6m_lab1 - EXPERIMENT til'rl-l: FLUIDS Introduction The...

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Unformatted text preview: EXPERIMENT til'rl-l: FLUIDS Introduction The subject of fluids is yast, complex, and beautiful. As the reader can easily imagine, it is also extremely important in the sciences, and in eyeryday life. The subject of stationary fluids is called liuid statics, and the subject of fluids in motion is called fluid dynamics. Although hydrostatics is a fairly straightforward subject, hydrodynamics can be extremely complex, leading to a host of phenomena that at first sight are often counterintuitiye. We hope that you will gain some appreciation for the beauty and complexity of fluids in these experiments. in this lab you are expected to do the Archimedes Principle experiment. You are also expected to do some, but riot necessarily all, of the other fwc other experiments, which are mainly qualitatiye demonstrations. (This doesn’t mean that you can finish a couple of them and then leaye early, but simply that you should focus more on the quality ofyour reasoning than in the quantity ofexperiments you get through.) Since there are only free Archimedes stations, you should plan to spend either the first half or the second halfofthe lab period doing it, and the other half on the one or more demonstration experiments. 1. Archimedes‘s Principle {Required} (Knight §lS-4} Imagine an irregular object that is partially or fully submerged in a tank of fluid somewhere on the surface of the earth (so that the fluid feels the earth’s grayity}. There may be many forces acting on the object, including the force of gravity acting on the mass of the object. There is always an additional force, called the buoyant force, which acts in the opposite direction as the force of grayity. The magnitude of this force is given by the following simple formula: Fe : prf'g = Wt In this formula, p is the density of the fluid, if} is the volume of fluid that is displaced by the object (not necessarily the total yolume of the object, because it may be only partly submerged), g = 9.3 this1 is the familiar acceleration of grayity, and Wyis the weight ofthe displaced fluid. It is remarkable that the buoyant force depends only upon the weight ofthe fluid displaced; all other properties ofthe object or ofthe fluid are irrelcyant except insofar as they determine the weight of the fluid displaced. Experiments: l. At your table you will find an irregularly shaped object. Using the oyerflow can, a graduated cylinder, and the balance, measure and record the yolume of water and the weight of the water that is displaced by the object when it is completely immersed. From your results of step (1}, compute the density of water. Is it close to the accepted yalue? Did you need this yalue to compute the buoyant force? 3. Use your results from steps (1) and (2} to predict the buoyant force that will act on the object if it is completely submerged in water. 4. Now, suspending the object from the balance, measure and record the weight of the object in air. Think about this result together with your prediction in step (3), and see if you can predict the apparent weight that the scale will read, if you weigh the object when submerged. 5. Finally, suspending the object from the balance, completely submerge the object in a beaker of water. Record the apparent weight of the object when submerged. How well does this result match your prediction from step (4)? 6. Using any or all ofyour preyious measurements, calculate the density of the object. There is more titan one way to do this. By referring to a table of the densities of common substances, can you guess what material the object is made of? to 2. The venturi Effect {Knight ere-5) Both this experiment and the next one involve Bernouiii’s Principle, which you have seen discussed in lecture. Qttalitatively, Bernoulli’s Principle encompasses two effects: in a connected region of fluid, [Uthe points at lower altitude will tend to have higher pressure, and (2} the points where the fluid is moving faster will tend to have lower pressure. Phenomenon (l) mayr seem very counterintuitive, think through the discussion given in lecture and in the text before tackling this lab! We can make these tendencies quantitative by using Bernouii'i ’3 Equation: Ifyou- label any two points within the connected region oftluid, then i 2 1 2 Pi + Epvl + 933’] :19: +5.01"): +93)”: Note that this equation is based on several assumptions which may or may not be true. The fluid must he incompressible (which is almost always a good approximation for liquids, and works well for gases as long as they are moving far slower than the speed of sound), it must be irrotational {no whirlpools or vortiees}, and it must be non-viscous {essentially meaning that we neglect the role of“friction" in the flowing fluid.) In this eitperiment, air from a blower passes through a ‘v’enturi tube, which is shown in figure 1. The Venturi tube consists of a glass tube that has a narrower region in the middle. Any fluid that passes through the tube must move faster in the narrow region. (This, too, you can make quantitative if you want, using the Continuity Equation, discussed both in lecture and in Knight: Aw,» -—' ,4ng where the A’s represent the cross—sectional area ofthe tube at different points.) The tube segments are connected to ports that allow one to monitor the pressure at two or more points along the tube. Since the elevation of the tube is constant, Bernoulli’s formula for_the difference in pressure between points i and 2 along the horizontal axis ofthe tube becomes 1 *1 pr ‘19: =E {1"}: “Fa (And you can do a similar analysis to connect points 2 and 3). It is clear from the geometry that v; is greater than v., because the same volume of fluid per second must pass through each of the three regions. Thus we immediately conclude that the pressure in region i should be higher than the pressure in region 2, so the manometer fluid level at point I will be lower than the fluid level at point 2. By the same token, the pressure in region 3 should be higher than the pressure in region 2. .F k? V - flfl‘b ' a. El". fi‘f ..- ‘ fi—t?’ CH— r e). —e— M. wea‘f‘f'r' Figure 1. Schematic View of the Venturi Tube Experiment: At your lab bench is a conventional blower, like the exhaust port of an ordinary household vacuum cleaner. In addition, there is a ‘v’enturi tube, which is connected to three manometer tubes, so that you can measure the relative pressures of three points within the tube. The experiment is very simple: Admit air from the blower into one end of the Venturi tube, and observe the elevations of the fluid in the three manometer tubes, as you vary the flow rate {by moving the blower hose back and forth}. Required: Qualitative interpretation: The most important qualitative observation is the behavior of the pressure in the middle of the Venturi tube, as compared with the pressure at the exhaust end ofthe 'v'enturi tube. You should explain the answers to {at least) the following questions: Based on your observations of the fluid levels in the manometer tubes. is the pressure at point 2 {the narrow region of the Venturi tube) higher or lower than the pressure in the other two regions? How does the pressure at point 3 {the wide region after the constriction} compare to the pressure at point I {the wide region before the constriction}? Do these results match your prediction based on Bernoulli‘s Principle? You should be able to easily imagine that ifyou could significantly increase the flow rate, you would draw the manometer fluid all the way up into the air stream {please don’t try it!). Optional: Quantitative Analysis: Based on the measured levels of fluid in the three manometer tubes, calculate the exact pressure difference between points 1 and 2 in the ‘v’enturi tubes. If you‘re feeling especially ambitious, see ifyou can calculate the velocity ofthe air as it enters the wide part ofthe tube. 3. Examples of Bernoulli’s Equation (Knight §15-5) This experiment investigates also investigates Bernoulli’s Principle, which was briefly explained in the introduction to the Venturi Tube experiment above. This one is a purely qualitative experiment — you will likely make no numerical measurements at all + but is one of the most dramatic demonstrations of Bernoulli’s Principle that you’ll ever see. a) Using the exhaust of the blower, see if you can suspend a ping-pong ball on the jet of air. is the ball stable against tapping it sideways with a pencil? {In other words, does it return to the center of the air stream when displaced slightly off-center?) ls the ball stable when you tilt the jet ofair significantly from the vertical? Draw lines representing the air flow contours for two cases: when the ball is exactly on axis, and when the ball is slightly off-axis. Can you explain why the ball is stable? b) New connect the output of the blower to a large funnel and point the blower hose downward. What happens ifyou gently push a ping-pong ball into the funnel? Explain. c) Similarly, place a stopper with a hole in it into the outlet ofthe blower, so that the air is forced through the small hole in the stopper. Point the blower hose and stopper downward. Now take a piece of 3” by 5“ card stock, which has a thumb tack in the middle, and hold the card against the stopper, with the sharp end of the tack pointing into the air stream. What happens? Explain. d) Make a sandwich of a 3” by 5" card and a 3” by 5" slip of paper, with the card on top and the slip of paper falling limp. New blow gently between the card and the slip of paper. What happens to the slip of paper? Explain. 4. Magdeburg Plates {Knight §15—2) If two smooth plates are separated by an o—ring, and the enclosed space is evacuated, one plate will be attracted to the other with a force equal to the external air pressure times the area of the plate. In familiar units, atmospheric pressure is about l4? pounds per square inch, so two plates each of area 10 square inches will be pushed together by a force of about 150 pounds. Since the lab bench is fairly flat, using the hand pump provided, pump the air out of a “Magdeburg Plate" that is face down on the table. Can you lift the plate from the table without sliding the plate horizontally? The “Magdeburg Plate” demonstrates the principle ofthe powerful “suction cups” used to lift plate glass. 5. PreSSure vs. Elevation (Knight §15-2) It is well known that the pressure of the atmosphere is a maximum at the surface of the earth; the pressure diminishes with altitude because the pressure is just the weight of a 1 square meter column of air above the observation point. It turns out that the difference in pressure between the first floor and the third floor of Thiniann Labs can be easily measured with a manometer and an empty jug. Roll the manometer and jug into the elevator on the first floor. Before pressing the “up” button, open and then close the stopcock so that the manometer reads 0 pressure difference. Now ride the elevator up to the third floor, and record the change in pressure between the air and the bufferjug. licpeat the experiment a couple oftimes to confirm that the effect is indeed caused by the change in elevation. From the change in pressure, calculate the difference in elevation between the first and third floors ofThimann Laboratories. 6. The Weight of Air {Knight §15-l) It seems hard to believe that 1 cubic meter ofair weighs 1.2 kg. In this experiment we test this hypothesis. Using the mechanical vacuum pump provided, evacuate the Bell jar. Weigh the Bell jar in its evacuated state; then let the air back in by opening the valve. Then weigh the filled Bell jar. From the difference in these two measurements, you can deduce the mass of the air that you removed from thejar. From this and the volume ofthejar, you can estimate the density of air. Before you actually make your measurements, make a prediction: will your measured density of air be a little higher or a little lower than the “accepted” valuepm-r = 1.2 Ice/ml? Why? (Hint: how much money do you think the Regents give us to buy state-of—the-art vacuum pumps?) Then try the experiment, and see how well your results match your prediction. Pro-laboratory Questions 1. What is the minimum radius of a “Magdeburg Plate” that is needed to lift a 100 pound piece of plate glass? 2. What is the change in weight of a hollow cylinder of height 10 cm and radius 4 cm when the air is pumped out ofit? _ 3. Show that the difference in pressure between the top and the bottom of a column of water 1.00 inches tall is equal to 248.9 Pa. 4. Assume that there is a 3*!) foot difference in elevation between the first and the third floors of Thimann laboratories. What is the difference in atmospheric pressure between the two floors, expressed in Pascals‘? From your result in part 3, how high a column of water would this pressure difference support? ...
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This lab report was uploaded on 04/16/2008 for the course PHYS 6M taught by Professor Graham during the Winter '07 term at University of California, Santa Cruz.

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6m_lab1 - EXPERIMENT til'rl-l: FLUIDS Introduction The...

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