Video Transcript
The diagram shows the flow of a
fluid past a line perpendicular to the flow. The gray lines represent the
direction of fluid flow. Black regions represent solid
obstacles to the flow. In which of the regions within the
dashed lines is the fluid flow faster? In which of the regions within the
dashed lines is the fluid flow steadier?
Okay, so we see in our diagram
fluid flowing along. And we can say that it’s moving
from left to right as we’re looking at it. As the fluid moves along, there’s
an obstacle in its path right here, something solid in the way that won’t move. In response, and we can see this in
the flow lines, the fluid changes direction to avoid this obstacle. Downstream of the obstacle, we have
these two regions marked out one and two. We want to know, first, in which of
the two regions is the fluid flow faster and, secondly, in which of the two is it
steadier.
Now, actually, it’s a bit easier to
answer this second part of this question before we answer the first. Let’s consider whether fluid flow
is steadier in region one or in region two. And to help us figure that out, we
can recall that fluid flow is steadier when the fluid’s speed and direction change
less. So in a given region, if the fluid
there isn’t changing much in speed or direction, then that indicates a fairly steady
fluid flow.
If we look at region one in our
diagram, we can see right away that the fluid direction is changing significantly in
this region. In this region, there is part of a
closed loop of fluid flow. These closed loops show the
direction of fluid changing drastically and are hallmarks of turbulent flow. By contrast, the streamlines in
region two are nearly parallel with one another. They don’t change direction much at
all and also show us that the speed of fluid in this region doesn’t change much
either.
This clarifies our answer to the
second part of this question. We can say that it’s in region two
that the fluid flow is steadier because it’s in this region that fluid speed and
direction change less.
And now for the first part of our
question, which asks in which of the two regions the fluid flow is faster, now it’s
a bit counterintuitive. But actually, there’s a correlation
between steady fluid flow and faster fluid speed. The reason for this is that when
fluid is flowing steadily along, that means its direction isn’t changing very
much. It’s not interfering with
itself. The effect of that interference,
the fluid pushing against itself, would be to slow down the average speed of the
fluid.
For example, consider the fluid in
region one in our diagram. We can assume that in this closed
loop we see, the fluid is flowing in one direction in one part of the loop and in
the other direction in the other part. The fact that within this region
some fluid is flowing one way and some is flowing in the opposite direction shows us
that fluid in this region is strongly interfering with itself. It’s not able to establish a steady
flow. And therefore, it doesn’t have much
opportunity to pick up speed. And that means that the average
speed of the fluid in this region is lower than that of a region within the same
flow but where the fluid is not pushing against itself quite so much.
So not only is region two the place
where fluid flow is steadier, it’s also the region where fluid flow is faster. In general, the steadier a fluid
flow is, the faster it can move along.
