Wrapping your head around the concept of viscosity (Fluid Dynamics w/ Olivier Cleynen)

How do you wrap your head around the concept of viscosity? Usually people start by telling you that viscosity is the stickiness of fluid. Honey, sugar syrup, is very sticky, it’s very viscous compared to say water. And that’s easy to understand. And all goes well until people start dumping that kind of equation on you like mu is defined by tau divided by some difference in velocity divided by some difference in height over here and then they add insult to injury by telling you that it’s easy it’s just a ratio between shear and strain. So let’s see what this means in practice. And for this we need to make a conceptual experiment we’re going to take a brick of fluid. So imagine inside fluid, you cut out a box brick-shaped piece of fluid.

This box has 00:50 - on top an area A, yeah? And it has in height and height Delta Y. And what we’re going to do to this brick of fluid is we’re going to strain it. We’re going to deform it continuously at some fixed velocity. So what we do is we apply here a velocity difference between the top and the bottom, yeah, we write it Delta V. Whatever the velocity the bottom is going at, we add to this a delta velocity Delta V, so this strains is the box. and to do this we need to apply some force F.

01:29 - We need to pull the top surface with us so that we strain the fluid. We want in this experiment to be able to quantify F and relate F with the stickiness or the viscosity of the fluid. So let’s take a look at this what this would look like. We have this little box over here and now we know that F, or we guess that F will increase with different parameters. It will certainly increase with increasing A.

The larger the area, the more force you need to pull 02:04 - It will also increase with more Delta V: the faster you pull, the more force you will be required to apply. And lastly it will increase with decreasing [—] decreasing height so the shallower this brick of fluid is, and the more strain you’re applying for a given delta V. So the shallower the brick, and the higher the force, like so. And finally what we actually want to quantify, the force will increase with increasing stickiness or viscosity. So now, turn this around. You take the force that you have on top here and based on this force you want to quantify the stickiness or the viscosity of the fluid.

We want to take the force and remove the parameters 02:55 - that influence the force that are not the viscosity. So we’re going to take the force on top we’re going to divide it by the area, we’re gonna divide it by the Delta V; and we’re going to multiply it by the Delta Y. And this gives us the equation which is like so here. Viscosity mu, a Greek letter mu, is defined as the force per area on top, divided by the Delta V divided by the Delta Y, yeah? And so force by area here on top we write it tau we call it shear stress; and we’ll come back to this in the coming chapters, and the bottom term we call velocity gradient — the change in space of velocity Delta V over Delta Y. We will learn to write this a tiny bit more formally in the coming chapters. For now, that should be enough.

so I hope now it makes a little sense when 03:50 - people say it’s the ratio between shear and strain : it’s a ratio between shear which is tau here, the effort that you apply, yeah, and the strain, how [quickly] the thing will deform (that’s how quickly this thing will deform), which is Delta V over Delta Y, or more formally what dV dY here, it’s the deformation rate in time what you get. .