>> In this module, we're going to look
at some of the ideas of fluid statics.
And in this video, I'm going to introduce fluid
statics and the reasons why we're interested in.
Just as you would expect, fluid statics
is looking at the forces on fluids
that are static, that is they're not moving.
So, there's still lots of
interesting cases where we have fluids
that exert forces even though
the inertial forces,
those associated with velocity are pretty small.
Simplest example might be if we've dammed a
river like this so that we've got water backed
up behind the dam, it's not moving very much
even if maybe we have a little pipe coming
out here that's allowing some water to pour out.
It's not moving very much so we
can treat it as if it's static.
And by looking at that, we can figure out what
the pressure forces that are acting on this dam
that would tend to push it over like this.
We'd like to avoid having our
dam bursts, so we need to know
about the forces exerted by the pressure.
In order to know about the forces exerted by the
pressure, we need to be able to figure out what
that pressure actually is at
different locations in the fluid.
Now, if we consider this case and we
consider for example a swimming pool,
a very deep swimming pool, but not nearly
as big as the reservoir behind the dam,
we could ask ourselves the question,
is the pressure at location 1 significantly
different from the pressure at location 2?
So, I'd like you to pause for
a moment and ask yourself,
do you think those two pressures
are the same or different and why?
How about this case where
the walls aren't vertical,
where we're concentrating our reservoir
down onto a small area, water there
and we've got this small area down here?
What about location 3, is
the pressure there different
from the pressure at locations 1 and 2?
If you're like a lot of people, you'd
probably want to say that the pressure
at location 3 will be higher
than the pressure at location 2.
You might also want to argue that the pressure
at location 1 is greater than
the pressure at location 2.
And you might get to that by an intuitive sense
that it has to be higher because you've got all
of this mass up here pushing
down on this one little area.
But you would turn out not to be right.
Let's think about it for a moment.
Yes, the pressure is the result
of the fluid up above pressing
down on the fluid that's down below here.
But in these cases where we have a lot of fluid
either here or here and a small area there
or there, we also have this fluid being
supported by forces from all around.
So in addition to the pressure forces
putting-- pushing up on the bottom like that,
there are also pressure forces
acting perpendicular
to the surface all the way
around this reservoir.
The result is we aren't supporting
all of this weight on that small area.
We're supporting it spread over
the entire area of the reservoir.
Likewise, we aren't supporting all of the weight
of the water behind this wall on just the area
of the wall, we're also supporting a bunch of
it on this part of the reservoir back here.
So even if we made this reservoir much bigger
with a whole lot more weight of water behind it,
we still wouldn't increase the
pressure acting on this wall.
So now, we have some ideas
about what we'd like to know.
We've got a way of thinking about pressure.
We know that on any surface, the pressure
will act perpendicular to the surface
against the fluid on the one side.
And we have some tools that we've
developed in the previous modules to look
at how those forces interact with each other.
And they're going to be much simpler if
we can make the assumption that u is equal
to zero, that our fluid is static.
