Question Video: Understanding Fluid Flow around Obstacles | Nagwa Question Video: Understanding Fluid Flow around Obstacles | Nagwa

Question Video: Understanding Fluid Flow around Obstacles Physics • Second Year of Secondary School

The diagram shows the flow of a fluid past a circular obstacle. The gray lines represent the direction of the fluid flow. Black regions represent solid obstacles to the flow. In which of the two regions within the dashed lines is the fluid flow faster?

03:09

Video Transcript

The diagram shows the flow of the fluid past a circular obstacle. The gray lines represent the direction of the fluid flow. Black regions represent solid obstacles to the flow. In which of the two regions within the dashed lines is the fluid flow faster?

So we’re imagining here that the fluid in this diagram is flowing left to right. And as it does so, a solid obstacle to that flow, right here, comes up. We could imagine this as being something like a rock in a riverbed. And we know that such a rock causes the fluid around it to flow differently. And indeed, we see that the gray lines indicating the direction of fluid flow do change as the fluid avoids this solid obstacle. Downstream of that obstacle, we see these two regions marked out one and two. And we want to know in which of them is the fluid flow faster on average.

Before we answer this question though, of in which region the fluid flow is faster, let’s consider in which of the two regions is the fluid flow more turbulent. We can recall that fluid flow is more turbulent when a fluid’s speed and direction change more. So if we wanna figure out in which region, one or two, the flow is more turbulent, we can look to see in which one do the fluid speed and direction change more.

We can figure this out by considering the gray lines, what we could call the streamlines of the fluid in this flow. Notice how, in region one, these two flow lines approach one another across this region, while in region two, the flow lines are nearly parallel with one another. This might seem like a small difference. But the changes in fluid direction we see in region one greater than the direction changes we see in region two indicate a more turbulent flow in region one. And indeed, this agrees with our intuition.

We would expect a region in our fluid right behind a large solid obstacle to be more turbulent, whereas farther downstream, farther away from this obstacle, we expect the flow to smooth out. Okay, so if the flow in region one is more turbulent than that in region two, how does that help us answer this question of in which region does the fluid flow faster?

Consider again the streamlines in region one. If we were to draw exaggerated velocity vectors for parts of these streamlines in this region, they might look like this. These vectors that we’ve drawn in, even though they may overstate the motion of the fluid in this dimension, show us that, nonetheless, because of these streamlines getting closer and closer together, fluid in one part of this region will be pushing against fluid in the other part. That is, fluid on this side of our dashed line will be pushing on fluid on this side of the line, and vice versa.

Because the fluid in region one isn’t only moving left to right but is instead also moving up and down we could say from this perspective, some of that fluid velocity will be negated as the fluid flows against itself. This will lead on average across the whole region to a slowing down of this fluid. This is in contrast to the fluid in region two. Instead of some fluid in the region pushing against fluid in other parts of it, it’s all essentially moving in lockstep and therefore fairly rapidly from left to right. Because the fluid in region one resists its own motion more than the fluid in region two, we can say that it’s the fluid in region two which flows faster.

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