Video Transcript
Is the fluid flow shown in the
following figure turbulent in any part of the flow?
In order to answer this question,
we need to understand how this fluid’s flow can be modeled by these blue arrows and
what is meant by turbulent flow.
Recall that we can model the
overall motion of a fluid by representing the motion of different layers of the
fluid using streamlines, which is what’s shown by the blue arrows here. Different fluid layers can flow at
different speeds and in different directions.
Now, modeling a fluid
quantitatively can be very complicated. But we are able to describe fluid
flow qualitatively by observing its streamlines and characterizing the flow as
steady or turbulent. These terms mean opposite
things. Steady fluid flow is orderly and
smooth. We can see this in a fluid whose
layers generally move in the same direction and at the same speed as each other. When a fluid’s layers keep the same
distance apart from one another, we can tell that there’s not a significant
difference in speed between them. Conversely, turbulent fluid flow is
especially chaotic. We see turbulence in a fluid whose
layers change speed and direction rapidly, as shown by streamlines that are more
curved or bunched together.
Now, this question is asking us
whether the fluid shown in the figure is turbulent at any point in its flow. So let’s take a closer look at
it. As a whole, we can see that the
direction of the flow is changing because it’s moving around a bend. But this doesn’t necessarily mean
that the flow is turbulent. Notice that each layer of the fluid
changes its direction by the same amount. So the streamlines always stay the
same distance apart.
Therefore, the layers of the fluid
don’t have different directions relative to each other. This shows us that the fluid’s
layers are moving together in a nice and orderly way. So the flow here is steady, not
turbulent. So the answer to this question is
no. The fluid flow shown in the figure
is not turbulent in any part of the flow.
