# Viscosity - Absolute (Dynamic) vs. Kinematic

Viscosity is an important fluid property when analyzing liquid behavior and fluid motion near solid boundaries. The 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 inter-molecular 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

** Shear stress ** can be expressed

τ = μ dc / dy

= μ γ (1)

where

τ = shearing stress in fluid (N/m^{2})

μ = dynamic viscosity of fluid (N s/m^{2})

dc = unit velocity (m/s)

dy = unit distance between layers (m)

γ = dc / dy = shear rate (s^{-1})

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

* (1) * can be rearranged to express ** Dynamic viscosity ** as

* μ * = * τ dy / dc *

* = τ / γ (1b) *

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) = 0.67197 lb_{m}/(ft s) = 0.02088 slug /(ft s) = 0.02089 lb_{f}s/ft^{2}

Dynamic viscosity may also be 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 normally too large and the unit is therefore 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/m*^{2}

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

*one*-

*1 - centiPoise*.

Liquid | Absolute Viscosity ^{ *) } ( N s/m, Pa s) ^{2} |
---|---|

Air | 1.983 10 ^{ -5 } |

Water | 10^{-3} |

Olive Oil | 10^{-1} |

Glycerol | 10 ^{ 0 } |

Liquid Honey | 10 ^{ 1 } |

Golden Syrup | 10^{2} |

Glass | 10 ^{ 40 } |

*) at room temperature

### 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 like

ν = μ / ρ (2)

where

ν = kinematic viscosity (m^{2}/s)

μ = absolute or dynamic viscosity (N s/m^{2})

ρ = density (kg/m^{3})

In the SI-system the theoretical unit of kinematic viscosity is * m ^{2}/s * - or the commonly used

*where*

**Stoke (St)**

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

Stoke comes from the CGS (Centimetre Gram Second) unit system.

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}m^{2}/s = 1 mm^{2}/s

*1 m*^{2}/s = 10^{6}centiStokes

The specific gravity for water at * 20.2 ^{o}C (68.4 ^{o}F) * is almost

*one,*and the kinematic viscosity for water at

*20.2*is for practical purpose

^{o}C (68.4^{o}F)*1.0 mm*A more exact kinematic viscosity for water at

^{2}/s ( cStokes).*20.2*is

^{o}C (68.4^{o}F)*1.0038 mm*

^{2}/s (cSt).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 (ft^{2}/s)

μ = absolute or dynamic viscosity (cP)

γ = specific weight (lb/ft^{3})

### 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 ^{o}C * . For a distillate fluid the reference temperature is

*40*.

^{o}C- for a liquid - the kinematic viscosity
**decreases**with higher temperature - for a gas - the kinematic viscosity
**increases**with higher temperature

### Related Mobile Apps from The Engineering ToolBox

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^{o}F (37.8^{o}C)

B = 4.664 for temperature 210^{o}F (98.9^{o}C)μ = dynamic or absolute viscosity (cP)

SG = Specific Gravity

ν_{ centiStokes }= kinematic viscosity (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 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 ^{o}C * but sometimes

*50*) in a standardized

^{o}C or 100^{o}C*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 the viscosity decrease with increased 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, Convert between Kinematic and Absolute Viscosity

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

*40*is

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

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

ρ = p / (R T)

= (1 10^{5}N/m^{2}) / ( (287 J/(kg K)) ((273^{o}C) + (33^{o}C)) )

= 1.113 (kg/m^{3})

where

ρ = density (kg/m^{3})

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

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

T = absolute temperature (K)

The absolute viscosity can be calculated 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})

### Viscosity of some Common Liquids

centiStokes (cSt, 10^{-6} m^{2}/s, mm^{2}/s ) | Saybolt Second Universal (SSU, SUS) | Typical liquid |
---|---|---|

0.1 | Mercury | |

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 | 10000 | Honey |

6250 | 28000 | Mayonnaise |

19000 | 86000 | Sour cream |

Kinematic viscosity can be converted from * SSU * to * Centistokes * with

ν_{ Centistokes }= 0.226 ν_{ SSU }- 195 / ν_{ SSU }(4)

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

### Measuring Viscosity

Three types of devices are used to measure viscosity

- capillary tube viscometer
- Saybolt viscometer
- rotating viscometer

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