Dynamic, Absolute and Kinematic Viscosity

Dynamic, absolute and kinematic viscosity - and how to convert between CentiStokes (cSt), CentiPoises (cP), Saybolt Universal Seconds (SSU) and degree Engler

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The viscosity is an important fluid property when analyzing liquid behavior and fluid motion near solid boundaries. Viscosity of a fluid is a measure of its resistance to gradual deformation by shear stress or tensile stress. The shear resistance in a fluid is caused by intermolecular friction exerted when layers of fluid attempt to slide by one another.

• viscosity is the measure of a fluid's resistance to flow

• molasses is highly viscous
• water is medium viscous
• gas is low viscous

There are two related measures of fluid viscosity

• dynamic (or absolute)
• kinematic

Dynamic (absolute) Viscosity

Absolute viscosity - coefficient of absolute viscosity - is a measure of internal resistance. Dynamic (absolute) viscosity is the tangential force per unit area required to move one horizontal plane with respect to an other plane - at an unit velocity - when maintaining an unit distance apart in the fluid.
The shearing stress between the layers of a non turbulent fluid moving in straight parallel lines can be defined for a Newtonian fluid as

The dynamic viscosity can be expressed

τ = μ dc / dy         (1)
where
τ = shearing stress (N/m²)
μ = dynamic viscosity (N s/m²)
dc = unit velocity (m/s)
dy = unit distance between layers (m)

Equation (1) is known as the Newtons Law of Friction.
In the SI system the dynamic viscosity units are N s/m², Pa s or kg/(m s) - where

• 1 Pa s = 1 N s/m² = 1 kg/(m s)

Dynamic viscosity may also be expressed in the metric CGS (centimeter-gram-second) system as g/(cm s), dyne s/cm² or poise (p) where

• 1 poise = 1 dyne s/cm² = 1 g/(cm s) = 1/10 Pa s = 1/10 N s/m²

For practical use the Poise is normally too large and the unit is often divided by 100 - into the smaller unit centiPoise (cP) - where

• 1 p = 100 cP
• 1 cP = 0.01 poise = 0.01 gram per cm second = 0.001 Pascal second = 1 milliPascal second = 0.001 N s/m²

Water at 20.2^oC (68.4^oF) has the absolute viscosity of one - 1 - centiPoise.

Liquid	Absolute Viscosity *) (Pa s)
Air	1.983 x 10-5
Water	1 x 10-3
Olive Oil	1 x 10-1
Glycerol	1 x 100
Liquid Honey	1 x 101
Golden Syrup	1 x 102
Glass	1 x 1040

*) at room temperature

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Kinematic Viscosity

Kinematic viscosity is the ratio of - absolute (or dynamic) viscosity to density - a quantity in which no force is involved. Kinematic viscosity can be obtained by dividing the absolute viscosity of a fluid with the fluid mass density.

ν = μ / ρ        (2)
where
ν = kinematic viscosity (m²/s)
μ = absolute or dynamic viscosity (N s/m²)
ρ = density (kg/m³)

In the SI-system the theoretical unit of kinematic viscosity is m²/s - or Stoke (St) where

• 1 St (Stokes) = 10^-4 m²/s = 1 cm²/s

Since the Stoke is a large unit it is often divided by 100 into the smaller unit Centistoke (cSt) - where

• 1 St = 100 cSt
• 1 cSt (centiStoke) = 10^-6 m²/s = 1 mm²/s

The specific gravity for water at 20.2^oC (68.4^oF) is almost one, and the kinematic viscosity for water at 20.2^oC (68.4^oF) is for practical purpose 1.0 mm²/s (cStokes). A more exact kinematic viscosity for water at 20.2^oC (68.4^oF) is 1.0038 mm²/s (cStokes).

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A conversion from absolute to kinematic viscosity in Imperial units can be expressed as

ν = 6.7197 10^-4 μ / γ        (2a)
where
ν = kinematic viscosity (ft²/s)
μ = absolute or dynamic viscosity (cP)
γ = specific weight (lb/ft³)

Viscosity and Reference Temperature

The viscosity of a fluid is highly temperature dependent - and for dynamic or kinematic viscosity to be meaningful the reference temperature must be quoted. In ISO 8217 the reference temperature for a residual fluid is 100^oC. For a distillate fluid the reference temperature is 40^oC.

• for a liquid - the kinematic viscosity decreases with higher temperature
• for a gas - the kinematic viscosity increases with higher temperature

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This is a free app that can be used offline on mobile devices.

Other Viscosity Units

Saybolt Universal Seconds (or SUS, SSU)

Saybolt Universal Seconds (or SUS) is an alternative unit for measuring viscosity. The efflux time is Saybolt Universal Seconds (SUS) required for 60 milliliters of a petroleum product to flow through the calibrated orifice of a Saybolt Universal viscometer - under a carefully controlled temperature and as prescribed by test method ASTM D 88. This method has largely been replaced by the kinematic viscosity method. Saybolt Universal Seconds is also called the SSU number (Seconds Saybolt Universal) or SSF number (Saybolt Seconds Furol).
Kinematic viscosity in SSU versus dynamic or absolute viscosity can be expressed as

ν_SSU = B μ / SG 
  = B ν_centiStokes        (3)
where
ν_SSU = kinematic viscosity (SSU)
B = 4.632 for temperature 100 ^oF (37.8 ^oC)
B = 4.664 for temperature 210^oF (98.9 ^oC)
μ = dynamic or absolute viscosity (cP)

SG = Specific Gravity

ν_centiStokes = kinematic viscosity (centiStokes)

• SSU at other temperatures

Degree Engler

Degree Engler is used in Great Britain as a scale to measure kinematic viscosity. Unlike the Saybolt and Redwood scales, the Engler scale is based on comparing the flow of the substance being tested to the flow of another substance - water. Viscosity in Engler degrees is the ratio of the time of a flow of 200 cubic centimeters of the fluid whose viscosity is being measured  - to the time of flow of 200 cubic centimeters of water at the same temperature (usually 20^oC but sometimes 50^oC or 100^oC) in a standardized Engler viscosity meter.

Newtonian Fluids

A fluid where the shearing stress is linearly related to the rate of shearing strain - is designated as a Newtonian Fluid.
A Newtonian material is referred to as true liquid since the viscosity or consistency is not affected by shear such as agitation or pumping at a constant temperature. Most common fluids - both liquids and gases - are Newtonian fluids. Water and oils are examples of Newtonian liquids.

Shear-thinning or Pseudo-plastic Fluids

A Shear-thinning or pseudo-plastic fluid is a fluid where viscosity decreases with increasing shear rate. The structure is time-independent.

Thixotropic Fluids

A Thixotropic fluid has a time-dependent structure. The viscosity of a thixotropic fluid decreases with increasing time - at a constant shear rate.
Ketchup and mayonnaise are examples of thixotropic materials. They appear thick or viscous but are possible to pump quite easily.

Dilatant Fluids

A Shear Thickening Fluid - or Dilatant Fluid - increases the viscosity with agitation or shear strain. Dilatant fluids are known as non-Newton fluids.
Some dilatant fluids can become almost solid in a pump or pipe line. With agitation cream becomes butter and candy compounds. Clay slurry and similar heavily filled liquids do the same thing.

Bingham Plastic Fluids

A Bingham Plastic Fluid has a yield value which must be exceeded before it will start to flow like a fluid. From that point the viscosity decreases with increasing agitation. Toothpaste, mayonnaise and tomato ketchup are examples of such products.

Example - Air, Converting between Kinematic and Absolute Viscosity

Kinematic viscosity of air at 1 bar (1 10⁵ Pa, N/m²) and 40^oC is 16.97 cSt (16.97 10^-6 m²/s).
The density of the air can be estimated with the Ideal Gas Law

ρ  = p / (R T)
    = 1 10⁵ (N/m²) / ( 287 (J/(kg K)) (273 (^oC) + 33 ( ^oC)) )
    = 1.113 (kg/m³)
where
ρ = density (kg/m³)
p = absolute pressure (Pa, N/m²)
R = individual gas constant (J/(kg K))
T = absolute temperature (K)  

The absolute viscosity can be calculated as

μ = 1.113 (kg/m³) 16.97 10^-6 (m²/s)
    = 1.88 10^-5 (kg/(m s), N s/m²)

Viscosity of some Common Liquids

centiStokes (cSt)	Saybolt Second Universal (SSU, SUS)	Typical liquid
1	31	Water (20oC)
4.3	40	Milk SAE 20 Crankcase Oil SAE 75 Gear Oil
15.7	80	No. 4 fuel oil
20.6	100	Cream
43.2	200	Vegetable oil
110	500	SAE 30 Crankcase Oil SAE 85 Gear Oil
220	1000	Tomato Juice SAE 50 Crankcase Oil SAE 90 Gear Oil
440	2000	SAE 140 Gear Oil
1100	5000	Glycerine (20oC) SAE 250 Gear Oil
2200	10,000	Honey
6250	28,000	Mayonnaise
19,000	86,000	Sour cream

Kinematic viscosity can be converted from SSU to Centistokes as

ν_Centistokes = 0.226 ν_SSU - 195 / ν_SSU
where
ν_SSU < 100
ν_Centistokes = 0.220 ν_SSU - 135 / ν_SSU
where
ν_SSU > 100

Viscosity and Temperature

Kinematic viscosity of fluids like water, mercury, oils SAE 10 and oil no. 3 - and gases like air, hydrogen and helium are indicated in the diagram below. Note that

• for liquids viscosity decreases with temperature
• for gases viscosity increases with temperature