasculopathy, and aortic valve calcification. Lift and drag properties of golf balls are customized by

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3024-433: The atmosphere. Upwelling in stratified coastal estuaries warrant the formation of dynamic eddies which distribute nutrients out from beneath the boundary layer to form plumes. Shallow waters, such as those along the coast, play a complex role in the transport of nutrients and pollutants due to the proximity of the upper-boundary driven by the wind and the lower-boundary near the bottom of the water body. Eddies are common in

3096-425: 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

3168-420: 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, the viscosity of a Newtonian fluid does not vary significantly with the rate of deformation. Zero viscosity (no resistance to shear stress )

3240-602: 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

3312-491: The cooler cyclones. Even though these anticyclonic eddies resulted in lower levels of chlorophyll in comparison to the cyclonic eddies, the warmer waters at deeper depths may allow for a deeper mixed layer and higher concentration of diatoms which in turn result in higher rates of primary productivity. Furthermore, the prey populations could be distributed more within these eddies attracting these larger female sharks to forage in this mesopelagic zone. This diving pattern may follow

3384-463: The critical Reynolds number, the critical velocity is represented as These are turbulence models in which the Reynolds stresses, as obtained from a Reynolds averaging of the Navier–Stokes equations , are modelled by a linear constitutive relationship with the mean flow straining field, as: where Hemodynamics is the study of blood flow in the circulatory system. Blood flow in straight sections of

3456-465: 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

3528-584: The eddy. That is, the water within an eddy usually has different temperature and salinity characteristics to the water outside the eddy. There is a direct link between the water mass properties of an eddy and its rotation. Warm eddies rotate anti-cyclonically, while cold eddies rotate cyclonically. Because eddies may have a vigorous circulation associated with them, they are of concern to naval and commercial operations at sea. Further, because eddies transport anomalously warm or cold water as they move, they have an important influence on heat transport in certain parts of

3600-457: 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

3672-409: 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

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3744-459: 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

3816-426: 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

3888-743: The globe. While the transport of organisms, such as phytoplankton , are essential for the preservation of ecosystems, oil and other pollutants are also mixed in the current flow and can carry pollution far from its origin. Eddy formations circulate trash and other pollutants into concentrated areas which researchers are tracking to improve clean-up and pollution prevention. The distribution and motion of plastics caused by eddy formations in natural water bodies can be predicted using Lagrangian transport models. Mesoscale ocean eddies play crucial roles in transferring heat poleward, as well as maintaining heat gradients at different depths. Modeling eddy development, as it relates to turbulence and fate transport phenomena,

3960-413: 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 the internal frictional force between adjacent layers of fluid that are in relative motion. For instance, when a viscous fluid

4032-529: 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

4104-421: The manipulation of dimples along the surface of the ball, allowing for the golf ball to travel further and faster in the air. The data from turbulent-flow phenomena has been used to model different transitions in fluid flow regimes, which are used to thoroughly mix fluids and increase reaction rates within industrial processes. Oceanic and atmospheric currents transfer particles, debris, and organisms all across

4176-435: 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

4248-465: The movement and diving behavior of two female white sharks (Carcharodon carcharias) within the eddies. The eddies were defined using sea surface height (SSH) and contours using the horizontal speed-based radius scale. This study found that the white sharks dove in both cyclones but favored the anticyclone which had three times more dives as the cyclonic eddies. Additionally, in the Gulf Stream eddies,

4320-404: The obstacle flowing upstream, toward the back of the obstacle. This phenomenon is naturally observed behind large emergent rocks in swift-flowing rivers. An eddy is a movement of fluid that deviates from the general flow of the fluid. An example for an eddy is a vortex which produces such deviation. However, there are other types of eddies that are not simple vortices. For example, a Rossby wave

4392-533: The ocean contains a sea surface height gradient this creates a jet or current, such as the Antarctic Circumpolar Current . This current as part of a baroclinically unstable system meanders and creates eddies (in much the same way as a meandering river forms an oxbow lake ). These types of mesoscale eddies have been observed in many major ocean currents, including the Gulf Stream , the Agulhas Current ,

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4464-549: The ocean, and range in diameter from centimeters to hundreds of kilometers. The smallest scale eddies may last for a matter of seconds, while the larger features may persist for months to years. Eddies that are between about 10 and 500 km (6 and 300 miles) in diameter and persist for periods of days to months are known in oceanography as mesoscale eddies. Mesoscale eddies can be split into two categories: static eddies, caused by flow around an obstacle (see animation) , and transient eddies, caused by baroclinic instability. When

4536-448: The ocean. The sub-tropical Northern Atlantic is known to have both cyclonic and anticyclonic eddies that are associated with high surface chlorophyll and low surface chlorophyll, respectively. The presence of chlorophyll and higher levels of chlorophyll allows this region to support higher biomass of phytoplankton, as well as, supported by areas of increased vertical nutrient fluxes and transportation of biological communities. This area of

4608-471: The open ocean and how the removal of fish in this region may impact this pelagic food web is crucial for the fish populations and apex predators that may rely on this food source in addition to making better ecosystem-based management plans. Viscosity#Dynamic viscosity Viscosity is a measure of a fluid's rate-dependent resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to

4680-515: 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 }}

4752-555: 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

4824-715: 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

4896-583: 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

4968-513: 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

5040-403: 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

5112-571: 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

5184-500: 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),

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