Video Transcript
The following figure shows the
direction of fluid flow over an obstacle. Within which of the regions shown,
if any, is there some turbulent flow? (A) Region 1 only, (B) region 2
only, (C) region 3 only, (D) all of the regions shown, (E) none of the regions
shown.
Studying this example of fluid
flow, we want to pick which of these four regions, if any of them, show some
turbulent flow. The idea is that there is a flowing
fluid whose movement is represented by these streamlines. And as this fluid flows from left
to right, it passes by this obstacle. Region 1, we see, is just upstream
of the obstacle, region 2 is at the obstacle, region 3 is just downstream of it, and
region 4 is farther downstream.
To figure out which, if any, of
these regions show us turbulent flow, let’s recall that turbulence arises due to
friction between adjacent layers of flowing fluid. In a smooth or laminar flow
situation, these layers stay separate from one another. However, if the friction between
them is great enough, then the layers begin to mix. This mixture is a sign of
turbulence. If we look at the streamlines in
our diagram, we see that at no point does the fluid flowing in any given layer, say
this one here, mix with the fluid flowing in the layers adjacent to it. No matter which layer we pick and
which of our four regions we choose, we don’t see any signs of mixing of adjacent
fluid layers. Even though these layers are
diverted due to the obstacle, they still remain intact without mixing with one
another.
If there was turbulent flow in any
of these four regions, it would be evidenced by something like we see here. The streamlines, which we can take
as boundaries between adjacent layers of fluid, would be disrupted and not follow a
smooth left-to-right flow pattern. Because we don’t see this anywhere
in our diagram, we can’t say that we see any signs of turbulent flow. For our answer then, we’ll choose
option (E). In none of the regions shown do we
see any signs of turbulent flow.