If you have ever gone diving underwater without the aid of scuba equipment, you know that as you go deeper, it becomes harder to hold your breath. The reason is that as you go deeper, all of the water above you is exerting pressure on you. The deeper you go, the more water on top of you, and therefore the greater the pressure on your lungs to give up its supply of air. At a depth of 10 meters (over 30 feet), if you are swimming horizontally, you have the equivalent to about 60-70 people lying on top of you. Such pressures would seem deadly.
Yet, you live in a world in which such pressures are applied to you 24 hours a day. How can it be when the only thing above us is air, and air is so light? While air is not that dense, there is over 50 miles of air above us. How come we do not notice such pressure? Simply put, we do not notice it since we have always lived under such pressures. Our bodies are permeable to air, and therefore, the gases in our body are at the same pressure as the surroundings. They therefore exert a force equal and opposite to the force of the air on us.
In today's discussions, we will study this phenomenon of fluid pressure and factors that affect it. We will start by looking at the pressure exerted by several known objects. When calculating pressures, we should keep in mind that there are several systems used for measuring. For instance, the pressure in your tires is measured in pounds per square inch (ex. 32 psi means the pressure due to a 32-pound weight exerted on a surface of 1 square inch). The weather people report atmospherically in inches or millimeters of mercury (i.e., the pressure due to a column of mercury that is that many inches or millimeters tall). The units that most scientist use are the pascal or the kilopascal. The pascal is quite small, being the pressure exerted by a 1 Newton weight (about .22 pounds) spread over 1 square meter. A kilopascal is a much more realistic unit for the work that we will be doing. One atmosphere of pressure is 101.3 kilopascals.
Another way to see how great atmospheric pressure is is with the following demonstration. For this, you will need an empty soda can, a large bucket or beaker full of water, a hot plate, and a pair of tongs. Pour about .5 cm of water into the soda and place it on the hot plate. When the water has just begun to boil, remove the can with the tongs. Invert the can and submerge it into the bucket of water. What happens? If all goes well, the can should be crushed very violently. Why did this occur? When the water began to boil, the air normally in the can was replaced with steam. When the can was placed in the cool water, the steam in the can condensed back to water. However, the approximately 300 milliliters of steam in can will condense to .3 milliliters of water. Since air is not allowed back into the can when this occurs (remember, the top is underwater) a vacuum is created within the can by the condensing steam. The great pressure difference between atmospheric pressure and the vacuum within the can causes it to crush rapidly.
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To see a Quicktime movie of the demonstration, click here. |
Evaluation: Very exciting demonstration. The can crushes very quickly, causing the class to jump a little in their seats. Needs good explanation, though, to make sure that students do not misunderstand what happened.
A slower way to show the same effect is to do the following demonstration. We will need a large beaker, an Erlenmeyer flask, a one hole stopper to fit the flask, glass tubing (between .2-.5 meters long), water, a ring stand holder with a support ring, and a hot plate. Fill the beaker with water and place it beneath the support ring, which should be at a height several centimeters higher than the glass tubing. Put a small amount of water in the flask and place it on the hot plate without the stopper and glass tubing. When the water has reached boiling, remove the flask from the plate and insert the one-hole stopper that has been fitted with one end of the glass tubing. Invert the flask and glide it through the support ring so that the other end of the glass tubing is in the beaker of water and the flask is supported by the ring. As the flask cools, water will condense, creating a partial vacuum and drawing water up the tubing. When the cool water reaches the flask, the steam will begin to condense quicker and draw the water up faster, creating a water fountain. To make the effect more dramatic, add food coloring to the water in the beaker to make the water more visible to the students.
Evaluation: This is another crowd-pleasing demonstration. Since it goes a little slower than the crushing can, it is better to use for explaining as the experiment is happening. To make it go really slow, use a small inner diameter piece of tubing.
How do we measure air pressure? The weather people usually report it in terms of how tall a column of mercury the air can support (ex. 75 mm of mercury). In fact, you should be able to find an example of such a measuring device in the laboratory. However, since mercury is such a toxic substance, having such a device in a high school or middle grades classroom is inadvisable. Instead, we will look at two different ways to measure air pressure.
Experiment 1: For this experiment, we will need a glass jar with a wide mouth, a balloon (mylar, if possible), rubber bands, glue or tape, and a straw. Stretch the balloon over the mouth of the jar until it is tight as a drum. Secure it in place with the rubber bands. Glue or tape one end of the straw to the middle of the balloon and allow the straw to rest on the edge of the mouth jar. Place the jar near a wall to which a piece of graph paper has been taped. Point the straw at the paper and record its height on the paper with a pen. Assuming that the balloon does not leak, as the air pressure drops, the "drum" head should expand since the balloon/jar is filled with air at the same pressure as when the balloon was put in place. This will cause the straw to point downward. If the air pressure increases, vice versa. You should observe the changes for several days to see if and how the pressure changes.
Evaluation: In just one days time, we were able to see a difference in the position of the marker (The measured difference with a barometer in the room was .2 inches of mercury). This experiment is good for a long term project (several weeks).
Experiment 2: For this experiment, we will need a length of clear tubing (small inner diameter) that is over 11 meters long, a bucket of water, and two hose clamps. Immerse the hose in the bucket of water and "bleed" it of any air. Apply the clamps to both ends and secure tightly. Take the hose out of the bucket and lower one end out an overhang that is higher than the length of the tubing. Have someone go to the other end of the tubing and release the clamp. What happens? The water level in the tubing should drop slightly, but it should stop dropping when the atmospheric pressure is great enough to support a column of water that tall. Mark the level of the water and measure the length of the tubing to that point.
Evaluation: This did not work well since we could not find a location on that side of campus that we could safely drop a line 33 feet downward (intended spot only turned out to be 28 feet).
Compressibility vs. Incompressibility
Some fluids, when put in a container and placed under pressure, exhibit the property that the volume that they occupy gets smaller (vice-versa is true). This is known as the compressibility of the fluid. Air is an example of a fluid that exhibits this behavior. For a test of this, close off the end of a bicycle pump and notice that the volume gets smaller as the pressure increases. Because of this property, the density of air is not a constant as one ascends into the atmosphere. As the air pressure decreases, the volume of air "expands", decreasing the mass per unit volume. This is why you have so much trouble breathing at high altitudes.
However, not all fluids are as compressible as air. Water is almost totally incompressible.
Therefore, as one goes deeper into water, the density of the water almost stays the same. A demonstration showing the difference between the compressibilities between air and water is the Cartesian Diver. For this demonstration, we will need a two liter soda bottle (with cap), an eyedropper that will fit in the hole of the soda bottle, and water. Fill the soda bottle almost to the top with water. Place the eyedropper in the bottle with the rubber bulb up. The eyedropper should float in the water. If it does not, check the eyedropper for leaks and/or replace it. Screw the cap onto the bottle very tightly. Squeeze the sides of the soda bottle. What happens? As you squeeze the bottle, the water does not compress, but the air in the top of the bottle does since it has no way to leak out of the bottle. As the volume decreases, the pressure in the air increases. This increased pressure is transmitted through the fluid, increasing the pressure in the water everywhere by an amount equal to the increase in the air pressure. Since the pressure in the eyedropper is at atmospheric pressure, a pressure difference exists between the water and air in the dropper. The water, therefore, compresses the air in the dropper, decreasing its volume. Water enters the dropper, thereby increasing its overall density and causing the dropper to sink.
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For a Quicktime movie of this demonstration, click here. |
Evaluation: This demonstration worked well for showing the compressibility of air. The participants were able to see the water being pushed up into the eyedropper.
The air pressure that we measure here at the surface is different from the air pressure that we would measure at some distance above the Earth's surface. The reason for this is simple. As we go higher into the air, there is less air above us and, therefore, less air pushing down upon us. We notice this difference when we go up in an elevator or an airplane. However, for most classrooms, this is hard to show without very accurate barometers. Another way to show it is by using water. Since water is much denser than air, a small variation in the height of a water column results in a much greater pressure difference. As we learned in the last experiment, water is also almost incompressible. Thus, the pressure anywhere in the water is given by P = gh, where is the density of the water, g is the acceleration due to gravity, and h is the depth of the water. For this experiment, we will need a 2 liter soda bottle, a nail, tape, a ruler, and water.
On the cylindrical shaped portion of the bottle, mark the positions for three holes to be placed: one near the top, one near the middle, and one near the bottom. Make sure that the holes are offset vertically from one another. Using the small nail, poke a hole at each mark. Apply tape over each hole and fill the bottle with water to the top of the cylindrical portion. Place the bottle near a sink or a large pan. Pull the tape off each hole and note where the stream of water from each hole hits the ground. Which hole appeared to have water moving the fastest from it? How is this speed of the water affected by the pressure of the water at the hole?
Measure the heights of the holes from the water level and call these h1, h2, and h3. Calculate the pressure at each hole using the formula P = gh. Now measure the height of the hole above the sink or pan, labeling these values y1, y2, and y3. Measure the distance of the water from each hole, and label these values d1, d2, and d3. Calculate the initial velocity at each hole using the formula v = d (.5g/y)1/2. Compare the values of the velocities and the pressures. Do you see any relationship? Plot v vs. P.
Evaluation: This experiment is a good demonstration of hydrostatic pressures. To ensure that the velocities you get match with Bernoulli's equation, make sure that the water levels are measured accurately. The water should also be kept below the top of the bottle where it curves. The holes should also be small enough to keep the water level from dropping to quickly, but not so small that the edge effects drastically alter the flow. A small nail does the trick well.
When a fluid moves, the pressure within it is no longer that just do to all of the weight above it. Instead, the fluid will begin to lose pressure according to Bernoulli's equation. This equation states that P + gh + .5v2 = constant within a fluid. Thus, if at the same height, the fluid is moving faster in one section of the fluid than in another, the pressure there must be less (You might want to check your results from the previous experiment with this equation.). This fact can be used to our advantage in many situations. First, we will demonstrate the principle with a few examples.
Demonstration 1: For this demonstration, we will need a ping pong ball and a hair blower (cool setting) or the exhaust from a vacuum cleaner. Turn the blower on, turn it so that it is blowing upward, and place the ball in the airstream. As most students will guess, the ball will be suspended in air. Now, slowly turn the direction of the airstream so that it is not pointing directly upward. What happens to the ball?
Demonstration 2: Hold a piece of paper near the top of the sheet so that the other end of the paper is drooping downward, away from you. Blow over the top of the paper. What happens?
Demonstration 3: For this demonstration, we will need a ping pong ball, a funnel, a straw that fits on the end of the funnel, and a lot of breath. Attach the straw to the end of the funnel, hold it upright, and place the ball in the funnel. Blow into the straw. What happens? Now, with the ball held in the funnel, turn the funnel upside down. While blowing into the straw, release the ball. What happens?
Demonstration 4: For this demonstration, we will need two ping pong balls, two equal length pieces of string, and tape. Tape each ball to one end of each string. Tape the other ends of the strings to a horizontal support such that the balls are 10-15 centimeters apart. Blow between the balls. What happens?
Evaluation: The first two demonstrations worked well; the other two, not so well. It was pointed out that the first one also works with a small beach ball and a large fan. Another variation of the second demonstration is to have the students try to blow a flat piece of paper off a table top. The funnels that we used for the third demonstration made it difficult to perform. The openning was so large that you ran out of breath within 2 seconds, not giving you enough time to show the effect very well. In the fourth demonstration, as the two balls came together, they were struck by the airflow and pushed away from the blower.
Now that we have seen that a faster moving fluid has a decreased pressure, we will now look at some applications. One of these is an atomizer. This is a device that sprays a fluid from a reservoir by blowing air over a tube. To make one, we will need a plastic straw and either a knife or a pair of scissors. First, make a cut midway up the straw almost all of the way trough, but leaving a small piece that keeps the two halves attached. Bend the straw at this point so that it forms a 90 degree angle. Place one end of the straw into a glass of water and blow very hard into the other end. What happens? As the air blows across the top of the straw, the air pressure is reduced. Atmospheric pressure at the surface of the water outside the straw pushed down on the water and forces it up the straw to the lower pressure. As the water reaches the top of the straw, it is sprayed out. This type of device has been used for many years to spray fluids such as perfume.
Evaluation: The straws that we used were too large in diameter. It took a very deep and quickly exhaled breath to get the water near the top of the straw. A smaller diameter (like a stirring straw) straw should be used.
Another demonstration of the Bernoulli effect is in the flight of rough surfaced balls (Note: Since the ball is spinning, and therefore, adding energy to the system, you cannot use Bernoulli's equation to explain this phenomenom. However, the effect of pressure differences being created by two air masses moving at different speed around an object is the same.). For instance, a curve ball in baseball is caused by the spinning action of the ball as it moves through the air. The side of the ball that is moving forward due to the spinning tends to slow the air flow; the side moving backward tends to speed up the flow of air around the ball. Therefore, the pressure is reduced on the backward moving side relative to the forward moving side, causing the ball to be pushed in this direction and curving the path of the ball. In golf, a similar thing occurs, except it is the top of the ball that is moving backwards and the bottom of the ball that is moving forward. This causes the ball to be pushed upward, producing lift (This is the reason for the dimples on the golf ball, which enhance the slowing down and speeding up of air.).
For this activity, we will need a golf ball, tape, one meter of string, and a meter stick. Tape the ball to one end of the string. Tape the other end of the string to the edge of a table, making sure that the ball clears the floor by a couple of centimeters. Lay the meter stick on the floor in the direction that the ball will initially be swung. Twist the string about 50-80 times in the counterclockwise direction. Pull the ball back along the direction of the meter stick and release. Note what happens to the ball. After several swings back and forth, catch the ball as it reaches its peak height and hold it in place. Measure the angle at which the ball is now spinning relative to the meter stick.
Evaluation: This worked very well. A line needs to be drawn on the ball so that the students can see which direction it is spinning. The ball should be caught as soon as it stops spinning in the initial direction or else it will begin to curve backward.