Question Video: Understanding Fluid Flow around Obstacles Physics

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

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Video Transcript

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

Okay, so we see in our diagram fluid flowing along. And we can say that it’s moving from left to right as we’re looking at it. As the fluid moves along, there’s an obstacle in its path right here, something solid in the way that won’t move. In response, and we can see this in the flow lines, the fluid changes direction to avoid this obstacle. Downstream of the obstacle, we have these two regions marked out one and two. We want to know, first, in which of the two regions is the fluid flow faster and, secondly, in which of the two is it steadier.

Now, actually, it’s a bit easier to answer this second part of this question before we answer the first. Let’s consider whether fluid flow is steadier in region one or in region two. And to help us figure that out, we can recall that fluid flow is steadier when the fluid’s speed and direction change less. So in a given region, if the fluid there isn’t changing much in speed or direction, then that indicates a fairly steady fluid flow.

If we look at region one in our diagram, we can see right away that the fluid direction is changing significantly in this region. In this region, there is part of a closed loop of fluid flow. These closed loops show the direction of fluid changing drastically and are hallmarks of turbulent flow. By contrast, the streamlines in region two are nearly parallel with one another. They don’t change direction much at all and also show us that the speed of fluid in this region doesn’t change much either.

This clarifies our answer to the second part of this question. We can say that it’s in region two that the fluid flow is steadier because it’s in this region that fluid speed and direction change less.

And now for the first part of our question, which asks in which of the two regions the fluid flow is faster, now it’s a bit counterintuitive. But actually, there’s a correlation between steady fluid flow and faster fluid speed. The reason for this is that when fluid is flowing steadily along, that means its direction isn’t changing very much. It’s not interfering with itself. The effect of that interference, the fluid pushing against itself, would be to slow down the average speed of the fluid.

For example, consider the fluid in region one in our diagram. We can assume that in this closed loop we see, the fluid is flowing in one direction in one part of the loop and in the other direction in the other part. The fact that within this region some fluid is flowing one way and some is flowing in the opposite direction shows us that fluid in this region is strongly interfering with itself. It’s not able to establish a steady flow. And therefore, it doesn’t have much opportunity to pick up speed. And that means that the average speed of the fluid in this region is lower than that of a region within the same flow but where the fluid is not pushing against itself quite so much.

So not only is region two the place where fluid flow is steadier, it’s also the region where fluid flow is faster. In general, the steadier a fluid flow is, the faster it can move along.

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