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Viscosity measures the resistance in the flow of a liquid which arises due to internal frictions between layers of the fluids. It typically occurs when a relative motion can be found between the layers of the fluid. Viscosity simply represents “the opposition to flow”. The reciprocal of the viscosity is known as “fluidity”, which can be defined as a measure of the ease of flow. The formula of Viscosity is: \(η = \frac{2ga^2(∆ρ)}{9v}\).
The Viscosity in a liquid decreases with the rise in temperature. When the temperature is high the kinetic energy of a molecule also rises which results in the slipping of the intermolecular through one another between the layers. Viscosity can be referred to as friction between the molecules of fluid.
The SI unit of Viscosity if Poiseiulle (PI). Viscosity has a dimensional formula of [ML-1T-1]. For instance, the viscosity of water at 27°C (81°F) is 0.85 × 10−3 and at 77°C (171°F) it is 0.36 × 10−3 pascal-second. However, the same for air at these temperatures are 1.85 × 10−5 and 2.08 × 10−5 pascal-second respectively.
Read More: Unit of Viscosity
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Key Terms: Viscosity, Newtonian Fluids, Non-Newtonian Fluids, Shear Stress, Pascal Second, Kinetic Energy, Viscometer
What is Viscosity?
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Viscosity is the measurement of a fluid’s resistance to a gradual distortion through tensile or shear stress. Viscosity exists when there is a relative motion in the layers of liquid. Most of this liquid is not ideal and offers some resistance to motion. This resistance to fluid motion is similar to internal friction which is analogous to friction when the solid moves to the surface.
The SI unit of viscosity is Poiseiulle (PI). It also has other units, known as newton-second per square metre (N s m-2) or pascal-second (Pa s.) Viscosity has a dimensional formula of [ML-1T-1].
Viscosity
Viscosity is a characteristic property of a liquid. When applying the same velocity to the liquids but a particular liquid is harder to move than the other liquid, then that liquid is known to be more viscous than others. The liquid which flows fast has lower resistance which means they are less viscous but the liquids which flow slower and show more resistance are more viscous which means they have more viscosity.
A fluid with greater viscosity opposes motion due to the strong intermolecular forces that provide internal friction, withstanding the movement of layers past each other. However, a fluid that has low viscosity can flow easily due to its molecular forces causing very little friction when it is in motion.
Note: Gases also show viscosity, but it is often very difficult to notice it.
Newtonian and Non-Newtonian FluidsTwo major factors, Temperature and pressure, are known to affect the viscosity of a fluid. With an increase in temperature, the viscosity of liquids increases rapidly as well. With the increase in pressure, the viscosity of liquid molecules increases as wellwith increase in liquid flow’s resistance. Assuming viscosity doesn’t change with pressure, it can be expressed as Newtonian fluid. However, if viscosity changes with a change in stress or temperature, then it is known as non-Newtonian fluid. While water is an example of Newtonian fluid, toothpaste can be an example of Non-Newtonian fluid. |
The video below explains this:
Viscosity Detailed Video Explanation:
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Examples of Viscosity
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The table below is some examples of the liquids which have high viscosity and which have lesser viscosity:
| High Viscosity | Low Viscosity |
|---|---|
| Honey | Water |
| Glycerin | Oil |
| Maple syrup | Gasoline |
| Motor oil SAE 50 | Ethyl alcohol |
| Tar | Vinegar |
| Sulfuric acid | Gases |
If we take a fluid like oil and place it between the two plates, where the bottom plate is fixed at one place and the top plate is moved with a constant velocity relative to the fixed place the resistance will be low and the oil will move easily.
But if the oil is replaced with honey, to move the same plate with the same velocity more force will be required as the friction and resistance will be high in the case of honey. The higher the viscosity the slower the flow of liquid.
Why does water flow faster than honey?
Honey has a higher viscosity as compared to water. In fact, it is also thicker than water. Honey comes with more cohesion (measures how strongly the particles in a fluid attract one another) than water. Therefore, it will take longer for honey to flow than water as water has lower cohesion and lower viscosity.
Difference in Viscosity between Water and Honey
Read More: Bernoullis Equation formula
Measurement of Viscosity
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Viscosity of a given matter is calculated in order to measure the behaviour of the matter in the actual world. Measuring the viscosity of any matter helps in determining and designing the production and transportation procedure. For example, if the viscosity of toothpaste is not appropriate it will either be very difficult to pump out the toothpaste or a lot of toothpaste will be pumped out in one go.
Viscosity Measurement
The primary way of measuring viscosity is to drop a sphere, such as a ball, in a fluid and simultaneously time the fall of it. The slower the ball will fall, the greater the viscosity it will have. However, an appropriate measure of viscosity can be given with the help of a viscometer.
U-Tube Viscometer
U-tube viscometers are also known as glass capillary viscometers or Ostwald viscometers. A viscometer comprises two reservoir bulbs and a capillary tube. The viscosity of a liquid can be defined as a measure of the resistance to deformation at a given speed.
A viscometer is an equipment that helps measure the viscosity of a fluid. To determine the viscosity of a Newtonian liquid, there are three ways:
- Capillary viscometer
- Rotational viscometer
- Falling Ball viscometer
Viscometer Diagram
Read Also: Sphygmomanometer
Types of Viscosity
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Types of viscosity are:
Dynamic Viscosity
When the viscosity is measured directly by measuring force. It is defined as the ratio of shear stress to the shear strain of the motion. Dynamic viscosity is used to calculate the rate of flow in liquid.
Kinematic Viscosity
In kinematic viscosity, there is no force involved. It can be referred to as the ratio between the dynamic viscosity and density of the fluid. It can be computed by dividing the dynamic viscosity of the fluid by fluid mass density. Kinematic viscosity is more useful than dynamic viscosity.
Laminar Flow
Laminar flow is the type of flow in which the fluid moves smoothly or in a regular path from one layer to the next. Laminar flow occurs in lower velocities. Laminar flow is seen in the fluid when there is no disturbance in the flowing of the liquid between the layers and the liquid flows in parallel layers.
Check Important PDF:
Viscosity PDF
Formula of Viscosity
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Formula of Viscosity is:
| η = \(\frac{2ga^2(Δρ)}{9v}\) |
Here
- Δρ = Difference in the density between a fluid and the sphere tested.
- a = Radius of the sphere.
- g = Acceleration caused by gravity
- v = Velocity of the sphere.
Note: “v can be considered as the distance travelled by a sphere divided by the time the sphere takes to travel that particular distance.”
Viscosity is calculated in Pascal seconds (Pa s). As explained above when a sphere has less speed, it has more viscosity. Any fluid which is highly viscous offers more resistance to any object that moves inside it. Although every liquid has viscosity to some extent, it can be measured as high or low considering the water viscosity as a benchmark.
The coefficient of viscosity is a measure of resistance to the flow of liquid. The coefficient of viscosity is a force when the velocity of the gradient is unity and the area of contact is unit area. It is viscous force per unit area per unit velocity gradient. ‘η’ is used to determine the viscosity coefficient.
Units of Viscosity
We are aware that:
| η = f.dx / A.dv |
Hence, η = dynes × cm / cm2 ×cm/sec.
η = dynes cm-2 sec
So, the unit of viscosity is dynes sec cm-2. This quantity is called 1 Poise.
f = m × a
⇒ η = (m × a × dx)/( A.dv)
Hence, η = g cm-1s-1
Therefore, η = 1 poise
In S.I. units, η = f .dx / A .dv
= N × m / ( m2 ×ms-1)
η = N s m-2 or Pascal seconds
So, the other units of Viscosity are N s m-2 or Pascal seconds (Ps)
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Things to Remember
- Viscosity measures the resistance in the flow of a liquid which arises due to internal frictions between layers of the fluids.
- The formula of Viscosity, η = \(\frac{2ga^2(Δρ)}{9v}\)
- The other units of Viscosity are N s m-2 or Pascal seconds (Ps)
- The coefficient of viscosity is a force when the velocity of the gradient is unity and the area of contact is unit area.
- Viscosity has a dimensional formula of [ML-1T-1].
Check More:
Previous Year Questions
- Raindrops are falling from a certain height … [DUET 2009]
- Two non-mixing liquids of densities … [NEET 2016]
- A large drop of oil density … [BITSAT 2012]
- A square plate of 0.1 m side moves parallel to a second plate … [AP EAPCET]
- A rain drop of radius 0.3mm has a terminal velocity … [VITEEE 2019]
- If Y, K and η are the values of Young's modulus … [JEE Mains 2021]
- The Young's modulus of steel is twice that of brass … [NEET 2015]
- Copper of fixed volume V … [NEET 2014]
- Two small spherical metal balls, having equal masses, are made … [NEET 2019]
- If a liquid does not wet glass, its angle of contact is …
- An object of mass 26 kg floats in air and it is in equilibrium state … [UPSEE 2017]
- Iceberg floats in water with part of it submerged … [KCET 2020]
- The coefficient of viscosity has following dimensions … [KCET 1994]
- The ratio of inertial force to viscous force of a fluid … [KEAM]
- When the temperature increases, the viscosity of … [JKCET 2006]
- Viscosity decreases with increase in temperature is the reason for … [COMEDK UGET 2009]
- The viscous force acting on a rain drop of radius … [COMEDK UGET 2004]
- Water is flowing through a very narrow tube …
- A vessel completely filled with water has holes …
- A hollow sphere of external radius …
- A 20 cm long capillary tube …
Sample Questions
Ques. Do gases have Viscosity? (1 Mark)
Ans: Yes, Gases do have viscosity and even semi-solids also have viscosity. When the temperature increases, the viscosity of the liquid decreases. But for gas, it will increase with the increase in the temperature.
Ques. How many types of Viscosity are there? (1 Mark)
Ans: There are two different ways of measuring a fluid's viscosity: Kinematic Viscosity and Dynamic Viscosity. In Kinematic viscosity, under the weight of gravity, the resistive flow of a fluid is measured. In Dynamic Viscosity, an external force is applied to measure the resistance flow of the liquid.
Ques. Why is measuring viscosity important? (1 Mark)
Ans: Manufacturers need to know the ground reality of a material’s behavior in the real world. So with the given material, they gather all the data of the viscosity. For Instance, if the viscosity of toothpaste is incorrect. Either it would be difficult to remove the paste from the tube or the whole paste will pump out in a single pressure. Moreover, the production and logistics processes are designed only when the viscosity of a material is precisely measured.
Ques. How is Viscosity measured? (1 Mark)
Ans: Pascal seconds (Pa s) is used to measure Viscosity. Every fluid/liquid has a different viscosity level. Most Newtonian liquids use kinematic viscosity measurement. To know the internal resistance of a fluid, dynamic viscosity is the measurement type.
Ques. What is the instrument used to measure Viscosity? (1 Mark)
Ans: The most common method used to measure kinematic viscosity is using a capillary tube in which the fluid is allowed to flow through it and the time taken is measured. The instrument used to measure dynamic viscosity is Rotational Viscometers.
Ques. Which fluid has the highest viscosity? (1 mark)
Ans. Honey has the highest viscosity.
Ques. What happens when the viscosity of liquid increases with the increase in temperature? (1 mark)
Ans. Viscosity and temperature are inversely proportional and viscosity of a liquid decreases with the increase in temperature.
Ques. What is the definition of a pseudoplastic liquid? (1 mark)
Ans. Pseudoplastic liquid can be referred to as a liquid that becomes less viscous as the rate of shear increases.
Ques. What is a good example of Viscosity? (1 mark)
Ans. The liquids like Honey, oil, etc., are good examples of viscosity.
Ques. What is the SI Unit of viscosity? (1 mark)
Ans. Poiseuille is the SI unit of viscosity.
Ques. (a) A flask contains glycerine and the other one contains water. Both are stirred rapidly and kept on the table. In which flask will the liquid come to rest earlier than the other one and why?
(b) What is the effect on the viscosity of a gas of the temperature? (2 marks)
Ans: (a) Glycerine will come to rest earlier than the water because the viscosity of the glycerine is greater than that of water.
(b) The viscosity of a gas decreases with the decrease in temperature and increases with an increase in temperature.
Ques. (a) What is the effect of pressure on the coefficient of viscosity of fluids?
(b) Why more viscous mobile oil is used in summer than in winter in scooters? (2 marks)
Ans: (a) With the increase in pressure, the viscosity of liquids increases, and the viscosity of water decreases, whereas the viscosity of gases remains unchanged.
(b) Due to high temperatures, the viscosity of the fluid decreases. So more viscous oil is used in summer than in winter.
Ques. Water is escaping from a vessel through a horizontal capillary tube 20 cm long and 0.2 mm radius at a point 100 cm below the free surface of the water in the vessel. Calculate the rate of flow if the coefficient of viscosity of water is 1 × 10-3 PaS. (2 marks)
Ans: Here, l = 20 cm = 0.20 m
r = 0.2mm = 2 × 104 m
h = 100 cm = 1 m
p = 103 kg m3
η = 1 × 103 PaS
∴ P = hpg= 1 × 103 × 9.8 Nm-2
Let V = rate of flow = volume of water flowing per second =?
Ques. The terminal velocity of a copper ball of radius 2.0 mm falling through a tank of oil at 20oC is 6.5 cm s-1. Compute the viscosity of the oil at 20oC. The density of oil is 1.5 ×103 kg m-3, the density of copper is 8.9 × 103 kg m-3. (3 marks)
Ans. We have,
vt = 6.5 × 10-2 ms-1
a = 2 × 10-3 m
g = 9.8 ms-2
ρ = 8.9 × 103 kg m-3
σ =1.5 ×103 kg m-3
η = 2/9 * [(2 x 10-3) m2 x 9.8 m s-2 x 7.4 x 103 kg m-3]/6.5 x 10-2 m s-1
= 9.9 x 10-1 kg m-1 s-1
Ques. (a) What is the effect of temperature on the viscosity of liquid?
(b) Why are machines sometimes jammed in winter?
(c) Why does a hot liquid move faster than a cold liquid? (3 marks)
Ans: (a) The temperature has a great effect on the viscosity of a liquid. The viscosity of a liquid decreases with the increase in temperature and when the temperature decreases the viscosity of liquid increases.
(b) When the temperature decreases, the viscosity of liquid increases. So, the machines are sometimes jammed in water because the fluid oil inside the machine becomes viscous in nature during the winter.
(c) A hot liquid moves faster than a cold liquid because of the viscosity of a liquid decreases with the increase in temperature and vice versa.
Ques. What is the largest average velocity of blood flow in an artery of radius 2 x 103 m if the flow must remain laminar?
(b) What is the corresponding flow rate? Take viscosity of blood to be 2.084 x 10-3 Pa-s. The density of blood is 1.06 x 103 kg/m3 . (3 marks)
Answer:
Ques. A metal block of an area of 0.10 m2 is connected to a 0.01 kg mass via a string that passes over an ideal 0.01 kg pulley (considered massless and frictionless). A liquid with a film thickness of 0.3 mm is placed between the block and the table. When released the block moves to the right with a constant speed of 0.085 m s-1. Find the coefficient of viscosity of the liquid. Take g as 10ms-2 (5 marks)
Ans. m = 0.01kg
1 = 0.3mm = = 0.3 * 10-3m
g = 10ms-2
v = 0.085ms-1
A = 0.1m2
The metal block shifts to the right side due to the tension present in the string. The tension T which is the magnitude is equal to the weight of the suspended mass m.
Thus the shear force F is,
F = T = mg
= 0.01 kg × 10 ms-2 = 0.1N
Shear stress on the fluid = F/A = 0.1N / 0.1m2
Strain rate: v/1 = 0.085ms-1 / 0.3*10-3m
η = Shear Stress / Strain rate
= (0.1N/0.1m2) * [(0.3 x 10-3m)/0.085ms-1]
= 3.5 x 10-3 Pa s
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