Under pressure

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.