Cartesian Diver: Difference between revisions

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== Age ==
{| class="wikitable" style="color:black; background-color:#ddd; margin-left: auto; float:right"
| [[Physics]]:
| Pressure, Buoyancy
|-
| Grade Range:
| [[Elementary School]], [[Middle School]]
|-
| Format:
| [[Hands-on]]
|}


Elementary School, Middle School
This demonstration is easy to make, easy to do, and easy to learn! All the parts can be found at home, so encourage students to try to make it at home and show their families how it works.


== Format ==
== Materials ==
 
* Cartesian Diver Bottle
 
Or, if being made:
* Eyedropper
* Empty two-liter bottle
* Water
* Duct tape
 
== Safety Precautions ==
 
Please read the [[Demonstration Safety]] page before performing this demonstration.
 
 
== Demonstration ==
 
Preparation: If making the Cartesian Diver, fill the bottle about 90% of the way with water, and have the eye dropper filled about 1/4 of the way with water. Place the eyedropper in the bottle, and adjust the amount of water in it if needed to ensure it floats in the bottle, with the open end facing downward. Close the bottle, and seal it with duct tape to prevent leaks.


Hands-on
# Show the bottle to the students, and allow them to squeeze the bottle to see the dropper sink.
# Show them that by squeezing slowly, you can watch the water level rise inside of the dropper. What causes the water level to rise, and the air to take up less space?


== Materials ==


    2-Liter Soda Bottle
== Why This Works ==
    The Cartesian Diver
 
    Water  
===Short Explanation===
There is just enough air in the diver to make it positively buoyant. Therefore, the diver floats at the water's surface. Squeezing the bottle increases the pressure inside the bottle. The air inside the bottle, including the eyedropper, is ''compressible''. This means that when pressure is put on air, it will take up less volume. However, the water is not. Water is seen as an ''in-compressible fluid'', meaning that it cannot be forced to take up less volume when pressure is put on it. Therefore, when the bottle is squeezed, the pressure on the water is distributed to all the air inside of the bottle, including the eyedropper. So the air in the eyedropper takes up less volume, which the water takes the place of it, resulting in the dropper becoming less buoyant until, when the pressure is high enough, the dropper sinks!


== Safety Precautions ==
===Full Explanation===
This demonstration follows the principles within '''''Pascal's law''''', and with that the '''''Ideal Gas Law'''''. Pascal's Law states that pressure exerted upon an in-compressible fluid will be transferred in all directions equally, such so that the variations in pressure throughout the fluid will stay the same. With this in mind, we can look at how buoyancy plays a role in this experiment, and with that the Ideal Gas Law. When the dropper is suspended in the water, it is experiencing buoyancy, or an equalization of the forces upon it due to gravity and those exerted upon the object due to the surrounding fluids. The force of air above it is much less than that of the water below, so the dropper will be suspended between the two, at a point where the downward force of gravity is equal to the upward buoyancy force exerted by the water.


Science Theatre demonstrators must keep the safety of themselves and their audience in mind at all times. All Science Theatre demonstrators must have read through the Safety Training page. The ST Safety Box with first aid kit, fire extinguisher, etc. should always be available to demonstrators. Always wear safety gloves, glasses, and a labcoat if handling chemicals; always perform potentially dangerous demonstrations at a safe distance from the audience; and always keep a very close eye on any volunteers you call from the audience. Add safety information
If we make it a closed system by sealing the lid, we can then show the effect of Pascal's law upon the water. Water, in most cases, behaves as an in-compressible fluid. Air, on the other hand, we can show to generally follow the '''''Ideal Gas Law''''', which states that:


== Preparation ==
'''PV''' = nR'''T'''


See [[#Demonstration]]
Where '''P''' = Pressure (Variable), '''V''' = Volume (Variable), n = Moles (Constant), R = Ideal Gas Constant, and '''T''' = Temperature (Variable).


== Demonstration ==
In this situation, we are only adjusting the '''P''' and '''V''' values, since we are not heating or cooling the system. By squeezing the bottle we increase the '''P''' value, which means that the '''V''' value needs to decrease when this happens. This results in the air taking up less space within the dropper, which allows the water to take up more space, and cause the dropper to sink. Now, you may wonder why the water takes up the space, instead of the top of the dropper compressing slightly and the air level within the dropper staying level. This is due to '''''Pascal's Law''''', which states:


The Cartesian diver experiment is set up by placing a "diver"—a small, rigid tube, open at one end, very similar to an eyedropper—in a larger container with some flexible component; for example, a two liter soft drink bottle. The larger container is partially filled with water, as you can see in the demonstration, and must be made airtight when closed. The "diver" is partially filled with a small amount of water, just enough to allow it to contain enough air so that it is nearly neutrally buoyant, but still buoyant enough that it floats at the top while being almost completely submerged. (This demonstration should be completely put together.)
d'''P''' = ''p''gd'''h'''


== What to Say ==  
Where d'''P''' = Change in Pressure (Variable), ''p'' = density of the fluid (constant), g = gravity (Constant), and d'''h''' = change in fluid height (Variable).


There is just enough air in the diver to make it positively buoyant. Therefore, the diver floats at the water's surface. As a result of Pascal's law, squeezing the airtight container increases the pressure of the air, part of which pressure is exerted against the water that constitutes one "wall" of the airtight container. This water in turn exerts additional pressure on the air bubble inside the diver; because the air inside the diver is compressible but the water is a incompressible fluid, the air's volume is decreased but the water's volume does not expand, such that the pressure external to the diver a) forces the water already in the diver further inward and b) drives water from outside the diver into the diver. Once the air bubble becomes smaller and more water enters the diver, the diver displaces a weight of water that is less than its own weight, so it becomes negatively buoyant and sinks in accordance with Archimedes’ principle. When the pressure on the container is released, the air expands again, increasing the weight of water displaced and the diver again becomes positively buoyant and floats.
Here we see that when the pressure increases within the water, the total height of the water level must increase, since the pressure change cannot cause the volume to decrease like in the Ideal Gas Law. This shows that, within the dropper, the increase in pressure should result in the water level increasing slightly, as the volume of the air decreases. That is what causes the dropper to sink!


== Why it is ==
== Additional Information ==


See [[#What to Say]]
* This demonstration pairs well with other hands-on demonstrations on pressure, such as [[Density Rainbow]] and [[Marshmallow Smashies]].
* This demonstration, as of yet, is not a part of the [[Pressure Show]], but it might in the future!

Latest revision as of 21:56, 14 October 2015

Physics: Pressure, Buoyancy
Grade Range: Elementary School, Middle School
Format: Hands-on

This demonstration is easy to make, easy to do, and easy to learn! All the parts can be found at home, so encourage students to try to make it at home and show their families how it works.

Materials

  • Cartesian Diver Bottle

Or, if being made:

  • Eyedropper
  • Empty two-liter bottle
  • Water
  • Duct tape

Safety Precautions

Please read the Demonstration Safety page before performing this demonstration.


Demonstration

Preparation: If making the Cartesian Diver, fill the bottle about 90% of the way with water, and have the eye dropper filled about 1/4 of the way with water. Place the eyedropper in the bottle, and adjust the amount of water in it if needed to ensure it floats in the bottle, with the open end facing downward. Close the bottle, and seal it with duct tape to prevent leaks.

  1. Show the bottle to the students, and allow them to squeeze the bottle to see the dropper sink.
  2. Show them that by squeezing slowly, you can watch the water level rise inside of the dropper. What causes the water level to rise, and the air to take up less space?


Why This Works

Short Explanation

There is just enough air in the diver to make it positively buoyant. Therefore, the diver floats at the water's surface. Squeezing the bottle increases the pressure inside the bottle. The air inside the bottle, including the eyedropper, is compressible. This means that when pressure is put on air, it will take up less volume. However, the water is not. Water is seen as an in-compressible fluid, meaning that it cannot be forced to take up less volume when pressure is put on it. Therefore, when the bottle is squeezed, the pressure on the water is distributed to all the air inside of the bottle, including the eyedropper. So the air in the eyedropper takes up less volume, which the water takes the place of it, resulting in the dropper becoming less buoyant until, when the pressure is high enough, the dropper sinks!

Full Explanation

This demonstration follows the principles within Pascal's law, and with that the Ideal Gas Law. Pascal's Law states that pressure exerted upon an in-compressible fluid will be transferred in all directions equally, such so that the variations in pressure throughout the fluid will stay the same. With this in mind, we can look at how buoyancy plays a role in this experiment, and with that the Ideal Gas Law. When the dropper is suspended in the water, it is experiencing buoyancy, or an equalization of the forces upon it due to gravity and those exerted upon the object due to the surrounding fluids. The force of air above it is much less than that of the water below, so the dropper will be suspended between the two, at a point where the downward force of gravity is equal to the upward buoyancy force exerted by the water.

If we make it a closed system by sealing the lid, we can then show the effect of Pascal's law upon the water. Water, in most cases, behaves as an in-compressible fluid. Air, on the other hand, we can show to generally follow the Ideal Gas Law, which states that:

PV = nRT

Where P = Pressure (Variable), V = Volume (Variable), n = Moles (Constant), R = Ideal Gas Constant, and T = Temperature (Variable).

In this situation, we are only adjusting the P and V values, since we are not heating or cooling the system. By squeezing the bottle we increase the P value, which means that the V value needs to decrease when this happens. This results in the air taking up less space within the dropper, which allows the water to take up more space, and cause the dropper to sink. Now, you may wonder why the water takes up the space, instead of the top of the dropper compressing slightly and the air level within the dropper staying level. This is due to Pascal's Law, which states:

dP = pgdh

Where dP = Change in Pressure (Variable), p = density of the fluid (constant), g = gravity (Constant), and dh = change in fluid height (Variable).

Here we see that when the pressure increases within the water, the total height of the water level must increase, since the pressure change cannot cause the volume to decrease like in the Ideal Gas Law. This shows that, within the dropper, the increase in pressure should result in the water level increasing slightly, as the volume of the air decreases. That is what causes the dropper to sink!

Additional Information

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