# Absolute, Dynamic and Kinematic Viscosity

## Dynamic, absolute and kinematic viscosities - convert between *CentiStokes (cSt), centipoises (cP), Saybolt Universal Seconds (SSU) and degree Engler*

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)

= dc / dy = shear rate (sγ^{-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/(ft s)*= 0.67197 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

*is for practical purpose*

*20.2*(68.4^{o}C^{o}F)*1.0*A more exact kinematic viscosity for water at

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

*20.2*(68.4^{o}C^{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

= Bν_{centiStokes}(3)

where

ν_{SSU}= kinematic viscosity (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 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}= 0.226ν_{SSU}- 195 /ν_{SSU }(4)_{}

where

ν_{SSU}< 100

ν_{Centistokes}= 0.220ν_{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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