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Today we're going to continue
with playing with liquids.

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If I have an object that floats,

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a simple cylinder
that floats in some liquid,

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the area is A here,
the mass of the cylinder is M.

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The density of the cylinder
is rho and its length is l

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and the surface area is A.

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So this is l.

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And let the liquid line be here,

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and the fluid has
a density rho fluid.

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I call this level y1,
this level y2.

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The separation is h,

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and right on top here, there is
the atmospheric pressure P2,

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which is the same
as it is here on the liquid.

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And here we have a pressure P1
in the liquid.

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For this object to float

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we need equilibrium between,
on the one hand, the force Mg

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and the buoyant force.

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There is a force up here
which I call F1,

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and there is a force down here
which I call F2--

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barometric pressure.

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The force is always
perpendicular to the surface.

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There couldn't be
any tangential component

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because then the air starts
to flow, and it's static.

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And here we have F1,

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which contains
the hydrostatic pressure.

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So P1 minus P2-- as we learned
last time from Pascal--

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equals rho of the fluid

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g to the minus y2 minus y1,
which is h.

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So that's the difference
between the pressure P1 and P2.

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For this to be in equilibrium,

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F1 minus F2 minus Mg
has to be zero,

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and this we call
the buoyant force.

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And "buoyant" is spelt in a
very strange way: b-u-o-y-a-n-t.

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I always have to think
about that.

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It's the buoyant force.

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F1 equals the area times P1
and F2 is the area times P2,

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so it is the area
times P1 minus P2,

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and that is rho fluids
times g times h.

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And when you look at this,

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this is exactly the weight
of the displaced fluid.

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The area times h

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is the volume of the fluid which
is displaced by this cylinder,

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and you multiply it by its
density, that gives it mass.

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Multiply it by g,
that gives it weight.

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So this is the weight
of the displaced fluids.

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And this is a very special case
of a general principle

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which is called
Archimedes' principle.

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Archimedes' principle
is as follows:

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The buoyant force on an immersed
body has the same magnitude

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as the weight of the fluid
which is displaced by the body.

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According to legend

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Archimedes thought about this
while he was taking a bath,

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and I have a picture
of that here--

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I don't know
from when that dates--

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but you see him there
in his bath,

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but what you also see
are there are two crowns.

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And there is a reason
why those crowns are there.

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Archimedes lived
in the third century B.C.

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Archimedes had been given
the task

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to determine whether a crown
that was made for King Hieron II

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was pure gold.

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The problem for him was

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to determine
the density of this crown--

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which is a very
irregular-shaped object--

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without destroying it.

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And the legend has it

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that as Archimedes was taking
a bath, he found the solution.

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He rushed naked
through the streets of Syracuse

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and he shouted,
"Eureka! Eureka! Eureka!"

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which means,
"I found it! I found it!"

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What did he find?

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What did he think of?

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He had the great vision
to do the following:

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You take the crown and you
weigh it in a normal way.

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So the weight of the crown--
I call it W1--

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is the volume of the crown times
the density of which it is made.

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If it is gold,
it should be 19.3, I believe,

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and so this is
the mass of the crown

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and this is the weight
of the crown.

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Now he takes the crown
and he immerses it in water.

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And he has a spring balance,
and he weighs it again.

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And he finds
that the weight is less

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and so now we have
the weight immersed in water.

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So what you get is

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the weight of the crown
minus the buoyant force,

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which is the weight
of the displaced fluid.

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And the weight
of the displaced fluid

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is the volume of the crown--
because the crown is where...

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the water has been removed
where the crown is--

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times the density
of the fluid--

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which is water, which he knew
very well-- times g.

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And so this part here is
weight loss.

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That's the loss of weight.

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You can see that, you can
measure that with a spring.

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It's lost weight,
because of the buoyant force.

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And so now what he does,

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he takes W1 and divides that
by the weight loss

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and that gives you this term
divided by this term,

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which immediately gives you

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rho of the crown divided
by rho of the water.

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And he knows rho of the water,
so he can find rho of the crown.

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It's an amazing idea;
he was a genius.

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I don't know
how the story ended,

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whether it was gold or not.

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It probably was, because chances
are that if it hadn't been gold

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that the king would have
killed him-- for no good reason,

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but that's the way these things
worked in those days.

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This method is also used

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to measure the percentage of fat
in persons' bodies,

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so they immerse them in water
and then they weigh them

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and they compare that
with their regular weight.

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Let's look at an iceberg.

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Here is an iceberg.

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Here is the water--
it's floating in water.

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It has mass M,
it has a total volume V total,

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and the density of the ice
is rho ice,

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which is 0.92 in grams
per cubic centimeter.

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It's less than water.

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This is floating,
and so there's equilibrium

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between Mg
and the buoyant force.

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So Mg must be equal
to the buoyant force.

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Now, Mg is the total volume
times rho ice times g,

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just like the crown.

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The buoyant force is the volume
underwater, which is this part,

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times the density of water,
rho water, times g.

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You lose your g, and so you find

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that the volume underwater
divided by the total volume

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equals rho ice divided
by rho of water, which is 0.92.

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That means 92% of the iceberg
is underwater,

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and this explains something
about the tragedy

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on April 15, 1912,
when theTitanic hit an iceberg.

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When you encounter an iceberg,

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you literally only see
the tip of the iceberg.

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That's where the expression
comes from.

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92% is underwater.

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I want to return now
to my cylinder,

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and I want to ask myself
the question,

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when does that cylinder float?

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What is the condition
for floating?

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Well, clearly,
for that cylinder to float

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the buoyant force must be Mg,
and the buoyant force

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is the area times h--
that's the volume underwater--

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multiplied by the density
of the fluid times g

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must be the total volume
of the cylinder,

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which is the area times l,

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because that was
the length of the cylinder,

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times the density
of the object itself times g.

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I lose my A, I lose my g,

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but I know that h
must be less than l;

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otherwise it wouldn't
be floating, right?

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The part below the water
has to be smaller

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than the length of the cylinder.

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And if h is less than l,

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that means that
the density of the fluid

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must be larger than
the density of the object,

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and this is a necessary
condition for floating.

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And therefore,
if an object sinks

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then the density
of the object is larger

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than the density of the fluid.

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And the amazing thing is that
this is completely independent

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of the dimensions of the object.

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The only thing that matters
is the density.

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If you take a pebble
and you throw it in the water,

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it sinks, because the density of
a pebble is higher than water.

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If you take a piece of wood,

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which has a density lower
than water,

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and you throw it on water,
it floats

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independent of its shape.

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Whether it sinks
or whether it floats,

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the buoyant force
is always identical

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to the weight
of the displaced fluid.

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And this brings up
one of my favorite questions

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that I have for you
that I want you to think about.

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And if you have

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a full understanding now
of Archimedes' principle,

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you will be able to answer it,

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so concentrate on what I am
going to present you with.

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I am in a swimming pool,
and I'm in a boat.

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Here is the swimming pool
and here is the boat,

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and I am sitting in the boat

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and I have a rock
here in my boat.

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I'm sitting in the swimming
pool, nice rock in my boat.

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I mark the waterline of the
swimming pool very carefully.

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I take the rock
and I throw it overboard.

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Will the waterline go up,
or will the waterline go down,

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or maybe the waterline
will stay the same?

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Now, use your intuition--
don't mind being wrong.

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At home you have
some time to think about it,

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and I am sure you will come up
with the right answer.

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Who thinks that the waterline
will go up the swimming pool?

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Who thinks that the waterline
will go down?

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Who thinks that
it will make no difference,

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that the waterline stays
the same?

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Amazing-- okay.

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Well, the waterline will change,
but you figure it out.

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Okay, you apply
Archimedes' principle

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and you'll get the answer.

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I want to talk about stability,
particularly stability of ships,

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which is a very
important thing-- they float.

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Suppose I have an object here
which is floating in water.

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Here is the waterline,

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and let here be the center
of mass of that object.

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Could be way off center.

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It could be an iceberg,

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it could be boulders, it could
be rocks in there, right?

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It doesn't have to be
uniform density.

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The center of mass could be
off the center...

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of the geometric center.

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So if this object has
a certain mass,

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then this is
the gravitational force.

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But now look at the center of
mass fluid that is displaced.

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That's clearly more here,

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somewhere here,
the displaced fluid.

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That is
where the buoyant force acts.

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And so now what you have...

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You have a torque on this object

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relative to any point
that you choose.

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It doesn't matter where you pick
a point, you have a torque.

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And so what's going to happen,

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this object is clearly going
to rotate in this direction.

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And the torque will only be zero
when the buoyant force

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and the gravitational force
are on one line.

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Then the torque becomes zero,
and then it is completely happy.

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Now, there are two ways that
you can get them on one line.

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We discussed that earlier
in a different context.

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You can either have the center
of mass of the object

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below the center of mass of
the displaced fluid or above.

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In both cases would they be
on one line.

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However, in one case, there
would be stable equilibrium.

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In the other, there would
not be a stable equilibrium.

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I have here an object which has
its center of mass very low.

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You can't tell that--
no way of knowing.

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All you know is that the weight
of the displaced fluid

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that you see here is the same
as the weight of the object.

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That's all you know.

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If I took this object
and I tilt it a little

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with the center of mass
very low--

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so here is Mg and here is
somewhere the waterline--

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so the center of mass
of the displaced fluid

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is somewhere here, so
Fb is here, the buoyant force,

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you can see
what's going to happen.

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It's going to rotate towards the
right-- it's a restoring torque,

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and so it's completely stable.

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I can wobble it back and forth
and it is stable.

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If I would turn it over,
then it's not stable,

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because now I would have
the center of mass

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somewhere here, high up,
so now I have Mg.

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And the center of the buoyant
force, the displaced water,

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is about here, so now I have
the buoyant force up,

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and now you see
what's going to happen.

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I tilt it to the side,
and it will rotate even further.

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This torque will drive it
away from the vertical.

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And that's very important,
therefore, with ships,

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that you always build the ship

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such that the center
of mass of the ship is

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as low as you can get it.

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That gives you
the most stable configuration.

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If you bring the center of mass
of ships very high--

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in the 17th century, they had
these very massive cannons

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which were very high
on the deck--

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then the ship can capsize,
and it has happened many times

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because the center of mass
was just too high.

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So here... the center of mass
is somewhere here.

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Very heavy, this part.

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And so now, if I lower it
in the water

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notice it goes into the water
to the same depth,

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because the buoyant force is,
of course, the same,

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so the amount of displaced water
is the same in both cases.

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But now the center of mass is
high and this is very unstable.

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When I let it go, it flips over.

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So the center of mass
of the object was higher

280
00:16:27 --> 00:16:33
than the center of mass
of the displaced fluid.

281
00:16:30 --> 00:16:36
And so with ships, you have
to be very careful about that.

282
00:16:34 --> 00:16:40
 

283
00:16:38 --> 00:16:44
Let's talk a little bit
about balloons.

284
00:16:41 --> 00:16:47
 

285
00:16:45 --> 00:16:51
If I have a balloon, the
situation is not too dissimilar

286
00:16:52 --> 00:16:58
from having an object
floating in a liquid.

287
00:16:56 --> 00:17:02
Let the balloon have a mass M.

288
00:16:59 --> 00:17:05
That is the mass of the gas
in the balloon

289
00:17:04 --> 00:17:10
plus all the rest, and what
I mean by "all the rest"...

290
00:17:08 --> 00:17:14
That is the material
of the balloon and the string--

291
00:17:11 --> 00:17:17
everything else
that makes up the mass.

292
00:17:13 --> 00:17:19
It has a certain volume v,

293
00:17:16 --> 00:17:22
and so there is a certain rho
of the gas inside

294
00:17:20 --> 00:17:26
and there is rho of air outside.

295
00:17:23 --> 00:17:29
And I want to evaluate

296
00:17:25 --> 00:17:31
what the criterion is
for this balloon to rise.

297
00:17:29 --> 00:17:35
Well, for it to rise,

298
00:17:30 --> 00:17:36
the buoyant force will have
to be larger than Mg.

299
00:17:34 --> 00:17:40
What is the buoyant force?

300
00:17:36 --> 00:17:42
That is the weight
of the displaced fluid.

301
00:17:39 --> 00:17:45
The fluid, in this case, is air.

302
00:17:41 --> 00:17:47
So the weight
of the displaced fluid

303
00:17:43 --> 00:17:49
is the volume times
the density of the air--

304
00:17:47 --> 00:17:53
that's the fluid
in which it is now--

305
00:17:50 --> 00:17:56
times g,
that is the buoyant force.

306
00:17:53 --> 00:17:59
That's... the weight
of the displaced fluid

307
00:17:56 --> 00:18:02
has to be larger than Mg.

308
00:17:59 --> 00:18:05
Now, Mg is the mass of the gas,

309
00:18:02 --> 00:18:08
which is the volume of the gas
times the density of the gas.

310
00:18:09 --> 00:18:15
That's the mass times g--

311
00:18:12 --> 00:18:18
because we have to convert it
to a force--

312
00:18:14 --> 00:18:20
plus all the rest, times g.

313
00:18:19 --> 00:18:25
I lose my g, and what you see...

314
00:18:24 --> 00:18:30
that this, of course,
is always larger than zero.

315
00:18:28 --> 00:18:34
There's always some mass
associated with the skin

316
00:18:32 --> 00:18:38
and in this case
with the string.

317
00:18:35 --> 00:18:41
But you see, the only way
that this balloon can rise

318
00:18:39 --> 00:18:45
is that the density of the gas
must be smaller

319
00:18:43 --> 00:18:49
than the density of air.

320
00:18:44 --> 00:18:50
Density of the gas must be less
than the density of the air.

321
00:18:49 --> 00:18:55
This is a necessary condition
for this to hold.

322
00:18:52 --> 00:18:58
It is not
a sufficient condition,

323
00:18:55 --> 00:19:01
because I can take a balloon,

324
00:18:57 --> 00:19:03
put a little bit
of helium in there--

325
00:18:59 --> 00:19:05
so the density of the gas is
lower than the density of air--

326
00:19:04 --> 00:19:10
but it may not rise, and
that's because of this term.

327
00:19:08 --> 00:19:14
But it is a necessary condition
but not a sufficient condition.

328
00:19:13 --> 00:19:19
Now I'm going to make you see

329
00:19:15 --> 00:19:21
a demonstration
which is extremely nonintuitive,

330
00:19:19 --> 00:19:25
and I will try, step by step,
to explain to you

331
00:19:23 --> 00:19:29
why you see what you see.

332
00:19:25 --> 00:19:31
What you're going to see,
very nonintuitive,

333
00:19:28 --> 00:19:34
so try to follow closely
why you see what you will see.

334
00:19:34 --> 00:19:40
I have here a pendulum
with an apple,

335
00:19:38 --> 00:19:44
and here I have a balloon
filled with helium.

336
00:19:42 --> 00:19:48
I cut this string
and I cut this string.

337
00:19:44 --> 00:19:50
Gravity is in this direction.

338
00:19:46 --> 00:19:52
The apple will fall,
the balloon will rise.

339
00:19:49 --> 00:19:55
The balloon goes
in the opposite direction

340
00:19:52 --> 00:19:58
than the
gravitational acceleration.

341
00:19:55 --> 00:20:01
If there were no gravity,
this balloon would not rise

342
00:20:00 --> 00:20:06
and the apple would not fall.

343
00:20:03 --> 00:20:09
Do we agree so far?

344
00:20:04 --> 00:20:10
Without gravity, apple would not
fall, balloon would not rise.

345
00:20:09 --> 00:20:15
Now we go in outer space.

346
00:20:11 --> 00:20:17
 

347
00:20:16 --> 00:20:22
Here is a compartment
and here is an apple.

348
00:20:21 --> 00:20:27
 

349
00:20:24 --> 00:20:30
I'm here as well.

350
00:20:28 --> 00:20:34
None of us have weight,
there's no gravity,

351
00:20:31 --> 00:20:37
and here is a helium-filled
object, a balloon,

352
00:20:35 --> 00:20:41
and there's air inside.

353
00:20:36 --> 00:20:42
We're in outer space,
there's no gravity.

354
00:20:39 --> 00:20:45
Nothing has any weight.

355
00:20:42 --> 00:20:48
We're all floating.

356
00:20:44 --> 00:20:50
 

357
00:20:46 --> 00:20:52
Now I'm going to accelerate.

358
00:20:48 --> 00:20:54
I have a rocket-- I'm going to
accelerate it in this direction

359
00:20:53 --> 00:20:59
with acceleration a.

360
00:20:55 --> 00:21:01
We all perceive, now,
a perceived gravity

361
00:21:00 --> 00:21:06
in this direction.

362
00:21:02 --> 00:21:08
I call it g.

363
00:21:04 --> 00:21:10
So the apple will fall.

364
00:21:07 --> 00:21:13
I'm standing there,
I see this apple fall.

365
00:21:09 --> 00:21:15
I'm in this compartment,
closed compartment.

366
00:21:11 --> 00:21:17
I see the apple go down.

367
00:21:12 --> 00:21:18
A little later,
the apple will be here.

368
00:21:14 --> 00:21:20
I myself fall;
a little later, I'm there.

369
00:21:17 --> 00:21:23
I can put a bathroom scale here

370
00:21:19 --> 00:21:25
and weigh myself
on the bathroom scale.

371
00:21:22 --> 00:21:28
My weight will be
M times this a,

372
00:21:24 --> 00:21:30
M being my mass,
a being this acceleration.

373
00:21:26 --> 00:21:32
I really think that it is
gravity in this direction.

374
00:21:30 --> 00:21:36
The air wants to fall,

375
00:21:34 --> 00:21:40
but the balloon wants to go
against gravity.

376
00:21:38 --> 00:21:44
The balloon will rise.

377
00:21:41 --> 00:21:47
 

378
00:21:45 --> 00:21:51
The air wants to fall,
so inside here

379
00:21:49 --> 00:21:55
you create a differential
pressure between the bottom, P1,

380
00:21:55 --> 00:22:01
and the top of the air, P2,
inside here.

381
00:21:59 --> 00:22:05
Just like the atmosphere
on earth--

382
00:22:01 --> 00:22:07
the atmosphere is pushing
down on us--

383
00:22:04 --> 00:22:10
the pressure is here
higher than there.

384
00:22:06 --> 00:22:12
So you get P1 is higher than P2.

385
00:22:11 --> 00:22:17
 

386
00:22:13 --> 00:22:19
So you create yourself
an atmosphere,

387
00:22:16 --> 00:22:22
and the balloon will rise.

388
00:22:18 --> 00:22:24
The balloon goes in the opposite
direction of gravity.

389
00:22:22 --> 00:22:28
If there were no air in there,

390
00:22:25 --> 00:22:31
then clearly
all of us would fall:

391
00:22:27 --> 00:22:33
The apple would fall,
I would fall,

392
00:22:29 --> 00:22:35
and the helium balloon
would fall.

393
00:22:31 --> 00:22:37
The only reason
why the helium balloon rises

394
00:22:34 --> 00:22:40
is because the air is there

395
00:22:36 --> 00:22:42
and because you build up
this differential pressure.

396
00:22:40 --> 00:22:46
Now comes my question to you:

397
00:22:42 --> 00:22:48
Instead of accelerating
it upwards

398
00:22:46 --> 00:22:52
and creating
perceived gravity down,

399
00:22:49 --> 00:22:55
I'm now going to accelerate
it in this direction,

400
00:22:53 --> 00:22:59
something that I'm going to do
shortly in the classroom.

401
00:22:58 --> 00:23:04
I'm going to accelerate all
of us in this direction a.

402
00:23:03 --> 00:23:09
In which direction
will the apple go?

403
00:23:05 --> 00:23:11
In which direction
will the balloon go?

404
00:23:08 --> 00:23:14
What do you think?

405
00:23:11 --> 00:23:17
The apple will go

406
00:23:13 --> 00:23:19
in the direction
that it perceives gravity.

407
00:23:16 --> 00:23:22
The apple will go like this.

408
00:23:18 --> 00:23:24
I will go like this.

409
00:23:20 --> 00:23:26
The air wants to go like this.

410
00:23:22 --> 00:23:28
But helium-- balloon-- goes

411
00:23:24 --> 00:23:30
in the opposite direction
of gravity,

412
00:23:27 --> 00:23:33
so helium goes
in this direction.

413
00:23:29 --> 00:23:35
In fact, what you're doing,

414
00:23:30 --> 00:23:36
you're building here
an atmosphere

415
00:23:32 --> 00:23:38
where pressure P1 here
will be higher

416
00:23:34 --> 00:23:40
than the pressure P2 there.

417
00:23:36 --> 00:23:42
The air wants to go
in this direction.

418
00:23:39 --> 00:23:45
The pressure here is higher
than the pressure there--

419
00:23:43 --> 00:23:49
larger than zero.

420
00:23:45 --> 00:23:51
 

421
00:23:47 --> 00:23:53
If there's no air in there,
we would all fall.

422
00:23:50 --> 00:23:56
Helium would fall...
helium balloon would fall,

423
00:23:54 --> 00:24:00
apple would fall,
and I would fall.

424
00:23:56 --> 00:24:02
 

425
00:23:59 --> 00:24:05
I have here
an apple on a string

426
00:24:06 --> 00:24:12
in a closed compartment,
not unlike what we have there

427
00:24:12 --> 00:24:18
except I can't take you out

428
00:24:14 --> 00:24:20
to an area
where we have no gravity.

429
00:24:17 --> 00:24:23
So here is
that closed compartment,

430
00:24:20 --> 00:24:26
and here is the apple.

431
00:24:22 --> 00:24:28
There is gravity
in this direction.

432
00:24:25 --> 00:24:31
It wants to fall

433
00:24:27 --> 00:24:33
in that direction of gravity
if I cut the wire.

434
00:24:30 --> 00:24:36
Now I'm going to accelerate it
in this direction,

435
00:24:33 --> 00:24:39
and when I do that, I add a
perceived component of gravity

436
00:24:37 --> 00:24:43
in the opposite direction.

437
00:24:39 --> 00:24:45
So I add a perceived component
of gravity in this direction.

438
00:24:43 --> 00:24:49
So this apple wants to fall down

439
00:24:45 --> 00:24:51
because of the gravity
that I cannot avoid,

440
00:24:48 --> 00:24:54
and it wants to fall
in this direction.

441
00:24:50 --> 00:24:56
So what will the string do?

442
00:24:52 --> 00:24:58
It's very clear, very intuitive,

443
00:24:54 --> 00:25:00
no one has any problem with
that-- the string will do this.

444
00:24:59 --> 00:25:05
Now I have a balloon here.

445
00:25:01 --> 00:25:07
 

446
00:25:06 --> 00:25:12
Helium.

447
00:25:07 --> 00:25:13
There is gravity
in this direction.

448
00:25:09 --> 00:25:15
That's why the balloon
wants to go up.

449
00:25:11 --> 00:25:17
It opposes gravity.

450
00:25:13 --> 00:25:19
I'm going to accelerate the car
in this direction.

451
00:25:16 --> 00:25:22
I introduce perceived gravity
in this direction.

452
00:25:18 --> 00:25:24
What does the balloon
want to do?

453
00:25:20 --> 00:25:26
It wants to go against gravity.

454
00:25:21 --> 00:25:27
I build up in here, and it must
be a closed compartment...

455
00:25:24 --> 00:25:30
I must build up there
a pressure differential.

456
00:25:27 --> 00:25:33
The air wants to fall
in this direction.

457
00:25:29 --> 00:25:35
I build up a pressure here

458
00:25:31 --> 00:25:37
which is larger
than the pressure there.

459
00:25:33 --> 00:25:39
That's why it has to be
a closed compartment.

460
00:25:36 --> 00:25:42
What will
the helium balloon do?

461
00:25:39 --> 00:25:45
It will go like that.

462
00:25:40 --> 00:25:46
That is very nonintuitive.

463
00:25:42 --> 00:25:48
So I accelerate this car.

464
00:25:44 --> 00:25:50
As I will do,
the apple will go back,

465
00:25:46 --> 00:25:52
which is completely consistent
with all our intuition,

466
00:25:49 --> 00:25:55
but the helium balloon
will go forward.

467
00:25:52 --> 00:25:58
 

468
00:25:54 --> 00:26:00
Let's first do it
with the apple,

469
00:25:56 --> 00:26:02
which is totally consistent
with anyone's intuition.

470
00:26:00 --> 00:26:06
I'm going to make sure that the
apple is not swinging too much.

471
00:26:07 --> 00:26:13
Now, it only happens
during the acceleration,

472
00:26:10 --> 00:26:16
so it's only during the very
short portion that I accelerate

473
00:26:14 --> 00:26:20
that you see the apple go back,

474
00:26:16 --> 00:26:22
and then of course it starts
to swing-- forget that part.

475
00:26:19 --> 00:26:25
So watch closely-- only
the moment that I accelerate

476
00:26:22 --> 00:26:28
the apple will come this way.

477
00:26:23 --> 00:26:29
It goes in the direction

478
00:26:24 --> 00:26:30
of the extra component
of perceived gravity.

479
00:26:26 --> 00:26:32
Ready?

480
00:26:27 --> 00:26:33
 

481
00:26:29 --> 00:26:35
Boy, it almost hit
this glass here.

482
00:26:31 --> 00:26:37
Everyone could see that, right?

483
00:26:32 --> 00:26:38
Okay.

484
00:26:34 --> 00:26:40
Now we're going to do it
with the balloon.

485
00:26:37 --> 00:26:43
We're going
to take this one off.

486
00:26:39 --> 00:26:45
 

487
00:26:42 --> 00:26:48
And now let's take one
of our beautiful balloons.

488
00:26:45 --> 00:26:51
 

489
00:26:54 --> 00:27:00
We're going to put
a balloon in here.

490
00:26:57 --> 00:27:03
Has to be a closed compartment

491
00:26:58 --> 00:27:04
so that the air can build up
the pressure differential.

492
00:27:05 --> 00:27:11
 

493
00:27:13 --> 00:27:19
There's always problems

494
00:27:14 --> 00:27:20
with static charges
on these systems.

495
00:27:18 --> 00:27:24
Okay.

496
00:27:20 --> 00:27:26
Only as long as I accelerate

497
00:27:22 --> 00:27:28
will the balloon go
in a forward direction,

498
00:27:24 --> 00:27:30
so I accelerate
in this direction,

499
00:27:26 --> 00:27:32
and what you're going to see
is really very nonintuitive.

500
00:27:29 --> 00:27:35
Every time I see it,
I say to myself,

501
00:27:31 --> 00:27:37
"I can reason it,
but do I understand it?"

502
00:27:34 --> 00:27:40
I don't know,
what is the difference

503
00:27:35 --> 00:27:41
between reasoning
and understanding?

504
00:27:36 --> 00:27:42
There we go.

505
00:27:37 --> 00:27:43
 

506
00:27:39 --> 00:27:45
The balloon went this way.

507
00:27:41 --> 00:27:47
You can do this
in your car with your parents.

508
00:27:44 --> 00:27:50
It's really fun to do it.

509
00:27:46 --> 00:27:52
Have a string with an apple
or something else

510
00:27:48 --> 00:27:54
and have a helium balloon.

511
00:27:50 --> 00:27:56
Close the windows.

512
00:27:52 --> 00:27:58
They don't have to be totally
closed, but more or less,

513
00:27:56 --> 00:28:02
and ask your dad or your mom
to slam the brakes.

514
00:27:59 --> 00:28:05
If you slam the brakes,
what will happen?

515
00:28:02 --> 00:28:08
The apple will go...
what do you think?

516
00:28:05 --> 00:28:11
If you slam the brakes,

517
00:28:07 --> 00:28:13
the apple will go forwards,
balloon will go backward.

518
00:28:09 --> 00:28:15
If you accelerate the car
all of a sudden,

519
00:28:11 --> 00:28:17
the apple will go backwards
and the balloon will go forward.

520
00:28:14 --> 00:28:20
You can do that at home.

521
00:28:16 --> 00:28:22
You can enjoy... entertain
your parents at Thanksgiving.

522
00:28:20 --> 00:28:26
They'll get some
of their $25,000 tuition back.

523
00:28:24 --> 00:28:30
(class laughs )

524
00:28:25 --> 00:28:31
 

525
00:28:29 --> 00:28:35
When fluids are moving,

526
00:28:32 --> 00:28:38
situations are
way more complicated

527
00:28:36 --> 00:28:42
than when they are static.

528
00:28:39 --> 00:28:45
And this leads

529
00:28:40 --> 00:28:46
to, again, very nonintuitive
behavior of fluids.

530
00:28:49 --> 00:28:55
I will derive in a short-cut way

531
00:28:55 --> 00:29:01
a very famous equation which
is called Bernoulli's equation,

532
00:29:00 --> 00:29:06
which relates kinetic energy

533
00:29:04 --> 00:29:10
with potential energy
and pressure.

534
00:29:09 --> 00:29:15
Suppose I have a fluid,
noncompressible, like so.

535
00:29:17 --> 00:29:23
This cross-sectional area is A2
and the pressure here is P2.

536
00:29:26 --> 00:29:32
And I have a velocity
of that liquid which is v2

537
00:29:34 --> 00:29:40
and this level is y2.

538
00:29:36 --> 00:29:42
Here I have
a cross-sectional area A1.

539
00:29:41 --> 00:29:47
I have a pressure P1.

540
00:29:43 --> 00:29:49
My level is y1;
this is increasing y.

541
00:29:48 --> 00:29:54
And I have
a much larger velocity

542
00:29:50 --> 00:29:56
because the cross-section is
substantially smaller there.

543
00:29:54 --> 00:30:00
Now, if this fluid were
completely static,

544
00:29:57 --> 00:30:03
if it were not moving--

545
00:29:59 --> 00:30:05
so forget about the v1
and forget about the v2;

546
00:30:02 --> 00:30:08
it's just sitting still--

547
00:30:04 --> 00:30:10
then P1 minus P2 would be
rho g times y2 minus y1

548
00:30:13 --> 00:30:19
if rho is the density
of the fluid.

549
00:30:16 --> 00:30:22
That's Pascal's Law.

550
00:30:18 --> 00:30:24
So it would
just be sitting still,

551
00:30:20 --> 00:30:26
and we know
that the pressure here

552
00:30:23 --> 00:30:29
would be lower
than the pressure there.

553
00:30:25 --> 00:30:31
This is also,
if you want to, rho gh

554
00:30:29 --> 00:30:35
if you call this distance h.

555
00:30:34 --> 00:30:40
 

556
00:30:36 --> 00:30:42
Rho gh--
that reminds me of mgh,

557
00:30:39 --> 00:30:45
and mgh is gravitational
potential energy.

558
00:30:43 --> 00:30:49
When I divide m by volume,
I get density.

559
00:30:47 --> 00:30:53
So this is really a term

560
00:30:50 --> 00:30:56
which is gravitational
potential energy

561
00:30:54 --> 00:31:00
per unit volume.

562
00:30:56 --> 00:31:02
That makes the m divided
by volume become density.

563
00:31:01 --> 00:31:07
Therefore, pressure itself
must also have

564
00:31:05 --> 00:31:11
the dimension of energy
per unit volume.

565
00:31:10 --> 00:31:16
And if we now set
this whole machine in motion,

566
00:31:13 --> 00:31:19
then there are three players:

567
00:31:16 --> 00:31:22
There is, on the one hand,
kinetic energy-- of motion--

568
00:31:20 --> 00:31:26
kinetic energy...
I take it, per unit volume.

569
00:31:24 --> 00:31:30
There is gravitational
potential energy...

570
00:31:28 --> 00:31:34
I will take it, per unit volume.

571
00:31:30 --> 00:31:36
And then there is pressure.

572
00:31:32 --> 00:31:38
They're equal partners.

573
00:31:34 --> 00:31:40
 

574
00:31:36 --> 00:31:42
And if I apply
the conservation of energy,

575
00:31:39 --> 00:31:45
the sum of these three
should remain constant.

576
00:31:42 --> 00:31:48
That's the idea
behind Bernoulli's law,

577
00:31:45 --> 00:31:51
Bernoulli's equation.

578
00:31:47 --> 00:31:53
When I take a fluid element

579
00:31:49 --> 00:31:55
and I move it from one position
in the tube to another position,

580
00:31:54 --> 00:32:00
it trades speed for
either height or for pressure.

581
00:31:58 --> 00:32:04
What is the kinetic energy
per unit volume?

582
00:32:01 --> 00:32:07
Well, the kinetic energy
is one-half mv squared.

583
00:32:05 --> 00:32:11
I divide by volume,
I get one-half rho v squared.

584
00:32:08 --> 00:32:14
What is gravitational
potential energy?

585
00:32:10 --> 00:32:16
That is mgy.

586
00:32:12 --> 00:32:18
I divide by volume,
and so I get rho gy

587
00:32:16 --> 00:32:22
plus the pressure
at that location y,

588
00:32:20 --> 00:32:26
and that must be a constant.

589
00:32:23 --> 00:32:29
And this, now, is
Bernoulli's equation.

590
00:32:30 --> 00:32:36
It is a conservation
of energy equation.

591
00:32:37 --> 00:32:43
And as I will show you,

592
00:32:39 --> 00:32:45
it has very
remarkable consequences.

593
00:32:42 --> 00:32:48
 

594
00:32:46 --> 00:32:52
First I will show you an example
whereby I keep y constant.

595
00:32:52 --> 00:32:58
So I have a tube
which changes diameter,

596
00:32:57 --> 00:33:03
but the tube is not changing
with level y, as I do there.

597
00:33:05 --> 00:33:11
So I come in here,
cross-sectional area A1.

598
00:33:12 --> 00:33:18
I widen it,
cross-sectional area A2.

599
00:33:17 --> 00:33:23
 

600
00:33:20 --> 00:33:26
This is y--
it's the same for both.

601
00:33:23 --> 00:33:29
I have here inside pressure P1

602
00:33:26 --> 00:33:32
and here inside
I have pressure P2

603
00:33:29 --> 00:33:35
and this is the density
of the fluid.

604
00:33:33 --> 00:33:39
There is here a velocity v2,
and there is here a velocity v1.

605
00:33:39 --> 00:33:45
And clearly v1 is
way larger than v2

606
00:33:42 --> 00:33:48
because A1 times v1
must be A2 times v2

607
00:33:46 --> 00:33:52
because the fluid
is incompressible.

608
00:33:50 --> 00:33:56
So the same amount of matter

609
00:33:52 --> 00:33:58
that flows through here
in one second

610
00:33:54 --> 00:34:00
must flow through here
in one second.

611
00:33:56 --> 00:34:02
And so these have to be
the same,

612
00:33:58 --> 00:34:04
and since A1 is
much smaller than A2,

613
00:34:01 --> 00:34:07
this velocity is
much larger than v2.

614
00:34:05 --> 00:34:11
 

615
00:34:08 --> 00:34:14
Now I'm going to apply
Bernoulli's equation.

616
00:34:12 --> 00:34:18
So the first term tells me
that one-half rho v1 squared...

617
00:34:17 --> 00:34:23
I can forget the second term

618
00:34:19 --> 00:34:25
because I get the same term
here as I get there

619
00:34:21 --> 00:34:27
because I measure
the pressure here

620
00:34:23 --> 00:34:29
and I measure
the pressure there.

621
00:34:24 --> 00:34:30
They have the same level of y.

622
00:34:25 --> 00:34:31
So I can ignore the second term.

623
00:34:29 --> 00:34:35
Plus P1 must be one-half rho
v2 squared plus P2.

624
00:34:36 --> 00:34:42
That's what
Bernoulli's equation tells me.

625
00:34:41 --> 00:34:47
Now, v1 is larger than v2.

626
00:34:47 --> 00:34:53
The only way that
this can be correct, then,

627
00:34:49 --> 00:34:55
is that P1 must be
less than P2.

628
00:34:51 --> 00:34:57
So you will say, "Big deal."

629
00:34:53 --> 00:34:59
Well, it's a big deal,
because I would have guessed

630
00:34:56 --> 00:35:02
exactly the other way around,
and so would you,

631
00:34:58 --> 00:35:04
because here is where
the highest velocity is,

632
00:35:00 --> 00:35:06
and all our instincts would say,

633
00:35:02 --> 00:35:08
"Oh, if the velocity is high,
there's a lot of pressure."

634
00:35:05 --> 00:35:11
It's exactly
the other way around.

635
00:35:07 --> 00:35:13
Here is the low pressure,
and here is the high pressure,

636
00:35:10 --> 00:35:16
which is one
quite bizarre consequence

637
00:35:12 --> 00:35:18
of Bernoulli's equation.

638
00:35:16 --> 00:35:22
 

639
00:35:20 --> 00:35:26
You must all have encountered
in your life

640
00:35:24 --> 00:35:30
what we call a siphon.

641
00:35:26 --> 00:35:32
They were used in the medieval
and they're still used today.

642
00:35:31 --> 00:35:37
You have here...

643
00:35:34 --> 00:35:40
A bucket in general is used
with water-- lakes.

644
00:35:38 --> 00:35:44
We have water here,
but it could be any liquid.

645
00:35:42 --> 00:35:48
And I stick in here a tube
which is small in diameter,

646
00:35:49 --> 00:35:55
substantially smaller
than this area here.

647
00:35:52 --> 00:35:58
And there will be water in here
up to this level--

648
00:35:58 --> 00:36:04
this level P2, y2.

649
00:36:04 --> 00:36:10
This is y1,
increasing value of y.

650
00:36:09 --> 00:36:15
This height difference is h.

651
00:36:11 --> 00:36:17
P2 is one atmosphere.

652
00:36:13 --> 00:36:19
I put a one there--
it's atmosphere.

653
00:36:16 --> 00:36:22
And here, if it's open,
then P1 is also one atmosphere.

654
00:36:21 --> 00:36:27
So there's air in here
and there's liquid in here.

655
00:36:26 --> 00:36:32
I take this open end in my mouth
and I suck the water in

656
00:36:31 --> 00:36:37
so that it's filled with this
water, full with this water.

657
00:36:37 --> 00:36:43
And strange as it may be, it's
like making a hole in this tank.

658
00:36:43 --> 00:36:49
If I take my finger off here,
the water will start to run out,

659
00:36:47 --> 00:36:53
and I will show you that.

660
00:36:48 --> 00:36:54
And you have here
a velocity v1.

661
00:36:52 --> 00:36:58
The water will stream down
into this here

662
00:36:55 --> 00:37:01
and the velocity here
is approximately zero,

663
00:36:59 --> 00:37:05
because this area is
so much larger

664
00:37:01 --> 00:37:07
than this cross-sectional area
that to a good approximation

665
00:37:06 --> 00:37:12
this water is going down
extremely slowly.

666
00:37:09 --> 00:37:15
 

667
00:37:11 --> 00:37:17
Let's call this
height difference d.

668
00:37:16 --> 00:37:22
I apply Bernoulli's law.

669
00:37:17 --> 00:37:23
So now we have a situation
where the y's are different

670
00:37:21 --> 00:37:27
but the pressure is the same,

671
00:37:23 --> 00:37:29
because right here
at this point of the liquid

672
00:37:26 --> 00:37:32
I have one atmosphere,
which is barometric pressure,

673
00:37:29 --> 00:37:35
and since this is open
with the outside world,

674
00:37:32 --> 00:37:38
P1 is also one atmosphere.

675
00:37:33 --> 00:37:39
So now I lose my P term.

676
00:37:35 --> 00:37:41
There I lost my y term;
now I lose my P term.

677
00:37:39 --> 00:37:45
So now I have
that one-half rho... rho--

678
00:37:43 --> 00:37:49
this is rho of the liquid--

679
00:37:47 --> 00:37:53
v1 squared plus rho g times y1
must be one-half rho v2 squared,

680
00:37:57 --> 00:38:03
but we agreed that that was
zero, so I don't have that term.

681
00:38:01 --> 00:38:07
So I only have rho gy2.

682
00:38:07 --> 00:38:13
I lose my g's...
no, I don't lose my g's.

683
00:38:10 --> 00:38:16
One-half rho v squared--
no, that's fine.

684
00:38:13 --> 00:38:19
And so... I lose my rho.

685
00:38:15 --> 00:38:21
This is one-half.

686
00:38:17 --> 00:38:23
I lose my rho.

687
00:38:18 --> 00:38:24
And so you get

688
00:38:20 --> 00:38:26
that one-half v1 squared equals
g times y2 minus y1, which is h.

689
00:38:27 --> 00:38:33
And so what do you find?

690
00:38:29 --> 00:38:35
That the speed with which this
water is running out here, v1,

691
00:38:33 --> 00:38:39
is the square root of 2gh.

692
00:38:36 --> 00:38:42
And you've seen that before.

693
00:38:39 --> 00:38:45
If you take a pebble and you
release a pebble from this level

694
00:38:43 --> 00:38:49
and you let it fall,

695
00:38:44 --> 00:38:50
it will reach this point here,
this level

696
00:38:47 --> 00:38:53
with the speed
the square root of 2gh.

697
00:38:50 --> 00:38:56
We've seen that many times.

698
00:38:52 --> 00:38:58
So what is happening here--

699
00:38:54 --> 00:39:00
since the pressure terms are
the same here and there,

700
00:38:57 --> 00:39:03
now there's only a conversion.

701
00:38:59 --> 00:39:05
Gravitational potential energy--

702
00:39:01 --> 00:39:07
which is higher here
than there--

703
00:39:02 --> 00:39:08
is now converted
to kinetic energy.

704
00:39:07 --> 00:39:13
This siphon would only work
if d is less than ten meters.

705
00:39:12 --> 00:39:18
Because of
the barometric pressure

706
00:39:14 --> 00:39:20
you can never suck up
this water--

707
00:39:16 --> 00:39:22
no one can;
a vacuum pump can't either--

708
00:39:18 --> 00:39:24
to a level that is higher
than ten meters.

709
00:39:21 --> 00:39:27
When I did the experiment
there with the cranberry juice,

710
00:39:24 --> 00:39:30
I was able to get it up
to five meters,

711
00:39:26 --> 00:39:32
but ten meters would have been
the theoretical maximum.

712
00:39:30 --> 00:39:36
So this has to be less than
ten meters that you go up.

713
00:39:33 --> 00:39:39
If I would have made a hole
in this tank here,

714
00:39:37 --> 00:39:43
just like this,
down to exactly this level,

715
00:39:40 --> 00:39:46
and I would have asked you
to calculate

716
00:39:42 --> 00:39:48
with what speed the water
is running out,

717
00:39:45 --> 00:39:51
you would have found
exactly the same

718
00:39:47 --> 00:39:53
if you had applied
Bernoulli's equation.

719
00:39:49 --> 00:39:55
This is a way that people...

720
00:39:51 --> 00:39:57
I've seen people steal
other people's gasoline

721
00:39:53 --> 00:39:59
in the time
that gasoline was very scarce

722
00:39:56 --> 00:40:02
and that there were no locks yet
on the gasoline caps.

723
00:39:59 --> 00:40:05
You would put a hose
in the gasoline tank

724
00:40:01 --> 00:40:07
and you would have
to suck on it a little--

725
00:40:03 --> 00:40:09
you have to sacrifice
a little bit--

726
00:40:04 --> 00:40:10
you get a little bit
of gasoline in your mouth,

727
00:40:07 --> 00:40:13
and then you can just empty
someone's gasoline tank

728
00:40:10 --> 00:40:16
by having a canister
or by having a jerrican

729
00:40:13 --> 00:40:19
and fill it with gasoline.

730
00:40:15 --> 00:40:21
And I'm going to show that now
to you by emptying...

731
00:40:19 --> 00:40:25
That's still cranberry juice, by
the way, from our last lecture.

732
00:40:26 --> 00:40:32
So let's put this up on a stool.

733
00:40:30 --> 00:40:36
 

734
00:40:32 --> 00:40:38
So there is the hose--
it's that thing--

735
00:40:39 --> 00:40:45
and I'm going to transfer
this liquid from here to here.

736
00:40:43 --> 00:40:49
So first I have to fill it
with cranberry juice.

737
00:40:46 --> 00:40:52
 

738
00:40:50 --> 00:40:56
And there it goes.

739
00:40:52 --> 00:40:58
And as long as this level
is below that level,

740
00:40:56 --> 00:41:02
it keeps running.

741
00:40:59 --> 00:41:05
Not so intuitive.

742
00:41:00 --> 00:41:06
I remember,
I was at a summer camp

743
00:41:03 --> 00:41:09
when I was maybe
six or seven years old.

744
00:41:05 --> 00:41:11
I couldn't believe it when
I saw this for the first time.

745
00:41:10 --> 00:41:16
We had these outdoor sinks

746
00:41:11 --> 00:41:17
where we washed ourselves
and brushed our teeth,

747
00:41:14 --> 00:41:20
and the sink was clogged,
it was full with water.

748
00:41:17 --> 00:41:23
And one of the camp leaders
took a hose, sucked up

749
00:41:21 --> 00:41:27
and it emptied itself.

750
00:41:22 --> 00:41:28
And I really thought, you know,

751
00:41:24 --> 00:41:30
you'd have to take spoonfuls
of water or maybe buckets

752
00:41:27 --> 00:41:33
and scoop it out.

753
00:41:28 --> 00:41:34
This is the way you do it.

754
00:41:30 --> 00:41:36
Very nonintuitive.

755
00:41:31 --> 00:41:37
The nonintuitive part is

756
00:41:33 --> 00:41:39
that it runs up
against gravity there.

757
00:41:36 --> 00:41:42
So we can let it sit there

758
00:41:37 --> 00:41:43
and we have a transfer, mass
transfer of cranberry juice.

759
00:41:42 --> 00:41:48
 

760
00:41:57 --> 00:42:03
Last time I was testing my lungs
to see how strong I was.

761
00:42:01 --> 00:42:07
I wasn't very good, right?

762
00:42:03 --> 00:42:09
I could only blow up
one meter of water

763
00:42:05 --> 00:42:11
and only suck one meter water.

764
00:42:08 --> 00:42:14
Differential pressure
only one-tenth of an atmosphere.

765
00:42:11 --> 00:42:17
Today I would like to test
one of the students

766
00:42:15 --> 00:42:21
who, no doubt, is
more powerful than I am.

767
00:42:19 --> 00:42:25
And I have here a funnel...

768
00:42:25 --> 00:42:31
with a Ping-Pong ball here,
very lightweight,

769
00:42:28 --> 00:42:34
and we're going
to have a contest

770
00:42:30 --> 00:42:36
to see who can blow it
the highest.

771
00:42:32 --> 00:42:38
I have two funnels,
so it's very hygienic.

772
00:42:35 --> 00:42:41
I will try it with this one.

773
00:42:37 --> 00:42:43
They're clean, they just...

774
00:42:38 --> 00:42:44
We just got them
from the chemistry department.

775
00:42:41 --> 00:42:47
And so I would like to see
a volunteer--

776
00:42:43 --> 00:42:49
woman or man, it doesn't matter.

777
00:42:45 --> 00:42:51
You want to try it, see whether
you can reach the ceiling?

778
00:42:50 --> 00:42:56
You don't want to try it?

779
00:42:52 --> 00:42:58
Come on! You want to try it?

780
00:42:54 --> 00:43:00
You're shy? You don't want to?

781
00:42:57 --> 00:43:03
Can I persuade you? I can.

782
00:43:00 --> 00:43:06
Okay, come along.

783
00:43:01 --> 00:43:07
Come right here.

784
00:43:03 --> 00:43:09
You think you can make it
to the ceiling?

785
00:43:06 --> 00:43:12
It's only
a very light Ping-Pong ball.

786
00:43:08 --> 00:43:14
So, you go like this,
blow as hard as you can.

787
00:43:12 --> 00:43:18
STUDENT:
Okay.

788
00:43:13 --> 00:43:19
LEWIN:
Try it, don't be nervous.

789
00:43:15 --> 00:43:21
STUDENT:
All right.

790
00:43:16 --> 00:43:22
LEWIN:
Straight up.

791
00:43:18 --> 00:43:24
STUDENT:
No...

792
00:43:19 --> 00:43:25
LEWIN:
Blow as hard as you can--
get it out.

793
00:43:21 --> 00:43:27
Amazing! Do it again.

794
00:43:23 --> 00:43:29
Come on, there must have been
something wrong.

795
00:43:25 --> 00:43:31
(class laughs )

796
00:43:26 --> 00:43:32
LEWIN:
You're not sick today, are you?

797
00:43:29 --> 00:43:35
Blow.

798
00:43:30 --> 00:43:36
Harder!

799
00:43:32 --> 00:43:38
STUDENT:
Is this a trick?

800
00:43:33 --> 00:43:39
LEWIN:
No, there's nothing,
there's no trick in here.

801
00:43:35 --> 00:43:41
I mean, my goodness--

802
00:43:36 --> 00:43:42
this is a Ping-Pong ball,
I'm not a magician.

803
00:43:38 --> 00:43:44
(class laughs )

804
00:43:39 --> 00:43:45
LEWIN:
Come on, blow it up!

805
00:43:42 --> 00:43:48
Hey, it doesn't work.

806
00:43:44 --> 00:43:50
It's amazing.

807
00:43:45 --> 00:43:51
Why don't you sit down?

808
00:43:47 --> 00:43:53
(class laughs )

809
00:43:50 --> 00:43:56
LEWIN:
Why doesn't it work?

810
00:43:52 --> 00:43:58
Why doesn't it work?

811
00:43:53 --> 00:43:59
The harder you blow,
the least it will work.

812
00:43:57 --> 00:44:03
Air is flowing here...

813
00:44:02 --> 00:44:08
and right here,
where there is very little room,

814
00:44:05 --> 00:44:11
the air will have
very high speed,

815
00:44:08 --> 00:44:14
way higher than it has
where it has lots of room.

816
00:44:11 --> 00:44:17
And so at the highest speed,
you get the lowest pressure.

817
00:44:16 --> 00:44:22
And so the Ping-Pong ball
is sucked in

818
00:44:19 --> 00:44:25
while you're blowing it.

819
00:44:21 --> 00:44:27
And to give you
the conclusive proof of that

820
00:44:24 --> 00:44:30
I will do it this way.

821
00:44:26 --> 00:44:32
 

822
00:44:29 --> 00:44:35
I will put
the Ping-Pong ball like so,

823
00:44:33 --> 00:44:39
and I'm going to blow like this,
and if I blow hard enough,

824
00:44:36 --> 00:44:42
the Ping-Pong ball
will stay in there

825
00:44:39 --> 00:44:45
because I generate
a lower pressure right here

826
00:44:43 --> 00:44:49
where the passage
is the smallest,

827
00:44:45 --> 00:44:51
but I have to blow quite hard.

828
00:44:47 --> 00:44:53
(inhales deeply, blowing hard )

829
00:44:51 --> 00:44:57
You see that?
Isn't that amazing?

830
00:44:53 --> 00:44:59
That's the reason
why she couldn't get it up.

831
00:44:56 --> 00:45:02
(inhales deeply, blowing hard )

832
00:45:01 --> 00:45:07
That's what Bernoulli
does for you.

833
00:45:03 --> 00:45:09
Not so intuitive, is it?

834
00:45:04 --> 00:45:10
 

835
00:45:07 --> 00:45:13
I have here an air flow,
a hose with air coming out,

836
00:45:13 --> 00:45:19
and I can show you there

837
00:45:14 --> 00:45:20
something that is
equally nonintuitive.

838
00:45:17 --> 00:45:23
 

839
00:45:21 --> 00:45:27
Let's start the air flow.

840
00:45:24 --> 00:45:30
(air hissing )

841
00:45:25 --> 00:45:31
It's coming out.

842
00:45:26 --> 00:45:32
 

843
00:45:29 --> 00:45:35
I take a Ping-Pong ball.

844
00:45:31 --> 00:45:37
 

845
00:45:34 --> 00:45:40
It stays there.

846
00:45:38 --> 00:45:44
Is that due
to Mr. Bernoulli? No.

847
00:45:41 --> 00:45:47
No, that's
more complicated physics,

848
00:45:44 --> 00:45:50
because it has to do
with turbulence.

849
00:45:46 --> 00:45:52
It has to do with vortices,
which is very difficult.

850
00:45:49 --> 00:45:55
What is happening here

851
00:45:51 --> 00:45:57
is that as the air flows,
you get turbulence above here

852
00:45:54 --> 00:46:00
and the turbulence creates
a lower pressure.

853
00:45:59 --> 00:46:05
So the vortices, which are the
turbulence, are keeping this up,

854
00:46:02 --> 00:46:08
because there's a lower pressure
here and there.

855
00:46:05 --> 00:46:11
But why is it so stable?

856
00:46:08 --> 00:46:14
I can see that I have...

857
00:46:10 --> 00:46:16
because of this turbulence,
that it's held up.

858
00:46:13 --> 00:46:19
Why is it so stable?

859
00:46:14 --> 00:46:20
If I give it a little push

860
00:46:15 --> 00:46:21
it doesn't...
it's sucked back in again.

861
00:46:20 --> 00:46:26
It's very stable--
that is Bernoulli.

862
00:46:22 --> 00:46:28
Because if I blow air,
like so...

863
00:46:28 --> 00:46:34
 

864
00:46:32 --> 00:46:38
then the velocity here
is the highest,

865
00:46:35 --> 00:46:41
because it's diverging
the air as it's coming out,

866
00:46:38 --> 00:46:44
but in the center,
it is the highest,

867
00:46:40 --> 00:46:46
and so when this Ping-Pong ball
goes to this side,

868
00:46:43 --> 00:46:49
it clearly has a lower pressure
here than there

869
00:46:46 --> 00:46:52
and so it's being sucked
back in again.

870
00:46:48 --> 00:46:54
So the stability is due
to Bernoulli,

871
00:46:50 --> 00:46:56
but the fact that it is held up
is more difficult physics.

872
00:46:54 --> 00:47:00
It is so stable
that I can even tilt this...

873
00:46:57 --> 00:47:03
 

874
00:47:01 --> 00:47:07
and it will still stay there.

875
00:47:04 --> 00:47:10
 

876
00:47:06 --> 00:47:12
Now I have something

877
00:47:07 --> 00:47:13
that I want you to show
your parents on Thanksgiving.

878
00:47:11 --> 00:47:17
It's a little present for them,

879
00:47:14 --> 00:47:20
and that is something that
you can very easily do at home.

880
00:47:19 --> 00:47:25
You take a glass and you fill
it with cranberry juice--

881
00:47:24 --> 00:47:30
not all the way, up to here.

882
00:47:30 --> 00:47:36
Take a thin piece of cardboard,

883
00:47:33 --> 00:47:39
the kind of stuff that you
have on the back of pads.

884
00:47:36 --> 00:47:42
You put it on top.

885
00:47:37 --> 00:47:43
The table is beautifully set--
turkey, everything is there--

886
00:47:41 --> 00:47:47
and you suggest to your parents
that you turn this over.

887
00:47:45 --> 00:47:51
Your mother will scream
bloody murder,

888
00:47:47 --> 00:47:53
because she would think

889
00:47:49 --> 00:47:55
that the cranberry juice
will fall out.

890
00:47:51 --> 00:47:57
In fact,
itmay actually fall out.

891
00:47:53 --> 00:47:59
I can't guarantee you
that it won't.

892
00:47:56 --> 00:48:02
(class laughs )

893
00:47:57 --> 00:48:03
 

894
00:47:59 --> 00:48:05
LEWIN:
But it may not, in which case

895
00:48:02 --> 00:48:08
you now have all the tools
to explain that.

896
00:48:06 --> 00:48:12
 

897
00:48:11 --> 00:48:17
Please do invite me
to your Thanksgiving dinner

898
00:48:14 --> 00:48:20
and I'll show it
to your parents.

899
00:48:15 --> 00:48:21

900
00:48:17 --> 00:48:23