**Continuum mechanics** |
| *Key topics* | Conservation of mass Conservation of momentum Navier-Stokes equations | *Classical mechanics* | Stress · Strain · Tensor
| *Solid mechanics* | Solids · Elasticity Plasticity · Hooke's law Rheology · Viscoelasticity Viscosity is a measure of the resistance of a fluid to deform under shear stress. ...
Continuum mechanics is a branch of physics (specifically mechanics) that deals with continuous matter, including both solids and fluids (i. ...
Image File history File links File links The following pages link to this file: Bernoullis equation ...
The law of conservation of mass/matter, also known as law of mass/matter conservation (or the Lomonosov-Lavoisier law), states that the mass of a closed system of substances will remain constant, regardless of the processes acting inside the system. ...
In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves. ...
The Navier-Stokes equations, named after Claude-Louis Navier and George Gabriel Stokes, are a set of equations which describe the motion of fluid substances such as liquids and gases. ...
Classical mechanics (commonly confused with Newtonian mechanics, which is a subfield thereof) is used for describing the motion of macroscopic objects, from projectiles to parts of machinery, as well as astronomical objects, such as spacecraft, planets, stars, and galaxies. ...
Stress is a measure of force per unit area within a body. ...
This article is about the deformation of materials. ...
In mathematics, a tensor is (in an informal sense) a generalized linear quantity or geometrical entity that can be expressed as a multi-dimensional array relative to a choice of basis; however, as an object in and of itself, a tensor is independent of any chosen frame of reference. ...
Solid mechanics is the branch of physics and mathematics that concern the behavior of solid matter under external actions (e. ...
For other uses, see Solid (disambiguation). ...
Elasticity is a branch of physics which studies the properties of elastic materials. ...
For other uses, see Plasticity. ...
Hookes law accurately models the physical properties of common mechanical springs for small changes in length. ...
Rheology is the study of the deformation and flow of matter under the influence of an applied stress. ...
Viscoelasticity, also known as anelasticity, describes materials that exhibit both viscous and elastic characteristics when undergoing plastic deformation. ...
| *Fluid mechanics* | Fluids · Fluid statics Fluid dynamics · **Viscosity** · Newtonian fluids Non-Newtonian fluids Surface tension | *Scientists* | Newton · Stokes · *others* Fluid mechanics is the subdiscipline of continuum mechanics that studies fluids, that is, liquids and gases. ...
A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. ...
Fluid statics (also called hydrostatics) is the science of fluids at rest, and is a sub-field within fluid mechanics. ...
Fluid dynamics is the sub-discipline of fluid mechanics dealing with fluids (liquids and gases) in motion. ...
A Newtonian fluid (named for Isaac Newton) is a fluid that flows like waterâ€”its shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear. ...
A non-Newtonian fluid is a fluid in which the viscosity changes with the applied strain rate. ...
Surface tension is an effect within the surface layer of a liquid that causes that layer to behave as an elastic sheet. ...
Sir Isaac Newton FRS (4 January 1643 â€“ 31 March 1727) [ OS: 25 December 1642 â€“ 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ...
Sir George Gabriel Stokes, 1st Baronet (13 August 1819â€“1 February 1903) was an Irish mathematician and physicist, who at Cambridge made important contributions to fluid dynamics (including the Navier-Stokes equations), optics, and mathematical physics (including Stokes theorem). ...
| This box: view • talk • edit | **Viscosity** is a measure of the resistance of a fluid to deform under either shear stress or extensional stress. It is commonly perceived as "thickness", or resistance to flow. Viscosity describes a fluid's internal resistance to flow and may be thought of as a measure of fluid friction. Thus, water is "thin", having a lower viscosity, while vegetable oil is "thick" having a higher viscosity. All real fluids (except superfluids) have some resistance to stress, but a fluid which has no resistance to shear stress is known as an **ideal fluid** or **inviscid fluid**.^{[1]} The study of viscosity is known as rheology. An object falling through a gas or liquid experiences a force in direction opposite to its motion. ...
A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. ...
Shear stress is a stress state where the stress is parallel or tangential to a face of the material, as opposed to normal stress when the stress is perpendicular to the face. ...
Stress is a measure of force per unit area within a body. ...
For other uses, see Friction (disambiguation). ...
Impact from a water drop causes an upward rebound jet surrounded by circular capillary waves. ...
It has been suggested that this article or section be merged with cooking oil. ...
Helium II will creep along surfaces in order to find its own level - after a short while, the levels in the two containers will equalize. ...
Stress is a measure of force per unit area within a body. ...
Rheology is the study of the deformation and flow of matter under the influence of an applied stress. ...
## Etymology
The word "viscosity" derives from the Latin word "viscum" for mistletoe. A viscous glue was made from mistletoe berries and used for lime-twigs to catch birds.^{[2]} For other uses, see Latin (disambiguation). ...
Families Santalaceae (Viscaceae) Loranthaceae Misodendraceae Mistletoe Viscum album is a plant parasitic on the branches of a tree or shrub. ...
## Viscosity coefficients When looking at a value for viscosity, the number that one most often sees is the coefficient of viscosity. There are several different viscosity coeffients depending on the nature of applied stress and nature of the fluid. They are introduced in the main books on hydrodynamics^{[3]}, ^{[4]} and rheology ^{[5]} Hydrodynamics is fluid dynamics applied to liquids, such as water, alcohol, oil, and blood. ...
Rheology is the study of the deformation and flow of matter under the influence of an applied stress. ...
**Dynamic viscosity** is viscosity coefficient that determines dynamics of incompressible Newtonian fluid; **Kinematic viscosity** is *dynamic viscosity* divided by density for Newtonian fluid; **Volume viscosity** is viscosity coefficient that determines dynamics of compressible Newtonian fluid; **Bulk viscosity** is the same as *volume viscosity* **Shear viscosity** is viscosity coefficient when applied stress is a shear stress, valid for non-Newtonian fluids; **Extensional viscosity** is viscosity coefficient when applied stress an extensional stress; valid for non-Newtonian fluids. *Shear and dynamic viscosity* are much more known than two others. That is why they are often reffered to as simply *viscosity*. Simply put, this quantity is the ratio between the pressure exerted on the surface of a fluid, in the lateral or horizontal direction, to the change in velocity of the fluid as you move down in the fluid (this is what is referred to as a velocity gradient). For example, at "room temperature", water has a nominal viscosity of 1.0 x 10^{-3} Pa∙s and motor oil has a nominal apparent viscosity of 250 x 10^{-3} Pa∙s.^{[6]} In mathematics, an incompressible surface is a kind of two-dimensional surface inside of a 3-manifold. ...
A Newtonian fluid (named for Isaac Newton) is a fluid that flows like waterâ€”its shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear. ...
Volume viscosity appears in Navier-Stokes equation if it is written for compressible fluid, as described in the most books on general hydrodynamics [1], [2], and the acoustics [3],[4]. where Î¼v is second viscosity coefficient. ...
A Newtonian fluid (named for Isaac Newton) is a fluid that flows like waterâ€”its shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear. ...
The pitch drop experiment at the University of Queensland. ...
Shear stress is a stress state where the stress is parallel or tangential to a face of the material, as opposed to normal stress when the stress is perpendicular to the face. ...
This article is about extensional viscosty. ...
Stress is a measure of force per unit area within a body. ...
For other uses, see Gradient (disambiguation). ...
*Extensional viscosity* is widely used for characterizing polymers. *Volume viscosity* is essentual for Acoustics in fluids, see Stokes' law (sound attenuation) ^{[7]} Acoustics is the branch of physics concerned with the study of sound (mechanical waves in gases, liquids, and solids). ...
This article is about sound attenuation in liquids. ...
## Newton's theory
Laminar shear of fluid between two plates. Friction between the fluid and the moving boundaries causes the fluid to shear. The force required for this action is a measure of the fluid's viscosity. This type of flow is known as a Couette flow.
Laminar shear, the non-linear gradient, is a result of the geometry the fluid is flowing through (e.g. a pipe). In general, in any flow, layers move at different velocities and the fluid's viscosity arises from the shear stress between the layers that ultimately opposes any applied force. laminar shear in fluid source: me File links The following pages link to this file: Viscosity Categories: GFDL images ...
laminar shear in fluid source: me File links The following pages link to this file: Viscosity Categories: GFDL images ...
The term Couette flow refers to the laminar flow of a viscous liquid in the space between two surfaces, one of which is moving relative to the other. ...
laminar shear-flow in a fluid File links The following pages link to this file: Viscosity Categories: Images with unknown source ...
laminar shear-flow in a fluid File links The following pages link to this file: Viscosity Categories: Images with unknown source ...
This article is about velocity in physics. ...
Isaac Newton postulated that, for straight, parallel and uniform flow, the shear stress, τ, between layers is proportional to the velocity gradient, ∂*u*/∂*y*, in the direction perpendicular to the layers. Sir Isaac Newton FRS (4 January 1643 â€“ 31 March 1727) [ OS: 25 December 1642 â€“ 20 March 1727][1] was an English physicist, mathematician, astronomer, natural philosopher, and alchemist. ...
Parallel is a term in geometry and in everyday life that refers to a property in Euclidean space of two or more lines or planes, or a combination of these. ...
This article is about velocity in physics. ...
For other uses, see Gradient (disambiguation). ...
Fig. ...
- .
Here, the constant η is known as the *coefficient of viscosity*, the *viscosity*, the *dynamic viscosity*, or the *Newtonian viscosity*. Many fluids, such as water and most gases, satisfy Newton's criterion and are known as Newtonian fluids. Non-Newtonian fluids exhibit a more complicated relationship between shear stress and velocity gradient than simple linearity. A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. ...
Impact from a water drop causes an upward rebound jet surrounded by circular capillary waves. ...
For other uses, see Gas (disambiguation). ...
A Newtonian fluid (named for Isaac Newton) is a fluid that flows like waterâ€”its shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear. ...
A non-Newtonian fluid is a fluid in which the viscosity changes with the applied strain rate. ...
The relationship between the shear stress and the velocity gradient can also be obtained by considering two plates closely spaced apart at a distance *y*, and separated by a homogeneous substance. Assuming that the plates are very large, with a large area *A*, such that edge effects may be ignored, and that the lower plate is fixed, let a force *F* be applied to the upper plate. If this force causes the substance between the plates to undergo shear flow (as opposed to just shearing elastically until the shear stress in the substance balances the applied force), the substance is called a fluid. The applied force is proportional to the area and velocity of the plate and inversely proportional to the distance between the plates. Combining these three relations results in the equation *F = η(Au/y)*, where η is the proportionality factor called the *absolute viscosity* (with units Pa·s = kg/(m·s) or slugs/(ft·s)). The absolute viscosity is also known as the *dynamic viscosity*, and is often shortened to simply *viscosity*. The equation can be expressed in terms of shear stress; *τ = F/A = η(u/y)*. The rate of shear deformation is *u* / *y* and can be also written as a shear velocity, *du/dy*. Hence, through this method, the relation between the shear stress and the velocity gradient can be obtained. Look up Heterogeneous in Wiktionary, the free dictionary. ...
In engineering mechanics, deformation is a change in shape due to an applied force. ...
In solid mechanics, elasticity is the property of materials which undergo reversible deformations under applied loads. ...
James Clerk Maxwell called viscosity *fugitive elasticity* because of the analogy that elastic deformation opposes shear stress in solids, while in viscous fluids, shear stress is opposed by *rate* of deformation. James Clerk Maxwell (13 June 1831 â€“ 5 November 1879) was a Scottish mathematician and theoretical physicist from Edinburgh, Scotland, UK. His most significant achievement was aggregating a set of equations in electricity, magnetism and inductance â€” eponymously named Maxwells equations â€” including an important modification (extension) of the AmpÃ¨res...
For other uses, see Solid (disambiguation). ...
A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. ...
## Viscosity Measurement *Dynamic viscosity* is measured with various types of viscometer. Close temperature control of the fluid is essential to accurate measurements, particularly in materials like lubricants, whose viscosity (-40 < sample temperature <0) can double with a change of only 5 deg. C. For some fluids, it is a constant over a wide range of shear rates. These are Newtonian fluids. A viscometer (also called viscosimeter) is an instrument used to measure the viscosity of a fluid. ...
A Newtonian fluid is a fluid in which shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear. ...
- The fluids without a constant viscosity are called Non-Newtonian fluids. They are better characterized with notion of
*shear viscosity*, which allows shear rate dependence. One of the most common methods of measuring kinematic viscosity is using the glass capillary viscometer. A non-Newtonian fluid is a fluid in which the viscosity changes with the applied strain rate. ...
In paint industries, viscosity is commonly measured with a Zahn cup, in which the efflux time is determined and given to customers. The efflux time can also be converted to kinematic viscosities (cSt) through the conversion equations. A Zahn cup is a viscosity measurement device widely used in the paint industry. ...
Also used in paint, a Stormer viscometer uses load-based rotation in order to determine viscosity. It uses units, Krebs units (KU), unique to this viscometer. A viscometer (also called viscosimeter) is an instrument used to measure the viscosity of a fluid. ...
Vibrating viscometers can also be used to measure viscosity. These models use vibration rather than rotation to measure viscosity.
*Extensional viscosity* can be measured with various rheometers that apply extensional stress Rheometers are viscometers which are able to measure visco-elastic properties of materials rather than viscosity alone. ...
Stress is a measure of force per unit area within a body. ...
Volume viscosity can be measured with acoustic rheometer. Volume viscosity appears in Navier-Stokes equation if it is written for compressible fluid, as described in the most books on general hydrodynamics [1], [2], and the acoustics [3],[4]. where Î¼v is second viscosity coefficient. ...
This article is about instrument for studying extensional rheology. ...
### Units of Measure #### Viscosity (dynamic/absolute viscosity) The IUPAC symbol for viscosity is the Greek symbol eta (η), and dynamic viscosity is also commonly referred to using the Greek symbol mu (μ). The SI physical unit of dynamic viscosity is the pascal-second (Pa·s), which is identical to 1 kg·m^{−1}·s^{−1}. If a fluid with a viscosity of one Pa·s is placed between two plates, and one plate is pushed sideways with a shear stress of one pascal, it moves a distance equal to the thickness of the layer between the plates in one second. The International Union of Pure and Applied Chemistry (IUPAC) is an international non-governmental organization devoted to the advancement of chemistry. ...
Look up si, Si, SI in Wiktionary, the free dictionary. ...
The definition, agreement and practical use of units of measurement have played a crucial role in human endeavour from early ages up to this day. ...
The pascal (symbol: Pa) is the SI derived unit of pressure or stress (also: Youngs modulus and tensile strength). ...
This article is about the unit of time. ...
â€œKgâ€ redirects here. ...
A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. ...
Shear stress is a stress state where the stress is parallel or tangential to a face of the material, as opposed to normal stress when the stress is perpendicular to the face. ...
The pascal (symbol: Pa) is the SI derived unit of pressure or stress (also: Youngs modulus and tensile strength). ...
This article is about the unit of time. ...
The name poiseuille (Pl) was proposed for this unit (after Jean Louis Marie Poiseuille who formulated Poiseuille's law of viscous flow), but not accepted internationally. Care must be taken in not confusing the poiseuille with the poise named after the same person. Jean Louis Marie Poiseuille (April 22, 1797 - December 26, 1869) was a French physician and physiologist. ...
Jean Louis Marie Poiseuille pwÃ¤z-wÄ“ (April 22, 1799 - December 26, 1869) was a French physician and physiologist. ...
The Poiseuilles law (or the Hagen-Poiseuille law also named after Gotthilf Heinrich Ludwig Hagen (1797-1884) for his experiments in 1839) is the physical law concerning the voluminal laminar stationary flow Î¦V of incompressible uniform viscous liquid (so called Newtonian fluid) through a cylindrical tube with the constant...
The poise (P; IPA: ) is the unit of dynamic viscosity in the centimetre gram second system of units. ...
The cgs physical unit for dynamic viscosity is the *poise*^{[8]} (P), named after Jean Louis Marie Poiseuille. It is more commonly expressed, particularly in ASTM standards, as *centipoise* (cP). The centipoise is commonly used because water has a viscosity of 1.0020 cP (at 20 °C; the closeness to one is a convenient coincidence). This article or section is in need of attention from an expert on the subject. ...
The definition, agreement and practical use of units of measurement have played a crucial role in human endeavour from early ages up to this day. ...
Jean Louis Marie Poiseuille pwÃ¤z-wÄ“ (April 22, 1799 - December 26, 1869) was a French physician and physiologist. ...
ASTM International is an international voluntary standards organization that develops and produces technical standards for materials, products, systems and services. ...
- 1 P = 1 g·cm
^{−1}·s^{−1} The relation between Poise and Pascal-second is: - 10 P = 1 kg·m
^{−1}·s^{−1} = 1 Pa·s - 1 cP = 0.001 Pa·s = 1 mPa·s
#### Kinematic viscosity: ν In many situations, we are concerned with the ratio of the viscous force to the inertial force, the latter characterised by the fluid density ρ. This ratio is characterised by the *kinematic viscosity* (ν), defined as follows: This article is about inertia as it applies to local motion. ...
A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. ...
For other uses, see Density (disambiguation). ...
- .
where μ is the (dynamic) viscosity, and ρ is the density. Kinematic viscosity (Greek symbol: ν) has SI units (m²·s^{−1}). The cgs physical unit for kinematic viscosity is the *stokes* (abbreviated S or St), named after George Gabriel Stokes. It is sometimes expressed in terms of *centistokes* (cS or cSt). In U.S. usage, *stoke* is sometimes used as the singular form. Sir George Gabriel Stokes, 1st Baronet (13 August 1819â€“1 February 1903) was an Irish mathematician and physicist, who at Cambridge made important contributions to fluid dynamics (including the Navier-Stokes equations), optics, and mathematical physics (including Stokes theorem). ...
- 1 stokes = 100 centistokes = 1 cm
^{2}·s^{−1} = 0.0001 m^{2}·s^{−1}. - 1 centistokes = 1 mm²/s
#### Dynamic versus kinematic viscosity Conversion between kinematic and dynamic viscosity, is given by νρ = η. Note that the parameters must be given in SI units not in P, cP or St. For example, if ν = 1 St (=0.0001 m²·s^{-1}) and ρ = 1000 kg m^{-3} then η = νρ = 0.1 kg·m^{−1}·s^{−1} = 0.1 Pa·s. A plot of the kinematic viscosity of air as a function of absolute temperature is available on the Internet.^{[9]}
#### Example: viscosity of water Because of its density of ρ = 1 g/cm^{3}, and its dynamic viscosity of 1 mPa·s, the viscosity values of water are all powers of ten: Dynamic viscosity: μ = 1 mPa·s = 10^{-3} Pa·s = 1 cP = 10^{-2} Poise Kinematic viscosity: ν = 1 cSt = 10^{-2} Stokes = 1 mm^{2}/s
## Molecular origins
Pitch has a viscosity approximately 100 billion times that of water. The viscosity of a system is determined by how molecules constituting the system interact. There are no simple but correct expressions for the viscosity of a fluid. The simplest exact expressions are the Green-Kubo relations for the linear shear viscosity or the Transient Time Correlation Function expressions derived by Evans and Morriss in 1985. Although these expressions are each exact in order to calculate the viscosity of a dense fluid, using these relations requires the use of molecular dynamics computer simulation. Image File history File links Size of this preview: 398 Ã— 599 pixelsFull resolution (1012 Ã— 1524 pixel, file size: 706 KB, MIME type: image/jpeg) Reworked version of Image:University_of_Queensland_Pitch_drop_experiment-6. ...
Image File history File links Size of this preview: 398 Ã— 599 pixelsFull resolution (1012 Ã— 1524 pixel, file size: 706 KB, MIME type: image/jpeg) Reworked version of Image:University_of_Queensland_Pitch_drop_experiment-6. ...
The University of Queensland pitch drop experiment, demonstrating the viscosity of bitumen. ...
Green-Kubo relations give exact mathematical expression for transport coefficients in terms of integrals of time correlation functions. ...
Molecular dynamics (MD) is a form of computer simulation wherein atoms and molecules are allowed to interact for a period of time under known laws of physics, giving a view of the motion of the atoms. ...
### Gases Viscosity in gases arises principally from the molecular diffusion that transports momentum between layers of flow. The kinetic theory of gases allows accurate prediction of the behaviour of gaseous viscosity. Within the regime where the theory is applicable: - Viscosity is independent of pressure and
- Viscosity increases as temperature increases.
#### Effect of temperature on the viscosity of a gas Sutherland's formula can be used to derive the dynamic viscosity of an ideal gas as a function of the temperature: An ideal gas or perfect gas is a hypothetical gas consisting of identical particles of zero volume, with no intermolecular forces. ...
where: - η = viscosity in (Pa·s) at input temperature
*T* - η
_{0} = reference viscosity in (Pa·s) at reference temperature *T*_{0} *T* = input temperature in kelvin *T*_{0} = reference temperature in kelvin *C* = Sutherland's constant for the gasous material in question Valid for temperatures between 0 < *T* < 555 K with an error due to pressure less than 10% below 3.45 MPa Sutherland's constant and reference temperature for some gases Look up air in Wiktionary, the free dictionary. ...
General Name, symbol, number nitrogen, N, 7 Chemical series nonmetals Group, period, block 15, 2, p Appearance colorless gas Standard atomic weight 14. ...
General Name, symbol, number oxygen, O, 8 Chemical series nonmetals, chalcogens Group, period, block 16, 2, p Appearance colorless (gas) pale blue (liquid) Standard atomic weight 15. ...
Carbon dioxide is a chemical compound composed of two oxygen atoms covalently bonded to a single carbon atom. ...
Carbon monoxide, with the chemical formula CO, is a colorless, odorless, and tasteless gas. ...
General Name, Symbol, Number hydrogen, H, 1 Chemical series nonmetals Group, Period, Block 1, 1, s Appearance colorless Atomic mass 1. ...
For other uses, see Ammonia (disambiguation). ...
Sulfur dioxide (or Sulphur dioxide) has the chemical formula SO2. ...
#### Viscosity of a dilute gas The Chapman-Enskog equation^{[10]} may be used to estimate viscosity for a dilute gas. This equation is based on semi-theorethical assumption by Chapman and Enskoq. The equation requires three empirically determined parameters: the collision diameter (σ), the maximum energy of attraction divided by the Boltzman constant (є/к) and the collision integral (ω(T*)). The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. ...
- ; T*=κT/ε
- η
_{0} = viscosity for dilute gas (uP) *M* = molecular weight (kg/m^3) *T* = temperature (K) - σ = the collision diameter (Å)
- ε / κ = the maximum energy of attraction divided by the Boltzman constant (K)
- ω
_{η} = the collision integral *T* * = reduced temperature (K) ### Liquids In liquids, the additional forces between molecules become important. This leads to an additional contribution to the shear stress though the exact mechanics of this are still controversial.^{[citation needed]} Thus, in liquids: - Viscosity is independent of pressure (except at very high pressure); and
- Viscosity tends to fall as temperature increases (for example, water viscosity goes from 1.79 cP to 0.28 cP in the temperature range from 0 °C to 100 °C); see temperature dependence of liquid viscosity for more details.
The dynamic viscosities of liquids are typically several orders of magnitude higher than dynamic viscosities of gases. The temperature dependence of liquid viscosity is usually expressed by one of the following models: // where T is temperature and and are coefficients. ...
#### Viscosity of blends of liquids The viscosity of the blend of two or more liquids can be estimated using the Refutas equation^{[11]}^{[12]}. The calculation is carried out in three steps. The first step is to calculate the Viscosity Blending Number (VBN) (also called the Viscosity Blending Index) of each component of the blend: - (1)
where *v* is the viscosity in centistokes (cSt). It is important that the viscosity of each component of the blend be obtained at the same temperature. The next step is to calculate the VBN of the blend, using this equation: - (2)
where *x*_{X} is the mass fraction of each component of the blend. In aerospace engineering, the mass fraction is an important measure of a rockets efficiency. ...
Once the viscosity blending number of a blend has been calculated using equation (2), the final step is to determine the viscosity of the blend by solving equation (1) for *v*: - (3)
where *V**B**N*_{Blend} is the viscosity blending number of the blend.
## Viscosity of materials The viscosity of air and water are by far the two most important materials for aviation aerodynamics and shipping fluid dynamics. Temperature plays the main role in determining viscosity.
### Viscosity of air The viscosity of air depends mostly on the temperature. At 15.0 °C, the viscosity of air is 1.78 × 10^{−5} kg/(m·s). You can get the viscosity of air as a function of altitude from the eXtreme High Altitude Calculator
### Viscosity of water The viscosity of water is 8.90 × 10^{−4} Pa·s or 8.90 × 10^{−3} dyn·s/cm² at about 25 °C. As a function of temperature *T* (K): *μ*(Pa·s) = *A* × 10^{B/(T−C)} where *A*=2.414 × 10^{−5} Pa·s ; *B* = 247.8 K ; and *C* = 140 K.
### Viscosity of various materials
Example of the viscosity of milk and water. Liquids with higher viscosities will not make such a splash when poured at the same velocity. Some dynamic viscosities of Newtonian fluids are listed below: Image File history File links Download high-resolution version (886x1398, 155 KB) Milk dropping down in red liquid File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): Viscosity User:Henningklevjer ...
Image File history File links Download high-resolution version (886x1398, 155 KB) Milk dropping down in red liquid File links The following pages on the English Wikipedia link to this file (pages on other projects are not listed): Viscosity User:Henningklevjer ...
This is a file from the Wikimedia Commons, a repository of free content hosted by the Wikimedia Foundation. ...
This is a file from the Wikimedia Commons, a repository of free content hosted by the Wikimedia Foundation. ...
For other uses, see Honey (disambiguation). ...
Download high resolution version (1141x850, 247 KB)Peanut Butter in the jar. ...
Download high resolution version (1141x850, 247 KB)Peanut Butter in the jar. ...
Peanut butter in a jar. ...
Quasi-solid is the physical term for a semi-solid. ...
Gases (at 0 °C): For other uses, see Gas (disambiguation). ...
Celsius is, or relates to, the Celsius temperature scale (previously known as the centigrade scale). ...
Liquids (at 25 °C): General Name, Symbol, Number hydrogen, H, 1 Chemical series nonmetals Group, Period, Block 1, 1, s Appearance colorless Atomic mass 1. ...
Air redirects here. ...
General Name, Symbol, Number xenon, Xe, 54 Chemical series noble gases Group, Period, Block 18, 5, p Appearance colorless Standard atomic weight 131. ...
For other uses, see Liquid (disambiguation). ...
Celsius is, or relates to, the Celsius temperature scale (previously known as the centigrade scale). ...
* Data from CRC Handbook of Chemistry and Physics, 73^{rd} edition, 1992-1993. General Name, Symbol, Number nitrogen, N, 7 Chemical series nonmetals Group, Period, Block 15, 2, p Appearance colorless gas Standard atomic weight 14. ...
The chemical compound acetone (also known as propanone, dimethyl ketone, 2-propanone, propan-2-one and Î²-ketopropane) is the simplest representative of the ketones. ...
Methanol, also known as methyl alcohol, carbinol, wood alcohol, wood naptha or wood spirits, is a chemical compound with chemical formula CH3OH. It is the simplest alcohol, and is a light, volatile, colourless, flammable, poisonous liquid with a distinctive odor that is somewhat milder and sweeter than ethanol (ethyl alcohol). ...
For benzine, see petroleum ether. ...
Grain alcohol redirects here. ...
Impact from a water drop causes an upward rebound jet surrounded by circular capillary waves. ...
General Name, Symbol, Number mercury, Hg, 80 Chemical series transition metals Group, Period, Block 12, 6, d Appearance silvery Standard atomic weight 200. ...
// Tate & Lyle brand Corn Syrup being moved by tank car Corn syrup is a syrup, made using corn (maize) starch as a feedstock, and composed mainly of glucose. ...
Nitrobenzene, also known as nitrobenzol or oil of mirbane, is a poisonous organic compound with an almond odor and chemical formula C6H5NO2. ...
R-phrases , , S-phrases , , , , , Flash point 15 Â°C RTECS number UH8225000 Supplementary data page Structure and properties n, Îµr, etc. ...
Ethylene glycol (monoethylene glycol (MEG), IUPAC name: ethane-1,2-diol) is an alcohol with two -OH groups (a diol), a chemical compound widely used as an automotive antifreeze. ...
R-phrases S-phrases , , , Flash point Non-flammable Related Compounds Related strong acids Selenic acid Hydrochloric acid Nitric acid Related compounds Hydrogen sulfide Sulfurous acid Peroxymonosulfuric acid Sulfur trioxide Oleum Supplementary data page Structure and properties n, Îµr, etc. ...
For the Popeye character, see Olive Oyl. ...
Glycerine, Glycerin redirects here. ...
Binomial name Ricinus communis The castor bean (Ricinus communis) is not a true bean, but a member of the Euphorbiaceae or spurge family. ...
The pitch drop experiment. ...
Fluids with variable compositions, such as honey, can have a wide range of viscosities. A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. ...
For other uses, see Honey (disambiguation). ...
A more complete table can be found here, including the following: | viscosity [cP] | honey | 2,000–10,000 | molasses | 5,000–10,000 | molten glass | 10,000–1,000,000 | chocolate syrup | 10,000–25,000 | chocolate^{*} | 45,000–130,000 [1] | ketchup^{*} | 50,000–100,000 | peanut butter | ~250,000 | shortening^{*} | ~250,000 | * These materials are highly non-Newtonian. For other uses, see Honey (disambiguation). ...
Molasses or treacle is a thick syrup by-product from the processing of the sugarcane or sugar beet into sugar. ...
This article is about the material. ...
Chocolate syrup is a type of syrup that is usually added to food to increase the chocolate flavour. ...
For other uses, see Chocolate (disambiguation). ...
This article is about the condiment. ...
Peanut butter in a jar. ...
Shortening is a semisolid fat used in food preparation, especially baked goods, and is so called because it inhibits the formation of long gluten strands in wheat-based doughs, giving them a short texture (as in shortbread). ...
A non-Newtonian fluid is a fluid in which the viscosity changes with the applied strain rate. ...
## Viscosity of solids On the basis that all solids flow to a small extent in response to shear stress some researchers^{[13]}^{[14]} have contended that substances known as amorphous solids, such as glass and many polymers, may be considered to have viscosity. This has led some to the view that solids are simply liquids with a very high viscosity, typically greater than 10^{12} Pa•s. This position is often adopted by supporters of the widely held misconception that glass flow can be observed in old buildings. This distortion is more likely the result of glass making process rather than the viscosity of glass.^{[15]} Shear stress is a stress state where the stress is parallel or tangential to a face of the material, as opposed to normal stress when the stress is perpendicular to the face. ...
Wax and paraffin are amorphous. ...
This article is about the material. ...
A polymer is a long, repeating chain of atoms, formed through the linkage of many molecules called monomers. ...
For other uses, see Solid (disambiguation). ...
For other uses, see Liquid (disambiguation). ...
This article is about the material. ...
However, others argue that solids are, in general, elastic for small stresses while fluids are not.^{[16]} Even if solids flow at higher stresses, they are characterized by their low-stress behavior. Viscosity may be an appropriate characteristic for solids in a plastic regime. The situation becomes somewhat confused as the term *viscosity* is sometimes used for solid materials, for example Maxwell materials, to describe the relationship between stress and the rate of change of strain, rather than rate of shear. For other uses, see Solid (disambiguation). ...
A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. ...
For other uses, see Solid (disambiguation). ...
For other uses, see Solid (disambiguation). ...
For other uses, see Plasticity. ...
A Maxwell material is a viscoelastic material having the properties both of elasticity and viscosity. ...
These distinctions may be largely resolved by considering the constitutive equations of the material in question, which take into account both its viscous and elastic behaviors. Materials for which both their viscosity and their elasticity are important in a particular range of deformation and deformation rate are called *viscoelastic*. In geology, earth materials that exhibit viscous deformation at least three times greater than their elastic deformation are sometimes called rheids. Viscoelasticity, also known as anelasticity, describes materials that exhibit both viscous and elastic characteristics when undergoing plastic deformation. ...
This article includes a list of works cited but its sources remain unclear because it lacks in-text citations. ...
In geology, a rheid is a solid material that deforms by viscous flow. ...
## Viscosity of amorphous materials Viscous flow in amorphous materials (e.g. in glasses and melts) ^{[17]}^{[18]}^{[19]} is a thermally activated process: Wax and paraffin are amorphous. ...
This article is about the material. ...
where *Q* is activation energy, *T* is temperature, *R* is the molar gas constant and *A* is approximately a constant. The viscous flow in amorphous materials is characterised by a deviation from the Arrhenius-type behaviour: *Q* changes from a high value *Q*_{H} at low temperatures (in the glassy state) to a low value *Q*_{L} at high temperatures (in the liquid state). Depending on this change, amorphous materials are classified as either The Arrhenius equation is a simple, but remarkably accurate, formula for the temperature dependence of a chemical reaction rate, more correctly, of a rate coefficient, as this coefficient includes all magnitudes that affect reaction rate except for concentration. ...
- strong when:
*Q*_{H} − *Q*_{L} < *Q*_{L} or - fragile when:
The fragility of amorphous materials is numerically characterized by the Doremus’ fragility ratio:
*R*_{D} = *Q*_{H} / *Q*_{L} and strong material have whereas fragile materials have The viscosity of amorphous materials is quite exactly described by a two-exponential equation:
with constants *A*_{1},*A*_{2},*B*,*C* and *D* related to thermodynamic parameters of joining bonds of an amorphous material. Not very far from the glass transition temperature, *T*_{g}, this equation can be approximated by a Vogel-Tammann-Fulcher (VTF) equation or a Kohlrausch-type stretched-exponential law. The glass transition temperature is the temperature below which the physical properties of amorphous materials vary in a manner similar to those of a solid phase (glassy state), and above which amorphous materials behave like liquids (rubbery state). ...
If the temperature is significantly lower than the glass transition temperature, , then the two-exponential equation simplifies to an Arrhenius type equation:
with:
*Q*_{H} = *H*_{d} + *H*_{m} where *H*_{d} is the enthalpy of formation of broken bonds (termed configurons) and *H*_{m} is the enthalpy of their motion. The standard enthalpy of formation of a compound is the change of enthalpy that accompanies the formation of 1 mole of that substance from its component elements, at their standard states (the most stable form of the element at 25 degrees Celsius and 100 kilopascals). ...
Configuron is an elementary configurational excitation in an amorphous material which involves breaking of a chemical bond and associated strain-releasing local adjustment of centres of atomic vibration. ...
t In thermodynamics and molecular chemistry, the enthalpy or heat content (denoted as H or Î”H, or rarely as Ï‡) is a quotient or description of thermodynamic potential of a system, which can be used to calculate the useful work obtainable from a closed thermodynamic system under constant pressure. ...
When the temperature is less than the glass transition temperature, *T* < *T*_{g}, the activation energy of viscosity is high because the amorphous materials are in the glassy state and most of their joining bonds are intact. If the temperature is highly above the glass transition temperature, , the two-exponential equation also simplifies to an Arrhenius type equation:
with:
*Q*_{L} = *H*_{m} When the temperature is higher than the glass transition temperature, *T* > *T*_{g}, the activation energy of viscosity is low because amorphous materials are melt and have most of their joining bonds broken which facilitates flow.
## Volume (Bulk) viscosity The negative-one-third of the trace of the stress tensor is often identified with the thermodynamic pressure, In linear algebra, the trace of an n-by-n square matrix A is defined to be the sum of the elements on the main diagonal (the diagonal from the upper left to the lower right) of A, i. ...
Stress is a measure of force per unit area within a body. ...
In mathematics, a tensor is (in an informal sense) a generalized linear quantity or geometrical entity that can be expressed as a multi-dimensional array relative to a choice of basis; however, as an object in and of itself, a tensor is independent of any chosen frame of reference. ...
This article is about pressure in the physical sciences. ...
, which only depends upon the equilibrium state potentials like temperature and density (equation of state). In general, the trace of the stress tensor is the sum of thermodynamic pressure contribution plus another contribution which is proportional to the divergence of the velocity field. This constant of proportionality is called the volume viscosity. In physics and thermodynamics, an equation of state is a relation between state variables. ...
Volume viscosity appears in Navier-Stokes equation if it is written for compressible fluid, as described in the most books on general hydrodynamics [1], [2], and the acoustics [3],[4]. where Î¼v is second viscosity coefficient. ...
## Eddy viscosity In the study of turbulence in fluids, a common practical strategy for calculation is to ignore the small-scale *vortices* (or *eddies*) in the motion and to calculate a large-scale motion with an *eddy viscosity* that characterizes the transport and dissipation of energy in the smaller-scale flow (see *large eddy simulation*). Values of eddy viscosity used in modeling ocean circulation may be from 5x10^{4} to 10^{6} Pa·s depending upon the resolution of the numerical grid. In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic, stochastic property changes. ...
A fluid is defined as a substance that continually deforms (flows) under an applied shear stress regardless of the magnitude of the applied stress. ...
Large eddy simulation (LES) is a numerical technique used to solve the partial differential equations governing turbulent fluid flow. ...
Animated map exhibiting the worlds oceanic waters. ...
## Fluidity The reciprocal of viscosity is *fluidity*, usually symbolized by φ = 1 / η or *F* = 1 / η, depending on the convention used, measured in *reciprocal poise* (cm·s·g^{-1}), sometimes called the *rhe*. *Fluidity* is seldom used in engineering practice. Look up reciprocal in Wiktionary, the free dictionary. ...
A centimetre (American spelling centimeter, symbol cm) is a unit of length that is equal to one hundredth of a metre, the current SI base unit of length. ...
This article is about the unit of time. ...
BIC pen cap, about 1 gram. ...
Engineering is the applied science of acquiring and applying knowledge to design, analysis, and/or construction of works for practical purposes. ...
The concept of fluidity can be used to determine the viscosity of an ideal solution. For two components *a* and *b*, the fluidity when *a* and *b* are mixed is In chemistry, an ideal solution is a solution where the enthalpy of solution is zero. ...
which is only slightly simpler than the equivalent equation in terms of viscosity: where χ_{a} and χ_{b} is the mole fraction of component *a* and *b* respectively, and η_{a} and η_{b} are the components pure viscosities.
## The linear viscous stress tensor (See *Hooke's law* and *strain tensor* for an analogous development for linearly elastic materials.) Hookes law accurately models the physical properties of common mechanical springs for small changes in length. ...
The strain tensor, Îµ, is a symmetric tensor used to quantify the strain of an object undergoing a small 3-dimensional deformation: the diagonal coefficients Îµii are the relative change in length in the direction of the i direction (along the xi-axis) ; the other terms Îµij = 1/2 Î³ij (i...
Viscous forces in a fluid are a function of the rate at which the fluid velocity is changing over distance. The velocity at any point is specified by the velocity field . The velocity at a small distance from point may be written as a Taylor series: As the degree of the Taylor series rises, it approaches the correct function. ...
where is shorthand for the dyadic product of the del operator and the velocity:
This is just the Jacobian of the velocity field. Viscous forces are the result of relative motion between elements of the fluid, and so are expressible as a function of the velocity field. In other words, the forces at are a function of and all derivatives of at that point. In the case of linear viscosity, the viscous force will be a function of the Jacobian tensor alone. For almost all practical situations, the linear approximation is sufficient. In vector calculus, the Jacobian is shorthand for either the Jacobian matrix or its determinant, the Jacobian determinant. ...
In mathematics, a tensor is (in an informal sense) a generalized linear quantity or geometrical entity that can be expressed as a multi-dimensional array relative to a choice of basis; however, as an object in and of itself, a tensor is independent of any chosen frame of reference. ...
If we represent *x*, *y*, and *z* by indices 1, 2, and 3 respectively, the *i,j* component of the Jacobian may be written as where is shorthand for . Note that when the first and higher derivative terms are zero, the velocity of all fluid elements is parallel, and there are no viscous forces. Any matrix may be written as the sum of an antisymmetric matrix and a symmetric matrix, and this decomposition is independent of coordinate system, and so has physical significance. The velocity field may be approximated as: In linear algebra, a skew-symmetric (or antisymmetric) matrix is a square matrix A whose transpose is also its negative; that is, it satisfies the equation: AT = −A or in component form, if A = (aij): aij = − aji for all i and j. ...
In linear algebra, a symmetric matrix is a matrix that is its own transpose. ...
where Einstein notation is now being used in which repeated indices in a product are implicitly summed. The second term on the left is the asymmetric part of the first derivative term, and it represents a rigid rotation of the fluid about with angular velocity ω where: This article or section does not adequately cite its references or sources. ...
For such a rigid rotation, there is no change in the relative positions of the fluid elements, and so there is no viscous force associated with this term. The remaining symmetric term is responsible for the viscous forces in the fluid. Assuming the fluid is isotropic (i.e. its properties are the same in all directions), then the most general way that the symmetric term (the rate-of-strain tensor) can be broken down in a coordinate-independent (and therefore physically real) way is as the sum of a constant tensor (the rate-of-expansion tensor) and a traceless symmetric tensor (the rate-of-shear tensor): Isotropic means independent of direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. ...
where δ_{ij} is the unit tensor. The most general linear relationship between the stress tensor and the rate-of-strain tensor is then a linear combination of these two tensors:^{[20]} In mathematics, the Kronecker delta or Kroneckers delta, named after Leopold Kronecker (1823-1891), is a function of two variables, usually integers, which is 1 if they are equal, and 0 otherwise. ...
where ζ is the coefficient of bulk viscosity (or "second viscosity") and η is the coefficient of (shear) viscosity. The forces in the fluid are due to the velocities of the individual molecules. The velocity of a molecule may be thought of as the sum of the fluid velocity and the thermal velocity. The viscous stress tensor described above gives the force due to the fluid velocity only. The force on an area element in the fluid due to the thermal velocities of the molecules is just the hydrostatic pressure. This pressure term ( − *p*δ_{ij}) must be added to the viscous stress tensor to obtain the total stress tensor for the fluid. This article is about pressure in the physical sciences. ...
The infinitesimal force *d**F*_{i} on an infinitesimal area *d**A*_{i} is then given by the usual relationship: ## See also The Deborah number is a dimensionless number, used in rheology to characterize how fluid a material is. ...
A dilatant material is one in which viscosity increases with the rate of shear (also termed Shear thickening). ...
Hyperviscosity syndrome is an increase in the viscosity of the blood. ...
Rheology is the study of the deformation and flow of matter under the influence of an applied stress. ...
Thixotropy is the property of some non-newtonian pseudoplastic fluids to show a time-dependent change in viscosity; the longer the fluid undergoes shear, the lower its viscosity. ...
A viscometer (also called viscosimeter) is an instrument used to measure the viscosity of a fluid. ...
The basis for determination of molecular weight according to the Staudinger method (since replaced by the more general Mark-Houwink equation) is the fact that relative viscosity of suspensions depends on volumetric proportion of solid particles. ...
Viscosity Index (or VI) is a petroleum industry term. ...
## References **^** Symon, Keith (1971). *Mechanics*, Third Edition, Addison-Wesley. ISBN 0-201-07392-7. **^** The Online Etymology Dictionary **^** Happel, J. and Brenner , H. "Low Reynolds number hydrodynamics", *Prentice-Hall*, (1965) **^** Landau, L.D. and Lifshitz, E.M. "Fluid mechanics", *Pergamon Press*,(1959) **^** Barnes, H.A. "A Handbook of Elementary Rheology", Institute of Non-Newtonian Fluid mechanics, UK (2000) **^** Raymond A. Serway (1996). *Physics for Scientists & Engineers*, 4th Edition, Saunders College Publishing. ISBN 0-03-005932-1. **^** Dukhin, A.S. and Goetz, P.J. "Ultrasound for characterizing colloids", Elsevier, (2002) **^** IUPAC definition of the Poise **^** James Ierardi's Fire Protection Engineering Site **^** J.O. Hirshfelder, C.F. Curtis and R.B. Bird (1964). *Molecular theory of gases and liquids*, First Edition, Wiley. ISBN 0-471-40065-3. **^** Robert E. Maples (2000). *Petroleum Refinery Process Economics*, 2nd Edition, Pennwell Books. ISBN 0-87814-779-9. **^** C.T. Baird (1989), *Guide to Petroleum Product Blending*, HPI Consultants, Inc. HPI website **^** The Physics Hypertextbook, by Glen Elert, retrieved on August 1, 2007. **^** The Properties of Glass , page 6, retrieved on August 1, 2007 **^** "Antique windowpanes and the flow of supercooled liquids", by Robert C. Plumb, (Worcester Polytech. Inst., Worcester, MA, 01609, USA), J. Chem. Educ. (1989), 66 (12), 994-6 **^** Gibbs, Philip. Is Glass a Liquid or a Solid?. Retrieved on 2007-07-31. **^** R.H.Doremus (2002). "Viscosity of silica". *J. Appl. Phys.* **92** (12): 7619-7629. ISSN 0021-8979. **^** M.I. Ojovan and W.E. Lee (2004). "Viscosity of network liquids within Doremus approach". *J. Appl. Phys.* **95** (7): 3803-3810. ISSN 0021-8979. **^** M.I. Ojovan, K.P. Travis and R.J. Hand (2000). "Thermodynamic parameters of bonds in glassy materials from viscosity-temperature relationships". *J. Phys.: Condensed matter* **19** (41): 415107. ISSN 0953-8984. **^** L.D. Landau and E.M. Lifshitz (translated from Russian by J.B. Sykes and W.H. Reid) (1997). *Fluid Mechanics*, 2nd Edition, Butterworth Heinemann. ISBN 0-7506-2767-0. Year 2007 (MMVII) is the current year, a common year starting on Monday of the Gregorian calendar and the AD/CE era in the 21st century. ...
is the 212th day of the year (213th in leap years) in the Gregorian calendar. ...
ISSN, or International Standard Serial Number, is the unique eight-digit number applied to a periodical publication including electronic serials. ...
ISSN, or International Standard Serial Number, is the unique eight-digit number applied to a periodical publication including electronic serials. ...
ISSN, or International Standard Serial Number, is the unique eight-digit number applied to a periodical publication including electronic serials. ...
## Additional reading Look up **Viscosity** in Wiktionary, the free dictionary. - Massey, B. S. (1983).
*Mechanics of Fluids*, Fifth Edition, Van Nostrand Reinhold (UK). ISBN 0-442-30552-4. Wikipedia does not have an article with this exact name. ...
Wiktionary (a portmanteau of wiki and dictionary) is a multilingual, Web-based project to create a free content dictionary, available in over 150 languages. ...
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