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Statics of Fluids

  • B1-18: Center of Mass - Soda Can and Water

    B1-18
    To demonstrate how an object's behaviour can change when its center of mass does
    An empty soda can can sit upright on its bottom, or can be laid on its side, but cannot be at rest at any angle between these. However, this can be changed by adding a liquid to the system. Pour approximately 150ml of water into the can, and then try carefully balancing the can at an angle, as seen in the photo above. (This may require experimenting to find the exact right amount of water for any given can; we recommend doing this in front of the class so they can see the process.)

    Ask your students why this should happen? The mass has increased, but why does that change how it balances?

    The water moves when the can tilts, causing the center of mass to shift – with just the right amount of water, the new center of mass will be above the edge of the can, and so it will balance.

    Some cans will tend towards a particular orientation and will roll along the edge to that point, displaying a damped oscillation – invite students to hypothesize why this is.

  • F1-01 FLUID PRESSURE VS. DEPTH

    F1-01
    Demonstrates that fluid pressure increases linearly with depth and is isotropic.
    An L-shaped glass tube connected to a liquid manometer is inserted into a tank of water. The pressure in the water tank can be measured at any depth. Holding the tube at a particular depth and rotating it about the end will show no change in pressure, demonstrating that pressure is isotropic.
    F1, FS2

  • F1-02: FLUID PRESSURE VS DEPTH - ANEROID GAUGE

    F1-02
    Show water pressure versus depth with an aneroid gauge.
    An L-shaped glass tube, connected to an aneroid gauge, is immersed in water. The pressure at any depth is indicated directly on the gauge. This enables students to see the pressure at any level.

    Invite students to make predictions about the relationship between depth and pressure, and perhaps even sketch what they expect the graph of this relationship to look like. Then take a few data points and see what happens.
    F1

  • F1-03: PASCAL'S VASES

    F1-03
    Demonstrate that pressure is dependent only on depth, and not on the shape of the container.
    Three "vases" with different shapes can be connected to a water reservoir and pressure gauge assembly. Using the wire as a depth indicator, it is shown that the pressure in the vase depends only on the depth, not on the shape of the vase.

  • F1-04: EQUILIBRIUM TUBES

    F1-04
    Demonstrate that pressure is transmitted equally throughout a fluid.
    By raising and lowering the reservoir, one can show that the water level in all three vases will rise and fall together. From this one concludes that pressure is transmitted uniformly throughout the water.
    F1

  • F1-05: DOES WATER SEEK ITS OWN LEVEL?

    F1-05
    A trick to challenge the students.

    The liquid level in the left side of the U-tube is higher than that in the right side of the U-tube. How does one explain this?

    Two immiscible fluids of different density which are identical in physical appearance are in the two ends of the U-tube. The point where they meet (which could be easily seen) is covered by the clamp which holds the U-tube.

  • F1-06 WATER SEEKS ITS OWN LEVEL

    F1-06
    Shows that pressure is dependent on depth, not shape of container

    This set of conjoined glass tubes is filled with green-dyed water. The water level in the four different tubes is the same even though the volumes and shapes of the tubes are very different.

    Engagement Suggestion
    • For advanced students, consider tilting the tubes slightly, then plugging them with corks so that the different amounts of trapped air cause the water to be at different levels. Challenge students to analyze why this changes the results, then remove the corks to show what happens.
    Background

    This illustrates that the pressure in an open container of liquid is dependent only on the depth, not the shape or area.

  • F1-11: HYDRAULIC PRESS

    F1-11
    Demonstrate dramatically Pascal's Law and the large forces attainable using hydraulic systems.
    Place the provided 2x4 board between the jaws of the press as shown in the photograph. Tighten the pressure release valve and pump the handle to increase the force and crush the 2x4. Pressure is read directly in tons. DO NOT exceed 5 tons.

  • F1-12: PASCAL'S LAW - COILED TUBE PARADOX

    F1-12
    Illustrate Pascal's law in a dramatic way.
    Referring to the photograph on the right, pouring water (colored green) into the tube at the left in the photograph causes the asymmetric configuration shown due to the equalization of pressure in the central air bubble. Similarly, if one end of a three-turn loop of tubing is raised vertically, as in the photograph at the left above, water poured into the high end will never come out the bottom end, even when the bottom end is lying flat on the table, as seen in the left photograph.

    f1-12af1-12b

  • F1-13: CONSTANT WATER PRESSURE

    F1-13
    Demonstrate a mechanism which produces a constant water pressure.

    Air enters the aspirator bottle, initially almost filled with water, through a tube inserted through a sealed stopper into the water bath, while the water leaves through a nipple near the bottom of the bottle. This arrangement provides a constant water pressure head, which is equal to the height of the water column between the nipple and the bottom end of the tube. Thus the water jet will have the same range as the water level in the bottle falls from its initial level to the level of the bottom of the tube.

    The idea of this gizmo to provide water at a constant pressure, was first proposed by Edme Mariotte, a 17th century French scientist. A device called the Mariotte siphon, making use of this concept, is used in agriculture to provide irrigation at a constant flow rate and as a research tool in determining the properties of soil. His work is also cited in the Catholic Encyclopedia.

  • F1-14: PISTON DIAMETER VS TRAVEL - WORKING MODEL

    F1-14
    Show that with an incompressible fluid the bigger piston moves more slowly than the smaller piston.
    Raise or lower one of the bottles to observe the relative speeds of the changing water levels. This is what happens in a confined incompressible fluid with pistons on the two water surfaces.

  • F1-15: PRESSURE GLOBE

    F1-15
    To illustrate several interesting phenomena related to air pressure
    This is a glass sphere into which a balloon can be inserted to demonstrate effects of air pressure. The sphere can be sealed with a rubber stopper. Three ways to use the Pressure Globe:

    (1) Place a balloon into the lipped opening of the Pressure Globe. After stretching the mouth of the balloon over the lip, blow into the balloon until it conforms to the bottle's interior surface. Insert the stopper in the bottom hole while retaining the pressure inside the balloon. Once the stopper has been firmly inserted, remove your mouth from the balloon. Observe that the balloon does not deflate.

    (2) Place the balloon into the lipped opening of the Pressure Globe and place the stopper in the bottom hole. After stretching the balloon over the lip, have a student blow into the balloon. Air cannot be blown in. Discuss why not.

    (3) Prepare the Pressure Globe following the procedure in Step 1. Once the balloon has been fully inflated and the stopper placed in the bottom hole, pour approximately 100 ml of water into the balloon. With the large opening facing upward, place the Pressure Globe over a sink. Now remove the stopper. Observe what happens. Discuss what force causes the water to squirt out of the bottle.

    Note: Care must be taken to insert the rubber stopper far enough that it fully seals, but not so far that it cannot be grasped to be removed.

  • F1-21: LIPLESS STRAW

    F1-21
    Demonstrate the role of atmospheric pressure in the operation of a drinking straw.
    The initial configuration of the water in the bottles is seen in the photograph at the left above. When air is pumped out of the bell jar, water flows through the tube from the stoppered bottle into the open bottle, as seen in the photograph at the right. When air is allowed to flow back into the bell jar, the water flows back into the closed bottle, reproducing the initial water configuration.

    f1-21a

  • F2-01 ARCHIMEDES' PRINCIPLE

    F2-01
    Demonstrates the buoyant force on a body submerged in a fluid to be equal to the weight of the displaced fluid.
    Hanging from the balance are a hollow can and a solid cylindrical metal block of the same volume V. Lowering the metal block into a beaker of water results in a buoyant force equal to the weight of a volume V of water. Pouring the volume V of water into the can restores the original weight as read on the spring scale.
    FS2

  • F2-02: CARTESIAN DIVER

    F2-02
    Demonstrate a variety of fluid mechanics phenomena, including the compressibility of a gas, the incompressibility of water, Boyle's law, Pascal's law, and Archimedes' law.
    The diver is carefully weighted with water. When the rubber membrane on the top of the tube is pressed, the air in the diver is compressed, allowing enough water to enter the tube that its average density becomes greater than that of water, and the diver sinks. When the membrane is released the diver again rises to the top of the tube.
    F2

  • F2-03: CARTESIAN DIVER - EXPLICIT VERSION

    F2-03
    Demonstrate explicitly how a cartesian diver works by showing how the water enters the diver when the pressure in the cylinder is increased.
    When no additional pressure (above normal atmospheric pressure) is applied to the membrane on top of the cylinder, the diver floats at the surface of the water. The location of the water surface inside the diver is indicated by the orange bob floating in the diver tube. When additional force is applied to the membrane the pressure in the tube increases, forcing more water into the diver tube and compressing the air in the tube, as indicated by the bob. Because the average density of the diver becomes greater than that of water, the diver sinks to the bottom. When the force is released, the diver again rises.

    f2-03a

  • F2-04: BUOYANCY - SPHERE AND WATER

    F2-04
    Challenge the students' thinking about the buoyant force by considering the question: "Will a round object, without a flat top and bottom surface, experience a buoyant force, as does a cylinder?"
    A round steel ball and a hollow metal can hang from the scale. The pressure is always normal to the surface of a body and increases linearly as the depth increases. When the steel ball is immersed it too experiences a buoyant force, because the upward vertical component of pressure applied to the lower hemisphere is greater in magnitude than the downward vertical component of the pressure exerted on the upper hemisphere.

    f2-04a

  • F2-05 BUOYANCY - BOAT AND ROCK

    F2-05
    Illustrates buoyancy
    Boat and rock float in a closed pond. removing rock from boat and dropping it in pond will cause the water level of the pond to go down
    F2

  • F2-06: BUOYANCY - SINKING BOAT

    F2-06
    Illustrates buoyancy
    A heavy copper "boat" floats in a fish tank "pond," as seen in the photograph at the left. The water level in the pond is marked by the top of the black tape on either side of the tank. A cork is removed from a hole in the bottom of the boat, allowing the boat to fill with water and sink. As the boat sinks, the water level in the pond goes down

  • F2-07: BUOYANCY - PEPSI AND DIET PEPSI

    F2-07
    Show the difference in density between soft drinks with and without sugar.
    Unopened cans of Pepsi and Diet Pepsi are floated in water. The Pepsi sinks, while the Diet Pepsi floats. The density of the Pepsi is increased by the dissolved sugar, which occupies space between the water molecules. Diet Pepsi has no additional sugar, and is therefore less dense.