Lesson Video: Applications of Viscosity Physics

In this video, we will learn how to describe the effect of viscosity on fluid flow for vehicular, engineering, and medical applications.

11:56

Video Transcript

In this video, we’re talking about applications of viscosity. Viscosity is a property of fluids that affects how those fluids move as well as how other objects can move through those fluids.

To get a sense for what viscosity means practically, imagine that we have here a mixing bowl and a spoon and currently all the bowl has in it is some water. From experience, we know that if we were to stir this water up, it would be fairly easy to do. The water offers very little resistance to the movement of the spoon through it. When we see this, we can say it’s a result of the water having a low viscosity. And we can define this term by saying that it refers to the magnitude of internal friction of a fluid.

So, if we picture, say, all the layers of water in our mixing bowl, we know that as the spoon stirs the layers because this is a low viscosity fluid, there’s very little friction between the layers. And that actually means that the layers of this liquid tend to mix easily with one another. That’s because friction between the layers of a fluid actually helps to reinforce the boundaries of those layers. So, when there’s not much internal friction, as is the case for a low-viscosity fluid like water, the boundaries between fluid layers are weak and, therefore, the layers mix easily.

So, in the case of pure water, stirring up the water doesn’t take much effort, and it also results in significant mixing of the layers of this fluid. This means, by the way, that we could describe the flow of this fluid under these conditions as turbulent. So, we have this fairly thin, that is, low-viscosity fluid. But what if we add something to make it a bit thicker? Say we pour some flour into the water.

As our flour mixes in with the water, the viscosity of this mixture will go up. And we’ll probably be able to feel this difference as we continue stirring. The fluid will feel a little bit thicker, and it will take a little bit more effort to move the spoon through it. And here’s another thing we can say.

If we were to continue stirring with the same exact force on the spoon before and after adding the flour, then once the flour has been added, the different layers of our fluid — now, a water-flour mixture — would do a better job at maintaining their separate boundaries than the water did by itself before. That’s because the internal friction of our fluid is increased with the added flour, which means the boundaries between these layers of fluid are now stronger. They still do mix, but not as much as they did before.

And if we were to add even more flour to the mix, this trend would continue in the same direction. The fluid would get harder and harder to stir. But if we did continue stirring it with the same force as we had all along, then the layers of fluid would tend to keep more and more separate. They would flow more and more smoothly, that is.

By now, our fluid in the bowl is starting to get pretty thick. And when this happens, there’s a certain effect we may start to notice. Say that we were moving the spoon through our fluid at a very slow speed very gradually in circles. Our fluid, because of its viscosity, would resist that movement to some extent. Then, imagine that we rapidly increase the speed with which we’re stirring. So, the spoon is moving much more quickly round and round in circles through this mixture.

Now, here’s a question; in which case, with the slow stirring or the fast stirring, will we need to apply more force to the spoon? Well, we know from experience that it’s the fast stirring that takes more force, and not just because we’re moving the spoon with its mass more quickly. More than that, it’s because we’re working against something called the drag force. This is a friction force that’s applied to any object that’s in motion through a fluid. So, an airplane flying through the air experiences drag force, a fish swimming through the sea. And we can feel the drag force ourselves when we’re driving along in a car and put our hand out the window. We bring up this force because it turns out that the magnitude of this force depends on the speed with which an object moves through a fluid.

Getting back to our stirring spoon, we saw earlier that when we moved the spoon more quickly, then we encountered more resistance from the fluid, that is, more drag force. And therefore, we had to push the spoon harder to move it faster. This is generally true of objects moving through fluids. The faster the objects move, the more drag force they experience. And here’s something really interesting. If we consider the general case of some object moving through some fluid, then typically there’s some speed, we can call that speed 𝑣, where if the object is moving below that particular speed through the fluid, then the drag force on that moving object, we’ll call it 𝐹 sub D, is proportional to the instantaneous speed of that object, we’ll call it 𝑣 sub i.

So, what we’re saying so far is that if we have an object moving at less than this speed 𝑣 through some fluid, then the drag due to friction that that object experiences is proportional to its speed. So, if its speed doubled, assuming it remains below this cut-off speed 𝑣, then the drag force experienced by the object would double as well. But if the speed of our object is greater than 𝑣, then in that case we can say the drag force it experiences is actually proportional to the object’s instantaneous speed squared.

This means that once we’re beyond this cut-off speed, if we were to double the speed of our object, then we would quadruple the drag force it experiences. The tendency of drag force to behave like this has some really interesting consequences. For one thing, when aircraft are traveling at very high speeds — several times the speed of sound, say — then the thrust force that the engines need to provide to move the aircraft just a little bit faster goes up significantly. Because in this regime, the drag force on the aircraft goes with the square of the aircraft’s speed. In other words, it gets harder and harder to push the aircraft that much faster.

Now, it’s worth pointing out that this cut-off speed 𝑣 is different for every combination of fluid and object moving through that fluid. So, it’s not a fixed number that we might be able to look up, say, in a table. So, anyway, as the speed of an object moving through a fluid increases, so does the drag force on that object. And sometimes that drag force increases with the square of the object speed. This may be what we experience as we find the spoon harder and harder to move through this mixture at higher and higher speeds.

Now, getting back to our mixture, let’s see that we added a whole lot of flour to it. Our mixture, therefore, get substantially thicker, that is, more viscous. And now, if we were to look at the various layers of this fluid, we would see that there’s virtually no mixing between them. That is, as our spoon moves through this flour—water mixture, the layer boundaries stay intact. We could say then that our fluid is flowing, albeit very slowly, in a very smooth fashion. This is the opposite of turbulent flow.

And so, what we’re finding then is that as the thickness or the viscosity of a fluid increases — that is, as the friction between layers of the fluid goes up — then the tendency of that fluid to flow smoothly also increases. When this happens, we say that the deformation of the fluid is very low, where the deformation of a fluid is simply a change in its flow. This change could happen, for example, by layers of the fluid mixing together. A more viscous fluid has greater resistance to deformation.

Knowing all this, let’s get a bit of practice now through an example exercise.

If a fluid increases in viscosity, in which of the following ways does this change the fluid’s resistance to deformation? (a) The fluid has less resistance to deformation. (b) The fluid has greater resistance to deformation. (c) The resistance of the fluid to deformation is not affected.

To get started here, let’s imagine some fluid that increases in its viscosity. So, how about this? Say that we have a container that’s filled with honey. We know that honey is already a fairly viscous or thick fluid. And let’s say that we decrease the temperature of this honey. We cool it down so that it gets even thicker. By cooling the honey then, we’re increasing the viscosity of this fluid. We want to know how this changes our fluid’s resistance to deformation.

And we can recall that deformation refers to a change in the flow of a fluid. One way we could change the flow of this fluid, that is, deform it, is by mixing it, say, with a spoon. So, here’s the question: how does the honey’s resistance to the spoon’s movement through it change as the honey’s viscosity increases?

We know from experience that for a thicker, that is, more viscous fluid, the resistance to a change in flow, that is, the resistance to deformation, will increase. Simply speaking, it’s harder to stir a thicker or more viscous fluid. And we see that of our three answer options, option (b) describes this case. This tells us that as the viscosity of our fluid increases, so does the fluid’s resistance to deformation.

Let’s look now at a second example exercise.

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.

Let’s now summarize what we’ve learned about applications of viscosity. In this lesson, we saw that the term viscosity describes the magnitude of internal friction of a fluid. We also learned that objects moving through fluids experience what’s called a drag force and that this force is due to friction. At relatively lower speeds, this drag force, we can abbreviate it 𝐹 sub D, is proportional to the speed of the object 𝑣. Whereas at relatively higher speeds, the drag force is proportional to 𝑣 squared. Lastly, we saw that fluids with greater viscosity offer greater resistance to deformation, a change in the flow of a fluid.

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