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Dynamic Viscosity

We know that any substance can exist in solid, liquid and gaseous states. The difference in these three states can be noticed in ice, water and steam. Let’s discuss the molecular level of these three states. All states are composed of certain particles which have weak or strong intermolecular forces between them. These forces determine the states of matter. See the image given below. The particles in solid state are much closed to each other due to strong inter-molecular forces between them. That is the reason; they have least inter-molecular distance between them. Unlike solids, gaseous particles are far enough from each other that are because of weakest inter-molecular forces between constituent particles. 

Solids Liquids Gases

Let’s discuss the liquid state of matter. It is an intermediate state of matter in which the intermolecular distance and forces lie between solid and gaseous state. The constituent particles in this state have intermolecular attraction but also have enough space between them. So we can say that they do not have enough fixed position like solid state but also not have enough space like gaseous state. The intermolecular attraction between the liquid particles keeps the volume constant. Due to this, liquid state exhibits many special properties such as flow, surface tension, viscosity, cohesive and adhesive forces. The attraction force between same kinds of particles is called as cohesive force.

Because of cohesive forces, liquid particle tend to stick with each other and show surface tension. Surface tension is the property of liquid surface which can be defined as the tension between the surface molecules due to uneven force of attraction from bulk molecules. Surface tension is responsible for the spherical shape of water drops. 

Another force between liquid particles is adhesive forces. These forces exist between different types of particles. For example the adhesive force between liquid particles and glass tube causes the capillary action of liquid. Both of these forces cause a slight concave curve at the surface of most liquids that is called as meniscus. 


Dynamic Viscosity Definition

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Let’s continue with one of the most important properties of liquid known as viscosity. Viscosity can be defined as the measure of flow of a liquid. A more viscous liquid will flow slowly than a less viscous liquid. In other words, a liquid with low viscosity is thinner than the liquid with higher viscosity. Water and honey is one of the best examples for this. Water is thinner than honey so it can flow faster than honey. So we can say honey is more viscous liquid than water. This property of liquids can be explained with the help of laminar flow of layers in liquids. Viscosity can be classified as dynamic or absolute viscosity, kinematic viscosity, relative and apparent viscosity. 

Dynamic viscosity is represented with the symbol of eta $(\eta)$.  It is also called as absolute viscosity or shear viscosity. It can be formulated with the use of Newton's Law as given below.
$\tau$  = $\eta * \gamma$
or $\eta$ =  $\frac{\tau}{\gamma}$

Dynamic viscosity can be expressed as pascal-second or millipascal-second.
1 Pa.s = 1000 mPa.s
Other common unit for dynamic viscosity is poise [P] or centipoise [cP]:
1 P = 100 cP
1 cP = 1 mPa.s

Dynamic Viscosity of Water

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Dynamic viscosity or absolute viscosity is the expression of resistance to flow of a liquid.  The SI unit of it is pascal-second (Pa.s) or N.m-2.s whereas CGS unit is ‘poise’ or centipoise (cP). The dynamic viscosities of water at different temperatures are listed below.

 Temperature  (oC) 
 Dynamic Viscosity
 $(10^{-3}$ Pa s (N s/m2))  
 0  1.787
 5  1.519
 10  1.307
 20  1.002
 30  0.798
 40  0.653
 50  0.547
 60  0.467
 70  0.404
 90  0.315
 100  0.282

So we can say that dynamic viscosity decreases with increasing the temperature of water. 
Temperature and Dynamic Viscocity

Dynamic Viscosity of Air

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The dynamic viscosity of air can be formulated with the help of Sutherland’s formula as given below.

$\eta$ = $\eta 0 \frac{T}{T_{0}}^{1.5}  \frac{(T0 + 198.72}{T + 198.72}$

Here η is dynamic viscosity at T temperature.  The dynamic viscosity of air at different temperature values are listed below;

 Temperature  (oC) 
 Dynamic Viscosity
 (N s/m2)
 0  $1.717 x 10^{-5}$
 5  $1.741 x 10^{-5}$
 10  $1.767 x 10^{-5}$
 20  $1.817 x 10^{-5}$
 30  $1.864 x 10^{-5}$
 40  $1.910 x 10^{-5}$
 50  $1.954 x 10^{-5}$
 60  $2.001 x 10^{-5}$
 70  $2.044 x 10^{-5}$
 80  $2.088 x 10^{-5}$
 90  $2.131 x 10^{-5}$
 100  $2.174 x 10^{-5}$

Dynamic Viscosity of Oil

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Engine oils are formulated oils which consist of mineral and synthetic base oil with different additives. The quality of engine oil depends on properties and amount of additives present in it. Temperature-viscosity is the main property of engine oil. The variation in dynamic viscosity of SAE 15W-40 engine oil with temperature is listed below.

 Temp [°C]   Dyn. Viscosity[mPa.s] 
 0  1328.0  0.8916
 10  582.95  0.8851
 20  287.23  0.8787
 30  155.31  0.8725
 40  91.057  0.8663
 50  57.172  0.8602
 60  38.071  0.8539
 70  26.576  0.8477
 80  19.358  0.8414
 90  14.588  0.8352
 100  11.316  0.8291

Difference Between Kinematic and Dynamic Viscosity

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The ratio of dynamic viscosity and density of liquid is called as kinematic viscosity of liquid. It describes the flow behavior under the influence of gravity. The mathematical expression for kinematic viscosity is given below;

ν = $\frac{\eta}{\rho}$

The SI unit f kinematic viscosity is [m2/s] or [mm2/s]. 

1 m2/s = 1 000 000 mm2/s

It can also express as;
1 St = 100 cSt
1 cSt = 1 mm2/s

The differences between dynamic viscosity and kinematic viscosity are listed below.

   Dynamic viscosity 
 Kinematic viscosity 
 It is represented as $\eta$ or $\mu$.   It is represented as ν.
2  $\eta$ =  $\frac{\tau}{\gamma}$  $\nu$ = $\frac{\eta}{\rho}$
3  It does not depend on the density of liquid.   It depends on the density of liquid. 
4  It is mainly used to describe the behavior of fluids under stress.   It is mainly used for petrochemical fluids like fuels or lube oils.

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