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## Density and Pressure

Current time:0:00Total duration:9:46

# Pressure and Pascal's principle (part 1)

## Video transcript

Let's learn a little
bit about fluids. You probably have some notion of
what a fluid is, but let's talk about it in the physics
sense, or maybe even the chemistry sense, depending
on in what context you're watching this video. So a fluid is anything
that takes the shape of its container. For example, if I had a glass
sphere, and let's say that I completely filled this glass
sphere with water. I was going to say that we're in
a zero gravity environment, but you really don't
even need that. Let's say that every cubic
centimeter or cubic meter of this glass sphere is
filled with water. Let's say that it's not a glass,
but a rubber sphere. If I were to change the shape of
the sphere, but not really change the volume-- if I were
to change the shape of the sphere where it looks like this
now-- the water would just change its shape
with the container. The water would just change in
the shape of the container, and in this case, I
have green water. The same is also true if that
was oxygen, or if that was just some gas. It would fill the container,
and in this situation, it would also fill the newly
shaped container. A fluid, in general, takes the
shape of its container. And I just gave you two examples
of fluids-- you have liquids, and you have gases. Those are two types of fluid:
both of those things take the shape of the container. What's the difference between
a liquid and a gas, then? A gas is compressible, which
means that I could actually decrease the volume of this
container and the gas will just become denser within
the container. You can think of it as if I blew
air into a balloon-- you could squeeze that balloon
a little bit. There's air in there, and at
some point the pressure might get high enough to pop
the balloon, but you can squeeze it. A liquid is incompressible. How do I know that a liquid
is incompressible? Imagine the same balloon filled
with water-- completely filled with water. If you squeezed on that balloon
from every side-- let me pick a different color-- I
have this balloon, and it was filled with water. If you squeezed on this balloon
from every side, you would not be able to change the
volume of this balloon. No matter what you do, you would
not be able to change the volume of this balloon, no
matter how much force or pressure you put from any side
on it, while if this was filled with gas-- and magenta,
blue in for gas-- you actually could decrease the volume by
just increasing the pressure on all sides of the balloon. You can actually squeeze
it, and make the entire volume smaller. That's the difference between
a liquid and a gas-- gas is compressible, liquid isn't, and
we'll learn later that you can turn a liquid into a gas,
gas into a liquid, and turn liquids into solids, but we'll
learn all about that later. This is a pretty good working
definition of that. Let's use that, and now we're
going to actually just focus on the liquids to see if we
could learn a little bit about liquid motion, or maybe even
fluid motion in general. Let me draw something else--
let's say I had a situation where I have this weird shaped
object which tends to show up in a lot of physics books, which
I'll draw in yellow. This weird shaped container
where it's relatively narrow there, and then it goes
and U-turns into a much larger opening. Let's say that the area of this
opening is A1, and the area of this opening is A2--
this one is bigger. Now let's fill this thing with
some liquid, which will be blue-- so that's my liquid. Let me see if they have
this tool-- there you go, look at that. I filled it with liquid
so quickly. This was liquid-- it's not just
a fluid, and so what's the important thing
about liquid? It's incompressible. Let's take what we know about
force-- actually about work-- and see if we can come up with
any rules about force and pressure with liquids. So what do we know about work? Work is force times distance, or
you can also view it as the energy put into the system--
I'll write it down here. Work is equal to force
times distance. We learned in mechanical
advantage that the work in-- I'll do it with that I--
is equal to work out. The force times the distance
that you've put into a system is equal to the force
times the distance you put out of it. And you might want to review
the work chapters on that. That's just the little law of
conservation of energy, because work in is just the
energy that you're putting into a system-- it's measured
in joules-- and the work out is the energy that comes
out of the system. And that's just saying that
no energy is destroyed or created, it just turns into
different forms. Let's just use this definition: the force
times distance in is equal to force times distance out. Let's say that I pressed
with some force on this entire surface. Let's say I had a piston-- let
me see if I can draw a piston, and what's a good color for
a piston-- so let's add a magenta piston right here. I push down on this magenta
piston, and so I pushed down on this with a force of F1. Let's say I push it
a distance of D1-- that's its initial position. Its final position-- let's see
what color, and the hardest part of these videos is picking
the color-- after I pushed, the piston
goes this far. This is the distance that I
pushed it-- this is D1. The water is here and I push
the water down D1 meters. In this situation, my work
in is F1 times D1. Let me ask you a question: how
much water did I displace? How much total water
did I displace? Well, it's this volume? I took this entire volume and
pushed it down, so what's the volume right there
that I displaced? The volume there is going to
be-- the initial volume that I'm displacing, or the
volume displaced, has to equal this distance. This is a cylinder of liquid,
so this distance times the area of the container
at that point. I'm assuming that it's constant
at that point, and then it changes after that,
so it equals area 1 times distance 1. We also know that that liquid
has to go someplace, because what do we know about
a liquid? We can't compress it, you can't
change its total volume, so all of that volume is going
to have to go someplace else. This is where the liquid was,
and the liquid is going to rise some level-- let's say that
it gets to this level, and this is its new level. It's going to change some
distance here, it's going to change some distance there,
and how do we know what distance that's going to be? The volume that it changes
here has to go someplace. You can say, that's going to
push on that, that's all going to push, and that liquid
has to go someplace. Essentially it's going to end
up-- it might not be the exact same molecules, but that might
displace some liquid here, that's going to displace some
liquid here and here and here and here and all the way until
the liquid up here gets displaced and gets
pushed upward. The volume that you're pushing
down here is the same volume that goes up right here. So what's the volume-- what's
the change in volume, or how much volume did you
push up here? This volume here is going to be
the distance 2 times this larger area, so we could say
volume 2 is going to be equal to the distance 2 times
this larger area. We know that this liquid is
incompressible, so this volume has to be the same
as this volume. We know that these two
quantities are equal to each other, so area 1 times distance
1 is going to be equal to this area times
this distance. Let's see what we can do. We know this, that the force
in times the distance in is equal to the force out times
the distance out. Let's take this equation-- I'm
going to switch back to green just so we don't lose
track of things-- and divide both sides. Let's rewrite it--
so let's say I rewrote each input force. Actually, I'm about to run out
of time, so I'll continue this into the next video. See you soon.