Question Video: Identifying the Steadiest Area of a Fluid’s Flow Physics

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 the steadiest? [A] Region I [B] Region II [C] Region III [D] Region IV

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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 the steadiest?

Let’s begin by briefly recalling what we’re looking for in a steadier fluid flow. First, remember that a steady flow is the opposite of a turbulent flow. Turbulence is characterized by a fluid changing in speed and direction more than in a steady flow. Remember that these gray lines in the diagram called flow lines, or streamlines, illustrate the motion of different layers of the fluid. Remember too that different layers of the fluid exert forces on one another like a sort of friction. Thus, curvy flow lines indicate change in direction and also change in speed because the different layers of the fluid are bumping into each other and getting mixed up. On the other hand, steady flow in which the fluid has a more constant speed and direction is shown by flow lines that are more regular. Basically, the less chaotic the flow lines are, the less turbulent the flow.

Now, it’s up to us to determine whether the flow shown in region I, II, III, or IV is the least turbulent or the steadiest. And we have to remember that we’re describing the fluid qualitatively. So we just have to use our best judgment based on what we know about steady versus turbulent fluid flow. Now, all four regions show some degree of turbulence. So let’s use the process of elimination by identifying the most turbulent regions first. It looks like region I contains the most extreme curves, and notice too that the layers of fluid are sort of bunched up near the bottom of the region. These are good indicators of turbulence not steadiness, so let’s eliminate I.

We can see the same sorts of turbulent features in region IV. The lines are really wavy, and they get pretty close to each other down here in the bottom-right corner, so let’s also eliminate IV. Finally, II and III might look more similar to each other, but region II contains curvier lines, which also happen to be oriented at a more extreme angle relative to the overall direction of fluid flow in the diagram. By contrast, the lines in region III are curved only slightly, so it does appear to be more steady than region II and of course regions I and IV. Thus, we’ve seen how region III is the least turbulent or the region with the steadiest fluid flow.

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