Quarter Sub - AKA Cartesian Diver
by Rapslogan, published
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A simple toy to demonstrate Archimedes principle and Boyles law.
Archimedes principle states that a body immersed in a fluid experiences a buoyant force equal to the weight of the fluid it displaces. Using Boyle's law we then change the amount of fluid displaced to make the quarter sub rise and fall. This is achieved by simply squeezing the bottle which reduces the volume of air in the main chamber due to an increase in pressure and this in turn reduces its buoyant force (Boyle’s Law).
- The main chamber (8.2cm^3) Internal air cavity volume 11cm^3
- The basket (1.4cm^3)
- Displacement plugs (1 cm^3)
- A semi ridged bottle with good lid
- A couple of US Quarters or other weight.
This is a 3 part print. All parts are designed to be scaled and can be printed without a raft or any support material. For the Quarter Sub to work the main chamber must be sealed and not allow air to be squeezed out. I have used the following settings:
- ABS or PLA 100% fill at 0.2mm layers
- ABS 80% fill at 0.2mm layers using an Acetone rinse to seal the chamber.
The Experiment and Fine Tuning:
- Print the parts as above.
- Add a weight: 80% fill ABS 2 US Quarters (11.3 Grams); 100% fill ABS or PLA 1 US Quarter (5.7grams).
- Fill the bottle with water, gently drop the Quarter Sub in then close the lid.
- Squeeze the bottle to see the Quarter Sub Drop and release to watch it rise.
- If the Sub sinks use less weight. If it requires too much force or won't sink then you will need to add some displacement plugs. These will be required for ABS at 100%. Some trial and error may be required here.
The buoyant force of the Quarter Sub:
Fb = pfluid Vsubmergedg
In the system pfluid and g remain a constant. To change Vsubmerged we use Boyle's law which in short states: assuming the temperature of the gas does not change when the volume is halved, the pressure is doubled; and if the volume is doubled, the pressure is halved.
V submerged(For the air) = P1V1 = P2V2 because we have a closed system V1 is constant therefore V2 = (V1P1)/P2.
So by squeezing the bottle P2 increases and the volume of air in the chamber is reduced therefore the Quarter sub will begin to sink. Releasing the pressure increases the volume of air and restores its original buoyant force.
For the record my 3 year old couldn’t care less about the math but loves to make the sub rise and fall.
Density of PLA aprox 1.25 g/cm^3
Density of ABS aprox 1.04 g/cm^3
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Quarter Sub - AKA Cartesian Diver by Rapslogan is licensed under the Creative Commons - Attribution - Share Alike license.
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