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

Two fluids flow past an airfoil. 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? [A] Diagram A [B] Diagram B

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Video Transcript

Two fluids flow past an airfoil. 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?

In both of these two diagrams, we see fluid flowing past an airfoil. We’re told that the only difference between these two scenarios is the viscosity of the two fluids involved. The viscosity of a fluid is a measure of its resistance to flow. A fluid with a higher viscosity is harder to make it flow quickly — a fluid like this might be honey — while a less viscous fluid — say, for example, water — does flow easily.

Fluid flow is represented in these diagrams by gray lines. We see in diagram (A) the lines stay fairly straight, while in diagram (B) some of the lines experience sharper curves and we even have this closed flow line here. Closed lines of flow are a sign of turbulent flow. Turbulence is the opposite of laminar or smooth fluid flow.

We want to identify which of the diagrams shows the fluid with the greater viscosity. So we’d like to consider how these two concepts, viscosity and turbulence, are related. When a fluid is very thick, when it has a high viscosity like, for example, honey, it’s harder to agitate that fluid and to make its flow turbulent. On the other hand, if we have, say, a closed jar with water in it, it’s easy to shake up that jar, agitate the fluid inside, and make it flow in a turbulent way.

We can deduce from this that, in general, if a fluid has a low viscosity like water has a low viscosity, then its tendency towards turbulent fluid flow will be increased. It’s easier to make the flow of a fluid with a low viscosity more turbulent. And the opposite is true. For a highly viscous fluid, like honey, the turbulence of that fluid tends to be quite low.

So in our question, we’re searching for which fluid has the greater viscosity, that is, which is less likely to experience turbulence. While we do see signs of turbulence in diagram (B), we don’t in diagram (A). For our answer then, we choose diagram (A) as the one that shows the fluid with the greater viscosity.

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