IDS 102

Pressure

We use the word “pressure” a lot in our daily lives. We hear of pressure in school or on the job, peer pressure, and blood pressure. A high-pressure situation is thought of as intense, but the weather report says that low pressure means a storm. What’s going on?

Well we can’t do anything about pressure on your job, but when scientists use the word pressure and when forecasters use the phrase atmospheric pressure, they are using these words in a very specific way. The aim of this module is to learn more about what the word “pressure” really means. Before we get to pressure we have to understand a couple of other things.

WEIGHT:

Weight is a kind of force. In general a “force” can be any push or a pull between two objects. All objects on Earth have weight because the Earth is pulling down on them. Another name for “weight” is “the force of gravity” on an object.

Quick activity #1: Hold out your hand, palm up, and place a book or another object on your hand. Hold up the book with your palm. Answer the following questions without putting down the book. (Okay, you can put the book down if you want. Just imagine you are still holding it in the air.)

·  The force of gravity is still acting on the book, right? In which direction is the Earth pulling or pushing on the book?

·  So why doesn’t the book fall down? What must be happening here to keep the book from falling down?

·  How does the size of the force that you exert on the book compare to the size of the force that the Earth is exerting on the book? Explain your reasoning.

This is how we experience the weight of other objects. We try to lift them or support them in some way. Gravity pulls down and we have to push up just as hard. Technically the “weight” is the force of gravity pulling down, but we experience the size of that pulling force when we pull or push in the opposite direction.

Is there more to our perception of how hard or uncomfortable it is to lift something than the weight of the object alone? Sometimes there is…

Quick activity #2: Get a book (a heavy, solid book – not a paperback) and a small block of wood or metal. Hold out your hand, palm up, place the book on top of your palm, and place the block on top of the book.

·  How much force do you think you need to exert to hold the book in the air now? Discuss your answer with your classmates.

·  Rearrange the book and the block so that the block is sitting on your palm and the book is balanced on the block. How much force do you think you need to exert to hold the book and block in the air now? Discuss your answer with your classmates.

·  Your perception of your comfort level was probably very difference when you are holding the book and the block in the two different ways. What do you suppose was the important difference? (Was the force different? What was different?)

Don’t really try this, but imagine doing the experiment with a book and a carpentry nail. How easy is it to hold them up when the nail is on top of the book? How easy would it be if the book was on the head of the nail and the point of the nail was against your palm?

·  Again, what are the important factors that determine your comfort in supporting these objects? Weight (or force) is one of them, but what is the other one?

Think of other examples from daily life where these same factors come into play. (Hint: Think of the shoulder straps on purses and backpacks, or high heel shoes and snowshoes.)

·  Choose one example and describe how these two factors enter into the way that forces are perceived by humans or the effect the forces have on other objects.


PRESSURE

Pressure is defined to be "an amount of force per unit of area." If you have a book resting on your entire hand, your hand feels pretty comfortable. Since the force is spread over a large area, the pressure in any one spot is low. If you have the weight of the book resting on a small portion of your hand (such as the bottom of a small block) then the pressure is much higher and can start to feel uncomfortable. Try to calculate pressure for yourself:

·  If a 0.2 pound block rests on a 4.8-pound book, which rests on a ten square inch hand, what is the pressure on the hand? (Assume that the pressure is spread evenly over the hand.)

·  If a 4.8-pound book rests on a 0.2 pound block, and the one square inch base of the block rests on a ten square inch hand, what is the pressure on the hand? (What is the pressure on the part of the hand that is under the block?)

·  Explain in words why it is easier to split wood with a sharp axe than with a round club. (A round club would be wider, so it would split the wood more, right? What does the sharp edge of the axe do for you?)

A force can be a "push" or a "pull," but we usually associate the word pressure with pushing forces. In general, pressure can be calculated as:

,

and for many important applications, the force involved is weight.

One such application is fluid pressure in an open container, and one common form of fluid pressure is water pressure. If you have ever dived deep under water, you may have experienced an increase in the pressure on your ears. This is because your body was subjected to the weight of the water above you. That weight compresses you and the water equally, so the water squeezes your body on all sides. (Important point: Fluid pressure may be caused by weight, but it does not only push down! As the fluid is squeezed from above, the compressed fluid pushes in all directions.)

If you try to dive under water with a long snorkel, you find you can't breathe below a couple of feet of water. That is because your body can't overcome the pressure from the water above. The pressure on your body is so much greater than the pressure on the air above; you can't compensate enough to convince air to come down the snorkel.

·  Is your answer what you expected?

·  We have another tube with 4 feet of water in it, what is the pressure at the bottom in psi?

·  In the back room we found some of the LST liquid (density is 2.95 g/ml (or 0.11 lb/cubic inch at room temperature) for separating minerals (recall that from fall quarter?). If we put four feet of LST in a tube, what is the pressure on the bottom of the tube in psi?

·  So, what causes the pressure to change on the bottom of the tube?

A brief experiment with water pressure should be instructive, and anyway, it's fun.

WATER PRESSURE

·  We are going to fill two tubes with water. One of the tubes is 1.5 inches in diameter and the other is 2.25 inches in diameter. Each tube has a hole that is the same diameter in the side of tube. If we fill the water to the same level above the hole in each tube, which tube will shoot water farther? What is your reasoning? (This is a prediction—you can come back and modify your prediction if you want at a later time).

This activity is very messy, so we will do it as a whole class.


Find two long clear tubes with a stopper in one end of each tube. We need one person to hold the tube vertical, one person to read the vertical measurements on the tube, and another person to read the horizontal distance of the water stream coming from the tube.

1.5 inch tube
Vertical Height (ft) / Horizontal distance of water stream-
Trial 1 (ft) / Horizontal distance of water stream-
Trial 2 (ft) / Horizontal distance of water stream-
Trial 3 (ft) / Average horizontal distance (ft)
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5

·  We will re-run the experiment with the other tube—what is your prediction? Will the stream go farther if the diameter of the tube is greater? Why?

2.25 inch tube
Vertical Height (ft) / Horizontal distance of water stream-
Trial 1 (ft) / Horizontal distance of water stream-
Trial 2 (ft) / Horizontal distance of water stream-
Trial 3 (ft) / Average horizontal distance (ft)
5.5
5.0
4.5
4.0
3.5
3.0
2.5
2.0
1.5
1.0
0.5

·  For each tube, graph your horizontal distance data as a function of the vertical height of the water in the tube. Draw a trend line for these data.

·  Describe the trendline of your graph. Explain why the trendline is oriented and shaped in this way.

ANOTHER FLUID

We live our lives surrounded by the fluid we call air. (Although the word "fluid" is sometimes misused as a synonym for liquid, gases and liquids are fluids. Sometimes solids have fluid properties if we expand our observation timescale.) But does the air have any weight? Let's check…

·  Hold out your hand, palm up, and place some air on your hand. Oh. I guess the air was already there. Can you feel any weight of the air? Discuss your answer with your classmates.

If you can't feel the weight of the air, your first guess might be that the air doesn't have any weight, or certainly not very much. With the help of modern scientific equipment we can investigate that hypothesis. (Actually all of the equipment used in the following experiments can be found at food supply stores, but "modern scientific equipment" sounds much more professional.)

Somewhere in the room you should be able to find some soda bottles, some plastic jars, and some air pumps. You can do either the plastic jar experiment or the soda bottle experiment first, and the other one second. It doesn't matter.

Soda bottle experiment: Obtain a soda bottle equipped with an air pump that screws on the top. Open the soda bottle. Screw the cap and pump tightly onto the bottle but DO NOT start pumping. Find a balance and record the mass of the bottle and pump.

·  Record the mass of the bottle and pump before pumping:

Now start pumping. Pump, and pump, and pump: about 100 times… You can do it… Take turns if you want... All done?

·  Record the mass of the bottle and pump after pumping:

·  Were the two answers the same? Which was bigger? What do you think happened?

·  Loosen the cap of the soda bottle. What happens? Does this agree with your idea above of what happened while you were pumping?

Plastic jar experiment: Obtain a solid plastic jar with a pump. The pumps from the soda bottles don't fit the jars. You need a pump that fits down over the top of the rubber stopper on the top of the jar. Open the jar (if you can't open it, squeeze the sides of the rubber stopper and try again). Close the jar. Use a balance to find the mass of the jar.

·  Record the mass of the jar before pumping:

Now push the pump down onto the top of the rubber stopper at the top of the jar and start pumping. You have to push down on the pump the whole time you are pumping to get a good seal. Now pump, and pump, and pump: about 100 times… Hum dee dum… Keep going… Take turns if you want… All done?

·  Record the mass of the jar after pumping:

·  Were the two answers the same? Which was bigger? What do you think happened?

·  Pull on the lid. Does it come off of the jar? (DO NOT force it open. Do not use sharp tools that could damage the jar.) Does this agree with your idea above of what happened while you were pumping?

·  Squeeze the rubber stopper. What happens? Does this agree with your idea above of what happened while you were pumping?


Answer these questions after completing BOTH Experiments:

·  Does air have mass? Explain your reasoning.

·  When you hold out your hand, why can't you feel the weight of the air? (Hint: think about water pressure on a swimmer under the water.)

Discuss your results with Bob before moving on.

FIND THE DENSITY OF THE AIR

The density of the air around you depends on the temperature and the pressure (don't worry if this isn't obvious - we'll get to it soon enough). Fortunately, the temperature and pressure inside of our classrooms does not change too much, so we can make a pretty good estimate of the density of the air around us.

Note: this is an estimate! It does not make sense to keep three decimal places from your calculator when you are estimating. One "significant figure" is plenty for this estimate. (If you don't know what one significant figure is, ask your instructor.)

Look back at your data for the plastic jar. The volume of that jar is a little over one liter. If you really pumped that thing about 100 times, you pumped out most of the air. We can estimate that you pumped out one liter of ordinary room air.

·  What was the mass of the air that you removed from the jar?

·  Assuming that you removed one liter of air, what was the density of the "ordinary room air" in units of grams per liter?

·  Hold it! Isn't that about the same as the density of water? Surely air can't have the same density as water, right? What's going on here? (You might want to find the density of air in units that you are more accustomed to using!)

·  If you made it through that one, here is another mind boggler to think about (most people refuse to believe this, so it is a great piece of scientific info for winning bets). Find the mass of a cubic meter of air. (Remember, one liter is 1000 cm3.)

So we now know that air has mass, and in fact it has a lot more mass than most people will believe. What is the effect of all of that air piled up on top of you? A couple of calculations show how great the effect really is.


ATMOSPHERIC PRESSURE:

The atmosphere is a blanket of gases all around the Earth. It is about 75 miles thick. When compared to the heights of objects from our daily lives, the atmosphere is huge. Compared to the size of the Earth, it is a paper-thin coat on which all life depends.