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84-653: Spätzle is the Swabian and Alsacian diminutive of Spatz , thus literally 'little sparrow '. They are also known as Knöpfle (diminutive of button ). In Switzerland they are called Spätzli or Chnöpfli , in Hungarian Nokedli or Csipetke , in Slovenian Vaseršpacli or vodni žličniki and in Ladin Fierfuli . The Slovak Halušky ( Hungarian : Galuska ) is also similar. Before

168-435: 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

252-587: A " Swabian speciality" and are generally associated with the German state of Baden-Württemberg . In France, they are associated with Alsace and Moselle . Germany's estimated annual commercial production of Spätzle is approximately 40,000 tons. Pre-made Spätzle are also available internationally. Since March 2012, Swabian Spätzle and Swabian Knöpfle have been awarded the EU quality seal for protected geographical indication (PGI) and are protected throughout Europe as

336-671: A "Prince of Swabia" and integrated the Shrievalty of Swabia in the realm of Further Austria . The Swabian League of Cities was first formed on 20 November 1331, when twenty-two imperial cities of the former Duchy of Swabia banded together in support of the Emperor Louis IV , who in return promised not to mortgage any of them to any imperial vassal . Among the founding cities were Augsburg , Heilbronn , Reutlingen , and Ulm . The counts of Württemberg , Oettingen , and Hohenberg were induced to join in 1340. The defeat of

420-436: 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

504-586: A culinary specialty eaten on feast days. In a description of a Swabian farmers' village written in 1937, Spätzle are described as a festive food. The great importance of Schwäbische Spätzle/Schwäbische Knöpfle in Swabian cooking can be seen, inter alia, from the 1827 novel Die Geschichte von den Sieben Schwaben , according to which the custom in Swabia is "to eat five times a day, five times soup, twice with Knöpfle or Spätzle". Today, Spätzle are largely considered

588-506: 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

672-512: A knife, yet hold the initial shape for some seconds. If dropped into boiling water, the albumen will congeal quickly in the boiling water, while the yolk will keep the dough succulent. After the pasta has become firm, they are skimmed and put aside. Since this can be a cumbersome way to prepare Spätzle, several devices were invented to facilitate cooking that resemble a strainer or colander , potato ricer ( Spätzlepresse ), food mill , or coarse grater ( Spätzlehobel ). As with scraped Spätzle,

756-415: 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

840-521: A primary ingredient in dishes including: Savory Sweet Swabia Swabia is a cultural, historic and linguistic region in southwestern Germany . The name is ultimately derived from the medieval Duchy of Swabia , one of the German stem duchies , representing the historic settlement area of the Germanic tribe alliances named Alemanni and Suebi . This territory would include all of

924-418: A regional specialty. To be able to bear this sign, one of the production stages of the product must have taken place in the respectively defined region of origin. Spätzle is a type of dumpling or noodle. Its dough typically consists of few ingredients, principally eggs, flour, and salt. The Swabian rule of thumb is to use a number of eggs equal to the number of servings, plus one. Water is often added to produce

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1008-492: A runnier dough. The flour traditionally used for Spätzle is bread wheat (not the durum wheat used for Italian pasta ); however, a more coarsely milled type is used for Spätzle-making than for baking. This flour type is known as Dunst , similar to US " first clear " or Czech hrubá type. This gives a chewier texture but can produce a dough too crumbly for scraping if no water is added, particularly when cutting short on eggs for dietary reasons. If fine ("all-purpose") flour and

1092-416: 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

1176-664: 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;

1260-457: 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

1344-462: 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

1428-460: 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 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

1512-550: 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

1596-532: 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}

1680-457: 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

1764-448: 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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1848-540: 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

1932-576: 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 } }

2016-658: 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

2100-588: 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}

2184-408: 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

2268-425: 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

2352-611: 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

2436-554: 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

2520-993: Is traditionally spoken in the upper Neckar basin (upstream of Heilbronn ), along the upper Danube between Tuttlingen and Donauwörth , in Upper Swabia , and on the left bank of the Lech , in an area centered on the Swabian Alps roughly stretching from Stuttgart to Augsburg . Many Swabian surnames end with the suffixes -le , -(l)er , -el , -ehl , and -lin , typically from the Middle High German diminutive suffix -elîn (Modern Standard German -lein ). Examples would be: Schäuble , Egeler , Rommel , and Gmelin . The popular German surname Schwab as well as Svevo in Italy are derived from this area, both meaning literally "Swabian". Viscous Viscosity

2604-626: The Alemannic German area, but the modern concept of Swabia is more restricted, due to the collapse of the duchy of Swabia in the thirteenth century. Swabia as understood in modern ethnography roughly coincides with the Swabian Circle of the Holy Roman Empire as it stood during the early modern period , now divided between the states of Bavaria and Baden-Württemberg . Swabians ( Schwaben , singular Schwabe ) are

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2688-1003: The Baltic Sea the Mare Suevicum ("Suebian Sea") after the Suiones , and ends his description of the Suiones and Sitones with "Here Suebia ends" ( Hic Suebiae finis ). By the mid-3rd century, groups of the Suebi form the core element of the new tribal alliance known as the Alamanni , who expanded towards the Roman Limes east of the Rhine and south of the Main. The Alamanni were sometimes referred to as Suebi even at this time, and their new area of settlement came to be known as Suebia. In

2772-674: The British Royal Family that has ruled since 1714. Smaller feudal dynasties eventually disappeared, however; for example, branches of the Montforts and Hohenems lived until modern times, and the Fürstenberg survive still. The region proved to be one of the most divided in the empire, containing, in addition to these principalities, numerous free cities , ecclesiastical territories, and fiefdoms of lesser counts and knights . A new Swabian League ( Schwäbischer Bund )

2856-586: The Franconian War . The Reformation caused the league to be disbanded in 1534. The territory of Swabia as understood today emerges in the early modern period. It corresponds to the Swabian Circle established in 1512. The Old Swiss Confederacy was de facto independent from Swabia from 1499 as a result of the Swabian War , while the Margraviate of Baden had been detached from Swabia since

2940-611: The Great Interregnum . In the following years, the original duchy gradually broke up into many smaller units. Rudolf I of Habsburg , elected in 1273 as emperor, tried to restore the duchy, but met the opposition of the higher nobility who aimed to limit the power of the emperor. Instead, he confiscated the former estates of the Hohenstaufen as imperial property of the Holy Roman Empire, and declared most of

3024-633: The Kingdom of Württemberg , the Grand Duchy of Baden , and the Principality of Hohenzollern-Sigmaringen as sovereign states. Much of Eastern Swabia became part of Bavaria , forming what is now the Swabian administrative region of Bavaria. The Kings of Bavaria assumed the title Duke in Swabia , with the in indicating that only parts of the Swabian territory was ruled by them, unlike their other title Duke of Franconia which made clear that

3108-702: The Vosges Mountains in the west to the broad Lech river in the east: Like all of Southern Germany , what is now Swabia was part of the La Tène culture , and as such has a Celtic (Gaulish) substrate. In the Roman era, it was part of the Raetia province. The name Suebia is derived from that of the Suebi . It is used already by Tacitus in the 1st century, albeit in a different geographical sense: He calls

3192-589: 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

3276-425: 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

3360-568: The migration period , the Suebi (Alamanni) crossed the Rhine in 406 and some of them established the Kingdom of the Suebi in Galicia. Another group settled in parts of Pannonia , after the Huns were defeated in 454 in the Battle of Nedao . The Alemanni were ruled by independent kings throughout the 4th to 5th centuries but fell under Frankish domination in the 6th ( Battle of Tolbiac 496). By

3444-431: 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

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3528-469: The 18th century, although medieval illustrations are believed to place the noodle at an even earlier date. In 1725, Rosino Lentilio, a councillor and personal physician from Württemberg , concluded that Knöpflein and Spazen were "all the things that are made from flour". Spelt was grown widely in the Swabian-Alemannic area at the time. The cereal grew on poor soils and was very popular in

3612-491: 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

3696-468: 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

3780-646: The Duke of Württemberg was soon restored. The region was quite divided by the Reformation. While secular princes such as the Duke of Württemberg and the Margrave of Baden-Durlach , as well as most of the Free Cities, became Protestant , the ecclesiastical territories (including the bishoprics of Augsburg , Konstanz and the numerous Imperial abbeys ) remained Catholic , as did the territories belonging to

3864-685: The Habsburgs ( Further Austria ), the Sigmaringen branch of the House of Hohenzollern , and the Margrave of Baden-Baden . In the wake of the territorial reorganization of the empire of 1803 by the Reichsdeputationshauptschluss , the shape of Swabia was entirely changed. All the ecclesiastical estates were secularized, and most of the smaller secular states, and almost all of the free cities, were mediatized , leaving only

3948-425: 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

4032-471: The cities formerly belonging to Hohenstaufen to be Free Imperial Cities , and the more powerful abbeys within the former duchy to be Imperial Abbeys. The rural regions were merged into the Imperial Shrievalty ( Reichslandvogtei ) of Swabia, which was given as Imperial Pawn to Duke Leopold III of Austria in 1379 and again to Sigismund, Archduke of Austria in 1473/1486. He took the title of

4116-494: The city league by Count Eberhard II of Württemberg in 1372 led to the formation of a new league of fourteen Swabian cities on 4 July 1376. The emperor refused to recognise the newly revitalised Swabian League, seeing it as a rebellion, and this led to an " imperial war " against the league. The renewed league defeated an imperial army at the Battle of Reutlingen on 14 May 1377. Burgrave Frederick V of Hohenzollern finally defeated

4200-602: 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

4284-701: The dough drops into the boiling water. Those instruments that use muscle pressure in addition to gravity can be used with a firmer dough; that for a Spätzlehobel should be as "runny" as the one for scraping. For certain specialty dishes, the dough may be enriched with minced pork liver (resulting in Leberspätzle  [ de ] ), spinach or finely grated cheese. Spätzle typically accompanies meat dishes prepared with an abundant sauce or gravy, such as Zwiebelrostbraten  [ de ] , Sauerbraten , Jägerschnitzel or Rouladen . In Hungary, Spätzle often are used in soup. Spätzle also are used as

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4368-465: 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

4452-457: 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

4536-409: 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

4620-459: 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

4704-426: 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

4788-673: The former state of Württemberg (with the Prussian Hohenzollern Province ), or the modern districts of Tübingen (excluding the former Baden regions of the Bodenseekreis district), Stuttgart , and the administrative region of Bavarian Swabia . In the Middle Ages , the term Swabia indicated a larger area, covering all the lands associated with the Frankish stem duchy of Alamannia stretching from

4872-405: 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,

4956-428: The full amount of eggs are used, all fat and moisture in the dough is derived from these, and water is rarely necessary. Traditionally, Spätzle are made by scraping long, thin strips of dough off a wooden (sometimes wet) chopping board ( Spätzlebrett ) into boiling salted water, where they cook until they rise to the surface. Altogether, the dough should thus be as viscous as to slowly flow apart if cut into strips with

5040-409: 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

5124-713: The late 5th century, the area settled by the Alemanni extended to Alsace and the Swiss Plateau , bordering on the Bavarii to the east, the Franks to the north, the remnants of Roman Gaul to the west, and the Lombards and Goths , united in the Kingdom of Odoacer , to the south. The name Alamannia was used by the 8th century, and from the 9th century, Suebia was occasionally used for Alamannia , while Alamannia

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5208-659: The later Carolingian period , Swabia became once again de facto independent, by the early 10th century mostly ruled by two dynasties, the Hunfriding counts in Raetia Curiensis and the Ahalolfings ruling the Baar estates around the upper Neckar and Danube rivers. The conflict between the two dynasties was decided in favour of Hunfriding Burchard II at the Battle of Winterthur (919). Burchard's rule as duke

5292-769: The league in 1388 at Döffingen . The next year the city league disbanded according to the resolutions of the Reichstag at Eger . The major dynasties that arose out of medieval Swabia were the Habsburgs and the Hohenzollerns , who rose to prominence in Northern Germany. Also stemming from Swabia are the local dynasties of the dukes of Württemberg and the margraves of Baden . The Welf family went on to rule in Bavaria and Hanover , and are ancestral to

5376-529: 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

5460-435: 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

5544-431: The natives of Swabia and speakers of Swabian German . Their number was estimated at close to 0.8 million by SIL Ethnologue as of 2006, compared to a total population of 7.5 million in the regions of Tübingen , Stuttgart and Bavarian Swabia . Like many cultural regions of Europe, Swabia's borders are not clearly defined. However, today it is normally thought of as comprising the former Swabian Circle , or equivalently

5628-518: The region, which was home to small farmers and characterised by poverty. As spelt flour contains high levels of gluten protein, and the dough could therefore be made in times of hardship without the need for eggs, Schwäbische Spätzle/Schwäbische Knöpfle were mainly made from spelt. The product achieved fame in the Münsinger Alb upland area. As industrialisation began and prosperity increased, the noodles went from an ordinary, everyday food item to

5712-515: 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 }}

5796-471: The same product made from the same dough and are interchangeable. There is no clear distinction between how the two names are used, and usage varies from region to region (for example, in Alsace, Knöple are typically larger than Spätzle). The geographic origin of Spätzle is not precisely known; various regions claim to be the originators of the noodles. The tradition of making Spätzle can be traced back to

5880-555: 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

5964-715: 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

6048-534: The term. Baden's residents mostly refer to themselves as Alemanni (versus the Swabians ). SIL Ethnologue cites an estimate of 819,000 Swabian speakers as of 2006. This corresponds to roughly 10% of the total population of the Swabian region, or roughly 1% of the total population of Germany. As an ethno-linguistic group, Swabians are closely related to other speakers of Alemannic German , i.e. Badeners , Alsatians , and German-speaking Swiss . Swabian German

6132-583: 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

6216-581: The twelfth century. Fearing the power of the greater princes, the cities and smaller secular rulers of Swabia joined to form the Swabian League in the fifteenth century. The League was quite successful, notably expelling the Duke of Württemberg in 1519 and putting in his place a Habsburg governor, but the league broke up a few years later over religious differences inspired by the Reformation , and

6300-513: 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

6384-403: The use of mechanical devices, the noodles were shaped by hand or with a spoon, and the results resembled Spatzen (plural of Spatz , meaning ' sparrows ', 'sparrow' is Spatz or Sperling in German; Spätzle is the diminutive of Spatz , unchanged in plural). Knöpfle means 'small buttons' and describes the compact, round form of the noodle. In everyday language usage, the two names refer to

6468-403: 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

6552-609: 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"

6636-571: 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

6720-500: 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),

6804-472: The whole of Franconia had become part of their kingdom. In contemporary usage, Schwaben is sometimes taken to refer to Bavarian Swabia exclusively, correctly however it includes the larger Württemberg part of Swabia. Its inhabitants attach great importance to calling themselves Swabians. Baden, historically part of the duchy of Swabia and also of the Swabian Circle, is no longer commonly included in

6888-472: Was acknowledged as such by the newly elected king Henry the Fowler , and in the 960s the duchy under Burchard III was incorporated in the Holy Roman Empire under Otto I . The Hohenstaufen dynasty, which ruled the Holy Roman Empire in the 12th and 13th centuries, arose out of Swabia, but following the execution of Conradin , the last Hohenstaufen, on 29 October 1268, the duchy was not reappointed during

6972-697: Was formed in 1488, opposing the expansionist Bavarian dukes from the House of Wittelsbach and the revolutionary threat from the south in the form of the Swiss . In 1519, the League conquered Württemberg and sold it to Charles V after its duke Ulrich seized the Free Imperial City of Reutlingen during the interregnum that followed the death of Maximilian I. It helped to suppress the Peasants' Revolt in 1524–26 and defeat an alliance of robber barons in

7056-549: Was increasingly used to refer to Alsace specifically. By the 12th century, Suebia rather than Alamannia was used consistently for the territory of the Duchy of Swabia . Swabia was one of the original stem duchies of East Francia , the later Holy Roman Empire , as it developed in the 9th and 10th centuries. Due to the foundation of the important abbeys of St. Gallen and Reichenau , Swabia became an important center of Old High German literary culture during this period. In

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