# Video: Analyzing the Behavior of Viscous Fluids under the Effect of Rotation

Thin layers of equal area and thickness of two different-colored oils are placed onto the central region of the top surface of two identical solid disks, as shown in the diagram. The disks are then rotated with equal angular velocities and the oils spread over the surface of the disks. The oils have the same density but different viscosities. Which of the oils has the greater viscosity?

02:40

### Video Transcript

Thin layers of equal area and thickness of two different-colored oils are placed onto the central region of the top surface of two identical solid disks, as shown in the diagram. The disks are then rotated with equal angular velocities and the oils spread over the surface of the disks. The oils have the same density but different viscosities. Which of the oils has the greater viscosity?

Okay, so we see in our diagram these two disks. And we’re looking at them in what we could call before and after instances. First, we have the two discs stationery and these two oils are deposited onto the center regions of each one. We could call the oil on the top desk the orange oil and that on the bottom disk the yellow one. We’re told that the regions on these disks that are covered by the oils are of equal area and equal thickness. This means that the oil volumes are the same. So, there’s just as much orange oil on this disk as there is yellow oil on this one. And they cover the same amount of area at the center of each identical disk.

So, this is our before scenario. And then, the disks are set to rotating. Our problem statement tells us that they rotate with equal angular velocities, in other words, the same angular speed. And as a result of this, the two oils spread out over the surface of the disks. The oils, we’re told, have the same density, but they have different viscosities, that is, thicknesses. Based on how these two different oils respond to the rotation of these disks, we want to identify which one has the greater viscosity.

To begin figuring this out, we can recall that viscosity indicates the internal friction of a fluid. That is, the more friction between the layers of that fluid, the higher its viscosity is. We can also say that if the layers of a given fluid have a lot of friction between them, then it will be unlikely for those layers to move very much relative to one another. That’s because there’s such a strong resistance to movement through friction. So, related to our question, the oil with the greater viscosity will be the one that moves less or, we could say, deforms less in response to the rotation of these disks.

That will be the oil that, we could say, is held together more closely than the less viscous of the two oils. So, looking at this snapshot of our spinning disks, after the oils have had a chance to expand across those surfaces, we see that it’s the orange oil that has expanded less than the yellow one. That means this oil more strongly resists deformation and that resistance, we can assume, is due to higher levels of internal friction in this oil. In other words, this is the more viscous of the two. For our answer then, we can say that the orange oil has greater viscosity. And we say that because this oil was deformed the least of the two.