Introduction

This design allows students to learn about volume and displacement, specifically in recreating Archimedes' famous bathtub experiment, where he realized the approach to measure the volume of an object based on the water it displaces. (wikipedia link)

The model consists of a "bathtub", which can be filled with water and displaced with a displacement object. The size is carefully set such that the volume inside the tub and outside the tub (at the tub wall level) is identical.

Application

This design can be incorporated into a curriculum to instruct students at a variety of levels, starting with the basic concepts of cube volume and displacement, to more advanced topics in algebra, solving equations for variables and conditions, density, and 3D printing concepts/error analysis.

Volume/Displacement topics

• Have students measure volume of displacement cube, handle, bathtub, and express it in the appropriate units.
• Fill tub with water, displace it using the displacement cube, note identical (or not!) volume inside and outside the tub. Account for any discrepency.
• Fill tub to brim, and displace liquid with objects of unknown volume. Remove object and measure the cavity at the top of the tub to calculate volume.

Algebra

• Given a known inner-cube size, calculate the needed volume for the outer cube.
• In this example, the outer cube is not a perfect cube - dimensions are set set to match the tub volume, at the tub wall level. Derive an equation for this and solve for the length/width dimension given an inner cube size. Remember to account for the wall width! (Solution for this is in the openscad code).

Density/buoyancy

• Provide displacement objects of a variety of densities/infill percentages. Which object float? Calculate their density.

3D printing applications

• Using standard 3D printing parameters, calculate the infill % from mystery prints.
• Above experiments make a variety of assumptions, based on a perfect mathematical model. When we print out an object, it is definitely no longer perfect. What are some of the problems with this print? What assumptions cannot be made? How could this model be improved?

Cost/Commercial alternatives

• Tub uses approximately 60g of PLA, displacement cube about 13g, approximate cost $1.50
• No known commercial products available

Improvements/future work

• Passageways for escaping water could be cut into the displacement cube, allowing for higher tolerance parts.
• Graduations could be carved into the side of the objects, to allow for easier measurement