Introduction: Pythagorean Cup

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About: My name is Britt Michelsen. I am a chemical engineer from Germany especially interested in computational fluid dynamics. To balance all the theoretical work, I like to make stuff in my free time

In this instructable I'm going to show you a simple way to make a Pythagorean cup. If you are looking for a cool peace of science, or would like to prank your friends, you came to the right place.

The special thing about this cup is that it can be used as a normal drinking cup as long as it is only filled with a certain amount of fluid. If a person is to greedy thought and fills it up to much, the entire content will empty through a hole in the bottom of the cup. It is named after the famous Ionian Greek philosopher Pythagoras of Samos (b. about 570 – d. about 495 BC), you might know him from the Pythagorean Theorem. I did a bit of research and found just as many sources saying that he did invent the cup, as ones saying that say he didn't.

So how does it work?
As you can see in the schematic on the left, there is a channel with an opening near the bottom of the glass running all the way through the stem to the base of it. As long as the fluid level stays under the inside loop of the cup, it can be used as normal. If too much liquid is filled into it though, a siphon is created and the whole glass empties.
Basically it works because the weight of the fluid flowing out reduces the pressure inside the tube so that the fluid is pushed into the channel by its own weight (Honestly this is not the entire truth, because a siphon also works in a vacuum, but enough to understand the effect. If you would like a more in-depth scientific explanation how siphons work, follow this link).

If you are interested in finding out more about the cup take a look at the wikipedia article and here are some great photos of someone making it out of clay. By the way this is the first thing I will make should I be able to afford a 3D printer, since I would love to see a version with the siphon hidden in the handle or the side of the cup.

Step 1: What You Need

What you need

  • Plastic wine glass (best are non transparent ones)
  • Silicone glue
  • Straw (best is a transparent one)
  • Plastic test tube (slightly bigger than the straw)
  • Box cutter
  • Small saw

Step 2: Sawing

I used a transparent cup for you to better see what I am doing, but I suggest you use a non-transparent one.

Start by sawing off the bottom of the top part of the cup, as shown in the first picture. Make sure, that the straw fits through the hole. Afterwards use the box cutter to carefully drill a hole into the bottom, as shown in the third picture. The straw will have to fit through this hole as well.

Step 3: Glue Everything Together

The length of the straw defines the amount of fluid the cup can hold. Since it is difficult to cut it once it is glued in place, you should do it beforehand.

Fill the stem of the cup with silicone adhesive around the straw, to hold it in place and to prevent the liquid from flowing into it. As shown in the first two pictures above.

Afterwards you will have to cut the tube to the correct length. It has to be bit longer than the straw. Cut a small hole into the bottom, to allow the liquid to flow into it, as shown in the pictures. Then apply the silicone adhesive around the rim and place it above the straw. Let everything set and you are done.

Make sure not to use the cup above a valuable carpet or something similar. If you don't want the inside to be visible, just fill the cup with ice.

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