# Kinematic Viscosity

How would you define kinematic viscosity? What does it physically represent? Around the Internet I've found it defined as just a ratio, and that's it.

I saw in an answer that I can think of it as "diffusivity of momentum". What does this mean?

In mechanics, "kinematics" means describing the motion mathematically, so, for example, if the acceleration is known I can integrate to find the velocity and position. "Dynamics" means analyzing motion due to the influence of forces. The two are related through Newton's second law: F = ma (dynamics version) is the same as a = F/m (useful for kinematics).

In both cases, "coefficient of viscosity" refers to the effect on one part of the flow due to neighboring flow with a different speed, i.e. flow shear. That is, if you imagine yourself as one parcel of fluid and the next parcel over is moving in the same direction as you but faster, it will pull you along due to the effect of viscosity. "Dynamic viscosity" gives the force on your parcel (per unit volume), while "kinematic viscosity" gives the acceleration (force per unit mass).

(Diffusivity of momentum is also a valid way to think of it that is equivalent to this, but if you don't have any intuition about diffusivity to begin with that's not very helpful.)

ADDENDUM: Air and water make an interesting comparison: air has much lower dynamic viscosity than water (by a factor of 50), but due to its low density, it has much higher kinematic viscosity (by a factor of 17):

$\mu_\text{air} = 2\times 10^{-5}$ Pa s; $\;\mu_\text{water} = 1\times 10^{-3}$ Pa s

$\nu_\text{air} = 0.17 \text{cm}^2/\text{s}$; $\;\nu_\text{water} = 0.01 \text{cm}^2/\text{s}$

• That was awesome, thank you. Can you expand on the second point? I've always thought about the difference of those two terms, do you know maybe a source where it would be possible to read about it? Feb 4, 2015 at 22:36
• @Novalink - you're welcome! Which point do you mean by "the second point"?
– pwf
Feb 5, 2015 at 0:46
• Sorry, I mean "Kinematics" and "Dynamics", the difference of the two terms. I don't know why I called it "the second point" Feb 7, 2015 at 14:14
• @Novalink I don't think I have anything further to add. If you have a traditional mechanics textbook, you'll see that it starts off with a kinematics section (some books call it that, some don't) that involves mathematical description of motion, and later gets into dynamics, i.e. Newton's laws. The kinematics part usually involves finding $v(t)$ and $x(t)$ given $a$ (or $a(t)$), and the dynamics part tells you how to analyze the forces to get $a$.
– pwf
Feb 11, 2015 at 18:42

I think diffusivity of momentum is actually a pretty good way of describing kinematic viscosity. After all viscosity acts to transfer momentum from one region of a flow to another. This is analogous to other diffusivities and has the same dimensions, $$L^2T^{-1}$$. Another way of describing kinematic viscosity is molecular diffusivity, or diffusion of momentum-carrying molecules.

The equation for kinematic viscosity is:

$$\nu = \frac{\mu}{\rho}$$

According to college textbooks, it is called kinematic viscosity because force is not involved and if you analyze the units you'll see that. In my opinion, they had to name it something so they came up with that name. "Viscosity" is much easier to understand since it's defined as a fluid's ability to resist shear or angular deformation. When you divide viscosity by density, you end up with something that needs to be named something else. I have never seen it described as "diffusivity of momentum".

It would be interesting to plot viscosity versus density on a graph for different materials to see what the graph would look like. The slope would obviously be kinematic viscosity.