Significance of kinematic and dynamic viscosity

In summary, kinematic viscosity is the ratio of dynamic viscosity to density and is used in fluid mechanics equations for convenience. It is also known as momentum diffusivity, as it describes how momentum is diffused through a fluid. This is similar to the heat equation in heat transfer. The Navier-Stokes equations also use kinematic viscosity as a diffusivity constant for momentum.
  • #1
Waqar Amin
8
0
It is stated that kinematic viscosity is the ratio of dynamic viscosity to density. can anyone elaborate it further that what are the uses of both types of viscosities and why we differentiate them.does dynamic viscosity reates with static fluid?
 
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  • #2
It is really just a term of convenience. Oftentimes, the equations of fluid mechanics are manipulated such that you end up with [itex]\mu/\rho[/itex] terms, so it is simply much easier to carry around a [itex]\nu[/itex] instead of a fraction. This is commonly seen with the Reynolds number, which has a [itex]\mu/\rho[/itex] term in it.
 
  • #3
then how kinematic viscosity is termed as momentum diffusivity, i m very confused with these terms.
 
  • #4
Well, as with any sort of viscosity, it is really a measure of how momentum is diffused through a fluid. If you are familiar with the heat equation, you should notice some analogs between it and the Navier-Stokes equations.

The heat equation:
[tex]\frac{\partial \phi}{\partial t} = c^2\nabla^2 \phi[/tex]

The incompressible Navier-Stokes equation:
[tex]\frac{\partial \mathbf{v}}{\partial t} + \mathbf{v}\cdot\nabla\mathbf{v}=-\frac{1}{\rho}\nabla p + \nu\nabla^2\mathbf{v} + \mathbf{f}[/tex]

The heat equation is a simplified version of the diffusion equation that describes the diffusion of basically any quantity through a material. In heat transfer, [itex]c^2=\alpha=\frac{k}{\rho c_p}[/itex] is the thermal diffusivity.

In the Navier-Stokes equations, notice that the [itex]\nu\nabla^2\mathbf{v}[/itex] term takes the same form, only the N-S equations are a momentum balance, so the kinematic viscosity, [itex]\nu[/itex], is essentially a diffusivity constant that describes how momentum diffuses through the medium. In other words, it describes one particle's ability to affect the momentum of the adjacent particles.
 
  • #5
i have understand. thanxx for your help boneh3ad. :)
 

What is kinematic viscosity?

Kinematic viscosity is the measure of a fluid's resistance to flow under the influence of gravity. It is defined as the ratio of dynamic viscosity to density and is commonly represented by the symbol "ν".

What is dynamic viscosity?

Dynamic viscosity is a measure of a fluid's resistance to flow under an applied force. It is also known as absolute viscosity and is commonly represented by the symbol "η".

How are kinematic and dynamic viscosity related?

Kinematic and dynamic viscosity are related by the density of the fluid. Kinematic viscosity is equal to dynamic viscosity divided by the density of the fluid.

Why are kinematic and dynamic viscosity important?

Kinematic and dynamic viscosity are important in understanding the behavior of fluids, such as how they flow and resist flow. They are also important in various industries, including aviation, automotive, and manufacturing, as they can impact the efficiency and performance of machinery and processes.

How are kinematic and dynamic viscosity measured?

Kinematic and dynamic viscosity can be measured using various instruments, such as viscometers and rheometers. These instruments apply a force to the fluid and measure the resulting flow rate, which is used to calculate the viscosity. Alternatively, there are also theoretical equations that can be used to calculate viscosity based on fluid properties.

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