# Dynamic, Absolute and Kinematic Viscosity

## An introduction to dynamic, absolute and kinematic viscosity and how to convert between *CentiStokes (cSt), CentiPoises (cP), Saybolt Universal Seconds (SSU), degree Engler and more*

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The viscosity of a fluid is an important property in the analysis of liquid behavior and fluid motion near solid boundaries.

The viscosity is the fluid resistance to shear or flow and is a measure of the adhesive/cohesive or frictional fluid property. The resistance is caused by intermolecular friction exerted when layers of fluids attempt to slide by one another.

- Viscosity is a measure of a fluid's resistance to flow

The knowledge of viscosity is needed for proper design of required temperatures for storage, pumping or injection of fluids.

- Molasses is highly viscous
- Water is medium viscous
- Gases have a low viscosity

There are two related measures of fluid viscosity - known as **dynamic** (**or absolute**) and **kinematic** viscosity.

### Dynamic (absolute) Viscosity

Absolute viscosity or the coefficient of absolute viscosity is a measure of the internal resistance. Dynamic (absolute) viscosity is the tangential force per unit area required to move one horizontal plane with respect to the other at unit velocity when maintained a unit distance apart by the fluid.

The shearing stress between the layers of non turbulent fluid moving in straight parallel lines can be defined for a Newtonian fluid as:

The dynamic or absolute viscosity can be expressed like

τ = μ dc/dy (1)

where

τ = shearing stress

μ = dynamic viscosity

Equation (1) is known as the **Newtons Law of Friction**.

In the SI system the dynamic viscosity units are **N s/m ^{2}**,

**Pa.s**or

**kg/m.s**where

*1 Pa.s = 1 N s/m*^{2}= 1 kg/m.s

The dynamic viscosity is also often expressed in the metric CGS (centimeter-gram-second) system as * g/cm.s, dyne.s/cm^{2}* or

*where*

**poise (p)***1 poise = 1 dyne s/cm*^{2}= 1 g/cm.s = 1/10 Pa.s = 1/10 N.s/m^{2}

For practical use the *Poise* is to large and it's usual divided by *100* into the smaller unit called the * 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/m^{2}

Water at *68.4 ^{o}F (20.2^{o}C)* has an absolute viscosity of one -

*1 - centiPoise*.

Liquid | Absolute Viscosity at Room Temperature (Pa.s) |

Air | 1.983 x 10^{-5} |

Water | 1 x 10^{-3} |

Olive Oil | 1 x 10^{-1} |

Glycerol | 1 x 10^{0} |

Liquid Honey | 1 x 10^{1} |

Golden Syrup | 1 x 10^{2} |

Glass | 1 x 10^{40} |

### 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 it's mass density

ν = μ / ρ (2)

where

ν = kinematic viscosity

μ = absolute or dynamic viscosity

ρ = density

In the SI-system the theoretical unit is m^{2}/s or commonly used * Stoke (St) *where

*1 St (Stokes) = 10*^{-4}m^{2}/s = 1 cm^{2}/s

Since the *Stoke* is an unpractical large unit, it is usual divided by *100* to give the unit called * Centistokes (cSt)* where

*1 St = 100 cSt**1 cSt (centiStokes) = 10*^{-6}m^{2}/s = 1 mm^{2}/s

Since the specific gravity of water at* 68.4 ^{o}F (20.2^{o}C) *is almost

*one*, the kinematic viscosity of water at

*68.4*is for all practical purposes

^{o}F*1.0*The kinematic viscosity of water at

*mm*cSt).^{2}/s (*68°F (20°C)*is

*1.0038 mm*

^{2}/s (cSt).Conversion from absolute to kinematic viscosity can also be expressed as:

ν = 6.7197 10^{-4}μ / γ (2a)

where

ν = kinematic viscosity (ft^{2}/s)

μ = absolute or dynamic viscosity (cP)

γ= specific weight (lb/ft^{3})

### Viscosity and Reference Temperatures

The viscosity of a fluid is highly temperature dependent and for either 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 ^{o}C*. For a distillate fluid the reference temperature is

*40*.

^{o}C- For a liquid - the kinematic viscosity will
**decrease**with higher temperature - For a gas - the kinematic viscosity will
**increase**with higher temperature

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### Other Commonly used Viscosity Units

#### Saybolt Universal Seconds (or *SUS, SSU*)

Saybolt Universal Seconds (or *SUS*) is used to measure 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 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 versus dynamic or absolute viscosity can be expressed as

ν_{SSU}= B μ / SG

= Bν_{centiStokes}(3)

where

ν_{SSU}= kinematic vicosity (SSU)

B = 4.632 for temperature100^{o}F (37.8^{o}C)

B = 4.664 for temperature210^{o}F (98.9^{o}C)μ = dynamic or absolute viscosity (cP)

SG = Specific Gravity

= kinematic viscosity (centiStokes)ν_{centiStokes}

#### 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 a 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 centimetres* 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 ^{o}C* but sometimes

*50*) in a standardized Engler viscosity meter.

^{o}C or 100^{o}C### Newtonian Fluids

Fluids for which the shearing stress is linearly related to the rate of shearing strain are designated as **Newtonian Fluids.**

Newtonian materials are referred to as true liquids since their viscosity or consistency is not affected by shear such as agitation or pumping at a constant temperature. Fortunately most common fluids, both liquids and gases, are Newtonian. Water and oils are examples of Newtonian liquids.

**Shear-thinning or ****Pseudoplastic Liquids**

**Shear-thinning** or **pseudoplastic liquids** are those whose viscosity decreases with increasing shear rate. Their structure is time-independent.

### Thixotropic Fluids

**Thixotropic liquids** have a time-dependent structure. The viscosity of a thixotropic liquid 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

**Shear Thickening Fluids** or **Dilatant Fluids** increase their viscosity with agitation. Some of these liquids can become almost solid within a pump or pipe line. With agitation, cream becomes butter and Candy compounds, clay slurries and similar heavily filled liquids do the same thing.

### Bingham Plastic Fluids

**Bingham Plastic Fluids** have a yield value which must be exceeded before it will start to flow like a fluid. From that point the viscosity will decrease with increase of agitation. Toothpaste, mayonnaise and tomato catsup are examples of such products.

### Example - Converting between Kinematic and Absolute Viscosity for Air

Kinematic viscosity of air at *1 bar (10 ^{5} Pa, N/m^{2})* and

*40*is

^{o}C*16.97 cSt (16.97 10*.

^{-6}m^{2}/s)The density of air estimated with the Ideal Gas Law

ρ = p / R T

where

ρ = density (kg/m^{3})

p = absolute pressure (Pa, N/m^{2})

R = individual gas constant (J/kg.K)

T = absolute temperature (K)

ρ = (10^{5}N/m^{2}) / ((287 J/kg/K) ((273^{o}C) + (33^{o}C)))

= 1.113 (kg/m^{3})

Absolute viscosity can be expressed as

μ = (1.113 kg/m^{3}) (16.97 10^{-6 }m^{2}/s)

= 1.88 10^{-5}(kg/m s, N.s/m^{2}, P)

### Viscosity of some Common Liquids

centiStokes(cSt) | Saybolt Second Universal (SSU, SUS) | Typical liquid |

1 | 31 | Water (20^{o}C) |

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 (20^{o}C)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 like

ν_{Centistokes}= 0.226ν_{SSU}- 195 /ν_{SSU}

where

ν_{SSU}< 100

ν_{Centistokes}= 0.220ν_{SSU}- 135 /ν_{SSU}

where

ν_{SSU}> 100

### Viscosity and Temperature

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

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

### Viscosity Measurements

Three types of devices are used in viscosity measurements

- capillary tube viscometer
- Saybolt viscometer
- rotatiting viscometer

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