Video Transcript
The diagram shows the flow of a fluid past a point. The lines represent the direction of the fluid flow. The black region represents a solid obstacle to the flow. Which of the two regions within the dashed lines has a steadier fluid flow?
Let’s take a closer look at the diagram. We have a fluid flowing generally from left to right. But we can also see that there’s a small round obstacle in its way. Remember that these lines illustrate the motion of different layers of the fluid. And as the fluid encounters the obstacle, we see that the fluid has to get redirected around it. Thanks to the shape of the obstacle and the properties of whatever type of fluid this is, there aren’t any areas of great turbulence. The overall flow is pretty steady, as indicated by the relatively straight and parallel flow lines.
Recall that “steady” describes a fluid that doesn’t experience much change in speed and direction. It’s the opposite of a turbulent flow. Of course, we have to keep in mind that we aren’t using any numbers or mathematics to describe the fluid flow here. Properties of fluid motion, such as steadiness, are typically very complicated to express quantitatively. So here we have to rely on our judgment to describe the flow qualitatively.
Still, it’s up to us to determine which of these boxed-in regions, I or II, shows steadier fluid flow. Sometimes this is very easy to tell, for instance, if one region has really curved flow lines. But it might not be as immediately obvious looking at this particular diagram. Both regions I and II do show quite steady fluid flow, but one of the regions is a little more steady than the other.
Now, if somehow we were only shown the insides of these two regions and we couldn’t see the rest of the diagram, we might be more inclined to believe that they have equally steady fluid flow. But we have to think about the whole picture, literally. Notice that region I is located directly behind the obstacle, which we know is solid. And therefore, the fluid must get redirected around it. That’s why we see curved flow lines in the surrounding area.
Now, these curves don’t only indicate a change in direction. Recall that the different layers of the fluid, which are represented by these flow lines, exert force on each other, like a sort of friction. So, as one layer changes direction, it drags the surrounding layers along with it. And we can imagine how this disturbs the general flow of things. Fluid particles are bumping into each other, changing direction, and thus slowing down. So the fluid around the obstacle is flowing slower, which is actually represented by these lines here being less intense than the bulk of the flow shown in the diagram.
Knowing this, we can see how region I isn’t quite perfectly steady due to the presence of this obstacle. This is a good hint that region II is in fact steadier. And then after the obstacle, as the fluid moves along, it eventually evens itself out. And there are no more obstructions to mess up the flow. In this context, we can further understand how region II has a steadier flow than region I.
