Today we're going to continue
with playing with liquids.
If I have an object that floats,
a simple cylinder
that floats in some liquid,
the area is A here,
the mass of the cylinder is M.
The density of the cylinder
is rho and its length is l
and the surface area is A.
So this is l.
And let the liquid line be here,
and the fluid has
a density rho fluid.
I call this level y1,
this level y2.
The separation is h,
and right on top here, there is
the atmospheric pressure P2,
which is the same
as it is here on the liquid.
And here we have a pressure P1
in the liquid.
For this object to float
we need equilibrium between,
on the one hand, the force Mg
and the buoyant force.
There is a force up here
which I call F1,
and there is a force down here
which I call F2--
barometric pressure.
The force is always
perpendicular to the surface.
There couldn't be
any tangential component
because then the air starts
to flow, and it's static.
And here we have F1,
which contains
the hydrostatic pressure.
So P1 minus P2-- as we learned
last time from Pascal--
equals rho of the fluid
g to the minus y2 minus y1,
which is h.
So that's the difference
between the pressure P1 and P2.
For this to be in equilibrium,
F1 minus F2 minus Mg
has to be zero,
and this we call
the buoyant force.
And "buoyant" is spelt in a
very strange way: b-u-o-y-a-n-t.
I always have to think
about that.
It's the buoyant force.
F1 equals the area times P1
and F2 is the area times P2,
so it is the area
times P1 minus P2,
and that is rho fluids
times g times h.
And when you look at this,
this is exactly the weight
of the displaced fluid.
The area times h
is the volume of the fluid which
is displaced by this cylinder,
and you multiply it by its
density, that gives it mass.
Multiply it by g,
that gives it weight.
So this is the weight
of the displaced fluids.
And this is a very special case
of a general principle
which is called
Archimedes' principle.
Archimedes' principle
is as follows:
The buoyant force on an immersed
body has the same magnitude
as the weight of the fluid
which is displaced by the body.
According to legend
Archimedes thought about this
while he was taking a bath,
and I have a picture
of that here--
I don't know
from when that dates--
but you see him there
in his bath,
but what you also see
are there are two crowns.
And there is a reason
why those crowns are there.
Archimedes lived
in the third century B.C.
Archimedes had been given
the task
to determine whether a crown
that was made for King Hieron II
was pure gold.
The problem for him was
to determine
the density of this crown--
which is a very
irregular-shaped object--
without destroying it.
And the legend has it
that as Archimedes was taking
a bath, he found the solution.
He rushed naked
through the streets of Syracuse
and he shouted,
"Eureka! Eureka! Eureka!"
which means,
"I found it! I found it!"
What did he find?
What did he think of?
He had the great vision
to do the following:
You take the crown and you
weigh it in a normal way.
So the weight of the crown--
I call it W1--
is the volume of the crown times
the density of which it is made.
If it is gold,
it should be 19.3, I believe,
and so this is
the mass of the crown
and this is the weight
of the crown.
Now he takes the crown
and he immerses it in water.
And he has a spring balance,
and he weighs it again.
And he finds
that the weight is less
and so now we have
the weight immersed in water.
So what you get is
the weight of the crown
minus the buoyant force,
which is the weight
of the displaced fluid.
And the weight
of the displaced fluid
is the volume of the crown--
because the crown is where...
the water has been removed
where the crown is--
times the density
of the fluid--
which is water, which he knew
very well-- times g.
And so this part here is
weight loss.
That's the loss of weight.
You can see that, you can
measure that with a spring.
It's lost weight,
because of the buoyant force.
And so now what he does,
he takes W1 and divides that
by the weight loss
and that gives you this term
divided by this term,
which immediately gives you
rho of the crown divided
by rho of the water.
And he knows rho of the water,
so he can find rho of the crown.
It's an amazing idea;
he was a genius.
I don't know
how the story ended,
whether it was gold or not.
It probably was, because chances
are that if it hadn't been gold
that the king would have
killed him-- for no good reason,
but that's the way these things
worked in those days.
This method is also used
to measure the percentage of fat
in persons' bodies,
so they immerse them in water
and then they weigh them
and they compare that
with their regular weight.
Let's look at an iceberg.
Here is an iceberg.
Here is the water--
it's floating in water.
It has mass M,
it has a total volume V total,
and the density of the ice
is rho ice,
which is 0.92 in grams
per cubic centimeter.
It's less than water.
This is floating,
and so there's equilibrium
between Mg
and the buoyant force.
So Mg must be equal
to the buoyant force.
Now, Mg is the total volume
times rho ice times g,
just like the crown.
The buoyant force is the volume
underwater, which is this part,
times the density of water,
rho water, times g.
You lose your g, and so you find
that the volume underwater
divided by the total volume
equals rho ice divided
by rho of water, which is 0.92.
That means 92% of the iceberg
is underwater,
and this explains something
about the tragedy
on April 15, 1912,
when the Titanic hit an iceberg.
When you encounter an iceberg,
you literally only see
the tip of the iceberg.
That's where the expression
comes from.
92% is underwater.
I want to return now
to my cylinder,
and I want to ask myself
the question,
when does that cylinder float?
What is the condition
for floating?
Well, clearly,
for that cylinder to float
the buoyant force must be Mg,
and the buoyant force
is the area times h--
that's the volume underwater--
multiplied by the density
of the fluid times g
must be the total volume
of the cylinder,
which is the area times l,
because that was
the length of the cylinder,
times the density
of the object itself times g.
I lose my A, I lose my g,
but I know that h
must be less than l;
otherwise it wouldn't
be floating, right?
The part below the water
has to be smaller
than the length of the cylinder.
And if h is less than l,
that means that
the density of the fluid
must be larger than
the density of the object,
and this is a necessary
condition for floating.
And therefore,
if an object sinks
then the density
of the object is larger
than the density of the fluid.
And the amazing thing is that
this is completely independent
of the dimensions of the object.
The only thing that matters
is the density.
If you take a pebble
and you throw it in the water,
it sinks, because the density of
a pebble is higher than water.
If you take a piece of wood,
which has a density lower
than water,
and you throw it on water,
it floats
independent of its shape.
Whether it sinks
or whether it floats,
the buoyant force
is always identical
to the weight
of the displaced fluid.
And this brings up
one of my favorite questions
that I have for you
that I want you to think about.
And if you have
a full understanding now
of Archimedes' principle,
you will be able to answer it,
so concentrate on what I am
going to present you with.
I am in a swimming pool,
and I'm in a boat.
Here is the swimming pool
and here is the boat,
and I am sitting in the boat
and I have a rock
here in my boat.
I'm sitting in the swimming
pool, nice rock in my boat.
I mark the waterline of the
swimming pool very carefully.
I take the rock
and I throw it overboard.
Will the waterline go up,
or will the waterline go down,
or maybe the waterline
will stay the same?
Now, use your intuition--
don't mind being wrong.
At home you have
some time to think about it,
and I am sure you will come up
with the right answer.
Who thinks that the waterline
will go up the swimming pool?
Who thinks that the waterline
will go down?
Who thinks that
it will make no difference,
that the waterline stays
the same?
Amazing-- okay.
Well, the waterline will change,
but you figure it out.
Okay, you apply
Archimedes' principle
and you'll get the answer.
I want to talk about stability,
particularly stability of ships,
which is a very
important thing-- they float.
Suppose I have an object here
which is floating in water.
Here is the waterline,
and let here be the center
of mass of that object.
Could be way off center.
It could be an iceberg,
it could be boulders, it could
be rocks in there.
Right? It doesn't have to be
uniform density.
The center of mass could be
off the center...
of the geometric center.
So if this object has
a certain mass,
then this is
the gravitational force.
But now look at the center of
mass fluid that is displaced.
That's clearly more here,
somewhere here,
the displaced fluid.
That is
where the buoyant force acts.
And so now what you have...
You have a torque on this object
relative to any point
that you choose.
It doesn't matter where you pick
a point, you have a torque.
And so what's going to happen,
this object is clearly going
to rotate in this direction.
And the torque will only be zero
when the buoyant force
and the gravitational force
are on one line.
Then the torque becomes zero,
and then it is completely happy.
Now, there are two ways that
you can get them on one line.
We discussed that earlier
in a different context.
You can either have the center
of mass of the object
below the center of mass of
the displaced fluid or above.
In both cases would they be
on one line.
However, in one case, there
would be stable equilibrium.
In the other, there would
not be a stable equilibrium.
I have here an object which has
its center of mass very low.
You can't tell that--
no way of knowing.
All you know is that the weight
of the displaced fluid
that you see here is the same
as the weight of the object.
That's all you know.
If I took this object
and I tilt it a little
with the center of mass
very low--
so here is Mg and here is
somewhere the waterline--
so the center of mass
of the displaced fluid
is somewhere here, so
Fb is here, the buoyant force,
you can see
what's going to happen.
It's going to rotate towards the
right-- it's a restoring torque,
and so it's completely stable.
I can wobble it back and forth
and it is stable.
If I would turn it over,
then it's not stable,
because now I would have
the center of mass
somewhere here, high up,
so now I have Mg.
And the center of the buoyant
force, the displaced water,
is about here, so now I have
the buoyant force up,
and now you see
what's going to happen.
I tilt it to the side,
and it will rotate even further.
This torque will drive it
away from the vertical.
And that's very important,
therefore, with ships,
that you always build the ship
such that the center
of mass of the ship is
as low as you can get it.
That gives you
the most stable configuration.
If you bring the center of mass
of ships very high--
in the 17th century, they had
these very massive cannons
which were very high
on the deck--
then the ship can capsize,
and it has happened many times
because the center of mass
was just too high.
So here... the center of mass
is somewhere here.
Very heavy, this part.
And so now, if I lower it
in the water
notice it goes into the water
to the same depth,
because the buoyant force is,
of course, the same,
so the amount of displaced water
is the same in both cases.
But now the center of mass is
high and this is very unstable.
When I let it go, it flips over.
So the center of mass
of the object was higher
than the center of mass
of the displaced fluid.
And so with ships, you have
to be very careful about that.
Let's talk a little bit
about balloons.
If I have a balloon, the
situation is not too dissimilar
from having an object
floating in a liquid.
Let the balloon have a mass M.
That is the mass of the gas
in the balloon
plus all the rest, and what
I mean by "all the rest"...
That is the material
of the balloon and the string--
everything else
that makes up the mass.
It has a certain volume v,
and so there is a certain rho
of the gas inside
and there is rho of air outside.
And I want to evaluate
what the criterion is
for this balloon to rise.
Well, for it to rise,
the buoyant force will have
to be larger than Mg.
What is the buoyant force?
That is the weight
of the displaced fluid.
The fluid, in this case, is air.
So the weight
of the displaced fluid
is the volume times
the density of the air--
that's the fluid
in which it is now--
times g,
that is the buoyant force.
That's... the weight
of the displaced fluid
has to be larger than Mg.
Now, Mg is the mass of the gas,
which is the volume of the gas
times the density of the gas.
That's the mass times g--
because we have to convert it
to a force--
plus all the rest, times g.
I lose my g, and what you see...
that this, of course,
is always larger than zero.
There's always some mass
associated with the skin
and in this case
with the string.
But you see, the only way
that this balloon can rise
is that the density of the gas
must be smaller
than the density of air.
Density of the gas must be less
than the density of the air.
This is a necessary condition
for this to hold.
It is not
a sufficient condition,
because I can take a balloon,
put a little bit
of helium in there--
so the density of the gas is
lower than the density of air--
but it may not rise, and
that's because of this term.
But it is a necessary condition
but not a sufficient condition.
Now I'm going to make you see
a demonstration
which is extremely nonintuitive,
and I will try, step by step,
to explain to you
why you see what you see.
What you're going to see,
very nonintuitive,
so try to follow closely
why you see what you will see.
I have here a pendulum
with an apple,
and here I have a balloon
filled with helium.
I cut this string
and I cut this string.
Gravity is in this direction.
The apple will fall,
the balloon will rise.
The balloon goes
in the opposite direction
than the
gravitational acceleration.
If there were no gravity,
this balloon would not rise
and the apple would not fall.
Do we agree so far?
Without gravity, apple would not
fall, balloon would not rise.
Now we go in outer space.
Here is a compartment
and here is an apple.
I'm here as well.
None of us have weight,
there's no gravity,
and here is a helium-filled
object, a balloon,
and there's air inside.
We're in outer space,
there's no gravity.
Nothing has any weight.
We're all floating.
Now I'm going to accelerate.
I have a rocket-- I'm going to
accelerate it in this direction
with acceleration a.
We all perceive, now,
a perceived gravity
in this direction.
I call it g.
So the apple will fall.
I'm standing there,
I see this apple fall.
I'm in this compartment,
closed compartment.
I see the apple go down.
A little later,
the apple will be here.
I myself fall;
a little later, I'm there.
I can put a bathroom scale here
and weigh myself
on the bathroom scale.
My weight will be
M times this a,
M being my mass,
a being this acceleration.
I really think that it is
gravity in this direction.
The air wants to fall,
but the balloon wants to go
against gravity.
The balloon will rise.
The air wants to fall,
so inside here
you create a differential
pressure between the bottom, P1,
and the top of the air, P2,
inside here.
Just like the atmosphere
on earth--
the atmosphere is pushing
down on us--
the pressure is here
higher than there.
So you get P1 is higher than P2.
So you create yourself
an atmosphere,
and the balloon will rise.
The balloon goes in the opposite
direction of gravity.
If there were no air in there,
then clearly
all of us would fall:
The apple would fall,
I would fall,
and the helium balloon
would fall.
The only reason
why the helium balloon rises
is because the air is there
and because you build up
this differential pressure.
Now comes my question to you:
Instead of accelerating
it upwards
and creating
perceived gravity down,
I'm now going to accelerate
it in this direction,
something that I'm going to do
shortly in the classroom.
I'm going to accelerate all
of us in this direction a.
In which direction
will the apple go?
In which direction
will the balloon go?
What do you think?
The apple will go
in the direction
that it perceives gravity.
The apple will go like this.
I will go like this.
The air wants to go like this.
But helium-- balloon-- goes
in the opposite direction
of gravity,
so helium goes
in this direction.
In fact, what you're doing,
you're building here
an atmosphere
where pressure P1 here
will be higher
than the pressure P2 there.
The air wants to go
in this direction.
The pressure here is higher
than the pressure there--
larger than zero.
If there's no air in there,
we would all fall.
Helium would fall...
helium balloon would fall,
apple would fall,
and I would fall.
I have here
an apple on a string
in a closed compartment,
not unlike what we have there
except I can't take you out
to an area
where we have no gravity.
So here is
that closed compartment,
and here is the apple.
There is gravity
in this direction.
It wants to fall
in that direction of gravity
if I cut the wire.
Now I'm going to accelerate it
in this direction,
and when I do that, I add a
perceived component of gravity
in the opposite direction.
So I add a perceived component
of gravity in this direction.
So this apple wants to fall down
because of the gravity
that I cannot avoid,
and it wants to fall
in this direction.
So what will the string do?
It's very clear, very intuitive,
no one has any problem with
that-- the string will do this.
Now I have a balloon here.
Helium.
There is gravity
in this direction.
That's why the balloon
wants to go up.
It opposes gravity.
I'm going to accelerate the car
in this direction.
I introduce perceived gravity
in this direction.
What does the balloon
want to do?
It wants to go against gravity.
I build up in here, and it must
be a closed compartment...
I must build up there
a pressure differential.
The air wants to fall
in this direction.
I build up a pressure here
which is larger
than the pressure there.
That's why it has to be
a closed compartment.
What will
the helium balloon do?
It will go like that.
That is very nonintuitive.
So I accelerate this car.
As I will do,
the apple will go back,
which is completely consistent
with all our intuition,
but the helium balloon
will go forward.
Let's first do it
with the apple,
which is totally consistent
with anyone's intuition.
I'm going to make sure that the
apple is not swinging too much.
Now, it only happens
during the acceleration,
so it's only during the very
short portion that I accelerate
that you see the apple go back,
and then of course it starts
to swing-- forget that part.
So watch closely-- only
the moment that I accelerate
the apple will come this way.
It goes in the direction
of the extra component
of perceived gravity.
Ready?
Boy, it almost hit
this glass here.
Everyone could see that, right?
Okay.
Now we're going to do it
with the balloon.
We're going
to take this one off.
And now let's take one
of our beautiful balloons.
We're going to put
a balloon in here.
Has to be a closed compartment
so that the air can build up
the pressure differential.
There's always problems
with static charges
on these systems.
Okay.
Only as long as I accelerate
will the balloon go
in a forward direction,
so I accelerate
in this direction,
and what you're going to see
is really very nonintuitive.
Every time I see it,
I say to myself,
"I can reason it,
but do I understand it?"
I don't know,
what is the difference
between reasoning
and understanding?
There we go.
The balloon went this way.
You can do this
in your car with your parents.
It's really fun to do it.
Have a string with an apple
or something else
and have a helium balloon.
Close the windows.
They don't have to be totally
closed, but more or less,
and ask your dad or your mom
to slam the brakes.
If you slam the brakes,
what will happen?
The apple will go...
what do you think?
If you slam the brakes,
the apple will go forwards,
balloon will go backward.
If you accelerate the car
all of a sudden,
the apple will go backwards
and the balloon will go forward.
You can do that at home.
You can enjoy... entertain
your parents with Thanksgiving.
They'll get some
of their $25,000 tuition back.
(class laughs)
When fluids are moving,
situations are
way more complicated
than when they are static.
And this leads
to, again, very nonintuitive
behavior of fluids.
I will derive in a short-cut way
a very famous equation which
is called Bernoulli's equation,
which relates kinetic energy
with potential energy
and pressure.
Suppose I have a fluid,
noncompressible, like so.
This cross-sectional area is A2
and the pressure here is P2.
And I have a velocity
of that liquid which is v2
and this level is y2.
Here I have
a cross-sectional area A1.
I have a pressure P1.
My level is y1;
this is increasing y.
And I have
a much larger velocity
because the cross-section is
substantially smaller there.
Now, if this fluid were
completely static,
if it were not moving--
so forget about the v1
and forget about the v2;
it's just sitting still--
then P1 minus P2 would be
rho g times y2 minus y1
if rho is the density
of the fluid.
That's Pascal's Law.
So it would
just be sitting still,
and we know
that the pressure here
would be lower
than the pressure there.
This is also,
if you want to, rho gh
if you call this distance h.
Rho gh--
that reminds me of mgh,
and mgh is gravitational
potential energy.
When I divide m by volume,
I get density.
So this is really a term
which is gravitational
potential energy
per unit volume.
That makes the m divided
by volume become density.
Therefore, pressure itself
must also have
the dimension of energy
per unit volume.
And if we now set
this whole machine in motion,
then there are three players:
There is, on the one hand,
kinetic energy-- of motion--
kinetic energy...
I take it, per unit volume.
There is gravitational
potential energy...
I will take it, per unit volume.
And then there is pressure.
They're equal partners.
And if I apply
the conservation of energy,
the sum of these three
should remain constant.
That's the idea
behind Bernoulli's law,
Bernoulli's equation.
When I take a fluid element
and I move it from one position
in the tube to another position,
it trades speed for
either height or for pressure.
What is the kinetic energy
per unit volume?
Well, the kinetic energy
is one-half mv squared.
I divide by volume,
I get one-half rho v squared.
What is gravitational
potential energy?
That is mgy.
I divide by volume,
and so I get rho gy
plus the pressure
at that location y,
and that must be a constant.
And this, now, is
Bernoulli's equation.
It is a conservation
of energy equation.
And as I will show you,
it has very
remarkable consequences.
First I will show you an example
whereby I keep y constant.
So I have a tube
which changes diameter,
but the tube is not changing
with level y, as I do there.
So I come in here,
cross-sectional area A1.
I widen it,
cross-sectional area A2.
This is y--
it's the same for both.
I have here inside pressure P1
and here inside
I have pressure P2
and this is the density
of the fluid.
There is here a velocity v2,
and there is here a velocity v1.
And clearly v1 is
way larger than v2
because A1 times v1
must be A2 times v2
because the fluid
is incompressible.
So the same amount of matter
that flows through here
in one second
must flow through here
in one second.
And so these have to be
the same,
and since A1 is
much smaller than A2,
this velocity is
much larger than v2.
Now I'm going to apply
Bernoulli's equation.
So the first term tells me
that one-half rho v1 squared...
I can forget the second term
because I get the same term
here as I get there
because I measure
the pressure here
and I measure
the pressure there.
They have the same level of y.
So I can ignore the second term.
Plus P1 must be one-half rho
v2 squared plus P2.
That's what
Bernoulli's equation tells me.
Now, v1 is larger than v2.
The only way that
this can be correct, then,
is that P1 must be
less than P2.
So you will say, "Big deal."
Well, it's a big deal,
because I would have guessed
exactly the other way around,
and so would you,
because here is where
the highest velocity is,
and all our instincts would say,
"Oh, if the velocity is high,
there's a lot of pressure."
It's exactly
the other way around.
Here is the low pressure,
and here is the high pressure,
which is one
quite bizarre consequence
of Bernoulli's equation.
You must all have encountered
in your life
what we call a siphon.
They were used in the medieval
and they're still used today.
You have here...
A bucket in general is used
with water-- lakes.
We have water here,
but it could be any liquid.
And I stick in here a tube
which is small in diameter,
substantially smaller
than this area here.
And there will be water in here
up to this level--
this level P2, y2.
This is y1,
increasing value of y.
This height difference is h.
P2 is one atmosphere.
I put a one there--
it's atmosphere.
And here, if it's open,
then P1 is also one atmosphere.
So there's air in here
and there's liquid in here.
I take this open end in my mouth
and I suck the water in
so that it's filled with this
water, full with this water.
And strange as it may be, it's
like making a hole in this tank.
If I take my finger off here,
the water will start to run out,
and I will show you that.
And you have here
a velocity v1.
The water will stream down
into this here
and the velocity here
is approximately zero,
because this area is
so much larger
than this cross-sectional area
that to a good approximation
this water is going down
extremely slowly.
Let's call this
height difference d.
I apply Bernoulli's law.
So now we have a situation
where the y's are different
but the pressure is the same,
because right here
at this point of the liquid
I have one atmosphere,
which is barometric pressure,
and since this is open
with the outside world,
P1 is also one atmosphere.
So now I lose my P term.
There I lost my y term;
now I lose my P term.
So now I have
that one-half rho... rho--
this is rho of the liquid--
v1 squared plus rho g times y1
must be one-half rho v2 squared,
but we agreed that that was
zero, so I don't have that term.
So I only have rho gy2.
I lose my g's...
no, I don't lose my g's.
One-half rho v squared--
no, that's fine.
And so... I lose my rho.
This is one-half.
I lose my rho.
And so you get
that one-half v1 squared equals
g times y2 minus y1, which is h.
And so what do you find?
That the speed with which this
water is running out here, v1,
is the square root of 2gh.
And you've seen that before.
If you take a pebble and you
release a pebble from this level
and you let it fall,
it will reach this point here,
this level
with the speed
the square root of 2gh.
We've seen that many times.
So what is happening here--
since the pressure terms are
the same here and there,
now there's only a conversion.
Gravitational potential energy--
which is higher here
than there--
is now converted
to kinetic energy.
This siphon would only work
if d is less than ten meters.
Because of
the barometric pressure
you can never suck up
this water--
no one can;
a vacuum pump can't either--
to a level that is higher
than ten meters.
When I did the experiment
there with the cranberry juice,
I was able to get it up
to five meters,
but ten meters would have been
the theoretical maximum.
So this has to be less than
ten meters that you go up.
If I would have made a hole
in this tank here,
just like this,
down to exactly this level,
and I would have asked you
to calculate
with what speed the water
is running out,
you would have found
exactly the same
if you had applied
Bernoulli's equation.
This is a way that people...
I've seen people steal
other people's gasoline
in the time
that gasoline was very scarce
and that there were no locks yet
on the gasoline caps.
You would put a hose
in the gasoline tank
and you would have
to suck on it a little--
you have to sacrifice
a little bit--
you get a little bit
of gasoline in your mouth,
and then you can just empty
someone's gasoline tank
by having a canister
or by having a jerrican
and fill it with gasoline.
And I'm going to show that now
to you by emptying...
That's still cranberry juice, by
the way, from our last lecture.
So let's put this up on a stool.
So there is the hose--
it's that thing--
and I'm going to transfer
this liquid from here to here.
So first I have to fill it
with cranberry juice.
And there it goes.
And as long as this level
is below that level,
it keeps running.
Not so intuitive.
I remember,
I was at a summer camp
when I was maybe
six or seven years old.
I couldn't believe it when
I saw this for the first time.
We had these outdoor sinks
where we washed ourselves
and brushed our teeth,
and the sink was clogged,
it was full with water.
And one of the camp leaders
took a hose, sucked up
and it emptied itself.
And I really thought, you know,
you'd have to take spoonfuls
of water or maybe buckets
and scoop it out.
This is the way you do it.
Very nonintuitive.
The nonintuitive part is
that it runs up
against gravity there.
So we can let it sit there
and we have a transfer, mass
transfer of cranberry juice.
Last time I was testing my lungs
to see how strong I was.
I wasn't very good, right?
I could only blow up
one meter of water
and only suck one meter water.
Differential pressure
only one-tenth of an atmosphere.
Today I would like to test
one of the students
who, no doubt, is
more powerful than I am.
And I have here a funnel...
with a Ping-Pong ball here,
very lightweight,
and we're going
to have a contest
to see who can blow it
the highest.
I have two funnels,
so it's very hygienic.
I will try it with this one.
They're clean, they just...
We just got them
from the chemistry department.
And so I would like to see
a volunteer--
woman or man, it doesn't matter.
You want to try it, see whether
you can reach the ceiling?
You don't want to try it?
Come on! You want to try it?
You're shy? You don't want to?
Can I persuade you? I can.
Okay, come along.
Come right here.
You think you can make it
to the ceiling?
It's only
a very light Ping-Pong ball.
So, you go like this,
blow as hard as you can.
STUDENT:
Okay.
LEWIN:
Try it, don't be nervous.
STUDENT:
All right.
LEWIN:
Straight up.
STUDENT: (blows) No?
LEWIN:
Blow as hard as you can--
get it out.
STUDENT: (blows)
Amazing! Do it again.
Come on, there must have been
something wrong.
(class laughs)
LEWIN:
You're not sick today, are you?
Blow.
Harder!
STUDENT:
Is this a trick?
LEWIN:
No, there's nothing,
there's no trick in here.
My goodness, I mean
this is a Ping-Pong ball,
I'm not a magician.
(class laughs)
LEWIN:
Come on, blow it up!
Hey, it doesn't work.
It's amazing.
Why don't you sit down?
(class laughs )
LEWIN:
Why doesn't it work?
Why doesn't it work?
The harder you blow,
the least it will work.
Air is flowing here...
and right here,
where there is very little room,
the air will have
very high speed,
way higher than it has
where it has lots of room.
And so at the highest speed,
you get the lowest pressure.
And so the Ping-Pong ball
is sucked in
while you're blowing it.
And to give you
the conclusive proof of that
I will do it this way.
I will put
the Ping-Pong ball like so,
and I'm going to blow like this,
and if I blow hard enough,
the Ping-Pong ball
will stay in there
because I generate
a lower pressure right here
where the passage
is the smallest,
but I have to blow quite hard.
(inhales deeply, blowing hard )
You see that?
Isn't that amazing?
That's the reason
why she couldn't get it up.
(inhales deeply, blowing hard )
That's what Bernoulli
does for you.
Not so intuitive, is it?
I have here an air flow,
a hose with air coming out,
and I can show you there
something that is
equally nonintuitive.
Let's start the air flow.
(machine starts)
It's coming out.
(air hissing)
I take a Ping-Pong ball.
It stays there.
Is that due
to Mr. Bernoulli? No.
No, that's
more complicated physics,
because it has to do
with turbulence.
It has to do with vortices,
which is very difficult.
What is happening here
is that as the air flows,
you get turbulence above here
and the turbulence creates
a lower pressure.
So the vortices, which are the
turbulence, are keeping this up,
because there's a lower pressure
here and there.
But why is it so stable?
I can see that I have...
because of this turbulence,
that it's held up.
Why is it so stable?
If I give it a little push
it doesn't...
it's sucked back in again.
It's very stable--
that is Bernoulli.
Because if I blow air,
like so...
then the velocity here
is the highest,
because it's diverging
the air as it's coming out,
but in the center,
it is the highest,
and so when this Ping-Pong ball
goes to this side,
it clearly has a lower pressure
here than there
and so it's being sucked
back in again.
So the stability is due
to Bernoulli,
but the fact that it is held up
is more difficult physics.
It is so stable
that I can even tilt this...
and it will still stay there.
Now I have something
that I want you to show
your parents on Thanksgiving.
It's a little present for them,
and that is something that
you can very easily do at home.
You take a glass and you fill
it with cranberry juice--
not all the way, up to here.
Take a thin piece of cardboard,
the kind of stuff that you
have on the back of pads.
You put it on top.
The table is beautifully set--
turkey, everything is there--
and you suggest to your parents
that you turn this over.
Your mother will scream
bloody murder,
because she would think
that the cranberry juice
will fall out.
In fact,
it may actually fall out.
I can't guarantee you
that it won't.
(class laughs)
LEWIN:
But it may not, in which case
you now have all the tools
to explain that.
Please do invite me
to your Thanksgiving dinner
and I'll show it
to your parents.
See you Friday.
