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## Measurement

Current time:0:00Total duration:6:39

# Under pressure

## Video transcript

Do you feel that? Do you feel the weight of the
atmosphere pushing down on you? Actually, you, like most people,
have probably not thought about how heavy the
atmosphere actually is and about the pressure it
pushes on you every day. In fact, you have
about 14.7 pounds of force pushing on you per
every square inch of you. But where does this
pressure come from? For the answer to
that question, science had to wait till the middle
of the 17th century, when Pascal had an hypothesis. You see he thought that the
atmospheric pressure that we experience every day is actually
due to the massive column of air that towers
above us and the weight that it exerts by gravity. To test this, he devised
a very simple experiment. He took an instrument
called a barometer that measures atmospheric pressure
and made a measurement at several locations in
the lowest part of town, at the top of a church tower. And he even climbed
a local mountain to measure the pressure
at the top with the idea that if the height
of the column of air stayed the same pressure, the
pressure should stay the same in each of those locations. But if the height of the column
decreases at each location, then the pressure
should decrease as well. I'm going to show you how
to build a simple pressure measuring device
called a manometer. First, I'll need two
relatively stiff tubes. I used two plastic pipe heads
I had lying around the lab. I got one end off to
make room for the plug. You'll also need a plug to
plug one end and a piece of relatively stiff tube. Now to make the
manometer, you need to connect the tubing
to each of the pipe heads or plastic tubes. Once they're connected,
you'll have a U-shaped device. You can then fill
it with water, add some food coloring if
you like, and then plug one end to fix the pressure. There you go. You have a manometer,
and you're ready to make pressure measurements. At the beginning,
the pressure exerted on each column of
liquid is equal so the liquid levels in tube
A and B are equal as well. If the pressure on tube A
increases, the water in tube A will fall, and the water
in tube B will rise. If the pressure over
tube A decreases, then the water in tube B will
fall, and the water in tube A will rise. For our first measurement,
we went to Constitution Park in Boston. Here we show that the
pressure is greater than it was in the lab
but using our manometer to show that column A is 12
millimeters below column B. But what's the pressure going to
be up on Bunker Hill Monument? Well, let's find out. After climbing 275
stairs, we were able to take a measurement
at the top of Bunker Hill Monument. Here we are able to show
that the column A is just six millimeters below column B. For our final measurement,
we drove about 20 miles south to the great Blue Hill. After climbing for
about a mile and a half, we reached the top
with our stunning views of Boston and the ocean. Here we get our lowest
measurement yet. Column A is actually three
millimeters above column B. Now for some resulting
calculations-- getting from changes
in water levels to pressure calculations. For starters, the air in Tube
B is constrained by the plug. Because of this,
it's an ideal gas and obeys the ideal
gas law, which states the pressure times
the volume equals nRT. Now nRT remains constant
through all measurements. Because of this, we can then
produce a nice relationship, and that is, P1 times
V1 equals P2 times V2. Or in other words, the pressure
times the volume at one state must equal the pressure and
the volume at another state. But how do we get from
differences in the water levels that we measured in
the field to changes in the volume of Tube
B, which is what we need for our actual calculations. Well, from my device,
I've calculated that for each 1 millimeter
change in the water level that that corresponds to a
change in volume of 0.133 ml, with half of that
volume change occurring in column A and the other
half occurring in column B. So to calculate the change
in volume of Tube B only, we can take my conversion factor
of 0.133 ml per millimeter and multiply it by half
of the height change. Therefore, the final volume in
Tube B that we saw in the field is V2 equals the
initial volume, V1 of 22 ml minus the
change in volume. So using this
formula, I went ahead and calculated the final volume
to be at each of our locations. At Constitution Park, the final
volume of Tube B was 20.4 ml, at Bunker Hill
Monument, 21.2 ml, and at Great Blue Hill, 22.4 ml. Now we can take
this relationship and rearrange it
to actually solve for the pressure in
each of these locations. Using the initial conditions
of the air in Tube B, of P1 equals 101.6 kilopascals,
which is the pressure the day that I built my manometer and
the initial volume of Tube B, that is the air
volume of 22 miles. Using this equation, we get
an actual atmospheric pressure at Constitution Park
of 109.6 kilopascals, at Bunker Hill
Monument 105.5 pascals, and at the Great Blue
Hill of 99.8% kilopascals. But how do these
atmospheric pressures relate to the elevations
that we measured them. Well just as pascal showed, we
see that the pressure decreases with increased
elevation at a very linear relationship over the
elevations that we measured. Finally, I'd like to
leave you with some tips when you make your
own measurement. First, be patient. it can take time for the
manometer to reach equilibrium as you change pressures. Second, take multiple
measurements. This will greatly
increase your accuracy. And third, pay attention
to weather as things like changes in temperature. Or incoming weather
systems can have a dramatic effect on the
pressures that you measure. Some final questions
to think about based on what you've
learned today. First, what would happen to
the water in the manometer if it went to 5,000 meters,
or what about the moon? And second, what
would happen if you made a measurement on an
airplane at 10,000 meters? Think about these things as
you think about pressure.