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Statics of Fluids

  • F2-08: BUOYANCY - BATTLESHIP IN BATHTUB

    F2-08
    Illustrate Archimedes' Law in a counterintuitive manner.

    A block of wood is "floated" in a volume of water much smaller than the volume of the wood block. The water is poured into a container the same shape, but slightly larger than the wood block, then the wood block is inserted.

    In the wonderland world of the physicist, a battleship could be floated in a bathtub using one cup of water, if the tub were the right shape!

    f2-08a

  • F2-10: BUOYANT BUBBLES

    F2-10
    Demonstrate buoyancy and diffusion in an interesting way.

    A block of dry ice is placed in the bottom of a clear plastic cylinder sealed on the bottom, trapping carbon dioxide in the bottom of the container as the dry ice sublimates (evaporates). Bubbles produced with a standard soap bubble blowing gizmo will float on top of the more dense carbon dioxide. Some carbon dioxide diffuses into the bubbles, so they get larger and sink! Some of the bubbles freeze when they sink to the bottom of the container near the dry ice. The photograph at the right is a detail of the top of the container.

    It may be necessary to remove static electricity from the plastic container. A damp cloth or lit match may assist with this.

    f2-10a

  • F2-11: HYDROMETER

    F2-11
    Measure the density of a liquid.
    If the hydrometer is immersed in a graduated cylinder filled with water, the reading on the scale (center photograph) should be C(W) = 1000, indicating that the scale is calibrated for water. If the hydrometer is put into the saline solution (photograph at right), the number C(L) at the level of the liquid is read. The density D(L) of the unknown liquid is given by: D(L)=C(L)*D(W)/1000,where D(W) is the density of water in kg/m^3. One can measure densities between 0.7 and 2.0 using this device.
    F2

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  • F2-12: HOT AIR BALLOON

    F2-12
    Show that hot air is less dense than cold air by operating a hot air balloon.
    A 15-ampere hot air gun is used to inflate a hot air balloon. As the air inside is heated, its density decreases with respect to the cooler outside atmosphere. Within less than a couple of minutes, the buoyant force becomes sufficient that the balloon will rise.

    Invite students to predict what will happen as the air cools.

    OS4

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  • F2-13: BOUYANCY - EXPANDING BALLOON CONUNDRUM

    F2-13
    Conundrum involving weight of an expanding balloon.

    A flask containing vinegar is connected to a balloon containing baking soda. This system is balanced with a collection of weights on a pan balance as shown in the photograph above. The balloon is raised up so the baking soda falls into the vinegar, commencing a reaction that produces carbon dioxide and inflates the balloon. When the balloon becomes inflated, what happens to the balance? Will the balloon side go down, will the weight side go down, or will it remain balanced?

    Included here are before and after pictures for this experiment using an electronic balance, showing the weight in grams and tenths (of force), eg. 261.7g down to 258.4g for the balloon expanding to a diameter of about 18cm.

    f2-13af2-13b

  • F2-21 REACTION TO BUOYANT FORCE

    F2-21
    Demonstrates the reaction force using a liquid.
    A beaker of water is balanced by two brass weights. Stick your finger into the water about up to the first knuckle, the water side will go down. The water exerts a buoyant force on your finger, so your finger exerts a reaction to the buoyant force on the water, thereby causing the water side to go down.
    F2, ME1
  • F2-22: BUOYANCY PARADOX - ACCELERATED FRAME

    F2-22
    Illustrate dramatically the concept of buoyancy.
    A float is at rest in a water vessel suspended by a spring from a fixed point. The vessel is lifted up and released from rest, so that it oscillates vertically on the spring. In the picture above a band around the floater lies between the two bands around the larger vessel when the system is at rest.

    Q: How will the float move inside the water vessel as the vessel executes simple harmonic motion?

    A: Surprisingly, the float will remain at rest in the water vessel as it oscillates. It will even remain at rest when the vessel is stopped suddenly with your hand! See video 2 below. As the vessel oscillates, the weight density of both the floater and the water bath vary together, as the acceleration of the vessel varies, so the ratio of their densities remains the same, and they will continue to float with the same geometrical relationship!!

  • F2-23: BUOYANCY PARADOX - INVERTED BLOCK

    F2-23
    Illustrate buoyancy in a paradoxical way.
    A large styrofoam block with a smaller aluminum block mounted on top as in the picture at the left, floats with the center of the styrofoam block, marked by the black line, at the water level. Q: When this object is inverted, with the aluminum block in the water, will the water level on the styrofoam block be (a) above, (b) below, or (c) at the black line?

    A: The water level will be below the black line, as seen by clicking your mouse on either of the pictures above. Notice also that the water level in the tank remains the same, at the level of the top of the black tape.

    f2-23af2-23b

  • F2-24: ACCELERATED BUOYANT BALL

    F2-24
    Illustrate buoyancy in a paradoxical way.
    A ping pong ball is tethered by a spring to the bottom of a water container, which in turn hangs from a spring attached to a fixed point. At rest, the ping pong ball floats near the center of the water tank. Q: How does the ping pong ball move, if at all, when the water tank is raised vertically and released from rest, so that it executes simple harmonic motion? A: The ping pong ball moves out of phase with the motion of the water tank. The system functions as an accelerometer, where the ball moves (with respect to its equilibrium position) in the direction of the acceleration of the tank. The magnitude of the displacement is roughly proportional to the magnitude of the acceleration of the tank.

    f2-24a

  • F2-25: BALANCE PARADOX - BUOYANCY WITH CROSSOVER

    F2-25
    Present buoyancy in a paradoxical way.
    The balance is initially at equilibrium with a mass hanging from an arm on the left pan in balance with the water beaker on the right pan, as seen in the photograph at the left above. Q: If the mass is allowed to hang into the beaker of water, how does this effect the balance? In particular, what, if anything must be done to restore equilibrium? (Note that there are a 100 gram weight and two 50 gram weights available at the lower left of th picture, and these weights can be added to either side of the balance to restore equilibrium.) A: Because the volume of the block is 50 cm^3, the weight on the left side is reduced by 50 grams when the block is submerged in the water. Conversely, the weight on the right side is increased by 50 grams, the reaction force on that pan. To restore equilibrium, 100 grams must be added to the left pan, as seen in the photograph at the right above.

    f2-25a

  • F2-26: BUOYANCY PARADOX - BALL IN TWO LIQUIDS

    F2-26
    Demonstrate buoyancy with a counterintuitive element.
    A ball floats in a beaker of water (at left in picture above). The ball sinks in a beaker of mineral spirit paint thinner (at right above). The mineral spirit paint thinner is immiscible with water, and will float above the water when poured slowly on top of water. The ball then floats at a higher level because the mineral spirits in which the upper part of the ball is floating provide an additional buoyant force on the ball. If the ball is floating on water alone, the top part of the ball is immersed in air, which has a much smaller density.
    F2

    f2-26b

  • F2-27: Buoyancy Paradox - Two Spheres

    f2-27
    To illustrate an interesting brainteaser about bouyancy
    Each pan of a balance holds a beaker of water, filled to the same level. In one beaker, a ping-pong ball floats, tethered by a string to the bottom of the beaker. In the other beaker, a steel ball of equal volume hangs suspended from an outside support. The balance can be clamped to hold it level. Invite students to predict what will happen when the clamp is removed: Will the balance remain level, will the side with the ping-pong ball go down (that side is heaver), or will the side with the steel ball go down (that side is heavier)? Encourage students to explain their reasoning and discuss amongst themselves.
  • F2-31: BUOYANT BALLS IN BEANS

    F2-31
    Illustrate buoyancy in a surprising way.
    Begin with a heavy ball resting on dried beans in a bowl. Unbeknownst to the class, a ping pong ball has been placed under the surface of the beans. Shaking the bowl, the heavy ball sinks, while the ping pong ball rises to sit on the surface of the beans. Cover the bowl with a black cloth while shaking it, to make the whole thing more like a magic trick.
    F2, I6

    f2-31a

  • F2-32: FLOATING SQUARE BAR

    F2-32
    Illustrate buoyancy and the orientation in which a long square bar floats in a very dramatic way.
    A long square bar floats in a bath of methyl alcohol, with its sides horizontal and vertical, as shown in the center photograph. If water is added to the bath until the tank is almost full, the bar will rotate so that the sides are diagonal, as shown in the photograph at the right, due to the effective decrease in the density of the bar relative to the bath.

    f2-32af2-32b

  • F2-41: DENSITY - SLOPE OF MASS VS VOLUME GRAPH

    F2-41
    Determine the density of water.
    Starting with the container empty, pour in water a small amount at a time and plot the total mass vs. the volume of water in the container. The slope of the graph is the mass density of water.
  • I1-64: BURNING CANDLE - COMBUSTION PROCESS

    I1-63
    Demonstrate features of the burning process and to debunk myths about this supposedly well-known demonstration.

    A common pre-college experiment is to burn a candle inside of a bottle which has been turned upside down over a container of water. The water supposedly rises about one-fifth of the way up the bottle, indicating that the oxygen, about one-fifth of the air in the atmosphere, has been "used up" in the combustion process.

    The candle in our experiment is placed inside the sealed tube containing air above a colored water bath, and is then ignited by a hot wire (center photograph). The water level goes down initially, then returns to its original level just after the candle goes out. There is virtually NO CHANGE in the water level from before to after the experiment is performed (photograph at right).

    This is the CORRECT WAY to do this experiment. Two experimental errors are often made when performing this experiment: (1) if the candle is lit before the bottle is placed over it, the air is initially hot, and will pull the water up the bottle as it cools, and (2) when the bottle is placed over the candle, the hot air from the candle flame expands, and some of it might escape out of the bottom opening of the bottle. Analysis of the chemistry of this experiment shows that the final products of combustion are actually more voluminous than the initial air, but other things happen to yield no net difference in the water level.

    I1

    i1-64a

    i1-64b

  • I3-01: BAROMETER - ANEROID TYPE

    I3-01
    Indicate air pressure.
    The barometer measures air pressure in the closed system; squeezing the bulb increases the air pressure. Pressure readings below ambient atmospheric pressure can be obtained by removing the tube and holding the bulb squeezed while replacing the tube.
  • I3-02: BAROMETER - WEIGHT PARADOX

    I3-02
    Show how a barometer really works using a counterintuitive problem.

    A barometer tube filled with water hangs from a spring scale as in the photograph. The water reservoir (a beaker) rests on a table, with the bottom of the tube below the water surface. A hole on the top of the tube is opened, allowing air to enter the tube, so the water in the tube flows into the reservoir. Q: After the water in the tube has been replaced by air, is the reading on the spring scale (a) greater than, (b) less than, or (c) the same as the reading with water filling the tube? A: The answer is that the scale reads less, as can be seen in the photograph at the right.

    This is an interesting question for people who know that atmospheric air pressure is what keeps the water in the tube. They are then left with the problem of what exactly is the force which changes to reduce the spring scale reading after the water flows out of the barometer.

    i3-02a

  • I3-03: GALILEO'S THERMOSCOPE

    I3-03
    Measure very small pressure changes.
    Without touching the can, disconnect and reconnect the tubing from the Magnahelic gauge in order to set the gauge pressure to zero. Warming the can by placing your hand on it raises the pressure in the can about half of the full scale. Also try warming the can by breathing on it.
    I3

    i3-03a

  • I3-10: LUNG FUNCTION MODEL

    I3-10
    Show how air pressure differences cause the lungs to expand and contract.
    A classical bell jar model demonstrates the role of diaphragmatic contraction in causing the lungs to inflate.