In the last video, we learned that the pressure at some
depth in a fluid is equal to the density of the fluid times
how deep we are in the fluid, or how high is the column of
fluid above us times gravity.
Let's see if we can use that to solve a fairly typical
problem that you'll see in your physics class, or even on
an AP physics test.
Let's say that I have a bowl.
And in that bowl, I have mercury, and then I also have
this kind of inverted test tube that I stick in the
middle of-- this is the side view of the bowl, and I'll
draw everything shortly.
Let's say my test tube looks something like this.
Let's say I have no air in this test tube-- there's a
vacuum here-- but the outside of the bowl, this whole area
out here, this is exposed to the air.
We are actually on Earth, or actually in Paris, France, at
sea level, because that's what an atmosphere is defined as--
the atmospheric pressure.
Essentially, the way you could think about it-- the weight of
all of the air above us is pushing down on the surface of
this bowl at one atmosphere.
An atmosphere is just the pressure of all of the air
above you at sea level in Paris, France.
And in the bowl, I have mercury.
Let's say that that mercury-- there's no air in here, and it
is actually going to go up this column a little bit.
We're going to do the math as far as-- one, we'll see why
it's going up, and then we'll do the math to figure out how
high up does it go.
Say the mercury goes up some distance-- this
is all still mercury.
And this is actually how a barometer works; this is
something that measures pressure.
Over here at this part, above the mercury, but still within
our little test tube, we have a vacuum-- there is no air.
Vacuum is one of my favorite words, because it has
two u's in a row.
We have this set up, and so my question to you is-- how high
is this column of mercury going to go?
First of all, let's just have the intuition as to why this
thing is going up to begin with.
We have all this pressure from all of the air above us-- I
know it's a little un-intuitive for us, because
we're used to all of that pressure on our shoulders all
of the time, so we don't really imagine it, but there
is literally the weight of the atmosphere above us.
That's going to be pushing down on the surface of the
mercury on the outside of the test tube.
Since there's no pressure here, the mercury is going to
go upwards here.
This state that I've drawn is a static state-- we have
assumed that all the motion has stopped.
So let's try to solve this problem.
Oh, and there are a couple of things we have to know before
we do this problem.
It's mercury, and we know the specific gravity-- I'm using
terminology, because a lot of these problems, the hardest
part is the terminology-- of mercury is 13.6.
That's often a daunting statement on a test-- you know
how to do all the math, and all of a sudden you go, what
is specific gravity?
All specific gravity is, is the ratio of how dense that
substance is to water.
All that means is that mercury is 13.6
times as dense as water.
Hopefully, after the last video-- because I told you
to-- you should have memorized the density of water.
It's 1,000 kilograms per meter cubed, so the density of
mercury-- let's write that down, and that's the rho, or
little p, depending on how you want to do it-- is going to be
equal to 13.6 times the density of water, or times
1,000 kilograms per meter cubed.
Let's go back to the problem.
What we want to know is how high this
column of mercury is.
We know that the pressure-- let's consider this point
right here, which is essentially the base of this
column of mercury.
What we're saying is the pressure on the base of this
column of mercury right here, or the pressure at this point
down, has to be the same thing as the pressure up, because
the mercury isn't moving-- we're in a static state.
We learned several videos ago that the pressure in is equal
to the pressure out on a liquid system.
Essentially, I have one atmosphere pushing down here
on the outside of the surface, so I must have one atmosphere
pushing up here.
The pressure pushing up at this point right here-- we
could imagine that we have that aluminum foil there
again, and just imagine where the pressure is hitting-- is
one atmosphere, so the pressure down right here must
be one atmosphere.
What's creating the pressure down right there?
It's essentially this column of water, or it's this
formula, which we learned in the last video.
What we now know is that the density of the mercury, times
the height of the column of water, times the acceleration
of gravity on Earth-- which is where we are-- has to equal
one atmosphere, because it has to offset the atmosphere
that's pushing on the outside and pushing up here.
The density of mercury is this: 13.6 thousand, so 13,600
kilogram meters per meter cubed.
That's the density times the height-- we don't know what
the height is, that's going to be in meters-- times the
acceleration of gravity, which is 9.8
meters per second squared.
It's going to be equal to one atmosphere.
Now you're saying-- Sal, this is strange.
I've never seen this atmosphere before-- we've
talked a lot about it, but how does an atmosphere relate to
pascals or newtons?
This is something else you should memorize: one
atmosphere is equal to 103,000 pascals, and that also equals
103,000 newtons per meter squared.
One atmosphere is how much we're pushing down out here.
So it's how much we're pushing up here, and that's going to
be equal to the amount of pressure at this point from
this column of mercury.
One atmosphere is exactly this much, which equals 103,000
newtons per meters squared.
If we divide both sides by 13,609.8, we get that the
height is equal to 103,000 newtons per meter cubed, over
13,600 kilograms per meter cubed times 9.8 meters per
second squared.
Make sure you always have the units right-- that's the
hardest thing about these problems, just to know that an
atmosphere is 103,000 pascals, which is also the same as
newtons per meter squared.
Let's just do the math, so let me type this in-- 103,000
divided by 13,600 divided by 9.8 equals 0.77.
We were dealing with newtons, so height is
equal to 0.77 meters.
And you should see that the units actually work, because
we have a meters cubed in the denominator up here, we have a
meters cubed in the denominator down here, and
then we have kilogram meters per second squared here.
We have newtons up here, but what's a newton?
A newton is a kilogram meter squared per second, so when
you divide you have kilogram meters squared per second
squared, and here you have kilogram
meter per second squared.
When you do all the division of the units, all you're left
with is meters, so we have 0.77 meters, or roughly 77
centimeters-- is how high this column of mercury is.
And you can make a barometer out of it-- you can say, let
me make a little notch on this test tube, and that represents
one atmosphere.
You can go around and figure out how many atmospheres
different parts of the globe are.
Anyway, I've run out of time.
See you in the next video.