This equation shows that there is no relation between the pressure at a certain point in a column of fluid and the shape of the container that the fluid is in or the area of the column, only the height within the column of fluid at which you are measuring the pressure is relevant. Where is the change in pressure in the vertical column of water, is the density of the fluid, is gravitational acceleration ( ), and is the change in height through the column of fluid. We see this when we look at the equation for the vertical fluid pressure variation: This is because the amount of pressure that water can exert on it’s surrounding is due only to the height of the column of water, and not the shape or width of it. This can be explained by Pascal’s theorem of communicating vessels, which states that when water is poured into two vessels which are connected (so that water can flow between), they will come to equilibrium at the same height. Pascal’s Theorem of Communicating VesselsĪs water is poured into the cup, it rises and fills the central column. It will empty quicker if there is a smaller bubble of air at the bend of the siphon than if there is a larger cavity of air. Once it reaches the top of the smaller straw inside of the large central column, a siphon will form. Once the siphon in the Pythagorean cup has been “activated”, it will continue to run until all the water in the cup has been emptied in to the container below. As water is poured into the tupperware, it rises up through the central column. The Pythagorean cup, or “greedy” cup is a specially designed cup which will empty its contents once filled to a certain point. The video camera may be helpful with this demonstration because it is quite small. The siphon will ensure the majority of the water in the cup is evacuated into the large container. Slowly pour water into the cup until it starts to come out of the bottom. Put the cup into a larger container to ensure no water leaks out onto the demonstration surface.