Unit of Viscosity - Definition, Types, Unit, Example, FAQs

Viscosity Unit

The unit of viscosity or viscosity unit is Pascal seconds (Pa-s) or .

SI unit of viscosity

The SI unit of viscosity is given by Pascal seconds (Pa-s) or .

What is the viscosity unit?

Viscosity is defined as the property of a fluid which offers resistance to the movement of one layer of fluid over another adjacent layer of the fluid. When two layers of a fluid, a distance ‘dy’ apart, move one over the other at different velocities, let us say it ‘u’ and ‘u + du’. This viscosity together with the relative velocity causes a shear stress acting between the fluid layers. The top layer causes a shear stress on the adjacent lower layer while the lower layer causes a shear stress on the adjacent top layer. This shear stress is proportional to the rate of change of velocity with respect to ‘y’. It is denoted by symbol.

Mathematically,

…………………(i)

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Where (called mu), is the constant of proportionality and is known as the coefficient of dynamic viscosity or only viscosity. is the rate of shear strain or rate of shear deformation or velocity gradient.

Using equation (i) we can write,

Viscosity is also defined as the shear stress required to produce unit rate of shear strain.

Unit of viscosity

The units of viscosity is obtained by putting the dimensions of the quantities in equation (i)

In MKS system, the force is represented by kgf and the length is represented by metre (m), in CGS system, the force is represented by dyne and the length is represented by cm and in SI system the force is represented by Newton (N) and the length is represented by meter (m).

MKS unit of viscosity =

CGS unit of viscosity =

is also known as Pascal and is represented by ‘Pa’.

SI unit of viscosity = = .

SI unit of viscosity = Newton –sec/m2

The unit of viscosity in CGS is also called Poise which is equal to

The numerical conversion of the unit of viscosity from MKS unit to CGS unit is given below:

One Newton = one kg (mass) x one (m/s2)(acceleration)

=

If viscosity is given in Poise, it must be divided by 10 to get its equivalent numerical value in SI units. Sometimes a unit of viscosity as centipoise is used where

1 centipoise = 1/100 Poise

The viscosity of water atis 0.01 Poise or 1.0 centipoise.

Types of Viscosity

There are two types of viscosity

1. Kinematic viscosity

It is defined as the ratio between the dynamic viscosity and density of fluid. It is denoted by the Greek symbol () called ‘nu’. Mathematically, it can be represented by,

The unit of Kinematic viscosity is obtained as

In MKS and SI, the unit of Kinematic Viscosity is while in CGS units it is written as. In CGS units, Kinematic Viscosity is also known as stoke.

One stoke =

Centistoke = 1/100 stoke

2. Dynamic Viscosity

It is the ratio of Force multiplied by time to the Area.

It is expressed as

The factors on which viscosity depends are:-

a. area of contact of two adjacent layers,

b. velocity difference between two adjacent layers,

c. the distance between two adjacent layers.

Difference between Dynamic Viscosity and Kinematic Viscosity

Newton’s Law of Viscosity

Newton’s Law of Viscosity states that the shear stress on a fluid element layer is directly proportional to the rate of shear strain. This constant of proportionality is called the coefficient of viscosity. Mathematically, it can be expressed as

Fluids which obey the above equation are known as Newtonian fluids and the fluids which do not obey the above relation are called Non-Newtonian fluids.

Also Read:

• NCERT solutions for Class 11 Physics Chapter 10 Mechanical Properties of Fluids
• NCERT Exemplar Class 11 Physics Solutions Chapter 10 Mechanical Properties of Fluids
• NCERT notes Class 11 Physics Chapter 10 Mechanical Properties of Fluids

Practice Questions

Q.1 Determine the viscosity of a liquid having kinematic viscosity 6 stokes and specific gravity 1.9.

Sol) Given,

Kinematic Viscosity, s

Specific gravity of liquid = 1.9

Let the viscosity of the liquid be

No, specific gravity of a liquid = Density of the liquid/Density of water

1.9 = Density of the liquid/1000

Density of the liquid =

By using the relation, , we get

= Poise.

Also read -

• NCERT Solutions for Class 11 Physics
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NCERT Physics Notes:

• NCERT Notes Class 11th Physics
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• NCERT Notes For All Subjects