Question Video: Comparing the Turbulence and Steadiness of Regions of Fluid Flow Physics

Video Transcript

The diagram shows the flow of a fluid past a circular obstacle. The gray lines represent the direction of the fluid’s flow. The black region represents a solid obstacle to the flow. In which of the four regions within the dashed lines is the fluid’s flow most turbulent? In which of the four regions within the dashed lines is the fluid’s flow steadiest?

Let’s take a closer look at the diagram. We have some fluid flowing around this black circular obstacle. We can understand this fluid to be flowing generally from left to right. And these gray flow lines or streamlines illustrate how the fluid flows past this circular obstacle.

Now, if there were no obstacle to the flow, we would expect to see flow lines that are relatively straight and parallel to one another. But with this object being in the way, we see the fluid moving in different directions, indicating turbulence. Recall that a turbulent flow is the opposite of a steady flow, since turbulence corresponds to a flow that is changing direction and speed more rapidly. For the first part of this question, we need to determine whether the flow shown in region I, II, III, or IV shows the most turbulence.

Now, all four of these regions do show some degree of turbulence, since the streamlines are all pretty wavy, meaning that the fluid is changing direction and speed. But there is a feature in one of the regions that indicates a great deal of turbulence, that is, the presence of these closed loops just behind the obstacle. Remember, the more a fluid changes direction, the more turbulent it is. And for a fluid to flow along a complete loop, it has to point in every direction before it gets back to where it started on the loop. Since number I is the only region that contains any loops in the flow, we know that the fluid’s flow is most turbulent in region I.

The next part of this question basically asks the opposite thing. We need to pick which region is the steadiest or the least turbulent. Now, the answer might not be immediately obvious to us. After all, each of these regions has streamlines that are wavy. We have to keep in mind that certain properties of fluid flow, such as turbulence, can be quite difficult to model quantitatively. This is why instead of using numbers and mathematics, we’re more just using our judgment to describe the flow qualitatively.

Now, we know that region I is the most turbulent. So it can’t be the steadiest, and it won’t be our answer. After that, it looks like region III also has some pretty extreme waves in its flow. Further, recall that when different layers of the fluid, as shown by the streamlines, come into close contact, like they do right here, they exert forces on each other, like a sort of friction, which causes them to slow down and change direction. This means turbulence. So let’s eliminate region III as well.

Finally, we’ll compare regions II and IV. It looks like the lines in region IV are more bunched up and more curved. So they change direction and speed more than the relatively straighter lines contained in region II. Thus, we can say that region IV is a little more turbulent than region II. And because II is the least turbulent of the regions, the fluid’s flow is steadiest in region II.