“What is Viscosity” is a often asked term in fluid mechanics. Viscosity is a fluid property and very important for studying fluid flow behavior. All kinds of fluids, whether it is in liquid state or gaseous state possess viscosity. In this article, We will explore more details about the term “Viscosity”, Its definition, significance, units, equations, values.

## Definition of Viscosity

The term “viscosity” has its root in a Latin term “viscum” that refers to a viscous glue originated from mistletoe berries. In fluid mechanics, **Viscosity is defined as the measure of a fluid’s resistance to fluid flow under an applied force. For a fluid in motion, the viscosity describes the internal friction. So, a fluid having large viscosity provides more internal friction to resist flow whereas a fluid with lower viscosity provides little friction.** In general, liquids have more viscosity than gases.

The concept of viscosity will be more clear if we consider the following example. If we take water and honey in a pot and try to pour, we find that water is flowing more smoothly and quicker than honey. This is because honey is more viscous than water. So, honey is providing more resistance to motion than water and that is why water is moving more freely than honey.

## Significance of Viscosity

The viscosity of a fluid is opposite to the fluidity that denotes how easily a fluid can flow. It is basically the internal friction between the molecules comprising the fluid. For fluid transportation and lubrication engineering, injection molding, spraying and surface coating applications, viscosity plays a major role as it controls the flow of the liquid. Knowing the viscosity data is very important to predict the fluid behavior. For example, if the tomato ketchup inside the tube does not have the correct viscosity it may not flow from the tube or flow too much all of a certain.

## Symbol of Viscosity

Mathematically, viscosity can be defined as the ratio of viscous stress (shear stress) to the rate of change of deformation. The symbol of viscosity is µ (Greek letter mu). Hence,

**Viscosity, µ=Shear Stress/strain rate=τ / (du/dy)**

So, µ=τ / (du/dy)……(1)

So, µ=τ / (du/dy)……(1)

The above symbol for viscosity µ is widely used. However, some physicists and chemists prefer to use η (Greek letter eta) as the symbol of viscosity.

## Units of Viscosity

From the above mathematical equation, we know that viscosity=stress/strain rate. The unit of stress in SI unit=N/m^{2}. The unit of Strain rate=(m/s)/m.=1/s

Hence, the unit of viscosity=(N/m^{2})/(1/s)=N-s/m^{2} and the dimension of viscosity is (force X time/area).

The above viscosity discussed is also popular as dynamic viscosity or absolute viscosity.

Hence, the unit of viscosity or dynamic viscosity in SI system is N-s/m^{2} or pascal-second.

Often, the unit of viscosity is denoted by Poise or Centipoise. In , CGS unit system the unit of dynamic viscosity is “Poise” named after Jean Léonard Marie Poiseuille. The relation between Pascal-Second and poise is given below:

### 1 Pascal-Second= 10 Poise or 1Pa-s=10P

## What is Kinematic Viscosity?

Kinematic viscosity or momentum diffusivity is defined as the ratio of dynamic viscosity to the fluid density. The symbol of kinematic viscosity is ν (Greek letter nu). So, mathematically the formula for kinematic viscosity is given by ν=µ/ρ.

Now we just learned that the unit of dynamic viscosity=N-s/m^{2}. Unit of fluid density=Kg/m^{3}. Hence, the unit of kinematic viscosity =(N-s/m^{2})/(Kg/m^{3})=(Kg-m/s^{2})*(s/m^{2})*(m^{3}/Kg)=m^{2}/s.

Accordingly, the dimension of kinematic viscosity is (length^{2}/time). In fluid dynamics, working with kinematic viscosity is more convenient.

## Measuring Viscosity

As it is well known that measuring viscosity of fluids is very important to understand the flow characteristics of those fluids. There are various types of instruments by which viscosity can be measured. Those viscosity measuring devices are known as viscometers and rheometers. Common widely used instruments for measuring viscosity are:

- Capillary Viscometer
- Falling Sphere Viscometer
- Vibrating Viscometer
- Rotational Viscometer
- Microfluidic Rheometers
- Zahn Cup
- Fluorescence correlation spectroscopy
- Acoustic rheometer

## Factors Affecting Viscosity

There are various factors that affect the viscosity of a fluid. Those are:

**Fluid Temperature:**Usually the viscosity of liquids decreases with an increase in temperature. On the contrary, the viscosity of gases increase with increase in temperature.**Flow Conditions:**For laminar flow the viscosity of liquid remains constant while for turbulent flow viscosity changes.**Pressure:**With an increase in pressure, the viscosity of gases usually increase. Liquids being incompressible does not have much impact.**Multiphase flow:**The viscosity of multiphase flow is affected by the volume of each phase.**Suspended Particles:**Suspended materials increases the viscosity.

## Viscosity of Water

The viscosity of water at 20^{0} C is 1 centipoise or 1 cP. As for liquids, the viscosity decreases with an increase in temperature, the same is true for water. The following table provides the dynamic viscosity of water with respect to various temperatures.

Temperature (°C) | Viscosity (cP or mPa·s) |
---|---|

10 | 1.3059 |

20 | 1.0016 |

30 | 0.79722 |

50 | 0.54652 |

70 | 0.40355 |

90 | 0.31417 |

100 | 0.2822 |

**Table 1: Viscosity of Water with respect to Temperature**

### Kinematic Viscosity of water

The kinematic viscosity of water can easily be obtained by dividing the above dynamic viscosity values by the water density. Table 2 below provides the kinematic viscosity of water.

Temperature (°C) | Kinematic Viscosity (m^{2}/s X 10^{-6}) |

10 | 1.3059 |

20 | 1.004 |

30 | 0.801 |

50 | 0.553 |

70 | 0.413 |

90 | 0.326 |

100 | 0.294 |

**Table 2: Kinematic Viscosity of water with respect to temperature**

### Viscosity of Some Common Substances

The following table states the viscosity of some popular substances.

Substance | Temperature (°C) | Viscosity (mPa·s) |

Benzene | 25 | 0.604 |

Air | 25 | 18.5×10^{-3} |

Mercury | 25 | 1.526 |

Whole milk | 20 | 2.12 |

Dark beer | 20 | 2.53 |

Olive oil | 26 | 56.2 |

Honey | 20 | 2,000–10,000 |

Ketchup | 25 | 5,000–20,000 |

Peanut butter | – | 10^{4}–10^{6} |

Pitch | 10–30 (variable) | 2.3×10^{11} |

**Table 3: Viscosity of some common fluids**

## Newton’s law of Viscosity

The relationship between the shear stress and shear rate of fluid under mechanical stress is established by Newton’s law of viscosity. For a given temperature and pressure, Newton’s viscosity law states that the shear stress between two adjacent layers in a fluid is proportional to the velocity gradients between those layers. In another way, it can be stated that the ratio of shear stress to shear rate in a fluid is a constant, and is defined as the coefficient of viscosity. Newtonian fluids obey Newton’s law of viscosity. Non-Newtonian fluids do not follow Newton’s law of viscosity and hence their viscosity varies and is dependent on the shear rate. Dynamic viscosity is the coefficient of viscosity as defined in Newton’s law of viscosity. Equation 1 mentioned above is basically a mathematical representation of Newton’s law of viscosity.

## Practical Applications of Viscosity

The concept of Viscosity is used widely in science and technology. The following examples can easily substantiate the applications of viscosity:

- The molecular weight of organic liquids is determined using the knowledge of viscosity.
- In lubrication engineering viscosity data and its variation with temperature is an absolute necessity to decide suitable lubrication for specific equipment. For example, light machines use low viscous liquids whereas highly viscous oils are used in heavy machines.
- For preparing various medicines like syrups viscosity data is required.
- Cooking oils, fats, butter, etc are manufactured providing a specific viscosity.
- Gums, coolants, petrol as a cleaner, brake fluid, cosmetics, food products, etc all require viscosity data during production to work smoothly.
- Blood circulation inside our body depends on the viscosity of blood