Question Video: Comparing Fluid Viscosities Based on Fluid Flow around an Obstacle Physics

Two fluids flow past a circular obstacle. Gray lines represent the direction of fluid flow. Black regions represent solid obstacles to the flow. The only difference between the two fluids is their viscosity. Which of the diagrams shows the fluid with the greater viscosity?

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Video Transcript

Two fluids flow past a circular obstacle. Gray lines represent the direction of fluid flow. Black regions represent solid obstacles to the flow. The only difference between the two fluids is their viscosity. Which of the diagrams shows the fluid with the greater viscosity?

We see these diagrams (A) and (B), which consist of two fluids identical other than their viscosity flowing past a circular obstacle. In diagram (A), the lines that represent the flow of this fluid are fairly straight, indicating laminar or smooth flow. In diagram (B), some of the flow lines are fairly smooth, but some are not. And in particular, we see these closed flow lines. Whenever a flow line forms a closed loop, that’s an indication of what is called turbulent flow. Turbulence describes the agitated or disorganized flow of fluids.

In our question, though, we don’t want to pick which fluid flow is the most turbulent, but which of the two fluids is likely to have the greater viscosity. One way to think about viscosity is to think of it as the thickness of a fluid. For example, a fluid like honey, which is relatively thick, has a high viscosity. We can also think of viscosity as the resistance of a fluid to flowing. A thick viscous fluid, like honey, does not flow easily, while a thinner fluid with a relatively lower viscosity, like water, does flow fairly easily.

The two ideas represented within are viscosity and turbulence, and these two concepts actually are connected. A very viscous thick fluid is unlikely to flow in an agitated or disorganized way. Thinking again of honey as an example of a highly viscous fluid, imagine stirring a large quantity of honey in a container. No matter how hard we stir, that honey will likely flow in a fairly smooth way. That is, the higher the viscosity of the fluid, the less likely it is to experience turbulence. But now, in that same picture of stirring a fluid, replace the honey with water. This relatively low-viscosity fluid will be much more likely to experience turbulence as we stir it.

Therefore, the diagram that shows us the fluid with the greatest viscosity is the one that indicates the least amount of turbulence. The flow in diagram (A) is significantly smoother, that is, less turbulent, than that in diagram (B). And therefore, it’s diagram (A) that shows us the fluid with the greater viscosity.

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