Unit of Viscosity

Do you know what will happen if you pour 1000 ml of water on a person's head? The water flows through the person's hair and then over the face. Now, let us consider another situation in which you pour 1000 ml of honey on a person's head.  In this particular scenario, the honey poured will take its own time running down the hair and face of that person. Do you know the difference between both the cases? The answer lies in the property of fluids, known as viscosity.


Understanding the Term Viscosity 

The term 'Viscosity' in physics refers to the measure of the resistance of a fluid to gradual deformation by tensile stress (the force acting along the axis of force, which is responsible for the stretching or elongation of a material) or shear stress (the external force on an object or surface area parallel to the plane or slope in which the object lies). To be specific, viscosity defines a fluid's resistance to flow. In the example we discussed earlier concerning honey and water, we can say that honey is thicker than water due to which it is more viscous than water as well.

So, we can say that the viscosity of a fluid refers to the measure of its resistance to gradual deformation at a given rate. For instance - the viscosity of syrup is higher than that of water.

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How to Calculate Viscosity

The viscosity of a fluid is measured in terms of the ratio of its shearing stress (if the direction of external force on an object is parallel to the plane of an object, then the deformation will be along that plane, and the stress on the object will be shear stress) to its velocity gradient (the difference between the adjacent layers of a fluid). If we drop a sphere into a fluid, we can calculate the viscosity using the formula specified below:

η = 2ga2(Δρ)/9v

In this formula,

η = viscosity (represented by the symbol η or “eta”)

 Δρ = difference in the density of the fluid and the sphere tested

a = radius of the sphere 

g = acceleration due to gravity 

v = velocity of the sphere 

We can, in turn, calculate v as the distance travelled by the sphere per unit time.

We measure viscosity in Pascal seconds that is Pa s. From the formula mentioned above, it is quite evident that if the velocity of the sphere increases, the viscosity will be more. Furthermore, the more viscous a fluid is, the more resistance shall it offer to any object flowing or moving inside it. The viscosity of water is 0.001 Pa s, that of motor oil is 1, and that of air is 0.000019 Pa s. It is also essential to make a point of the fact that in the case of gases, with the increase in the temperature, the viscosity will also increase. On the other hand, in the case of liquids, the viscosity shall decrease as the temperature increases.


Different Types of Viscosity

We already know that viscosity refers to the friction of fluids. We can measure a fluid's viscosity using two ways, which are as follows:

  1. Dynamic Viscosity or Absolute Viscosity 

  2. Kinematic Viscosity

The primary difference between the two types of viscosity is that dynamic or absolute viscosity is the measure of the internal resistance of the fluids to the flow while kinematic viscosity is the ratio of dynamic or absolute viscosity to the density. Also, kinematic viscosity is more useful than dynamic or absolute viscosity for a few applications.


SI Unit of Viscosity 

Pascal seconds (Pa s) is the SI unit of dynamic or absolute viscosity.  

We know that Pa is the SI unit of pressure. 

Pressure = Pa = Force/Area

Force = Mass * Acceleration

Force = kg ms-2

Area = m2

By substituting these values in the formula of pressure, we get:

Pressure = Pa = kg ms-2/ m2

Pressure = Pa = kg m-1s-2

So, Pa s = kg m-1s-2 s = kg m-1s-1

Therefore, the SI unit of dynamic or absolute viscosity = Pa s = kg m-1s-1

Now, Kinematic viscosity = dynamic or absolute viscosity/density and density = mass/volume = kg m-3

So, kinematic viscosity = kg m-1s-1/ kg m-3 = m2s-1

So, the SI unit of kinematic viscosity = m2s-1


CGS Unit of Viscosity

Poise (P) is the CGS unit of dynamic or absolute viscosity, named in honor of Jean Léonard Marie Poiseuille, a French physiologist. Poise (P) is particularly used in ASTM standards as centipoises (cP). 

Stokes (St) is the CGS unit of kinematic viscosity, named after Sir George Gabriel Stokes, an Irish physicist and mathematician. The unit centistokes (cST) also has its uses in various fields.