## What is meant by viscosity?

The measure of the resistance of a fluid to flow is known as viscosity. Most fluids have some resistance to motion, the resistance provided by the fluid is called viscosity. This resistance is created by the force of attraction between the fluid molecules. If you pour water through a funnel, it flows easily and quickly, because it has very little resistance. But if you pour honey through a funnel, it may take a little time longer, as the density of honey is high.

## Introduction to viscosity

Viscosity is also referred to as fluid thickness. It is produced by the internal friction that takes place between the molecules. Friction is very important for these types of flows because there is a resistance to the relative motion. When a layer of liquid is moving in order to the next layer, there exists friction between the layers. The amount of friction depends on the fluid viscosity and the relative velocity between the layers (velocity gradient). A high-viscosity liquid flows slowly, while a low-viscosity liquid flows rapidly.

The viscosity of the liquid is defined as how easily the liquid flows under the stress. A fluid that is in motion adheres to the wall of the container. Hence, the velocity of the liquid is zero at the walls of the container. If the velocity of the liquid increases, away from the vessel surface, the fluid moves through the vessel in layers.

The fluid deformation is called shear. A fluid is said to be sheared when it moves through a solid surface.

## Types of viscosity

There are two kinds of viscosity. They are dynamic viscosity and kinematic viscosity.

### Dynamic viscosity

Dynamic viscosity or absolute viscosity or viscosity is defined as the ratio of shearing stress (F/A) to the velocity gradient of the fluid.

$Vis\mathrm{cos}ity=\frac{Shearstress}{Velocitygradient}\phantom{\rule{0ex}{0ex}}\mu =\frac{{\displaystyle F}}{{\displaystyle A\left(\frac{dv}{dx}\right)}}$

Where,

$\mu $=Dynamic viscosity

F=Force

A=Area

dv=Velocity of the liquid

dx=Thickness or density of the liquid

The SI units of dynamic viscosity are Pascal second (Pas) and dynes second per square centimeter (dyne s/cm^{2}) or poise (P), which is defined by Jean Poiseuille who discovered viscosity.

1Pa s=10 poise

1 millipasacal second (mPa s)= 10 poise

1 mPa s= 1 centiPoise

### Kinematic viscosity

The kinematic viscosity ($\nu $) is defined as the ratio of the viscosity of a fluid to its density. It is a measure of the resistance flow of a fluid under the influence of gravity. When two different fluids of equal amount are taken in an identical viscometer and allowed to flow under the influence of gravity, the liquid which is more viscous takes a longer time than the low viscous fluid.

$Kinematicvis\mathrm{cos}ity=\frac{Dynamicvis\mathrm{cos}ity}{Density}\phantom{\rule{0ex}{0ex}}\nu =\frac{\mu}{\rho}$

Where,

$\mu $ = dynamic viscosity.

$\rho $= density of the liquid.

The SI units ae meter square per second $({m}^{2}/s)$ and centimeter square per second $(c{m}^{2}/s)$ or stokes (St).

$1c{m}^{2}/s=1St\phantom{\rule{0ex}{0ex}}1{m}^{2}/s=10000St$

## Newton’s law of viscosity

The law states that the shear stress is directly proportional to the velocity gradient. The shear stress between the two adjacent layers of the fluid is directly proportional to the negative gradient velocity between the two adjacent layers of the fluid.

The two types of fluids based on newton’s law of viscosity are:

- Newtonian fluids.
- Non-newtonian fluids.

### Newtonian fluids

In this type, the viscosity of the fluid remains constant. It is independent of the shear stress applied to them in respect to time. The relationship between the shear stress and viscosity is linear for this type of fluid.

Examples are water, mineral oil, alcohol, gasoline.

### Non-newtonian fluids

In this type, the viscosity changes, when the shear stress is applied. It is completely opposite to Newtonian fluids.

Examples are toothpaste, paint, ketchup shampoo, butter yogurt.

### Types of non-newtonian fluids

There are four types of non-newtonian fluids. They are:

**Shear- thinning or dilatant:**When shear stress is applied, viscosity increases.**Shear-thickening or Pseudoplastic:**When shear stress is applied, viscosity decreases.**Rheopectic:**When shear stress is applied, viscosity increases with time.**Thixotropic:**When shear stress is applied, viscosity decreases with time.

## Factors affecting viscosity

The major factors which affect viscosity are,

**Temperature**: When the temperature is high, the liquid has low viscosity There is an inverse relationship between the temperature and viscosity. When the temperature is increased, its density decreases, thus the fluid becomes less viscous.

**Pressure**: When pressure increases, viscosity increases in liquids. For water, the viscosity decreases, and in gases, it remains the same.

Sometimes, the shape and size of the molecule can affect viscosity. If the molecules are in round shape, they can easily move each other compared to the molecules which are shapeless or non-uniform.

## Instruments

The instruments used to measure viscosity are viscometers and rheometers. Viscometers are used to measure the viscosity only when the flow is conditional. Rheometers are used when the viscosities of the flow vary with the flow condition. It is considered as one type of special of viscometer.

The fluid which flows through the meter must be stationary and the object moves through it or the object must be stationary and the fluid moves through the meter. The drag caused by the relative motion of the fluid and a surface is a measure of the viscosity. If the flow is laminar, then the flow must satisfy the Reynolds number in a small value.

## Formulas

The formula of dynamic viscosity is,

$\mu =\frac{{\displaystyle F}}{{\displaystyle A\left(\raisebox{1ex}{$dv$}\!\left/ \!\raisebox{-1ex}{$dx$}\right.\right)}}$

The formula of kinematic viscosity is,

$\nu =\frac{\eta}{\rho}$

## Context and Applications

This topic is the basic and important topic for all the graduates, especially for bachelors of science (physics) and bachelors of technology (mechanical engineering).

## Practice Problems

**Question 1**: Viscosity is measured in _____.

a. Newton second

b. Pascal second

c. Tesla second

d. None of these

**Answer:** The correct option is b.

**Explanation**: The unit of viscosity is Newton-second per meter. But it is generally measured in Pascal second (Pa s).

**Question 2: **Which of the following liquid has high viscosity?

a. Water

b. Cooking oil

c. Honey

d. Juice

**Answer:** The correct option is c.

**Explanation:** From the following options, honey is high viscous compared with others. Whereas water, cooking oil, and juice have low viscosity compared to honey, and they are easy to flow.

**Question 3**: If the viscosity of the liquid is 0.049 poise and its kinematic viscosity is 0.10 stokes, find the density of the liquid.

$a.490kg/{m}^{3}\phantom{\rule{0ex}{0ex}}b.325kg/{m}^{3}\phantom{\rule{0ex}{0ex}}c.475kg/{m}^{3}\phantom{\rule{0ex}{0ex}}d.256kg/{m}^{3}$

**Answer**: The correct option is a.

**Explanation:**

**Given data:**

Viscosity $\mu =0.049poise=0.0049Ns/{m}^{2}$

Kinematic viscosity $\nu =0.10stokes=0.10\times {10}^{-4}{m}^{2}/s$

**Solution:**

The density of the liquid is found from the formula,

$\nu =\frac{\mu}{\rho}\phantom{\rule{0ex}{0ex}}\rho =\frac{\mu}{\nu}=\frac{0.0049Ns/{m}^{2}}{0.10\times {10}^{-4}{m}^{2}/s}\phantom{\rule{0ex}{0ex}}\rho =490kg/{m}^{3}$

**Question 4**: The measure of the resistance of a fluid to gradual deformation by shear stress is ______.

a. Capacitance

b. Resistance

c. Viscosity

d. None of these

**Answer:** The correct option is c.

**Explanation:** The resistance offered by the fluid to flow and the deformation of the fluid that takes place by the shear stress is called viscosity.

**Question 5**: Water is an example of __.

a. Newtonian fluid

b. Pseudoplastic

c. Rheopectic

d. dilatant

**Answer:** The correct option is a.

**Explanation:** Water is an example of a newtonian fluid because its viscosity is not affected by the shear stress. The viscosity does not change even when we apply shear stress to them. Hence, water is an example of a newtonian fluid.

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