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What is Viscosity?

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Viscosity is the measurement of the resistance of the flowing liquid. Let us learn more about viscosity with an example suppose we take two bowls, one bowl contains water and the other has honey in it, we drop the content of both bowls then we see that water flows much faster than honey which concludes that honey is more viscous than water. 

Viscosity is the property of the liquids that prevents liquids from spreading. The force generated due to viscosity is called Viscous Force. Since this force is between the layers of liquids, it is also called internal friction. In this article, we will learn about viscosity its formula, measurement, and much more in detail.

What is Meaning of Viscosity?

The property of a liquid by virtue of which an opposing force (internal friction) comes into play between different layers of a liquid, whenever there is a relative motion between these layers of the liquid is called viscosity.

Imagine a fluid moving parallel to it on the horizontal plane. The fluid may be thought to consist of several layers. If the flow of the fluid is sharp, then the layer that is in contact with the horizontal plane will have a velocity of about zero. But as the distance of the layer from the horizontal plane increases, the velocity of the flow of the layer will increase the topmost layer of fluid has maximum velocity.

Thus, there is always a difference in the velocity of the two adjacent layers of the fluid. One layer is flowing faster than the other layer, due to their relative motion, the opposing frictional force acts between them. This force is called a viscous force and the property is called Viscosity.

Viscosity Definition

Viscosity of any liquid is defined as,

“The measure of the resistance of the flow of the liquid.”

Viscosity is the property of any liquid which tells us how a liquid flow under the action of gravity. It tells that any liquid with a lower viscosity flows easily whereas the liquid with high viscosity flows with great difficulties.

Unit of Viscosity

SI unit for measuring the viscosity of liquid is Poiseiulle (PI). Other units used for measuring viscosity are Newton-Second per Square Metre (Nsm-2) or Pascal-Second (Pas)

Viscosity Dimensional Formula

Dimensional formula of the viscosity is [ML-1T-1]

Viscosity Formula

Viscosity is defined as the measure of the ratio of “shearing stress to the velocity gradient of the given fluid”. For example when a sphere is dropped into a fluid, then the viscosity of the liquid is determined using the formula:

η = 2ga2(∆ρ) / 9v

where,

  • g is Acceleration due to Gravity
  • a is Radius of Sphere
  • ∆ρ is Density difference between fluid and sphere tested
  • v is Velocity of Sphere

Types of Viscosity

We can measure Viscosity by two methods and the viscosity measured by these two methods is called the types of viscosity. The two types of viscosity are:

  • Dynamic Viscosity (Absolute Viscosity)
  • Kinematic Viscosity

One way is to measure the fluid’s resistance to flow when an external force is applied. This is known as Dynamic Viscosity. And the other way is to measure the resistive flow of a fluid under the weight of gravity. We call this measure of fluid viscosity kinematic viscosity.

The Formula for Dynamic Viscosity is given as

Dynamic Viscosity = Shearing Stress/Shearing Rate Change

The Kinematic Viscosity Formula is given as

Kinematic Viscosity = Absolute Viscosity/Density of the Liquid

Learn more about, Dynamic Viscosity and Kinematic Viscosity

Co-efficient of Viscosity

According to Newton’s law of viscosity, the viscous drag, between these layers is,

  • Directly proportional to area (A) of the layer F ∝ A
  • Directly proportional to velocity gradient (dv/dx) between the layers F ∝ (dv/dx)

Therefore, it can be written as:

F ∝ A (dv/dx)

Lets remove the proportionality sign by introducing a proportionality constant η.

F = η A (dv/dx)

Here, η is called the coefficient of viscosity. 

If A = 1 m2 and dv/dx = 1 s-1 then the above expression becomes: 

F = η

Thus, the coefficient of viscosity of a liquid is defined as the viscous drag or force acting per unit area of the layer having a unit velocity gradient perpendicular to the direction of the flow of the liquid. 

Viscosity Co-efficient Units

Co-efficient of Viscosity is measured in various units as,

  • In the CGS system, the unit of coefficient of viscosity is dynes s cm-2 or Poise
  • In the SI system the unit of coefficient of viscosity N s m-2 or deca-poise
  • Dimensional formula for the coefficient of viscosity is [ML-1 T-1]

Variation of Viscosity

The coefficient of viscosity depends on the following mentioned factors.

  • Effect of Temperature on Viscosity: The viscosity of liquids decreases with an increase in temperature. The viscosity of gases increases with an increase in temperatures as η ∝ √T.  
  • Effect of Pressure on Viscosity: The coefficient of viscosity of liquids rises as pressure increases, although there is no relationship to explain the phenomenon thus far.

The table given below lists some fluids and their coefficient of viscosity at different temperatures:

Fluid

Temperature (in °C)

η (deca-poise)

Air

20

0.018 × 10-3

Water

0

1.8 × 10-3

20

1.0 × 10-3

Blood

100

0.3 × 10-3

37

2.7 × 10-3

Engine Oil

30

250 × 10-3

Glycerine

0

10

20

1.5

Newtonian and Non-Newtonian Fluids

The viscosity of any liquid is directly influenced by the change in pressure and temperature in the liquid. So on this basis we have two types of liquid that are,

  • Newtonian Fluids
  • Non-Newtonian Fluids

Now let’s learn about them in detail.

Newtonian Fluids

Any fluid whose viscosity remains constant when the amount of shear is applied at a constant temperature is called Newtonian fluid. There is a linear relationship between viscosity and shear stress in the case of Newtonian Fluid.

Examples: Water, Alcohol, Petroleum, and others.

Non-Newtonian Fluids

Non-Newtonian fluids are the opposite of Newtonian fluids i.e. on applying shear, the viscosity of non-Newtonian fluids changes, depending on the fluid. 

Examples: Ketchup, Quicksand, Silly Putty, etc.

Measurement of Viscosity

Viscosity of any liquid is measured by dropping a metal ball through the liquid and measuring the time of the fall of the metal ball. The slower the metal ball falls, the greater the viscosity of the liquid. This method doesn’t provide an accurate idea of the viscosity for accurate measurement U-Tube Viscometer is used.

U-Tube Viscometer

U-tube viscometers are generally called Glass Capillary Viscometers or Ostwald Viscometers.

A viscometer consists of two reservoir bulbs and a capillary tube. In one arm of the U is the capillary, a vertical section of a precise narrow bore. Above, is a bulb, and with it is another bulb lower down on the other arm, as shown in the image.

In use, the upper bulb draws the liquid by suction, and then the liquid is made to flow down through the capillary into the lower bulb. Two marks (one above and one below the upper bulb) indicate a known volume. The time taken for the liquid to pass between these marks is proportional to the kinematic viscosity.

Most commercial units are provided with a conversion factor. The time taken by the test liquid to flow between two points is measured. By multiplying the time measured by the factor of the viscometer, the kinematic viscosity is obtained.

Applications of Viscosity

Knowledge of the viscosity of various liquids and gases has been put to use in daily life. Some applications of its knowledge are discussed as under:

  • The coefficient of viscosity of organic liquids is used to calculate their molecular weights.
  • Knowing the coefficient of viscosity and how it varies with temperature allows us to select the best lubricant for each machine. Thin oils with low viscosity (for example, lubricating oil used in clocks) are utilized in light machinery. Highly viscous oils (for example, grease) are employed in heavy machinery. Viscosity is the most important quality of lubricating oils in lubrication, and it is also highly important in greases, which is frequently overlooked. The resistance to movement is defined as viscosity. Water has a low viscosity because it flows quickly, but honey has a high viscosity. 
  • The viscosity of a few drugs, such as the numerous solutions used to eradicate moles, has also been reduced to make application simpler. To coat the throat, drug firms provide treatments with a high viscosity yet are still drinkable, such as cough syrup. 
  • The viscosity of paints, varnishes, and other home items is tightly controlled so that they may be applied smoothly and uniformly with a brush roller.
  • Viscosity is an important factor in food preparation and serving. Cooking oils’ viscosity may or may not vary as they heat, but many become considerably more viscous when they cool. When fats are cold, they become solid because they are viscous when heated.
  • To function properly, manufacturing equipment needs the use of appropriate lubricant. Too viscous lubricants can block and block pipes. Lubricants that are excessively thin provide insufficient protection for moving components.
  • Coating viscosity is one of the important characteristics that determine the success of the coating technique. Because the uniformity and repeatability of the coating operation are frequently connected to the viscosity of the coating, it is an important parameter to regulate.

Bernoulli’s Theorem

When an incompressible and non-volatile fluid i.e. an ideal fluid flows in a torrent stream in a tube, the total energy of its unit volume or unit mass is fixed at each point of its path. This is called Bernoulli’s Theorem. 

The theorem is written in the form of equations and the equations are as follows:

For Unit Volume: 

P + 1/2dv2 + dgh = Constant

For Unit Mass:

P/d + 1/2 dv2 + gh = Constant

where,

  • P is the Pressure
  • d is the Density
  • v is the Velocity of Flowing Fluid
  • g is the Gravitational Acceleration
  • h is the Height of Water from Earth

Learn more about Bernoulli’s Principle

Solved Examples on Viscosity

Example 1: There is a 3 mm thick layer of glycerin between a flat plate and a large plate. If the viscosity coefficient of glycerin is 2 N s/m2 and the area of the plane plate is 48 cm. How much force is required to move the plate at a speed of 6 cm/s? 

Solution:

Given,

  • Thickness of the layer, dx = 3 mm = 3 × 10-3 m.
  • Coefficient of viscosity, η = 2 N s/m2 
  • Change in speed, dv = 6 cm/s = 6 × 10-2 m/s.
  • Area of the plate, A = 48 cm2 = 48 × 10-4 m2

Formula to calculate the force required to move the plate is, 

F = ηA × (dv/dx)

Substitute the given values in the above expression as:

F = 2 N s/m2 × 48 × 10-4 m2 × (6 × 10-2 m/s / 3 × 10-3 m)

  = 192 × 10-3 N

  = 0.192 N

Example 2: The diameter of a pipe is 2 cm. what will be the maximum average trick of water for level flow? The viscosity coefficient for water is 0.001 N-s/m2.

Solution: 

Given,

  • Diameter of the pipe, D = 2 cm = 0.02 m
  • Viscosity coefficient, η = 0.001 N-s/m2
  • Density of water, ρ = 1000 kg/m3

Since, the maximum value of K for level flow is 2000

Therefore, the formula to calculate the maximum speed of water is,    

v = Kη / ρD

Substitute the given values in the above expression to calculate v as,

v = 2000 × 0.001 N-s/m2 / 1000 kg/m3 × 0.02 m

   = 0.1 m/s 

Example 3: The shear stress at a point in a liquid is found to be 0.03 N/m2. The velocity gradient at the point is 0.21 s-1. What will be its viscosity?

Solution:

Given,

  • Shear stress, F/A is 0.03 N/m2
  • Velocity gradient, dv/dx is 0.21 s-1

Formula to calculate the viscous force is,

F = -ηA (dv/dx)

η = -(F/A) / (dv/dx)

Substitute the given values in the above expression to calculate η

η = – 0.03 N/m2 / 0.21 s-1

   = – 0.14 N s/m2

Example 4: Water is flowing slowly on a horizontal plane, the viscosity coefficient of water is 0.01 poise, and its surface area is 100 cm2. What is the external force required to maintain the velocity gradient of the flow 1 s-1?

Solution: 

Given,

  • Viscosity coefficient of water, η = 0.01 poise = 0.001 kg/ms
  • Surface area, A = 100 cm2 = 10-2 m2
  • Velocity gradient of the flow, dv/dx = 1 s-1

Formula to calculate the viscous force, 

F = -ηA (dv/dx)

Substitute the given values in the above expression to calculate F

F = 0.001 kg/ms × 10-2 m2 × 1 s-1

   = 10-5

Read, More,

Viscosity – FAQs

1. What is Viscosity?

Viscosity is the measure of a fluid’s resistance to the flow of liquid.

2. What is Unit for Coefficient of Viscosity?

SI unit of the coefficient of viscosity is N s m-2.

3. What is Viscosity of Water?

Viscosity of water at 20 degrees Celsius is roughly equal to 0.01 poise or 10-3 Pa. s (Pascal seconds)

4. How is Viscosity Measured?

Viscosity of a liquid is measured using the Viscometer.

5. How does Viscosity Vary with Temperature?

Viscosity of liquids decreases with the increase in temperature, and viscosity of gases increases with the increase in temperature.

6. What is Newton’s Law of Viscosity?

Newton’s Law of Viscosity states that the shear stress applied between the two layers of fluid is directly proportional to the velocity gradient between the two layers.

7. What is Viscosity Index?

Viscocity Index is an Imperical measure of the viscosity of lubricating oil whose change in temperature is Viscocity Index.

8. What is Viscosity of Blood?

The normal viscosity of blood is, between 3.5 and 5.5 cP

9. What is Viscocity for Air?

The viscosity of air at 15°C is 1.81 × 10-5 kg/(m·s) OR 18.1 μPa·s.

10. What is Honey Viscosity?

Honey is a highly viscous material and it has a viscosity of 10000 cps.

11. What is Viscocity of Water?

Viscocity of water at 20°C is 0.01 poise OR 10-3 Pa.s



Last Updated : 16 Oct, 2023
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