The diagram shows a cross section of the streamlines of a liquid flowing around a cylinder. Before the fluid reaches the cylinder, the flow is laminar. After the flow passes behind the cylinder, there is a region of turbulent flow. However, after the region of turbulent flow, the flow becomes laminar again. Which of the following statements most correctly explains why the turbulent flow returns to a laminar flow condition? (A) The flowing liquid expands in the turbulent region. The fluid compresses as it exits the turbulent region. (B) In turbulent flow regions, the kinetic energy of the fluid is dissipated by viscous friction, reducing the average speed of the fluid. As the fluid slows, it becomes less turbulent. (C) The dynamic viscosity of the liquid is increased in the turbulent region. The fluid decreases in viscosity as it exits the turbulent region.
In our diagram, we see streamlines indicating a cross section of fluid flow. In general, the fluid flows from left to right, but it encounters an obstacle in this cylinder. Before the flowing liquid reaches the cylinder, the flow is laminar, or smooth. To the right of the cylinder though, just downstream, there’s a region of turbulent flow, which is then followed by a region of laminar flow. We want to choose which of these three answer options best explains why the turbulent flow in this region transitions to laminar flow.
Answer option (A) says that this happens because the flowing liquid expands in the turbulent region and then compresses as it exits that region. It’s indeed the case that our flowing fluid is a liquid, and liquids, we recall, are considered incompressible. That is, for a given change in pressure, the change in density of a liquid is negligibly small. This means that as our liquid flows, it does not expand or compress, since that would violate its incompressibility. Based on this, we know that answer option (A) can’t be our best answer.
Option (B) says that in the turbulent flow region, the kinetic energy of the fluid is dissipated by viscous friction, which reduces the fluid speed. As the fluid slows, this option says, it becomes less turbulent. This indeed is a good description of what’s going on. Turbulent fluid flows are typically associated with higher fluid speeds, and therefore the various layers of the fluid experience more friction with one another. This friction results in a dissipation of energy, which slows the fluid down. A slower-moving fluid will tend to flow more smoothly. That is, its flow is likely to be laminar. Option (B) then looks like it might be our best answer.
Before deciding this for sure, let’s consider answer option (C). This option talks about the dynamic viscosity of the liquid, both increasing and decreasing in various parts of its flow. We know this won’t happen because the dynamic viscosity, or just viscosity for short, of a liquid is a fixed quantity. Unlike, say, a liquid’s speed or pressure, this is not something that can either increase or decrease depending on how the liquid is flowing. We can eliminate then answer option (C) from consideration.
We’ve confirmed that answer choice (B) is the best explanation for why the region of turbulent flow in our diagram transitions to a region of laminar flow. In turbulent flow regions, the kinetic energy of the fluid is dissipated by viscous friction, reducing the average speed of the fluid. As the fluid slows, it becomes less turbulent.