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Let's learn a little
bit about fluids.

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You probably have some notion of
what a fluid is, but let's

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talk about it in the physics
sense, or maybe even the

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chemistry sense, depending
on in what context you're

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watching this video.

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So a fluid is anything
that takes the

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shape of its container.

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For example, if I had a glass
sphere, and let's say that I

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completely filled this glass
sphere with water.

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I was going to say that we're in
a zero gravity environment,

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but you really don't
even need that.

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Let's say that every cubic
centimeter or cubic meter of

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this glass sphere is
filled with water.

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Let's say that it's not a glass,
but a rubber sphere.

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If I were to change the shape of
the sphere, but not really

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change the volume-- if I were
to change the shape of the

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sphere where it looks like this
now-- the water would

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just change its shape
with the container.

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The water would just change in
the shape of the container,

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and in this case, I
have green water.

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The same is also true if that
was oxygen, or if that was

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just some gas.

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It would fill the container,
and in this situation, it

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would also fill the newly
shaped container.

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A fluid, in general, takes the
shape of its container.

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And I just gave you two examples
of fluids-- you have

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liquids, and you have gases.

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Those are two types of fluid:
both of those things take the

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shape of the container.

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What's the difference between
a liquid and a gas, then?

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A gas is compressible, which
means that I could actually

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decrease the volume of this
container and the gas will

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just become denser within
the container.

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You can think of it as if I blew
air into a balloon-- you

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could squeeze that balloon
a little bit.

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There's air in there, and at
some point the pressure might

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get high enough to pop
the balloon, but

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you can squeeze it.

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A liquid is incompressible.

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How do I know that a liquid
is incompressible?

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Imagine the same balloon filled
with water-- completely

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filled with water.

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If you squeezed on that balloon
from every side-- let

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me pick a different color-- I
have this balloon, and it was

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filled with water.

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If you squeezed on this balloon
from every side, you

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would not be able to change the
volume of this balloon.

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No matter what you do, you would
not be able to change

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the volume of this balloon, no
matter how much force or

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pressure you put from any side
on it, while if this was

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filled with gas-- and magenta,
blue in for gas-- you actually

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could decrease the volume by
just increasing the pressure

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on all sides of the balloon.

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You can actually squeeze
it, and make the

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entire volume smaller.

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That's the difference between
a liquid and a gas-- gas is

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compressible, liquid isn't, and
we'll learn later that you

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can turn a liquid into a gas,
gas into a liquid, and turn

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liquids into solids, but we'll
learn all about that later.

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This is a pretty good working
definition of that.

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Let's use that, and now we're
going to actually just focus

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on the liquids to see if we
could learn a little bit about

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liquid motion, or maybe even
fluid motion in general.

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Let me draw something else--
let's say I had a situation

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where I have this weird shaped
object which tends to show up

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in a lot of physics books, which
I'll draw in yellow.

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This weird shaped container
where it's relatively narrow

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there, and then it goes
and U-turns into

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a much larger opening.

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Let's say that the area of this
opening is A1, and the

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area of this opening is A2--
this one is bigger.

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Now let's fill this thing with
some liquid, which will be

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blue-- so that's my liquid.

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Let me see if they have
this tool-- there

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you go, look at that.

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I filled it with liquid
so quickly.

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This was liquid-- it's not just
a fluid, and so what's

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the important thing
about liquid?

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It's incompressible.

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Let's take what we know about
force-- actually about work--

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and see if we can come up with
any rules about force and

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pressure with liquids.

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So what do we know about work?

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Work is force times distance, or
you can also view it as the

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energy put into the system--
I'll write it down here.

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Work is equal to force
times distance.

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We learned in mechanical
advantage that the work in--

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I'll do it with that I--
is equal to work out.

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The force times the distance
that you've put into a system

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is equal to the force
times the distance

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you put out of it.

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And you might want to review
the work chapters on that.

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That's just the little law of
conservation of energy,

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because work in is just the
energy that you're putting

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into a system-- it's measured
in joules-- and the work out

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is the energy that comes
out of the system.

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And that's just saying that
no energy is destroyed or

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created, it just turns into
different forms. Let's just

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use this definition: the force
times distance in is equal to

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force times distance out.

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Let's say that I pressed
with some force

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on this entire surface.

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Let's say I had a piston-- let
me see if I can draw a piston,

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and what's a good color for
a piston-- so let's add a

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magenta piston right here.

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I push down on this magenta
piston, and so I pushed down

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on this with a force of F1.

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Let's say I push it
a distance of D1--

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that's its initial position.

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Its final position-- let's see
what color, and the hardest

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part of these videos is picking
the color-- after I

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pushed, the piston
goes this far.

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This is the distance that I
pushed it-- this is D1.

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The water is here and I push
the water down D1 meters.

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In this situation, my work
in is F1 times D1.

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Let me ask you a question: how
much water did I displace?

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How much total water
did I displace?

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Well, it's this volume?

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I took this entire volume and
pushed it down, so what's the

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volume right there
that I displaced?

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The volume there is going to
be-- the initial volume that

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I'm displacing, or the
volume displaced, has

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to equal this distance.

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This is a cylinder of liquid,
so this distance times the

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area of the container
at that point.

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I'm assuming that it's constant
at that point, and

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then it changes after that,
so it equals area 1 times

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distance 1.

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We also know that that liquid
has to go someplace, because

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what do we know about
a liquid?

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We can't compress it, you can't
change its total volume,

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so all of that volume is going
to have to go someplace else.

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This is where the liquid was,
and the liquid is going to

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rise some level-- let's say that
it gets to this level,

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and this is its new level.

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It's going to change some
distance here, it's going to

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change some distance there,
and how do we know what

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distance that's going to be?

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The volume that it changes
here has to go someplace.

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You can say, that's going to
push on that, that's all going

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to push, and that liquid
has to go someplace.

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Essentially it's going to end
up-- it might not be the exact

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same molecules, but that might
displace some liquid here,

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that's going to displace some
liquid here and here and here

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and here and all the way until
the liquid up here gets

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displaced and gets
pushed upward.

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The volume that you're pushing
down here is the same volume

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that goes up right here.

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So what's the volume-- what's
the change in volume, or how

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much volume did you
push up here?

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This volume here is going to be
the distance 2 times this

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larger area, so we could say
volume 2 is going to be equal

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to the distance 2 times
this larger area.

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We know that this liquid is
incompressible, so this volume

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has to be the same
as this volume.

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We know that these two
quantities are equal to each

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other, so area 1 times distance
1 is going to be

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equal to this area times
this distance.

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Let's see what we can do.

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We know this, that the force
in times the distance in is

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equal to the force out times
the distance out.

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Let's take this equation-- I'm
going to switch back to green

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just so we don't lose
track of things--

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and divide both sides.

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Let's rewrite it--
so let's say I

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rewrote each input force.

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Actually, I'm about to run out
of time, so I'll continue this

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into the next video.

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See you soon.