Dynamic and kinematic viscosity and how they relate

[mitch_1211]

I have been looking into how the overall viscosity of a liquid/gas is related to kinematic and dynamic viscosities.

I have used n_water = 1e-3 Pa.s
n_air = 17.4e-6 Pa.s
density_water = 1000 kgm^-3
density_air = 1.3 kgm^3

and kinematic viscosity v = n/density

So v_air ~ 1.4e-5
v_water ~ 1e-6

So here the dynamic viscosity of water is greater than that of air, but the kinematic viscosity for water is less that that of air.

Does this mean that air is the more viscous fluid? How would one use there two properties to describe the overall viscosity of a fluid?

Mitch

 

[cjl]

Typically, when people refer to viscosity, they are referring to the dynamic viscosity, not the kinematic viscosity. So, I would describe water as more viscous than air.

 

[boneh3ad]

Typically, when people refer to viscosity, they are referring to the dynamic viscosity, not the kinematic viscosity. So, I would describe water as more viscous than air.

To add onto this, viscosity's chief use, relating velocity gradients in a fluid to shear stresses, involves dynamic viscosity, $\mu$. Kinematic viscosity is more of a value of convenience used because it can help simplify the notation sometimes. Dynamic viscosity is the more physically meaningful quantity in the most basic sense.

 

[mitch_1211]

I was thinking that was the case. Thank you both for the explanations.

 

[PJC01]

ell, thank you for bringing up this topic. I can provide some insights into the relationship between dynamic and kinematic viscosity and how they contribute to the overall viscosity of a fluid.

First, let's define dynamic and kinematic viscosity. Dynamic viscosity is a measure of a fluid's resistance to flow under an applied force or stress. It is typically represented by the symbol "n" and has units of Pa.s (Pascal seconds). On the other hand, kinematic viscosity is a measure of a fluid's resistance to flow due to its internal friction and is represented by the symbol "v". It has units of m^2/s (square meters per second).

The relationship between these two viscosities can be described by the equation v = n/p, where "p" is the density of the fluid. As you have correctly calculated, the kinematic viscosity of water is lower than that of air, despite water having a higher dynamic viscosity. This is because water is denser than air, resulting in a lower kinematic viscosity.

To answer your question, the overall viscosity of a fluid cannot be determined solely by its dynamic or kinematic viscosity. Both properties play a role in determining the fluid's resistance to flow. In fact, the overall viscosity of a fluid is a combination of these two viscosities, along with other factors such as temperature and pressure.

In summary, dynamic and kinematic viscosity are important properties that help us understand the behavior of fluids. While they may seem contradictory at first, they both contribute to the overall viscosity of a fluid and cannot be used interchangeably. Further research and experimentation are necessary to fully understand the complexities of fluid viscosity.