Coefficient of Viscosity - Definition, Formula, Types, Application, FAQs

Edited By Team Careers360 | Updated on Jul 02, 2025 04:28 PM IST

Viscosity is defined as the degree to which a fluid resists flow when subjected to a force; it is calculated by dividing the tangential friction force acting per unit area by the velocity gradient under streamlined flow circumstances. Viscosity is an important rheological measurement that is directly related to flow resistance. A fluid's viscosity is defined as its resistance to flow.

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Viscosity Measurement
The Coefficient of Viscosity Formula
Numerically
Applications of Viscosity

Coefficient of Viscosity - Definition, Formula, Types, Application, FAQs

The coefficient of viscosity of liquids such as the coefficient of viscosity of water, alcohols, petrol, and others flow more readily and quickly than glycerin solution, honey, and oil. This is due to its viscosity, which is a physical attribute. It illustrates the fluid's flow resistance in simple terms.

Viscosity Measurement

The coefficient of viscosity is used to calculate the viscosity. It is constant for a liquid and is determined by the type of the liquid. When a liquid flows through a tube at varied pressures, Poiseuille's method is formally employed to estimate the coefficient of viscosity.

Fluid's coefficient of viscosity decreases as temperature rises, whereas gases' coefficient of viscosity rises in the opposite direction. While the coefficient of viscosity of gases increases as the temperature rises. The fluid's temperature rises, loosening the connections between molecules. These bonds are directly related to viscosity, resulting in a drop in the coefficient.

The Coefficient of Viscosity Formula

The coefficient of viscosity is the ratio of the shearing force to the fluid's velocity gradient.

The symbol of the coefficient of viscosity is η. As a result, the viscosity coefficient is given by,

η = F.d / A .ⅴ

Here, F is the tangential force needed to maintain a unit velocity gradient between two parallel liquid layers of equal area.

v stands for velocity.

A stands for the area.

d is the distance between the two liquid layers skidding over one another.

The velocity gradient is defined as the differential in velocity between neighboring layers of a fluid stream.

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Numerically

Coefficient of viscosity (η) = Fd/Av, where F denotes extraneous power, d denotes layer separation, and v denotes speed.

Force Dimensional Formula = M¹L¹T-²

Area Dimensional Formula = MºL²Tº

Distance Formula in Dimensions = MºL¹Tº

MºL¹T-¹is the dimensional formula for velocity.

Combining these traits in the preceding criteria we get

[η]= [M¹L¹T-²] [MºL¹Tº]/[MºL²Tº] [MºL¹T-¹] = [M¹L-¹T-¹]

Types of Viscosity

Dynamic and kinematic viscosities are the two distinct estimates of viscosity used to depict fluids.

These depict the growth of the liquid in various ways viscosity depends on how they are approximated; nevertheless, if the liquid viscosity is known, they are compatible.

Unique viscosity and kinematic viscosity v are the two types of viscosity that are commonly used.

Dynamic Viscosity

The shear worry to the shear rate for a liquid is measured using dynamic viscosity.

The condition μ = ρν where ρ is the viscosity of the liquid, identifies dynamic viscosity with kinematic viscosity.

The centipoise is the unit of dynamic viscosity is μ. If liquid viscosity is measured in grams per cubic centimeter, kinematic viscosity is measured in centistoke.

As a result, 1 centistoke becomes 1 centipoise when separated by 1 g/cc.

Kinematic Viscosity

The ratio of viscous power to inertial power on a liquid is measured by kinematic viscosity.

The diffusivity of mass as well as warmth which is the diffusivity of energy, can be compared to kinematic viscosity.

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Applications of Viscosity

Vehicles with oil

When it comes to putting oil in the car or truck, one should be aware of its viscosity. This is because factors affecting viscosity grating, and erosion factors affecting viscosity heat as a result.

Some oils have a constant viscosity, while others respond to heat or cold; if the oil's viscosity list is low, it may become thinner as it warms, causing problems when the car is working on a hot summer day.

Cooking

Viscosity plays an important role in the preparation and serving of food. Cooking oils viscosity can alter as they heat, and many become significantly more viscous as they cool.

When fats are warmed, they become viscous, but when they are cold, they become powerful. The viscosity of sauces, soups, and stews also influences different cooking styles.

Assembling

To run smoothly, adequate oil is required while assembling hardware. Oils that are excessively thick can clog pipelines and cause them to shut down. Ointments that are excessively thin provide insufficient protection for moving parts.

Gel Medicine (Medication)

As liquids are injected into the body intravenously, viscosity is crucial in medicine.

Blood viscosity is a significant problem: excessively thick blood might form dangerous internal clusters, but blood that is too thin won't clump, resulting in dangerous blood misfortune and even death.

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Frequently Asked Questions (FAQs)

1. What are the units of the coefficient of viscosity?

The coefficient of viscosity is typically expressed in units of Pascal-seconds (Pa·s) in the SI system. In the CGS system, it is expressed in poise (P), where 1 P = 0.1 Pa·s. Additionally, the centipoise (cP) is a commonly used unit, where 1 cP = 0.001 Pa·s.

2. What Causes Viscosity?

Thesintermolecular interactions hinder the fluid's shearing movement, and the strength of these forces is related to the fluid's viscosity. Internal friction increases when the force of attraction between the molecules in the liquid becomes stronger. As a result, the viscosity of a fluid is named after the property of friction. It's usually measured in centipoise (cP), which is equal to 1 metre of pressure (millipascal second).

3. Write Some Examples of Viscosity.

There are some real-life examples that can be used to explain viscosity.

i. Viscous items (dishwasher or hand wash) are used in daily life since the viscosity of the fluid determines how successful it is at washing hands and utensils.

ii. Another example is oil, which, when a drop of it falls on the surface, forms a tiny spherical shape on the surface.

4. What is kinematic viscosity?

The ratio of viscous power to inertial power on a liquid is measured by kinematic viscosity.

The diffusivity of mass as well as warm which is diffusivity of energy, can be compared to kinematic viscosity.

5. Explain the coefficient of viscosity.

The coefficient of viscosity is a measure of a fluid's resistance to flow. It quantifies how thick or sticky a fluid is. Higher values indicate greater resistance to flow, while lower values indicate a more fluid behavior.

6. What's the difference between dynamic viscosity and kinematic viscosity?

Dynamic viscosity (η) is the coefficient of viscosity we've been discussing, which measures a fluid's resistance to flow. Kinematic viscosity (ν) is the ratio of dynamic viscosity to the fluid's density (ν = η / ρ). Kinematic viscosity is often used in fluid dynamics calculations.

7. How do non-Newtonian fluids differ from Newtonian fluids?

Non-Newtonian fluids have a viscosity that changes depending on the shear rate or shear stress applied. They can be further classified as shear-thinning (viscosity decreases with increased shear rate) or shear-thickening (viscosity increases with increased shear rate). Examples include ketchup (shear-thinning) and cornstarch in water (shear-thickening).

8. What is the significance of the coefficient of viscosity in fluid dynamics?

The coefficient of viscosity is crucial in fluid dynamics as it helps predict fluid behavior in various situations. It's used in calculations involving fluid flow, heat transfer, and the design of pipes, pumps, and other fluid-handling equipment.

9. How does temperature affect the coefficient of viscosity in liquids?

In general, as temperature increases, the coefficient of viscosity of liquids decreases. This is because higher temperatures increase the kinetic energy of molecules, reducing intermolecular forces and making the liquid flow more easily.

10. What are Newtonian fluids?

Newtonian fluids are fluids whose viscosity remains constant regardless of the shear rate applied to them. In other words, the relationship between shear stress and shear rate is linear. Examples include water and most gases.

11. What is the unit of measurement for the coefficient of viscosity in the SI system?

In the SI system, the unit of measurement for the coefficient of viscosity is the pascal-second (Pa·s). One pascal-second is equal to one newton-second per square meter (N·s/m²).

12. How does the coefficient of viscosity relate to Reynolds number?

The coefficient of viscosity is inversely related to the Reynolds number, a dimensionless quantity used to predict flow patterns. The Reynolds number is calculated as Re = (ρvL) / η, where ρ is density, v is velocity, L is a characteristic length, and η is the coefficient of viscosity. Lower viscosity leads to higher Reynolds numbers, indicating more turbulent flow.

13. What is the Poiseuille equation and how does it relate to viscosity?

The Poiseuille equation describes the flow rate of a fluid through a pipe: Q = (πr⁴ΔP) / (8ηL), where Q is flow rate, r is pipe radius, ΔP is pressure difference, η is viscosity, and L is pipe length. This equation shows how viscosity directly affects fluid flow in pipes.

14. How does pressure affect the coefficient of viscosity in liquids?

For most liquids, pressure has a relatively small effect on viscosity compared to temperature. However, at very high pressures, the viscosity of liquids generally increases as molecules are forced closer together, increasing intermolecular forces.

15. How does the coefficient of viscosity of gases differ from that of liquids?

Gases typically have much lower coefficients of viscosity than liquids due to their lower density and weaker intermolecular forces. Unlike liquids, the viscosity of gases tends to increase with temperature due to increased molecular collisions at higher temperatures.

16. What is the coefficient of viscosity?

The coefficient of viscosity, also known as dynamic viscosity, is a measure of a fluid's resistance to flow. It quantifies how much force is required to move one layer of fluid over another. The higher the coefficient, the more viscous or "thick" the fluid is.

17. How is the coefficient of viscosity represented in equations?

The coefficient of viscosity is typically represented by the Greek letter η (eta) or μ (mu) in equations. It's usually expressed in units of pascal-seconds (Pa·s) or poise (P) in the CGS system.

18. What is the formula for calculating the coefficient of viscosity?

The coefficient of viscosity (η) can be calculated using the formula: η = (F * d) / (A * v), where F is the force applied, d is the distance between layers, A is the area of the layers, and v is the relative velocity between the layers.

19. Can you explain the concept of shear stress in relation to viscosity?

Shear stress is the force per unit area required to move one layer of fluid in relation to another. It's directly related to viscosity: the higher the viscosity, the more shear stress is needed to induce flow. The relationship is described by Newton's law of viscosity: τ = η * (dv/dy), where τ is shear stress and dv/dy is the velocity gradient.

20. Why do some liquids have higher coefficients of viscosity than others?

The coefficient of viscosity depends on the strength of intermolecular forces in the liquid. Liquids with stronger intermolecular forces (like hydrogen bonding or van der Waals forces) tend to have higher viscosities because their molecules resist flowing past each other more.

21. How is viscosity measured experimentally?

Viscosity can be measured using various methods, including:

22. What is the difference between absolute viscosity and relative viscosity?

Absolute viscosity is the actual coefficient of viscosity of a fluid, measured in units like Pa·s. Relative viscosity is the ratio of a fluid's absolute viscosity to the viscosity of a reference fluid (often water). Relative viscosity is dimensionless and used to compare viscosities of different fluids.

23. What is extensional viscosity and how does it differ from shear viscosity?

Extensional viscosity, also known as elongational viscosity, measures a fluid's resistance to stretching or extensional deformation. It differs from shear viscosity, which measures resistance to shearing flows. Some fluids, especially polymer solutions, can have extensional viscosities much higher than their shear viscosities. This property is important in processes involving stretching, like fiber spinning or film blowing.

24. What is the Trouton ratio and what does it tell us about a fluid?

The Trouton ratio is the ratio of extensional viscosity to shear viscosity. For Newtonian fluids, this ratio is typically around 3. Deviations from this value can indicate non-Newtonian behavior or the presence of complex molecular structures. A high Trouton ratio often suggests the presence of long, flexible molecules like polymers in the fluid.

25. What is the significance of the glass transition temperature in relation to viscosity?

The glass transition temperature (Tg) is the temperature at which an amorphous solid (like many polymers) transitions from a hard, glassy state to a more flexible, rubbery state. This transition is marked by a dramatic change in viscosity. Below Tg, the material has extremely high viscosity, behaving like a solid. Above Tg, the viscosity decreases significantly, allowing for more molecular movement.

26. 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, there isn't a direct correlation, as some liquids (like mercury) have low viscosity but high surface tension.

27. What is the Maxwell model of viscoelasticity?

The Maxwell model is a simple representation of viscoelastic behavior, combining viscous and elastic elements in series. It's represented by a dashpot (viscous element) and a spring (elastic element) connected end-to-end. This model helps describe materials that exhibit both viscous and elastic properties, showing how they respond to stress over time.

28. What is the relationship between molecular size and viscosity?

Generally, larger molecules lead to higher viscosities. This is because larger molecules have more surface area for intermolecular interactions, making it harder for them to flow past each other. This is why oils (with large hydrocarbon molecules) are typically more viscous than water.

29. How does the concept of viscosity apply to the movement of glaciers?

Glaciers, despite being solid ice, can flow very slowly due to their immense mass. This flow can be modeled using concepts from fluid dynamics, including viscosity. The "viscosity" of ice in a glacier depends on factors like temperature, pressure, and crystal structure, affecting how quickly the glacier moves.

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

Viscosity directly affects terminal velocity. As viscosity increases, the drag force on a falling object increases, resulting in a lower terminal velocity. This relationship is described by Stokes' law for spherical objects: v = (2gr²(ρs - ρf)) / (9η), where v is terminal velocity, g is gravity, r is radius, ρs and ρf are densities of the sphere and fluid, and η is viscosity.

31. What is viscous dissipation?

Viscous dissipation is the process by which the kinetic energy of a flowing fluid is converted into heat due to viscosity. This occurs as work is done against viscous forces, causing energy loss in the fluid and potentially increasing its temperature.

32. How does the coefficient of viscosity relate to lubrication in mechanical systems?

The coefficient of viscosity is crucial in lubrication. Lubricants with appropriate viscosity form a thin film between moving parts, reducing friction and wear. The viscosity must be high enough to maintain the film under pressure but low enough to allow smooth movement. Viscosity also affects how well the lubricant can be pumped and distributed in a system.

33. What is thixotropy and how does it relate to viscosity?

Thixotropy is a property of certain non-Newtonian fluids where their viscosity decreases over time when subjected to constant shear stress, but returns to a higher viscosity when the stress is removed. This behavior is seen in some gels and colloids, like paint, which become less viscous when stirred but thicken again when left to stand.

34. How does the concept of viscosity apply to the Earth's mantle?

Although the Earth's mantle is solid rock, over geological time scales it behaves like a very viscous fluid. The concept of viscosity is used to model mantle convection, which drives plate tectonics. The mantle's effective viscosity varies with depth, temperature, and pressure, affecting how quickly convection currents move.

35. How does the presence of dissolved substances affect a liquid's viscosity?

Dissolved substances can significantly affect a liquid's viscosity. In general, dissolving solids in a liquid increases its viscosity by introducing more particles that interfere with fluid flow. However, the effect depends on the nature of both the solute and solvent. For example, adding salt to water slightly increases its viscosity, while adding sugar increases it more substantially.

36. How does viscosity affect the formation of bubbles in liquids?

Viscosity plays a crucial role in bubble formation and stability. In more viscous liquids, it's harder for bubbles to form and rise to the surface due to greater resistance to flow. However, once formed, bubbles in viscous liquids tend to be more stable as the higher viscosity slows down the drainage of liquid films between bubbles, delaying their coalescence or bursting.

37. How does the coefficient of viscosity affect heat transfer in fluids?

The coefficient of viscosity significantly influences heat transfer in fluids. Higher viscosity typically reduces convective heat transfer by slowing fluid motion. However, it can increase conductive heat transfer near solid boundaries by creating a thicker boundary layer. In forced convection systems, higher viscosity increases pumping power requirements but can lead to more uniform heating or cooling.

38. How does viscosity affect the formation and behavior of emulsions?

Viscosity plays a crucial role in emulsion stability and formation. Higher viscosity in the continuous phase can slow down the movement of dispersed droplets, reducing coalescence and separation. This makes it easier to form and maintain stable emulsions. However, very high viscosities can make it difficult to initially disperse one phase into another during emulsion formation.

39. What is the relationship between viscosity and diffusion in liquids?

Viscosity and diffusion are inversely related in liquids. The Stokes-Einstein equation describes this relationship: D = (kT) / (6πηr), where D is the diffusion coefficient, k is Boltzmann's constant, T is temperature, η is viscosity, and r is the radius of the diffusing particle. Higher viscosity leads to slower diffusion as molecules face more resistance to movement.

40. How does the concept of viscosity apply to blood flow in the human body?

Blood viscosity is crucial in understanding circulation. Blood is a non-Newtonian fluid, with viscosity that decreases at higher shear rates (shear-thinning). This property allows blood to flow easily through large vessels but become more viscous in smaller capillaries, aiding in functions like gas exchange. Factors like hematocrit (percentage of red blood cells) significantly affect blood viscosity.

41. How does viscosity affect the atomization of liquids in sprays?

Viscosity significantly influences liquid atomization in sprays. Higher viscosity liquids require more energy to break into droplets, resulting in larger droplet sizes and potentially poorer spray quality. This is important in applications like fuel injection, where fine atomization is crucial for efficient combustion. Lower viscosity generally allows for finer atomization and more uniform spray patterns.

42. What is viscous fingering and under what conditions does it occur?

Viscous fingering is an instability that occurs when a less viscous fluid displaces a more viscous fluid in a porous medium or between close plates. It results in finger-like intrusions of the less viscous fluid into the more viscous one. This phenomenon is important in oil recovery, where water (less viscous) is used to displace oil (more viscous) from reservoirs, potentially reducing extraction efficiency.

43. How does the presence of long polymer chains affect a liquid's viscosity?

Long polymer chains significantly increase a liquid's viscosity. These chains can entangle with each other, creating a complex network that resists flow. As the molecular weight of the polymer increases, viscosity typically increases exponentially. This property is used in many applications, such as thickening agents in foods and viscosity modifiers in lubricants.

44. What is the relationship between viscosity and the Reynolds number in pipe flow?

Viscosity is inversely related to the Reynolds number in pipe flow. The Reynolds number is given by Re = (ρvD) / η, where ρ is density, v is velocity, D is pipe diameter, and η is viscosity. Lower viscosity leads to higher Reynolds numbers, indicating a greater tendency towards turbulent flow. This relationship is crucial in designing piping systems and predicting flow regimes.

45. How does supercritical fluid behavior relate to viscosity?

Supercritical fluids, which exist above their critical temperature and pressure, exhibit interesting viscosity behavior. Their viscosity is typically much lower than that of liquids but higher than gases. This low viscosity, combined with liquid-like densities, allows supercritical fluids to penetrate porous materials easily, making them useful in applications like extraction processes.

46. What is the concept of effective viscosity in multiphase flows?

Effective viscosity in multiphase flows refers to the apparent viscosity of a mixture of different phases (e.g., gas bubbles in a liquid or solid particles in a fluid). It's often higher than the viscosity of the continuous phase alone. The effective viscosity depends on factors like the volume fraction of dispersed phase, particle size, and interfacial tension, and is crucial in modeling complex flows in industries like oil and gas.

47. How does viscosity affect the formation and stability of foams?

Viscosity plays a dual role in foam formation and stability. Higher liquid viscosity can make initial foam formation more difficult as it resists the incorporation of air bubbles. However, once formed, foams in more viscous liquids tend to be more stable. The higher viscosity slows down liquid drainage between bubbles, delaying foam collapse. This balance is important in applications ranging from food products to firefighting foams.

48. What is the relationship between viscosity and the speed of sound in liquids?

Viscosity affects the speed of sound in liquids through its influence on bulk modulus (resistance to compression). In general, more viscous liquids tend to have a higher bulk modulus, which leads to a higher speed of sound. The relationship is described by the equation: c = √(K/ρ), where c is the speed of sound, K is the bulk modulus (influenced by viscosity), and ρ