# Viscosity

Today we are going to discuss about viscosity, cause of viscosity, examples of viscosity, coefficient of viscosity, comparison between viscous force and solid friction, variation of viscosity with temperature & pressure and practical applications of the knowledge of viscosity in daily life.

### What is viscosity ?

Viscosity is a property of fluid by virtue of which an internal force of friction comes into play when a fluid is in motion and which opposed the relative motion between its different layers.

The backward dragging force, called viscous drag or viscous force, acts tangentially on the layers of th fluid in motion and tends to destroy its motion.

### Cause of viscosity

Consider a liquid moving slowly and steadily over a fixed horizontal surface. Each layer mover parallel to fixed surface. The layer which is in contact with the fixed surface is at rest and the velocity of the every other layer increases uniformly upwards.

Consider any two adjacent layers 1 and 2. The upper fast moving layer 1 tends to accelerate the lower layer 2 while the slow moving layer 2 tends to retard the fast moving layer 1.

As a result, a backward dragging tangential force F, called viscous drag comes into play which tends to destroy the relative motion. To maintain the motion or movement, an external force has to be applied to overcome the backward viscous force.

### Some examples of viscosity

Here are some examples of viscosity.

• When we swim in a pool of water, we experience some resistance to our motion. This is on account of viscous forces of water

• If we pour water and honey in different funnels, water comes out readily from the hole in the funnel while honey trickles down drop by drop very slowly. This happens because the honey is much more viscous than the water. The relative motion between the layers of honey is strongly opposed.

• The cloud particles fall down very slowly on account of the viscosity of air and hence seen floating in the sky.

• we can talk fast in air, but not in water. This is because viscosity of air is much smaller than that of water.

### Coefficient of viscosity

Let us assume a liquid is flowing steadily in the form of parallel layers on a fixed horizontal surface.

Consider two layers P and Q at distances x and
x + dx from the solid surface and moving with velocities v and v + dv respectively.

The dv/dx is the rate of change of velocity with distance in the direction of increasing distance and is called velocity gradient.

According to Newton, a force of viscosity F acting tangentially between two layers is

• Proportional to the area A of the layers in contact.

F   is directly proportional to   A

• Proptional to the velocity gradient dv/dx between the two layers

F is directly proportional to dv/dx

F is directly proportional to Adv/dx

Where n is coefficient of viscosity of the liquid. It depends on the nature of the liquid and gives a measure of viscosity.

Negative sign shows that viscous force acts in a direction opposite to the direction of motion of the liquid.

If

A = 1 and dv/dx = 1

Then,

F = n   ( numerically )

Hence coefficient of viscosity of a liquid may be defined as the tangential viscous force required to maintain a unit velocity gradient between it's two parallel layers each of unit area.

#### Dimensions of coefficient of viscosity

dimension of coefficient of viscosity is

#### Units of coefficient of viscosity

• The CGS unit of coefficient of viscosity is
dyne s cm-² or g cm-¹ s-¹ and is called poise.

1 poise = 1 dyne s cm-²

The coefficient of viscosity of a liquid is said to be 1 poise if a tangential force of 1 dyne cm-² of the surface is required to maintain a relative velocity of 1 cm s-¹ between two layers of the liquid 1 cm apart.

• The SI unit of n is N s m-² or Kg m-¹ s-¹ and is called decapoise or poiseuille.

1 poiseuille = 1 N s m-²

The coefficient of viscosity of a liquid is said to be 1 poiseuille or 1 decapoise if a tangential force of 1Nm-² of the surface is required to maintain a relative velocity of 1Nm-¹ between two layers of the liquid 1m apart.

### Comparision between viscous force and solid friction

Here are some similarities and differences between viscous force and solid friction.

#### Similarities

• Both viscous force and solid friction come into play whenever therevis relative motion.

• Both oppose the motion.

• Both are due to molecular attraction.

#### Difference

• Viscous force is directly proportional to the area of layers in contact but solid friction is independent of the area of the surfaces in contact.

• Viscous force is directly proportional to the relative velocity but solid friction is independent to to relative velocity.

• Viscous force is independent to the normal reaction between the two liquid layers but solid friction is directly proportional to the normal reaction between the surface in contact.

### Variation of viscosity with

Variation of viscosity with temperature and pressure.

#### 1. Temperature

• When a liquid is heated, the kinetic energy of its molecules increases and the intermolecular attractions become weaker.

Hence the viscosity of liquid decreases with the increase in the temperature.

• Viscosity of gases is due to the diffusion of molecules from one moving layer to another. But the rate of diffusion of a gas is directly proportional to the square root of its absolute temperature, so viscosity of a gas increases with increase in temperature.

#### 2. Pressure

• Except water the viscosity of liquids increases with the increase in pressure. In case of water, viscosity decreases with the increase in pressure for first few hundred atmospheres of pressure.

• The viscosity of gases is independent of pressure.

### Practical applications of viscosity

Let's discuss about practical applications of knowledge of viscosity.

• The knowledge of viscosity and its variation with temperature helps us to select a suitable lubricant for a given machine in different seasons.

• Liquids of high viscosity are used as buffers for absorbing shocks during the shunting of trains.

• The knowledge of viscosity is used in determining the shape and molecular weight of some organic liquids like proteins, cellulose etc.

• The phenomenon of viscosity plays an important role in the circulation of blood through arteries and veins of human body.

• Millikan used the knowledge of viscosity in determining the charge on an electron.

## FAQ

Here are some frequently asked questions.

#### 1. What is viscosity formula ?

F = -n Adv/dx - this is the formula of viscosity.

#### 2. What causes viscosity ?

backward dragging tangential force F, called viscous drag comes into play which tends to destroy the relative motion. To maintain the motion or movement, an external force has to be applied to overcome the backward viscous force.

#### 3. What is liquid viscosity ?

We can also define viscosity by thickness. For eg. Water is a liquid which is not thick and viscosity of water is low, but in case of honey its thick and viscosity of honey is high as compared to water.

#### 4. What is viscosity in simple words ?

Viscosity is a property of fluid which describes the internal friction in a moving fluid.
Measure of fluid resistance to flow is called viscosity.

#### 5. Why viscosity is important ?

Viscosity is important because it plays a very important role in our day to day life. All the uses of viscosity are mentioned above.

#### 6. What is viscous force ?

The backward dragging force is called viscous drag or viscous force.

#### 7. Viscosity SI unit

The SI unit of coefficient of viscosity is N s m-² or
Kg m-¹ s-¹.

They are also called decapoise or poiseuille.