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A simulation of liquids with different viscosities.The liquid on the left has lower viscosity than the liquid on the right.Common symbols, SI unit.Pas Nsm. 2 kgsmDerivations fromother quantities Gt.The viscosity of a fluid is a measure of its resistance to gradual deformation by shear stress or tensile stress.For liquids, it corresponds to the informal concept of thickness for example, honey has a much higher viscosity than water.Viscosity is a property of the fluid which opposes the relative motion between the two surfaces of the fluid in a fluid that are moving at different velocities.When the fluid is forced through a tube, the particles which compose the fluid generally move more quickly near the tubes axis and more slowly near its walls therefore some stress such as a pressure difference between the two ends of the tube is needed to overcome the friction between particle layers to keep the fluid moving.For a given velocity pattern, the stress required is proportional to the fluids viscosity.A fluid that has no resistance to shear stress is known as an ideal or inviscid fluid.Zero viscosity is observed only at very low temperatures in superfluids.Otherwise, all fluids have positive viscosity, and are technically said to be viscous or viscid.In common parlance, however, a liquid is said to be viscous if its viscosity is substantially greater than that of water, and may be described as mobile if the viscosity is noticeably less than water.A fluid with a relatively high viscosity, such as pitch, may appear to be a solid.EtymologyeditThe word viscosity is derived from the Latin viscum, meaning mistletoe and also a viscous glue made from mistletoe berries.DefinitioneditDynamic shear viscosity edit.Laminar shear of fluid between two plates.Friction between the fluid and the moving boundariesplates causes the fluid to shear.The force required for this action is a measure of the fluids viscosity.In a general parallel flow such as could occur in a straight pipe, the shear stress is proportional to the gradient of the velocity.The dynamic shear viscosity of a fluid expresses its resistance to shearing flows, where adjacent layers move parallel to each other with different speeds.It can be defined through the idealized situation known as a Couette flow, where a layer of fluid is trapped between two horizontal plates, one fixed and one moving horizontally at constant speed udisplaystyle u.This fluid has to be homogeneous in the layer and at different shear stresses.The plates are assumed to be very large, so that one need not consider what happens near their edges.If the speed of the top plate is low enough, the fluid particles will move parallel to it, and their speed will vary linearly from zero at the bottom to u at the top.Each layer of fluid will move faster than the one just below it, and friction between them will give rise to a force resisting their relative motion.In particular, the fluid will apply on the top plate a force in the direction opposite to its motion, and an equal but opposite one to the bottom plate.An external force is therefore required in order to keep the top plate moving at constant speed.The magnitude F of this force is found to be proportional to the speed u and the area A of each plate, and inversely proportional to their separation y FAuy.Fmu Afrac uy. The proportionality factor in this formula is the viscosity specifically, the dynamic viscosity of the fluid, with units of Pasdisplaystyle Pacdot s pascal second.The ratio uy is called the rate of shear deformation or shear velocity, and is the derivative of the fluid speed in the direction perpendicular to the plates clarification needed.Isaac Newton expressed the viscous forces by the differential equationuy,displaystyle tau mu frac partial upartial y,where FA, and uy is the local shear velocity.This formula assumes that the flow is moving along parallel lines to x axis.Furthermore, it assumes that the y axis, perpendicular to the flow, points in the direction of maximum shear velocity.This equation can be used where the velocity does not vary linearly with y, such as in fluid flowing through a pipe.Use of the Greek letter mu for the dynamic stress viscosity is common among mechanical and chemical engineers, as well as physicists.However, the Greek letter eta is also used by chemists, physicists, and the IUPAC.Kinematic viscosityeditThe kinematic viscosity also called momentum diffusivity is the ratio of the dynamic viscosity to the density of the fluid.It is usually denoted by the Greek letter nu and has units m.It is a convenient concept when analyzing the Reynolds number, which expresses the ratio of the inertial forces to the viscous forces Reu.Lu. L,displaystyle mathrm Re frac rho u.Lmu frac u. Lnu ,where L is a typical length scale in the system.Bulk viscosityeditWhen a compressible fluid is compressed or expanded evenly, without shear, it may still exhibit a form of internal friction that resists its flow.These forces are related to the rate of compression or expansion by a factor called the volume viscosity, bulk viscosity or second viscosity.The bulk viscosity is important only when the fluid is being rapidly compressed or expanded, such as in sound and shock waves.Bulk viscosity explains the loss of energy in those waves, as described by Stokes law of sound attenuation.Viscosity tensoreditIn general, the stresses within a flow can be attributed partly to the deformation of the material from some rest state elastic stress, and partly to the rate of change of the deformation over time viscous stress.In a fluid, by definition, the elastic stress includes only the hydrostatic pressure.In very general terms, the fluids viscosity is the relation between the strain rate and the viscous stress.In the Newtonian fluid model, the relationship is by definition a linear map, described by a viscosity tensor that, multiplied by the strain rate tensor which is the gradient of the flows velocity, gives the viscous stress tensor.The viscosity tensor has nine independent degrees of freedom in general.For isotropic Newtonian fluids, these can be reduced to two independent parameters.The most usual decomposition yields the dynamic viscosity and the bulk viscosity.Newtonian and non Newtonian fluidsedit.Viscosity, the slope of each line, varies among materials.Newtons law of viscosity is a constitutive equation like Hookes law, Ficks law, Ohms law it is not a fundamental law of nature but an approximation that holds in some materials and fails in others.A fluid that behaves according to Newtons law, with a viscosity that is independent of the stress, is said to be Newtonian.Gases, water, and many common liquids can be considered Newtonian in ordinary conditions and contexts.There are many non Newtonian fluids that significantly deviate from that law in some way or other.For example Shear thickening liquids, whose viscosity increases with the rate of shear strain.Shear thinning liquids, whose viscosity decreases with the rate of shear strain.Thixotropic liquids, that become less viscous over time when shaken, agitated, or otherwise stressed.Rheopectic Dilatant liquids, that become more viscous over time when shaken, agitated, or otherwise stressed.Bingham plastics that behave as a solid at low stresses but flow as a viscous fluid at high stresses.Shear thinning liquids are very commonly, but misleadingly, described as thixotropic.Even for a Newtonian fluid, the viscosity usually depends on its composition and temperature.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 a magnetic field, possibly to the point of behaving like a solid.Viscosity in solidseditThe viscous forces that arise during fluid flow must not be confused with the elastic forces that arise 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.
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