Video Transcript
The diagram shows the flow of a fluid past a line perpendicular to the flow. The gray lines represent the direction of the fluid’s flow. The black region represents a solid obstacle to the flow. Which of the two regions within the dashed lines has a faster fluid flow?
Okay, so in the diagram the fluid is generally moving from left to right, but it encounters this big obstacle right in its path. Remember that these gray flow lines or streamlines illustrate the motion of different layers of the fluid. So, these curved lines show us how the fluid gets redirected around the obstacle. Now we’re not working with any numbers or mathematics here, but we can use the shapes of flow lines like these to qualitatively describe the nature of a fluid’s flow.
For instance, recall that a steady flow is characterized by more regular and parallel flow lines, like the ones we see over here in region II. This is in contrast to the more irregularly distributed and more curved lines seen in region I. Recall that the less steady a flow is, the more turbulent it is and that turbulence corresponds to areas of flow where the fluid is changing speed and direction more rapidly. Now the flow lines in this diagram aren’t very chaotic. But still this big perpendicular obstacle does cause the flow lines to curve and get scrunched up on either side of it.
Behind the obstacle in region I, we see the flow lines start to curve more gently. And then they continue to even out, resulting in the relatively steady flow we see in region II. But the question is asking us which region has a faster fluid flow. So, what does this all have to do with flow speed? To answer this, we have to recall that the different layers of the fluid as represented by the streamlines exert force on each other like a sort of friction.
So in more turbulent areas where layers are changing speed and direction and bumping into each other, things get more chaotic and the fluid interferes with itself. Between these two boxed-in regions, we’d expect to see this happening more in region I, whereas over here, in region II things are going with the flow. The different layers are basically all heading in the same direction at the same speed, so they don’t have to get slowed down by interfering with each other.
Thus, we can say that generally the steadier regions of a fluid have a faster flow than the more turbulent ones. We’ve determined that region II is steadier than region I. So, we can say that region II has a faster fluid flow.
