Unit of Viscosity

Edited By Team Careers360 | Updated on Jul 02, 2025 05:02 PM IST

Viscosity Unit

The unit of viscosity or viscosity unit is Pascal seconds (Pa-s) or .

SI unit of viscosity

The SI unit of viscosity is given by Pascal seconds (Pa-s) or .

What is the viscosity unit?

Viscosity is defined as the property of a fluid which offers resistance to the movement of one layer of fluid over another adjacent layer of the fluid. When two layers of a fluid, a distance ‘dy’ apart, move one over the other at different velocities, let us say it ‘u’ and ‘u + du’. This viscosity together with the relative velocity causes a shear stress acting between the fluid layers. The top layer causes a shear stress on the adjacent lower layer while the lower layer causes a shear stress on the adjacent top layer. This shear stress is proportional to the rate of change of velocity with respect to ‘y’. It is denoted by symbol.

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Viscosity Unit
What is the viscosity unit?
Unit of viscosity
Types of Viscosity

Unit of Viscosity - Definition, Types, Unit, Example, FAQs

Mathematically,

…………………(i)

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Where (called mu), is the constant of proportionality and is known as the coefficient of dynamic viscosity or only viscosity. is the rate of shear strain or rate of shear deformation or velocity gradient.

Using equation (i) we can write, 1641280054331

Viscosity is also defined as the shear stress required to produce unit rate of shear strain.

The units of viscosity is obtained by putting the dimensions of the quantities in equation (i)

1641280054439

In MKS system, the force is represented by kgf and the length is represented by metre (m), in CGS system, the force is represented by dyne and the length is represented by cm and in SI system the force is represented by Newton (N) and the length is represented by meter (m).

MKS unit of viscosity =

CGS unit of viscosity =

is also known as Pascal and is represented by ‘Pa’.

SI unit of viscosity = = .

SI unit of viscosity = Newton –sec/m2

The unit of viscosity in CGS is also called Poise which is equal to

The numerical conversion of the unit of viscosity from MKS unit to CGS unit is given below:

One Newton = one kg (mass) x one (m/s2)(acceleration)

If viscosity is given in Poise, it must be divided by 10 to get its equivalent numerical value in SI units. Sometimes a unit of viscosity as centipoise is used where

1 centipoise = 1/100 Poise

The viscosity of water atis 0.01 Poise or 1.0 centipoise.

Related Topics,

Types of Viscosity

There are two types of viscosity

1. Kinematic viscosity

It is defined as the ratio between the dynamic viscosity and density of fluid. It is denoted by the Greek symbol () called ‘nu’. Mathematically, it can be represented by,

The unit of Kinematic viscosity is obtained as

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In MKS and SI, the unit of Kinematic Viscosity is while in CGS units it is written as. In CGS units, Kinematic Viscosity is also known as stoke.

One stoke =

Centistoke = 1/100 stoke

2. Dynamic Viscosity

It is the ratio of Force multiplied by time to the Area.

It is expressed as

The factors on which viscosity depends are:-

a. area of contact of two adjacent layers,

b. velocity difference between two adjacent layers,

c. the distance between two adjacent layers.

Difference between Dynamic Viscosity and Kinematic Viscosity

S.NO	Dynamic Viscosity	Kinetic Viscosity
1.	It is resistant to fluid flow and tells about the thickness of fluid. For example: - If the fluid is thinner, it will have less viscosity and if the thickness is more, it will have more viscosity.	It is the ratio of the fluid’s viscous force to the inertial force.
2.	Its symbol is .	Its symbol is .
3.	The unit of Dynamic Viscosity is.	The unit of Kinematic Viscosity is.
4.	Dynamic Viscosity is absolute viscosity or simply viscosity.	Kinematic Viscosity is momentum diffusivity.

Newton’s Law of Viscosity

Newton’s Law of Viscosity states that the shear stress on a fluid element layer is directly proportional to the rate of shear strain. This constant of proportionality is called the coefficient of viscosity. Mathematically, it can be expressed as

Fluids which obey the above equation are known as Newtonian fluids and the fluids which do not obey the above relation are called Non-Newtonian fluids.

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Practice Questions

Q.1 Determine the viscosity of a liquid having kinematic viscosity 6 stokes and specific gravity 1.9.

Sol) Given,

Kinematic Viscosity, s

Specific gravity of liquid = 1.9

Let the viscosity of the liquid be

No, specific gravity of a liquid = Density of the liquid/Density of water

1.9 = Density of the liquid/1000

Density of the liquid =

By using the relation, , we get

= Poise.

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NCERT Physics Notes:

Frequently Asked Questions (FAQs)

1. Pascal second is the unit of?

Pascal second is the unit of viscosity.

2. What is the difference between dynamic viscosity and kinematic viscosity?

Dynamic viscosity (μ) is the ratio of shear stress to shear rate in a fluid, measuring its resistance to flow. Kinematic viscosity (ν) is the ratio of dynamic viscosity to fluid density. While dynamic viscosity is an intrinsic property of the fluid, kinematic viscosity takes into account the fluid's density and is often used in fluid flow calculations.

3. What are the SI units for dynamic and kinematic viscosity?

The SI unit for dynamic viscosity is pascal-second (Pa·s) or newton-second per square meter (N·s/m²). For kinematic viscosity, the SI unit is square meters per second (m²/s). However, centipoise (cP) for dynamic viscosity and centistokes (cSt) for kinematic viscosity are also commonly used in practice.

4. What is viscosity and why is it important in fluid mechanics?

Viscosity is a measure of a fluid's resistance to flow. It's important in fluid mechanics because it determines how easily a fluid flows and affects phenomena like drag, energy dissipation, and heat transfer in fluids. Understanding viscosity is crucial for designing systems involving fluid flow, such as pipelines, lubricants, and blood flow in the body.

5. How does the concept of viscosity relate to Newton's law of viscosity?

Newton's law of viscosity states that the shear stress in a fluid is directly proportional to the shear rate, with the constant of proportionality being the dynamic viscosity. This law applies to Newtonian fluids, where viscosity remains constant regardless of the shear rate. The equation is τ = μ(du/dy), where τ is shear stress, μ is dynamic viscosity, and du/dy is the velocity gradient perpendicular to the direction of shear.

6. How is viscosity measured experimentally?

Viscosity can be measured using various methods, including:

7. How does the viscosity of a fluid affect its Reynolds number?

The Reynolds number (Re) is inversely proportional to viscosity. The equation for Reynolds number is Re = ρvL/μ, where ρ is density, v is velocity, L is a characteristic length, and μ is dynamic viscosity. As viscosity increases, the Reynolds number decreases, indicating a greater tendency towards laminar flow. Conversely, lower viscosity leads to higher Reynolds numbers and a greater likelihood of turbulent flow.

8. What is the relationship between viscosity and lubrication?

Viscosity plays a crucial role in lubrication by determining how well a lubricant can maintain a fluid film between moving surfaces. Higher viscosity lubricants can maintain thicker films and withstand higher loads, but may increase energy loss due to internal fluid friction. Lower viscosity lubricants flow more easily but may not provide adequate separation under high loads. The ideal viscosity for a lubricant depends on factors such as load, speed, and operating temperature.

9. What is the significance of the viscosity index in lubricating oils?

The viscosity index (VI) is a measure of how much an oil's viscosity changes with temperature. A high VI indicates that the oil's viscosity changes less with temperature, which is desirable for many applications. Oils with high VI:

10. How does temperature affect the viscosity of liquids and gases?

Temperature generally has opposite effects on the viscosity of liquids and gases. For liquids, viscosity typically decreases as temperature increases because the molecules have more thermal energy and can move more freely. For gases, viscosity usually increases with temperature due to increased molecular motion and collisions.

11. What is the relationship between viscosity and fluid flow rate in a pipe?

Viscosity is inversely related to fluid flow rate in a pipe. As viscosity increases, the flow rate decreases, assuming constant pressure difference and pipe dimensions. This relationship is described by the Hagen-Poiseuille equation for laminar flow, which states that the flow rate is inversely proportional to viscosity.

12. How does the molecular structure of a fluid influence its viscosity?

The molecular structure of a fluid greatly influences its viscosity through several factors:

13. How does viscosity affect the terminal velocity of an object falling through a fluid?

Viscosity directly influences the terminal velocity of an object falling through a fluid. As viscosity increases, the terminal velocity decreases. This is because the viscous drag force, which opposes the motion of the falling object, is proportional to the fluid's viscosity. The balance between this drag force and the gravitational force determines the terminal velocity. This relationship is described by Stokes' law for small, spherical objects in laminar flow conditions.

14. How does the presence of suspended particles affect a fluid's viscosity?

Suspended particles generally increase a fluid's viscosity. This effect depends on factors such as:

15. What is the relationship between viscosity and surface tension?

While viscosity and surface tension are distinct properties, they are both influenced by intermolecular forces. Generally, liquids with strong intermolecular forces tend to have both high viscosity and high surface tension. However, the relationship is not always straightforward, as viscosity is a bulk property (resistance to flow), while surface tension is a surface property (tendency to minimize surface area). Understanding both properties is crucial for phenomena like droplet formation, wetting, and fluid flow in small channels.

16. How does pressure affect the viscosity of liquids and gases?

The effect of pressure on viscosity differs for liquids and gases:

17. How does the viscosity of a fluid affect its ability to transmit sound waves?

Viscosity affects sound wave transmission in fluids by influencing wave attenuation and dispersion:

18. How does the concept of viscosity apply to plasmas?

Plasma viscosity is a complex concept due to the unique nature of plasmas as ionized gases. In plasmas:

19. What is the relationship between viscosity and the no-slip condition in fluid dynamics?

The no-slip condition states that fluid in direct contact with a solid boundary has zero velocity relative to the boundary. This condition arises due to fluid viscosity:

20. How does the concept of viscosity apply to non-fluid materials like glasses or amorphous solids?

While typically associated with fluids, viscosity is also relevant to non-fluid materials:

21. How does viscosity affect the formation and behavior of vortices in fluids?

Viscosity significantly influences vortex dynamics:

22. How does viscosity affect the phenomenon of cavitation in fluids?

Viscosity influences cavitation (formation and collapse of vapor bubbles in a liquid) in several ways:

23. What is the relationship between viscosity and the speed of sound in fluids?

While viscosity doesn't directly determine the speed of sound, there are some connections:

24. What are non-Newtonian fluids, and how do they differ from Newtonian fluids in terms of viscosity?

Non-Newtonian fluids are fluids whose viscosity changes with the applied shear rate or stress. Unlike Newtonian fluids, which have a constant viscosity, non-Newtonian fluids can exhibit various behaviors:

25. What is the significance of critical shear stress in relation to viscosity?

Critical shear stress is the minimum stress required to initiate flow in some non-Newtonian fluids, particularly Bingham plastics and yield-stress fluids. It's significant because it represents a threshold below which the fluid behaves like a solid and above which it flows like a liquid. This property is related to the fluid's internal structure and can be considered an extension of the concept of viscosity for these complex fluids.

26. What is the concept of apparent viscosity in non-Newtonian fluids?

Apparent viscosity is the effective viscosity of a non-Newtonian fluid at a specific shear rate or stress. Unlike Newtonian fluids, where viscosity is constant, the apparent viscosity of non-Newtonian fluids changes with shear rate or stress. It's calculated as the ratio of shear stress to shear rate at a given point. This concept allows for the characterization of complex fluid behaviors and is essential for understanding and predicting the flow properties of non-Newtonian fluids in various applications.

27. What is the concept of extensional viscosity, and how does it differ from shear viscosity?

Extensional viscosity is a measure of a fluid's resistance to stretching or extensional deformation, while shear viscosity (the commonly discussed viscosity) measures resistance to shear deformation. Extensional viscosity is important in processes involving stretching flows, like fiber spinning or droplet breakup. For Newtonian fluids, the extensional viscosity is three times the shear viscosity. However, for many non-Newtonian fluids, especially polymer solutions, the extensional viscosity can be much higher and exhibit complex behaviors.

28. How does the concept of viscosity apply to superfluids?

Superfluids, such as liquid helium below a critical temperature, exhibit zero viscosity, challenging our conventional understanding of fluid behavior:

29. What is the role of viscosity in the formation and stability of emulsions?

Viscosity plays a crucial role in emulsions (mixtures of immiscible liquids):

30. What is the significance of the Trouton ratio in fluid mechanics?

The Trouton ratio is the ratio of extensional viscosity to shear viscosity:

31. What is the concept of complex viscosity in viscoelastic fluids?

Complex viscosity is used to describe the viscous and elastic behavior of viscoelastic fluids: