Viscosities Blending Formula

VISCOSITY BLENDING FORMULA Viscosity (cst) of Components components 1 2 3 4 5 6 7 8 9 10 11 12

Quantity in bbls (preferably) in or m3 or ton mass unit

39.15 9.6 1 1 1 1 1 1 1 1 1 1

Viscosity of blend will be

10 20 0 0 0 0 0 0 0 0 0 0

14.45cst

30 wt fraction VBN

VBN(com)

0.33

9.98

29.94

0.67

15.56

23.34

0

0

3.25

0

0

3.25

0

0

3.25

0

0

3.25

0

0

3.25

0

0

3.25

0

0

3.25

0

0

3.25

0

0

3.25

0 1

0 25.54

3.25

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Viscosity From Wikipedia, the free encyclopedia

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Viscosity Measured in (SI unit):

Pa s = kg / (s m)

Commonly used symbols: Expressed in other quantities:

μ μ=G·t

For other uses, see Viscosity (disambiguation). "Fluidity" redirects here. For the ship, see MV Fluidity. Continuum mechanics [show]Laws Conservation of mass Conservation of momentum Conservation of energy Entropy Inequality [show]Solid mechanics Solids · Stress · Deformation · Finite strain theory · Infinitesimal strain theory · Elasticity · Linear elasticity · Plasticity · Viscoelasticity · Hooke's law · Rheology [show]Fluid mechanics Fluids · Fluid statics Fluid dynamics · Viscosity · Newtonian fluids

Non-Newtonian fluids Surface tension [show]Scientists Newton · Stokes · Navier · Cauchy· Hooke · Bernoulli This box: view • talk • edit

Illustration of viscosity; Green fluid to the left has higher viscosity than the clear liquid on the right.

Viscosity is a measure of the resistance of a fluid which is being deformed by either shear stress or extensional str

Contents [hide] 1 Etymology 2 Viscosity coefficients 3 Newton's theory 4 Viscosity measurement 4.1 Units of measure 4.1.1 Dynamic viscosity 4.1.2 Kinematic viscosity 4.1.3 Saybolt Universal viscosity 4.1.4 Relation to mean free path of diffusing particles 4.1.5 Dynamic versus kinematic viscosity 4.1.6 Example: viscosity of water 5 Molecular origins 5.1 Gases 5.1.1 Effect of temperature on the viscosity of a gas 5.1.2 Viscosity of a dilute gas 5.2 Liquids 5.2.1 Viscosity of blends of liquids 6 Viscosity of selected substances 6.1 Viscosity of air 6.2 Viscosity of water 6.3 Viscosity of various materials 7 Viscosity of solids 8 Viscosity of amorphous materials 9 Volume (bulk) viscosity 10 Eddy viscosity 11 Fluidity 12 The linear viscous stress tensor 13 See also 14 References 15 Additional reading 16 External links [edit] Etymology

The word "viscosity" derives from the Latin word "viscum" for mistletoe. A viscous glue was made from mistletoe be [edit] Viscosity coefficients

When looking at a value for viscosity, the number that one most often sees is the coefficient of viscosity. There are s Dynamic viscosity (or absolute viscosity) determines the dynamics of an incompressible Newtonian fluid; Kinematic viscosity is the dynamic viscosity divided by the density for a Newtonian fluid; Volume viscosity (or bulk viscosity) determines the dynamics of a compressible Newtonian fluid;

Shear viscosity is the viscosity coefficient when the applied stress is a shear stress (valid for non-Newtonian fluid Extensional viscosity is the viscosity coefficient when the applied stress is an extensional stress (valid for non-N

Shear viscosity and dynamic viscosity are much better known than the others. That is why they are often referred to Extensional viscosity is widely used for characterizing polymers. Volume viscosity is essential for acoustics in fluids, see Stokes' law (sound attenuation)[7] [edit] Newton's theory Laminar shear of fluid between two plates. Friction between the fluid and the moving boundaries causes the fluid to Laminar shear, the non-constant 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 betwe

Isaac Newton postulated that, for straight, parallel and uniform flow, the shear stress, τ, between layers is proportion Here, the constant μ is known as the coefficient of viscosity, the viscosity, the dynamic viscosity The relationship between the shear stress and the velocity gradient can also be obtained by considering two plates

James Clerk Maxwell called viscosity fugitive elasticity because of the analogy that elastic deformation opposes she [edit] Viscosity measurement

Dynamic viscosity is measured with various types of rheometer. Close temperature control of the fluid is essential to

The fluids without a constant viscosity are called non-Newtonian fluids. Their viscosity cannot be described by a sin One of the most common instruments for measuring kinematic viscosity is the glass capillary viscometer.

In paint industries, viscosity is commonly measured with a Zahn cup, in which the efflux time is determined and give

A Ford viscosity cup measures the rate of flow of a liquid. This, under ideal conditions, is proportional to the kinema

Also used in paint, a Stormer viscometer uses load-based rotation in order to determine viscosity. The viscosity is re Vibrating viscometers can also be used to measure viscosity. These models such as the Dynatrol Extensional viscosity can be measured with various rheometers that apply extensional stress. Volume viscosity can be measured with acoustic rheometer. [edit] Units of measure [edit] Dynamic viscosity

The usual symbol for dynamic viscosity used by mechanical and chemical engineers — as well as fluid dynamicists

The cgs physical unit for dynamic viscosity is the poise[13] (P), named after Jean Louis Marie Poiseuille. It is more co

1 P = 1 g·cm−1·s−1. The relation between poise and pascal-seconds is: 10 P = 1 kg·m−1·s−1 = 1 Pa·s, 1 cP = 0.001 Pa·s = 1 mPa·s.

The name 'poiseuille' (Pl) was proposed for this unit (after Jean Louis Marie Poiseuille who formulated Poiseuille's la [edit] Kinematic viscosity In many situations, we are concerned with the ratio of the viscous force to the inertial force, the latter characterised where μ is the dynamic viscosity (Pa·s), ρ is the density (kg/m3), and ν is the kinematic viscosity (m The cgs physical unit for kinematic viscosity is the stokes (St), named after George Gabriel Stokes. It is sometimes 1 stokes = 100 centistokes = 1 cm2·s−1 = 0.0001 m2·s−1. 1 centistokes = 1 mm2·s−1 = 10−6m2·s−1.

The kinematic viscosity is sometimes referred to as diffusivity of momentum, because it is comparable to and has th [edit] Saybolt Universal viscosity

At one time the petroleum industry relied on measuring kinematic viscosity by means of the Saybolt viscometer, and [edit] Relation to mean free path of diffusing particles

In relation to diffusion, the kinematic viscosity provides a better understanding of the behavior of mass transport of a

From fluid mechanics, shear stress, τ, on a unit area moving parallel to itself, is found to be proportional to the rate o for a unit area parallel to the x-z plane, moving along the x axis. We will derive this formula and show how Interpreting shear stress as the time rate of change of momentum, p, per unit area A (rate of momentum flux) of an where is the average velocity along x of fluid molecules hitting the unit area, with respect to the unit area. Further manipulation will show[16]

, assuming that molecules hitting the unit area come from all distances between 0 and λ (equally distributed), and where is the rate of fluid mass hitting the surface, ρ is the density of the fluid, ū is the average molecular speed (), μ is the dynamic viscosity. [edit] Dynamic versus kinematic viscosity

Conversion between kinematic and dynamic viscosity is given by ν ρ = μ. For example, if ν = 0.0001 m2·s−1 and ρ = 1000 kg m−3 then μ = ν ρ = 0.1 kg·m−1·s−1 = 0.1 Pa·s, if ν = 1 St (= 1 cm2·s−1) and ρ = g cm−3 then μ = ν ρ = 1 g·cm−1·s−1 = 1 P. [edit] Example: viscosity of water

Because of its density of ρ = 1 g/cm3 (varies slightly with temperature), and its dynamic viscosity is near 1 mPa·s (s Dynamic viscosity: μ = 1 mPa·s = 10−3 Pa·s = 0.001 kg/(m·s) = 1 cP = 10−2 poise. Kinematic viscosity: ν = 1 cSt = 10−2 stokes = 1 mm2/s. [edit] Molecular origins

Pitch has a viscosity approximately 230 billion (2.3 × 10 11) times that of water. [17] The viscosity of a system is determined by how molecules constituting the system interact. There are no simple but [edit] Gases Viscosity in gases arises principally from the molecular diffusion that transports momentum between layers of flow. Within the regime where the theory is applicable:

Viscosity is independent of pressure and Viscosity increases as temperature increases.

James Clerk Maxwell published a famous paper in 1866 using the kinetic theory of gases to study gaseous viscosity [edit] 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: where: μ = dynamic viscosity in (Pa·s) at input temperature T, μ0 = reference viscosity in (Pa·s) at reference temperature T0, T = input temperature in kelvin, T0 = reference temperature in kelvin, C = Sutherland's constant for the gaseous 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

Gas

air nitrogen oxygen carbon dioxide carbon monoxide hydrogen ammonia sulfur dioxide helium

C

T0

μ0

[K]

[K]

[10−6 Pa s ]

120 111 127 240 118 72 370 416 79.4 [19]

291.15 18.27 300.55 17.81 292.25 20.18 293.15 14.8 288.15 17.2 293.85 8.76 293.15 9.82 293.65 12.54 273 19 [20]

See also [1]. [edit] Viscosity of a dilute gas

The Chapman-Enskog equation [21] may be used to estimate viscosity for a dilute gas. This equation is based on sem with T* = κT/ε — reduced temperature (dimensionless), μ0 = viscosity for dilute gas (μP), M = molecular mass (g/mol), T = temperature (K),

σ = the collision diameter (Å), ε / κ = the maximum energy of attraction divided by the Boltzmann constant (K), ωμ = the collision integral. [edit] Liquids

Video showing three liquids with different Viscosities

In liquids, the additional forces between molecules become important. This leads to an additional contribution to the

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

The dynamic viscosities of liquids are typically several orders of magnitude higher than dynamic viscosities of gases [edit] Viscosity of blends of liquids The viscosity of the blend of two or more liquids can be estimated using the Refutas equation [22][23]

The first step is to calculate the Viscosity Blending Number (VBN) (also called the Viscosity Blending Index) of each (1)

where v is the kinematic viscosity in centistokes (cSt). It is important that the kinematic viscosity of each component The next step is to calculate the VBN of the blend, using this equation: (2) where xX is the mass fraction of each component of the blend.

Once the viscosity blending number of a blend has been calculated using equation (2), the final step is to determine (3) where VBNBlend is the viscosity blending number of the blend.

[edit] Viscosity of selected substances

The viscosity of air and water are by far the two most important materials for aviation aerodynamics and shipping flu [edit] 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) or 1.7 [edit] Viscosity of water Dynamic Viscosity of Water The dynamic viscosity of water is 8.90 × 10 −4 Pa·s or 8.90 × 10 −3 dyn·s/cm2 or 0.890 cP at about 25 °C. As a function of temperature T (K): μ(Pa·s) = A × 10B/(T−C) where A=2.414 × 10−5 Pa·s ; B = 247.8 K ; and C = 140 K. Viscosity of liquid water at different temperatures up to the normal boiling point is listed below. Temperature

Viscosity

[°C]

[Pa·s]

10 20 30 40 50 60 70 80 90 100 [edit] Viscosity of various materials

1.31E-03 1.00E-03 7.98E-04 6.53E-04 5.47E-04 4.67E-04 4.04E-04 3.55E-04 3.15E-04 2.82E-04

Example of the viscosity of milk and water. Liquids with higher viscosities will not make such a splash when poured

Honey being drizzled.

Peanut butter is a semi-solid and so can hold peaks. Some dynamic viscosities of Newtonian fluids are listed below: Gases (at 0 °C): viscosity [Pa·s]

hydrogen air xenon

8.40E-06 1.74E-05 2.12E-05

Liquids (at 25 °C): viscosity viscosity [Pa·s]

acetone[24] benzene[24]

3.06E-04 6.04E-04

[cP]

0.31 0.6

blood (37 °C)[25] castor oil[24] corn syrup[24] ethanol[24] ethylene glycol glycerol HFO-380 mercury[24] methanol[24] nitrobenzene[24] liquid nitrogen @ 77K propanol[24] olive oil pitch sulfuric acid[24] water

3e-3 to 4e-3 3–4 0.99 985 1.38 1380.6 1.07E-03 1.07 1.61E-02 16.1 1.5 1500 2.02 2022 1.53E-03 1.53 5.44E-04 0.54 1.86E-03 1.86 1.58E-04 0.16 1.95E-03 1.95 0.08 81 2.30E+08 2.30E+11 2.42E-02 24.2 8.94E-04 0.89

Fluids with variable compositions, such as honey, can have a wide range of viscosities. viscosity [cP]

honey molasses molten glass chocolate syrup molten chocolate* ketchup* peanut butter shortening*

2,000– 10,000 5,000– 10,000 10,000– 1,000,000 10,000– 25,000 45,000–130,000 [26] 50,000– 100,000 ~250,000 ~250,000

* These materials are highly non-Newtonian. [edit] Viscosity of solids

On the basis that all solids such as granite [27] flow to a small extent in response to small shear stress, some researc However, others argue that solids are, in general, elastic for small stresses while fluids are not. [30]

These distinctions may be largely resolved by considering the constitutive equations of the material in question, whi [edit] Viscosity of amorphous materials

Common glass viscosity curves.[31] Viscous flow in amorphous materials (e.g. in glasses and melts) [32][33][34] is a thermally activated process: 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 characterized by a deviation from the Arrhenius-type behavior: Q chang strong when: QH − QL < QL or fragile when: QH − QL ≥ QL. The fragility of amorphous materials is numerically characterized by the Doremus’ fragility ratio: and strong material have RD < 2 whereas fragile materials have RD ≥ 2. The viscosity of amorphous materials is quite exactly described by a two-exponential equation: with constants A1, A2, B, C and D related to thermodynamic parameters of joining bonds of an amorphous material.

Not very far from the glass transition temperature, Tg, this equation can be approximated by a Vogel-Tammann-Fulc

If the temperature is significantly lower than the glass transition temperature, T < Tg, then the two-exponential equa with:

where Hd is the enthalpy of formation of broken bonds (termed configurons) and Hm is the enthalpy of their motion. W

If the temperature is highly above the glass transition temperature, T > Tg, the two-exponential equation also simplif with:

When the temperature is higher than the glass transition temperature, T > Tg, the activation energy of viscosity is lo [edit] Volume (bulk) viscosity The negative-one-third of the trace of the stress tensor is often identified with the thermodynamic pressure,

which only depends upon the equilibrium state potentials like temperature and density (equation of state). In genera [edit] Eddy viscosity In the study of turbulence in fluids, a common practical strategy for calculation is to ignore the small-scale [edit] Fluidity

The reciprocal of viscosity is fluidity, usually symbolized by φ = 1 / μ or F = 1 / μ, depending on the convention used The concept of fluidity can be used to determine the viscosity of an ideal solution. For two components a and b, the which is only slightly simpler than the equivalent equation in terms of viscosity:

where χa and χb is the mole fraction of component a and b respectively, and μa and μb are the components pure visc [edit] The linear viscous stress tensor For more details on an analogous development for linearly elastic materials, see Hooke's law and strain tensor.

Viscous forces in a fluid are a function of the rate at which the fluid velocity is changing over distance. The velocity a where dv / dr 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 o 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

Any matrix may be written as the sum of an antisymmetric matrix and a symmetric matrix, and this decomposition is

where Einstein notation is now being used in which repeated indices in a product are implicitly summed. The second

For such a rigid rotation, there is no change in the relative positions of the fluid elements, and so there is no viscous

where δij is the unit tensor. The most general linear relationship between the stress tensor σ and the rate-of-strain t where ς is the coefficient of bulk viscosity (or "second viscosity") and μ 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 thoug The infinitesimal force dFi on an infinitesimal area dAi is then given by the usual relationship: [edit] See also Deborah number Dilatant Hyperviscosity syndrome Inviscid flow Physics of glass Reyn Reynold's number Rheology Thixotropy Viscometer Viscometry Viscoelasticity Viscosity index Joback method (Estimation of the liquid viscosity from molecular structure) [edit] References

1. ^ Symon, Keith (1971). Mechanics (Third ed.). Addison-Wesley. ISBN 0-201-07392-7. 2. ^ The Online Etymology Dictionary 3. ^ Happel, J. and Brenner , H. "Low Reynolds number hydrodynamics", Prentice-Hall, (1965) 4. ^ Landau, L.D. and Lifshitz, E.M. "Fluid mechanics", Pergamon Press,(1959) 5. ^ Barnes, H.A. "A Handbook of Elementary Rheology", Institute of Non-Newtonian Fluid mechanics, UK (2000) 6. ^ Raymond A. Serway (1996). Physics for Scientists & Engineers (4th ed.). Saunders College Publishing. ISBN 7. ^ Dukhin, A.S.; Goetz, P.J. (2002), Ultrasound for characterizing colloids, Elsevier, ISBN 0444511644 8. ^ ASHRAE handbook, 1989 edition 9. ^ Streeter & Wylie Fluid Mechanics, McGraw-Hill, 1981 10. ^ Holman Heat Transfer, McGraw-Hill, 2002 11. ^ Incropera & DeWitt, Fundamentals of Heat and Mass Transfer, Wiley, 1996 12. ^ IUPAC Gold Book, Definition of (dynamic) viscosity 13. ^ IUPAC definition of the Poise 14. ^ ASTM D 2161, Page one,(2005) 15. ^ Quantities and Units of Viscosity 16. ^ Salmon, R.L. (1998), Lectures on geophysical fluid dynamics, Oxford University Press, ISBN 0195108086 , 17. ^ Edgeworth,, R.; Dalton, B.J.; Parnell, T.. "The pitch drop experiment". University of Queensland. http://www 18. ^ Maxwell, J. C. (1866), "On the viscosity or internal friction of air and other gases", Philosophical Transaction 19. ^ data constants for sutherland's formula 20. ^ Viscosity of liquids and gases 21. ^ J.O. Hirshfelder, C.F. Curtis and R.B. Bird (1964). Molecular theory of gases and liquids 22. ^ Robert E. Maples (2000). Petroleum Refinery Process Economics (2nd ed.). Pennwell Books. ISBN 0-8781 23. ^ C.T. Baird (1989), Guide to Petroleum Product Blending, HPI Consultants, Inc. HPI website 24. ^ a b c d e f g h i j CRC Handbook of Chemistry and Physics, 73 rd edition, 1992–1993 25. ^ Viscosity. The Physics Hypertextbook. by Glenn Elert 26. ^ "Chocolate Processing". Brookfield Engineering website. http://www.brookfieldengineering.com/education/a 27. ^ Kumagai, Naoichi; Sadao Sasajima, Hidebumi Ito (15 February 1978). "Long-term Creep of Rocks: Results 28. ^ Elert, Glenn. "Viscosity". The Physics Hypertextbook. http://hypertextbook.com/physics/matter/viscosity/. 29. ^ "Antique windowpanes and the flow of supercooled liquids", by Robert C. Plumb, (Worcester Polytech. Inst. 30. ^ Gibbs, Philip. "Is Glass a Liquid or a Solid?". http://math.ucr.edu/home/baez/physics/General/Glass/glass.h 31. ^ Viscosity calculation of glasses 32. ^ R.H.Doremus (2002). "Viscosity of silica". J. Appl. Phys. 92 (12): 7619–7629. doi:10.1063/1.1515132. 33. ^ M.I. Ojovan and W.E. Lee (2004). "Viscosity of network liquids within Doremus approach". 34. ^ M.I. Ojovan, K.P. Travis and R.J. Hand (2000). "Thermodynamic parameters of bonds in glassy materials fr 35. ^ L.D. Landau and E.M. Lifshitz (translated from Russian by J.B. Sykes and W.H. Reid) (1997). [edit] Additional reading

Look up viscosity in Wiktionary , the free dictionary. Massey, B. S. (1983). Mechanics of Fluids (Fifth ed.). Van Nostrand Reinhold (UK). ISBN 0-442-30552-4. [edit] External links

Fluid Characteristics Chart A table of viscosities and vapor pressures for various fluids Gas Dynamics Toolbox Calculate coefficient of viscosity for mixtures of gases Glass Viscosity Measurement Viscosity measurement, viscosity units and fixpoints, glass viscosity calculation Kinematic Viscosity conversion between kinematic and dynamic viscosity. Physical Characteristics of Water A table of water viscosity as a function of temperature Project Trajectory Java Web Start Application for simulation of moving bodies through different and user definabl Vogel–Tammann–Fulcher Equation Parameters Calculation of temperature-dependent dynamic viscosities for some common components [show] v•d•e

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uid on the right.

er shear stress or extensional stress. In everyday terms (and for fluids only), viscosity is "thickness." Thus, water is "thin," having a lower vis

glue was made from mistletoe berries and used for lime-twigs to catch birds. [2]

oefficient of viscosity. There are several different viscosity coefficients depending on the nature of applied stress and nature of the fluid. The

mpressible Newtonian fluid;

le Newtonian fluid;

ss (valid for non-Newtonian fluids); extensional stress (valid for non-Newtonian fluids).

t is why they are often referred to as simply viscosity. Simply put, this quantity is the ratio between the pressure exerted on the surface of a

ng 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 wing through (e.g. a pipe).

rises from the shear stress between the layers that ultimately opposes any applied force.

ss, τ, between layers is proportional to the velocity gradient, ∂ u /∂y, in the direction perpendicular to the layers.

amic viscosity, or the Newtonian viscosity. Many fluids, such as water and most gases, satisfy Newton's criterion and are known as Newtonia

tained by considering two plates closely spaced apart at a distance y, and separated by a homogeneous substance. Assuming that the plat elastic deformation opposes shear stress in solids, while in viscous fluids, shear stress is opposed by rate of deformation.

control of the fluid is essential to accurate measurements, particularly in materials like lubricants, whose viscosity can double with a change

sity cannot be described by a single number. Non-Newtonian fluids exhibit a variety of different correlations between shear stress and shear

s capillary viscometer.

efflux time is determined and given to customers. The efflux time can also be converted to kinematic viscosities (cSt) through the conversion

ons, is proportional to the kinematic viscosity.

mine viscosity. The viscosity is reported in Krebs units (KU), which are unique to Stormer viscometers.

as the Dynatrol use vibration rather than rotation to measure viscosity.

rs — as well as fluid dynamicists — is the Greek letter mu ( μ)[8][9][10][11]. The symbol η is also used by chemists and IUPAC [12]. The SI physica

uis Marie Poiseuille. It is more commonly expressed, particularly in ASTM standards, as centipoise (cP). Water at 20 °C has a viscosity of 1

uille who formulated Poiseuille's law of viscous flow), but not accepted internationally.

[citation needed]

Care must be taken in not confusing the poi

al force, the latter characterised by the fluid density ρ. This ratio is characterised by the kinematic viscosity (Greek letter nu,

atic viscosity (m2/s).

Gabriel Stokes. It is sometimes expressed in terms of centistokes (cSt or ctsk). In U.S. usage, stoke is sometimes used as the singular form

use it is comparable to and has the same unit (m 2s−1) as diffusivity of heat and diffusivity of mass. It is therefore used in dimensionless numb

ns of the Saybolt viscometer, and expressing kinematic viscosity in units of Saybolt Universal seconds (SUS). [14] Other abbreviations such a

e behavior of mass transport of a dilute species. Viscosity is related to shear stress and the rate of shear in a fluid, which illustrates its depe

nd to be proportional to the rate of change of velocity with distance perpendicular to the unit area:

formula and show how μ is related to λ.

A (rate of momentum flux) of an arbitrary control surface gives

espect to the unit area.

0 and λ (equally distributed), and that their average velocities change linearly with distance (always true for small enough λ). From this follo

amic viscosity is near 1 mPa·s (see Viscosity of water section), the viscosity values of water are, to rough precision, all powers of ten:

nteract. There are no simple but correct expressions for the viscosity of a fluid. The simplest exact expressions are the Green–Kubo relation

mentum between layers of flow. The kinetic theory of gases allows accurate prediction of the behavior of gaseous viscosity.

gases to study gaseous viscosity. [18] To understand why the viscosity is independent of pressure consider two adjacent boundary layers (A

s a function of the temperature:

an 10% below 3.45 MPa.

as. This equation is based on semi-theorethical assumption by Chapman and Enskoq. The equation requires three empirically determined p

o an additional contribution to the shear stress though the exact mechanics of this are still controversial.[citation needed] Thus, in liquids:

es 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.

han dynamic viscosities of gases.

s equation [22][23]. The calculation is carried out in three steps.

Viscosity Blending Index) of each component of the blend:

matic viscosity of each component of the blend be obtained at the same temperature.

(2), the final step is to determine the kinematic viscosity of the blend by solving equation (1) for v:

on aerodynamics and shipping fluid dynamics. Temperature plays the main role in determining viscosity.

air is 1.78 × 10−5 kg/(m·s) or 1.78 × 10−4 P. One can get the viscosity of air as a function of temperature from the Gas Viscosity Calculator

0 cP at about 25 °C.

make such a splash when poured at the same velocity.

small shear stress, some researchers [28] have contended that substances known as amorphous solids, such as glass and many polymers, m

uids are not. [30] Even if solids flow at higher stresses, they are characterized by their low-stress behavior. This distinction can become mudd

s of the material in question, which take into account both its viscous and elastic behaviors. Materials for which both their viscosity and their

ly activated process:

s approximately a constant.

Arrhenius-type behavior: Q changes from a high value QH at low temperatures (in the glassy state) to a low value QL at high temperatures (i

ragility ratio:

al equation:

bonds of an amorphous material.

mated by a Vogel-Tammann-Fulcher (VTF) equation or a Kohlrausch-type stretched-exponential law. , then the two-exponential equation simplifies to an Arrhenius type equation:

g

m

is the enthalpy of their motion. When the temperature is less than the glass transition temperature, T < Tg, the activation energy of viscosi

exponential equation also simplifies to an Arrhenius type equation:

activation energy of viscosity is low because amorphous materials are melt and have most of their joining bonds broken which facilitates flow

hermodynamic pressure,

sity (equation of state). In general, the trace of the stress tensor is the sum of thermodynamic pressure contribution plus another contribution

ignore the small-scale vortices (or eddies) in the motion and to calculate a large-scale motion with an eddy viscosity that characterizes the

epending on the convention used, measured in reciprocal poise (cm·s·g−1), sometimes called the rhe. Fluidity is seldom used in engineering

For two components a and b, the fluidity when a and b are mixed is

d μb are the components pure viscosities.

ooke's law and strain tensor.

ging over distance. The velocity at any point r is specified by the velocity field v(r). The velocity at a small distance dr from point r may be wr

so are expressible as a function of the velocity field. In other words, the forces at r are a function of v(r) and all derivatives of v(r) at that poin

the Jacobian may be written as ∂i vj where ∂i is shorthand for ∂/∂xi. Note that when the first and higher derivative terms are zero, the velocity

matrix, and this decomposition is independent of coordinate system, and so has physical significance. The velocity field may be approximat

re implicitly summed. The second term from the right is the asymmetric part of the first derivative term, and it represents a rigid rotation of th

ments, and so there is no viscous force associated with this term. The remaining symmetric term is responsible for the viscous forces in the tensor σ and the rate-of-strain tensor is then a linear combination of these two tensors: [35]

cient of (shear) viscosity.

ocity of a molecule may be thought of as the sum of the fluid velocity and the thermal velocity. The viscous stress tensor described above giv

e-Hall, (1965)

nian Fluid mechanics, UK (2000) aunders College Publishing. ISBN 0-03-005932-1. evier, ISBN 0444511644

ersity Press, ISBN 0195108086 , pp. 23–26. ersity of Queensland. http://www.physics.uq.edu.au/physics_museum/pitchdrop.shtml. Retrieved on 31-03-2009. . A copy of: gases", Philosophical Transactions of the Royal Society of London 156: 249–268, doi:10.1098/rstl.1866.0013

es and liquids (First ed.). Wiley. ISBN 0-471-40065-3. ). Pennwell Books. ISBN 0-87814-779-9. Inc. HPI website

fieldengineering.com/education/applications/laboratory-chocolate-processing.asp. Retrieved on 2007-12-03. ng-term Creep of Rocks: Results with Large Specimens Obtained in about 20 Years and Those with Small Specimens in about 3 Years". com/physics/matter/viscosity/. lumb, (Worcester Polytech. Inst., Worcester, MA, 01609, USA), J. Chem. Educ. (1989), 66 (12), 994–6 z/physics/General/Glass/glass.html. Retrieved on 2007-07-31.

29. doi:10.1063/1.1515132. mus approach". J. Appl. Phys. 95 (7): 3803–3810. doi:10.1063/1.1647260. rs of bonds in glassy materials from viscosity-temperature relationships". J. Phys.: Condensed matter 19 (41): 415107. doi:10.1088/0953-8 W.H. Reid) (1997). Fluid Mechanics (2nd ed.). Butterworth Heinemann. ISBN 0-7506-2767-0.

K). ISBN 0-442-30552-4.

ts, glass viscosity calculation

ough different and user definable media.

ering and science | Viscosity | Petroleum engineering | Oilfield terminology g Latin language text | All articles with unsourced statements | Articles with unsourced statements from September 2008 | Articles with unso

dditional terms may apply. See Terms of Use for details. rofit organization.

is "thin," having a lower viscosity, while honey is "thick" havi ng a higher viscosity. Viscosity describes a fluid's internal resistance to flow an

and nature of the fluid. They are introduced in the mai n books on hydrodynamics [3][4] and rheology.[5]

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

s type of flow is known as a Couette flow.

and are known as Newtonian fluids. Non-Newtonian fluids exhibit a more complicated relationship between shear stress and velocity gradie

nce. 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, le

y can double with a change of only 5 °C. For some fluids, it is a constant over a wide range of shear rates. These are Newtonian fluids.

een shear stress and shear rate.

cSt) through the conversion equations.

d IUPAC [12]. The SI physical unit of dynamic viscosity is the pascal-second (Pa·s), which is identical to kg·m −1·s−1. If a fluid with a viscosity of

at 20 °C has a viscosity of 1.0020 cP.

en in not confusing the poiseuille with the poise named after the same person.

ek letter nu, ν), defined as follows:

es used as the singular form.

sed in dimensionless numbers which compare the ratio of the diffusivities.

Other abbreviations such as SSU (Saybolt Seconds Universal) or SUV (Saybolt Universal Viscosity) are sometimes used. Kinematic viscos

d, which illustrates its dependence on the mean fre e path, λ, of the diffusing particles.

l enough λ). From this follows:

on, all powers of ten:

are the Green–Kubo relations for the linear shear viscosity or the Transient Time Correlation Function expressions derived by Evans and M

djacent boundary layers (A and B) moving with respect to each other. The internal friction (the viscosity) of the gas is determined by the prob

ee empirically determined parameters: the collision diameter (σ), the maximum energy of attraction divided by the Boltzmann constant (

needed] Thus, in liquids:

viscosity for more details.

he Gas Viscosity Calculator

lass 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 v

tinction can become muddled if measurements are continued over long time periods, such as the Pitch drop experiment. Viscosity may be a

both their viscosity and their elasticity are important in a particular range of deformation and deformation rate are called viscoelastic

QL at high temperatures (in the liquid state). Depending on th is change, amorphous materials are classified as either

activation energy of viscosity is high because the amorphous materials are in the glassy state and most of their joining bonds are intact.

broken which facilitates flow.

on plus another contribution which is proportional to the d ivergence of the velocity field. This constant of proportionality is called the volume

osity that characterizes the transport and dissipation of energy in the smaller-scale flow (see large eddy simulation). Values of eddy viscosi

eldom used in engineering practice.

e dr from point r may be written as a Taylor ser ies:

rivatives of v(r) at that point. In the case of lin ear viscosity, the viscous force will be a function of the Jacobian tensor alone. For almost all

terms are zero, the velocity of all fluid elements is parallel, and there are no viscous forces.

ty field may be approximated as:

resents a rigid rotation of the fluid about r with angular velocity ω where:

or the viscous forces in the fluid. Assuming the fluid i s isotropic (i.e. its properties are the same in all directions), then the most general way

tensor described above gives the force due to the flui d velocity only. The force on an area element in the fluid due to the thermal velocities

. . A copy of: European Journal of Physics (1984) pp. 198–200.

imens in about 3 Years". Journal of the Society of Materials Science (Japan) (Japan Energy Society) 27 (293): 157–161. http://translate.goo

15107. doi:10.1088/0953-8984/19/41/415107.

er 2008 | Articles with unsourced statements from February 20 07

ternal resistance to flow and may be thought of as a measure of fluid friction. For example, high-viscosity magma will create a tall, steep str

move down in the fluid (this is what is referred to as a velocity gradient). For example, at room temperature, water has a nominal dynamic v

ar stress and velocity gradient than simple linearity.

at 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 shea

se are Newtonian fluids.

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 m

mes used. Kinematic viscosity in centistoke can be converted from SUS according to the arithmetic and the reference table provided in ASTM

ns derived by Evans and Morriss in 1985. Although these expressions are each exact in order to calculate the viscosity of a dense fluid, usin

as is determined by the probability a particle of layer A enters layer B with a corresponding transfer of momentum. Maxwell's calculations sh

e Boltzmann constant ( є/к) and the collision integral (ω(T*)).

ply liquids with a very high viscosity, typically greater than 10

12

Pa·s. This position is often adopted by supporters of the widely held misconc

periment. Viscosity may be an appropriate characteristic for solids in a plastic regime. The situation becomes somewhat confused as the te

e called viscoelastic. In geology, earth materials that exhibit viscous deformation at least three times greater than their elastic deformation a

oining bonds are intact.

ionality is called the volume viscosity.

on). Values of eddy viscosity used in modeling ocean circulation may be from 5x10 4 to 106 Pa·s depending upon the resolution of the nume

ensor alone. For almost all practical situations, the linear approximation is sufficient.

then the most general way that the symmetric term (the rate-of-strain tensor) can be broken down in a coordinate-independent (and theref

due to the thermal velocities of the molecules is just the hydrostatic pressure. This pressure term (−p δij) must be added to the viscous stre

57–161. http://translate.google.com/translate?hl=en&sl=ja&u=http://ci.nii.ac.jp/naid/110002299397/&sa=X&oi=translate&resnum=4&ct=resu

a will create a tall, steep stratovolcano, because it cannot flow far before it cools, wh ile low-viscosity lava will create a wide, shallow-sloped

er has a nominal dynamic viscosity of 1.0 × 10−3 Pa·s and motor oil has a nominal apparent dynamic viscosity of 250 × 10 −3 Pa·s.

he plates to undergo shear flow (as opposed to just shearing elastically until the shear stress in the substance balances the applied force),

ar stress of one pascal, it moves a distance equal to the thickness of the layer between the plates in one second.

ence table provided in ASTM D 2161. I t can also be converted in computerized method, or vice versa. [15]

scosity of a dense fluid, using these relations requires the use of molecular dynamics computer simulations.

m. Maxwell's calculations showed him that the viscosity coefficient is proportional to both the density, the mean free path and the mean veloc

of the widely held misconception that glass flow can be observed in old buildings. This distortion is more likely the result of the glass makin

mewhat confused as the term viscosity is sometimes used for solid materials, for example Maxwell materials, to describe the relationship be their elastic deformation are sometimes called rheids.

the resolution of the numerical grid.

e-independent (and therefore physically real) way is as the sum of a constant t ensor (the rate-of-expansion tensor) and a traceless symme

added to the viscous stress tensor to obtain the total stress tensor for the flu id.

anslate&resnum=4&ct=result&prev=/search%3Fq%3DIto%2BHidebumi%26hl%3Den. Retrieved on 2008-06-16.

ate a wide, shallow-sloped shield volcano. Put simply, the less viscous something is, the greater its ease of movement (fluidity).

250 × 10 −3 Pa·s.[6] (kinematic viscosity is measured in m 2s-1).

alances the applied force), the substance is called a fluid. The a pplied force is proportional to the area and velocity of the plate and inverse

ee path and the mean velocity of the atoms. On the other hand, the mean free path is inversely proportional to the density. So an increase

he result of the glass making process rather than the viscosity of glass.[29]

describe the relationship between stress and the rate of change of strain, rather than rate of shear.

or) and a traceless symmetric tensor (the rate-of-shear tensor):

ement (fluidity). [1] All real fluids (except superfluids) have some resistance to stress, but a fluid which has no resistance to shear stress is kn

city of the plate and inversely proportional to the distance between the plates. Combining these three relations results in the equation

he density. So an increase of pressure doesn't result in any change of the viscosity.

stance to shear stress is known as an ideal fluid or inviscid fluid. The study of viscosity is known as rheology.

sults in the equation F = μ (Au/y), where μ is the proportionality factor called the dynamic viscosity (also called absolute viscosity

bsolute viscosity, or simply viscosity). The equation can be expressed in terms of shear stress; τ = F/A = μ (u / y). The rate of shear deforma

). 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

method, the relation between the shear stress and the velocity gradient can be obtained.