Viscosity

What is viscosity? It is defined as the measure of the resistance of a fluid (gas or liquid) to any change in shape or motion. In simple words, how easily a fluid can flow is determined by its viscosity. If fluid can flow freely, it is said to be less viscous. An example is water. However, if it is flowing slowly and with difficulty, the viscosity is said to be high. Examples include honey, sugar syrups, etc. Mathematically, viscosity can be determined from a formula that relates shearing stress to the velocity gradient.

What is viscosity?

A fluid can be thought of as a stack of layers that are sliding on one another. Let’s take honey, for example. When you drop honey down on a slant wooden board, it flows down slowly. This is because honey consists of several layers, and it moves due to the movement of one layer over the other. If the force of friction between two adjacent layers is high, then the movement would be hindered.

Intermolecular forces exist between two layers. When these forces are strong, the forces of friction between the layers are high, and fluid flow is restricted. On the other hand, when these intermolecular forces between two layers are weak, the fluid flows without any restriction.

Viscosity definition is a measure of the resistance of fluid flow. Its SI unit is newton-second per metre square (N s m-2) or poiseuille (P). The opposite of viscosity is fluidity, which is defined as the ease with which a fluid flows.

Here, it is to be noted that fluid means both liquid and gas. However, the internal friction of gases is minimal due to which gases are free flowing.

Factors affecting viscosity

Viscosity is dependent on several factors, the major being temperature. For liquids, it is inversely proportional to temperature, i.e., it decreases with an increase in temperature and increases with a decrease in temperature.

You can try this experiment at home. Heat honey in a microwave or over a stove. It would start to flow more easily and quickly than the room temperature honey due to a decrease in viscosity.

For gases, viscosity is directly proportional to the square root of temperature, i.e., it increases with the rise in temperature.

A change in pressure can also affect the viscosity of liquids—the viscosity of liquid increases with an increase in pressure as the resistance to the liquid flow increases. Sometimes, the viscosity of a fluid is independent of pressure. Such fluids are known as Newtonian fluids. An example is water.

However, it does not depend upon the amount of material. One litre of honey would be just as viscous as ten litres of honey.

Mathematical formula

Viscosity is the ratio of shearing stress to the velocity gradient in a fluid. Shearing stress is defined as the force between two layers in contact with each other, moving in opposite directions.

η = F∆z/A∆v; where η is viscosity, F/A is shearing stress, ∆v/∆z is the velocity gradient.

As per this formula, the shear of fluid is inversely proportional to its viscosity. 

In a real-life experiment, viscosity is determined by dropping a spherical metal ball down the fluid. The time taken by the ball to reach from one point to another is noted down.

The viscous drag force on a sphere of radius r moving with a velocity v  in a fluid of viscosity η  is given by Stokes’ law 

F=6πηrv

When the ball attain a terminal velocity, the equation can be  rewritten as,

η = 2a2g∆ρ/9v; here ∆ρ is the density difference between the fluid and sphere, a is the radius of the sphere, g is the acceleration due to gravity, and v is the velocity of the sphere.

The velocity is determined by dividing the distance between two points by the time taken by the ball to travel between these two points. The slower the ball moves in the fluid, the more is the viscosity.

Types of viscosity

Dynamic or absolute viscosity: It is the ratio of shearing stress to the velocity gradient of a fluid. It is measured by the fluid’s resistance to flow upon application of external pressure.

Kinematic viscosity: It is the ratio of the viscosity of a fluid to its density. It is measured by the fluid’s resistance to flow under the gravitational force. It is measured by an apparatus called capillary viscometer. Its unit of measurement is strokes.

Capillary viscometer

It is an open-ended U-tube with two bulbs used to measure kinematic viscosity. Both of the bulbs are at different heights. The liquid in the upper bulb is drawn through suction. Then, it is allowed to flow down to the lower level bulb under the action of gravity. More is the time taken by the liquid to flow down through the tube, and more is the viscosity.

Conclusion 

Viscosity is a property of fluids, i.e., gases and liquids. Viscosity definition is how much a fluid resists the movement of flow. Its SI unit is poise. A simple example is that the viscosity of sugar syrup is more than that of water. It depends on the temperature but not on the amount of fluid. Its opposite is fluidity. Viscosity can be determined by a simple ball experiment in which a ball is allowed to flow down a liquid.