We can tell that diameter of the tube influence the pressure of the water at the bottom.

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1 IDS 102 Pressure Part II You may have found that there is a slight difference in the distance of the two streams, but this is due to frictional forces between the water and the tube, not the different diameters of the tubes. We can tell this because the area of the opening of larger tube is.about 2.25 times greater than the area of opening of the smaller tube. If the diameter of the tube were the primary factor in determining the pressure on the water, the stream from the larger tube should have gone about 2 times farther and it did not. We can tell that diameter of the tube influence the pressure of the water at the bottom. Let s do some figuring using the two tubes to the right. The larger tube is 3 inches in diameter (inside diameter) and the smaller tube is 2 inches in diameter. If the water is 3 feet high in each tube, what is the pressure on the bottom of the tube due to the water in pounds per square inch (psi)? (Some data you will need include the density of water in English units which is pounds per cubic inch and the volume of a cylinder is r 2 h. We have another tube with 4 feet of water in it, what is the pressure at the bottom in psi? 4

2 One technique to separate the minerals in a rock is to crush the rock and pour it into liquids of different densities. Some minerals will float on the liquid and others sink. One such liquid is called LST. The LST liquid has a density of 2.95 g/ml (or 0.11 lb/cubic inch) at room temperature. If we replace the water with LST (there is now four feet of LST in a tube), what is the pressure on the bottom of the tube in psi? In summary, what two things cause the pressure to change on the bottom of the tube? 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. 5

3 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. The mass of the bottle and pump before pumping is: Now start pumping. Pump, and pump, and pump: about 100 times You can do it Take turns if you want... All done? The mass of the bottle and pump after pumping is: The mass of the bottle after pumping minus the initial mass = 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? 6

4 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. Mass = 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. Mass = 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? 7

5 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? 8

6 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 cm 3.) 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. Although the atmosphere extends about 75 miles up, the air gets pretty thin above a few miles. Mount Everest is a little less than six miles high, and even experienced mountain climbers have to carry oxygen to the top. In fact, if we were to squeeze that entire 75 mile layer until it had the same density as our "ordinary room air" it would only be 6.2 miles thick. This information gives us a way to calculate the weight of the air above us. For the following calculation, we will pretend that the atmosphere is a uniform blanket of air, six miles thick. In reality, the atmosphere is NOT UNIFORM and it is much thicker than six miles, but the weight of the air above us is the same as the weight of a 6.2 mile thick blanket of "ordinary room air." We have seen that the mass of a cubic meter of the air around us is about one kilogram. Find the volume of one pound of air. No, don't. Just kidding. We'll tell you. One pound of ordinary room air has a volume of 27,000 cubic inches. Imagine a rectangular column of air with a one square inch base and a volume of 27,000 cubic inches. How tall would it be in inches? How tall would it be in miles? (There are 5280 feet in a mile and twelve inches in a foot.) 9

7 Now you know the height of a column of air with a weight of one pound. The air above you would actually fill a column 6.2 miles high. How heavy would it be? According to this "back of the envelope" calculation, what is ordinary "atmospheric pressure" in pounds per square inch? (Think about this! This is how much force the air around you exerts on every square inch of your body!) What would be different about this calculation if we did it in Denver, "the mile high city?" (How tall is the column of air above Denver? How does that influence the atmospheric pressure in Denver?) Discuss your results with your instructors before moving on. 10

8 End of Module Questions 1. Imagine two tall glass tubes filled with water. Both tubes are 60 inches high, but one tube has a diameter of 3 in, while the other has a diameter of 9 in. Compare the pressure exerted by the water in each of these tubes. Clearly explain your reasoning. 2. A 2 inch by 2 inch by 6 inch block of wood is resting on a table. The density of the wood is pounds per cubic inch. a) If the block is resting on its side, as shown in the diagram at right, what is the pressure (in pounds per square inch) that the block exerts on the table? b) If the block is standing on end, as shown in the diagram at right, what is the pressure (in pounds per square inch) that the block exerts on the table? c) Atmospheric pressure at sea level is about 15 pounds per square inch. How tall would the two inch by two inch block of wood need to be to exert a pressure of 15 pounds per square inch on the table (when the block is standing on end)? 11

9 3. Three rectangular containers are full of water. Each container has a square base. The container on the left has a base that is 8 inches by 8 inches and it is 4 inches high. The middle container is 8 inches by 8 inches at the base and two inches high. The container on the right is 4 inches by 4 inches and also 4 inches high. The situation is shown below. 4 in A B 8 in 8 in 2 in C A D A 8 in 8 in 4 in E F 4 in 4 in The points labeled A, B, C, D, E, and F are all inside of the containers and below the surface of the water. Each of the points labeled B, D, and F is at the bottom of a container. Each of the points labeled A, C, and E is halfway between the bottom and the top of a container. Note: to answer these questions you do not need to numerically compute the water pressure at any of the points if you do not want to. a) List all of the points (if any) where the water pressure will be greater than it is at point A. Explain your reasoning. b) List all of the points (if any) where the water pressure will be the same as it is at point A. Explain your reasoning. c) List all of the points (if any) where the water pressure will be less than it is at point A. Explain your reasoning. 4. Three containers of liquid are shown in the diagram below. All three containers are open to the atmosphere. The containers on the left contain water and the container on the right contains mercury (which is about 13 times more dense than water). There are seven points labeled inside the liquid in the containers. The heights of these points are shown in inches at the right, as is the height of the surface of each liquid Water Mercury 4 inches A F 3 inches B D G 2 inches C E 1 inch a) List all of the points where you would expect the pressure to be greater than it is at point D. Explain your reasoning. 12

10 b) List all of the points where you would expect the pressure to be greater than it is at point E. Explain your reasoning. c) List a pair of points where you would expect the pressure to be just about equal. Explain your reasoning. 5. We have seen that the density of air at sea level is about 1 kg/m 3. The density of water (at sea level and elsewhere) is about 1,000 kg/m 3. The amount of pressure we call "one atmosphere" (an "atmosphere" is a unit of pressure) is the same as the pressure that would be created by a blanket of air with the same density as the air at sea level, 10,000 meters thick. a) How thick would a blanket of water need to be to exert a pressure of one atmosphere? b) How deep below the surface of the ocean would you need to dive to experience a pressure of two atmospheres? (Hint: you experience a pressure of one atmosphere before you get into the water.) 13