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# Kinematic Viscosity

Matter can exist in three physical states; solids, liquids and gases. All physical states are composed of certain particles which are arranged in a manner that determine their physical state. Some intermolecular forces of attraction also exist between constituent particles such as solid particles are bonded with strong force of attraction whereas weakest force of attraction is found in gaseous state of matter. Liquid state is intermediate state of matter in which substance occupies the volume and shape of container. Liquid particles can move freely like gaseous particles due to weaker intermolecular force than solid state. Some other properties such as viscosity, surface tension make the liquids different from other two states. Because of different intermolecular forces, liquids can be different types. Some common examples of liquids are water, honey, alcohol, petrol etc.

Viscosity is the property of liquids which characterized the thickness of that liquid. On molecular level, it represents the resistance of flow of layers. Solids and gases do not show this property. This is because, in solid state the particles are arranged in a regular packed manner and do not show any movement. They can only vibrate at their mean position in the solid lattice. In gaseous state, the particles have high kinetic energy and can move randomly move. The laminar flow of liquid molecules explains the properties like viscosity, surface tension etc.

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## Kinematic Viscosity Definition

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To analyze the liquid behavior and fluid motion near solid boundaries, we can use viscosity. It is measurement of resistance to gradual deformation by tensile stress. In liquids the resistance is caused by inter molecular friction between molecular layers. The viscosity of liquid can be measured as absolute viscosity and kinematic viscosity. Kinematic viscosity can be defined as the ratio of absolute viscosity and density of liquid at given temperature.

## Kinematic Viscosity of Water

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At different temperatures, the values of kinematic viscosity of water are listed below.

 Temperature (oC) Kinematic Viscosity (10-6 m2/s) 0 1.787 5 1.519 10 1.307 20 1.004 30 0.801 40 0.658 50 0.553 60 0.475 70 0.413 80 0.365 90 0.326 100 0.294

## Kinematic Viscosity Formula

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Kinematic viscosity is the ratio of dynamic viscosity and density of liquid. Te mathematical expression for it is;
ν = $\frac{\mu}{\rho}$
•    ν = kinematic viscosity
•   $\mu$ = absolute viscosity
•    $\rho$ = density

Unit of kinematic viscosity:
The theoretical unit of kinematic viscosity in SI system is m2/s or Stoke (St).  The relation between these two units is;
1 St (Stokes) = 10-4 m2/s = 1 cm2/s
It can also expressed as Centistoke (cSt) here
1    St = 100 cSt
And 1 cSt (centiStoke) = 10-6 m2/s = 1 mm2/s

Since the specific gravity for water at 20.2oC is 1 so the kinematic viscosity for water at that temperature will be 1.0 mm2/s (cStokes). The exact value of kinematic viscosity is 1.0038 mm2/s (cStokes) at 20.2 oC temperature. The imperial units of kinematic viscosity are ft2/s. We know that;

Dynamic viscosity (μ)   = $\frac{lb. s}{ft^{2}}$

And density (ρ) = $\frac{slugs}{ft^{3}}$

Here slug = $\frac{lb}{32.174 ft. s 2}$

So density (ρ) = (lb /32.174 ft.s2) / ft3 = (lb/32.174. s2) / ft4

Kinematic Viscosity ν = (lb. s / ft2) / (slugs / ft3)

Or v = (lb. s / ft2)/ (lb.s2 /ft4) = ft2 /s

## Difference Between Dynamic and Kinematic Viscosity

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The fundamental material property which describes the flow of fluid is known as viscosity. Viscosity can be classified as dynamic and kinematic viscosity. The measurement of the fluidâ€™s internal resistance to flow is called as dynamic viscosity or absolute viscosity whereas kinematic viscosity is ratio of dynamic viscosity to density. Two fluids can have same dynamic viscosities whereas kinematic viscosity value depends on density of liquid. Dynamic viscosity represents the force needed to make the flow of fluid at a certain rate. Kinematic viscosity indicates the flow of the fluid at a certain force. The dynamic viscosity is a force involved in displacing a fluid which is proportional to:

F = $\eta A \times S$

Here;
â€¢    S = Shear rate
â€¢    A = Surface area
â€¢    $\eta$ = Dynamic viscosity

The variation of dynamic viscosity with temperature is shown below. The unit of dynamic viscosity is;
$\frac{Force}{area * time}$

$\mu$=  $\frac{lb . s}{ft^{2}}$

The unit of kinematic viscosity;

Î½ = $\frac{Area}{time}$ = $\frac{ft^{2}}{s}$

The units of dynamic viscosity and kinematic viscosity are below.

 Dynamic viscosity Unit Equivalent 1 mPa-s 1 cP 1 P (Poise) 100 cP 1 Pa-s 1000 cP

Kinematic viscosity  Unit Equivalent 1 cm2/s
100 cSt
1 St
100 cSt 1 m2/s 1,000,000 cSt

Dynamic and kinematic viscosity values of some of the common fluids are given below.

 Fluids Dynamic viscosity [cP] Kinematic viscosity [cSt] Temperature [â„ƒ] Water 1 1 20 Water 0.894 0.894 25 Air 0.018 13.9 27 Honey 5000 3500 25 Mercury 1.526 0.11 25 Ethanol 1.074 1.36 25

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