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Difference Between Kinematic and Dynamic Viscosity

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  • Last Updated : 15 May, 2022
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The viscosity of a fluid is a measure of its resistance to deformation at a certain rate. It corresponds to the informal notion of “thickness” in liquids. For example, syrup has a higher viscosity than water.

Viscosity measures the internal frictional force between neighbouring layers of fluid in relative motion. When a viscous fluid is forced into a tube, it flows faster towards the axis than it does towards the walls. Experiments have demonstrated that maintaining the flow requires a source of stress (such as a pressure difference between the tube’s two ends). This is because a force is required to overcome the friction between the fluid layers that are in relative motion. The compensating force in a tube with a constant rate of flow is proportional to the viscosity of the fluid.

 

What is Kinematic Viscosity?

Kinematic viscosity is a measurement of a fluid’s internal resistance when subjected to the gravitational forces of a planet. For measurement, the capillary inside a calibrated viscometer is kept at a consistent temperature. A fixed amount of fluid must flow over a known distance in a fixed amount of time to estimate the kinematic viscosity at the given conditions. The results of this test are only valid under particular circumstances, such as temperature.

Kinematic viscosity is used to express both inertia and viscous force. Kinematic viscosity is denoted by the letter “ν”. Kinematic viscosity can be computed by multiplying dynamic viscosity by density. In terms of density dependency, kinematic viscosity is determined by the fluid’s density. In kinematics, viscosity is also known as momentum diffusivity, and it is usually used to refer to kinematic viscosity. Kinematic viscosity is used when both inertia and viscosity forces are present. The m2/s is the standard unit for kinematic viscosity.

Formula For Kinematic Viscosity

ν = μ/ρ

Where, 

ν = kinematic viscosity

μ = dynamic viscosity

ρ = density

What is Dynamic Viscosity?

Dynamic viscosity is the resistance that occurs when one layer of fluid flows across another layer of fluid. It is proportional to the density of a fluid. The higher the viscosity of a fluid, the higher its density and thickness. Temperature fluctuations have an impact on viscosity. As the temperature rises, the viscosity tends to fall quickly. The other temperature in the state of gas that controls dynamic viscosity tends to rise as the temperature rises.

The viscous force of fluid is represented by its dynamic viscosity. The symbol “η” is used to denote dynamic viscosity. In dynamic viscosity calculations, the shear stress to shear strain ratio is used. It is unaffected by the presence of dynamic viscosity. Dynamic viscosity is also known as absolute viscosity. When the viscosity force is the only one that matters, dynamic viscosity is used. Ns/m2 is the unit of dynamic viscosity.

Formula For Dynamic Viscosity

η = τ/γ

Where,

η = Dynamic Viscosity

τ = Shearing stress

γ= Shear rate

Difference Between Kinematic and Dynamic Viscosity

 

Kinematic Viscosity

Dynamic Viscosity

1. Inertia and viscous force are both represented by kinematic viscosity. The viscous force of the fluid is represented by dynamic viscosity.
2. Its symbol is ν. Its symbol is η.
3. It is the dynamic viscosity to density ratio. It is the shear stress to shear strain ratio.
4. Kinematic viscosity density is dependent. Dynamic viscosity density is independent.
5. Kinematic viscosity is a fundamental property. Dynamic viscosity is a derived property.
6. The unit is m2/s. The unit is Ns/m2.
7. It is also called the diffusivity of momentum. It is also called absolute viscosity.

Sample Problems

Problem 1: A fluid with an absolute viscosity of 0.98 Ns/m2 and a kinematic viscosity of 3 m2/s. How can you calculate a fluid’s density?

Solution:

Given,

ν = 3 m2/s

μ = 0.098 Ns/m2

Using the Kinematic Viscosity Formula,

ν= μ/ρ

Substituting values in the equation,

ρ =  ν/μ 

   = 3/0.98

   = 3.0612 kg/m3

So, the density of fluid is 3.0612 kg/m3.

Problem 2: Calculate the density of a fluid with a kinematic viscosity of 2 m2/s and absolute viscosity of 0.89 Ns/m2.

Solution:

Given,

ν = 2  m2/s

μ = 0.89 Ns/m2

Using Kinematic Formula,

ν =  μ/ρ

Substituting values in the equation,

ρ =  ν/μ 

   = 2/0.89

   = 0.445 kg/m3

So, the density of a fluid is 0.445 kg/m3.

Problem 3: With a shear rate of 0.35 s-1 and dynamic viscosity of 0.018 Pa s, what pressure is necessary to move a plane of fluid?

Solution:

Given,

Shear rate γ = 0.35 s-1

dynamic viscosity  η = 0.018 Pa s

Using the Dynamic Viscosity Formula,

η = τ /γ

Substituting values in the given equation,

  τ = η×γ

   = (0.018 ×0.35)

   = 0.0063 Pa

So, the pressure required is 0.0063 Pa

Problem 4: With a shear rate of 0.35 s-1 and dynamic viscosity of 0.018 Pa s, what pressure is necessary to move a plane of fluid?

  • Water: 1 Pa s
  • Air: 0.018 Pa s
  • Mercury: 1.526 Pa s

Solution:

Given,

Shearing stress  τ = 0.76 N/m2

Shearing rate γ = 0.5 s-

Using Dynamic Viscosity Formula,

η = τ /γ

   = 0.76/0.5

   = 1.52 Pa s

Therefore, the fluid corresponds to 1.52 Pa s.

Question 5: When a fluid with a constant specific gravity is transferred to a planet with three times the acceleration due to gravity as Earth, what variation in kinematic viscosity may we observe?

Answer:

Kinematic viscosity is influenced by both density and dynamic viscosity. Density and dynamic viscosity are unaffected by gravitational acceleration. As a result, gravity’s acceleration has no effect on kinematic viscosity.

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