# Cartesian diver

Last updated
Dancing Cartesian Devil
Hand blown glass toy from Lauscha, Thuringian Forest
In the bottle

A Cartesian diver or Cartesian devil is a classic science experiment which demonstrates the principle of buoyancy (Archimedes' principle) and the ideal gas law. The first written description of this device is provided by Raffaello Magiotti, in his book Renitenza certissima dell'acqua alla compressione (Very firm resistance of water to compression) published in 1648. It is named for René Descartes as the toy it is said to have been invented by him.[ citation needed ]

Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe.

Buoyancy or upthrust, is an upward force exerted by a fluid that opposes the weight of an immersed object. In a column of fluid, pressure increases with depth as a result of the weight of the overlying fluid. Thus the pressure at the bottom of a column of fluid is greater than at the top of the column. Similarly, the pressure at the bottom of an object submerged in a fluid is greater than at the top of the object. The pressure difference results in a net upward force on the object. The magnitude of the force is proportional to the pressure difference, and is equivalent to the weight of the fluid that would otherwise occupy the volume of the object, i.e. the displaced fluid.

Archimedes of Syracuse was a Greek mathematician, physicist, engineer, inventor, and astronomer. Although few details of his life are known, he is regarded as one of the leading scientists in classical antiquity. Generally considered the greatest mathematician of antiquity and one of the greatest of all time, Archimedes anticipated modern calculus and analysis by applying concepts of infinitesimals and the method of exhaustion to derive and rigorously prove a range of geometrical theorems, including the area of a circle, the surface area and volume of a sphere, and the area under a parabola.

The principle is used to make small toys often called "water dancers" or "water devils". The principle is the same, but the eyedropper is instead replaced with a decorative object with the same properties which is a tube of near-neutral buoyancy, for example, a blown-glass bubble. If the tail of the glass bubble is given a twist, the flow of the water into and out of the glass bubble creates spin. This causes the toy to spin as it sinks and rises. An example of such a toy is the red "devil" shown here. The device also has a practical use for measuring the pressure of a liquid.

Glassblowing is a glassforming technique that involves inflating molten glass into a bubble with the aid of a blowpipe. A person who blows glass is called a glassblower, glassmith, or gaffer. A lampworker manipulates glass with the use of a torch on a smaller scale, such as in producing precision laboratory glassware out of borosilicate glass.

Pressure is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure is the pressure relative to the ambient pressure.

A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of the four fundamental states of matter, and is the only state with a definite volume but no fixed shape. A liquid is made up of tiny vibrating particles of matter, such as atoms, held together by intermolecular bonds. Like a gas, a liquid is able to flow and take the shape of a container. Most liquids resist compression, although others can be compressed. Unlike a gas, a liquid does not disperse to fill every space of a container, and maintains a fairly constant density. A distinctive property of the liquid state is surface tension, leading to wetting phenomena. Water is, by far, the most common liquid on Earth.

Plastic divers were given away in British cereal boxes as free gifts in the 1950s, and "Diving Tony," a version of the toy modeled after Kellogg's Frosted Flakes mascot Tony the Tiger, was made available in the 1980s.

A cereal box prize, also known as a cereal box toy in the UK and Ireland, is a form of advertising that involves using a promotional toy or small item that is offered as an incentive to buy a particular breakfast cereal. Prizes are found inside or sometimes on the cereal box. The term "cereal box prize" is sometimes used as a broader term to also include premiums that can be ordered through the mail from an advertising promotion printed on the outside of the cereal box.

Frosted Flakes or Frosties is a breakfast cereal, produced by the Kellogg Company and consisting of sugar-coated corn flakes. It was introduced in the United States in 1952, as Sugar Frosted Flakes. The word "sugar" was dropped from the name in 1983.

Tony the Tiger is the advertising cartoon mascot for Kellogg's Frosted Flakes breakfast cereal, appearing on its packaging and advertising. Tony has also been the mascot for related cereals such as Tony's Cinnamon Krunchers and Tiger Power. Since his debut in 1952, the character has spanned several generations and become a breakfast cereal icon.

## Experiment description

The experiment requires a large water-filled bottle, inside which is a "diver": a small, rigid tube, open at one end, very similar to an eyedropper with just enough air so that it is nearly neutrally buoyant, but still buoyant enough that it floats at the top while being almost completely submerged. Two alternative "divers" can be constructed. One sealed but a flexible bulb, and the other a sealed glass bulb (flashlight minus metal base) with wool threads trailing below. The flexible one will compress reducing volume, and the solid glass one will not change, but air bubbles will be trapped in the fibres, and be exposed to the pressure – thus will change volume.

A pipette is a laboratory tool commonly used in chemistry, biology and medicine to transport a measured volume of liquid, often as a media dispenser. Pipettes come in several designs for various purposes with differing levels of accuracy and precision, from single piece glass pipettes to more complex adjustable or electronic pipettes. Many pipette types work by creating a partial vacuum above the liquid-holding chamber and selectively releasing this vacuum to draw up and dispense liquid. Measurement accuracy varies greatly depending on the style.

Neutral buoyancy occurs when a object's average density is equal to the density of the fluid in which it is immersed, resulting in the buoyant force balancing the force of gravity that would otherwise cause the object to sink or rise. An object that has neutral buoyancy will neither sink nor rise.

The "diving" occurs when the flexible part of the larger container is pressed inwards, increasing the pressure inside the larger container, causing the "diver" to sink to the bottom until the pressure is released, when it rises back to the surface. If the container is rigid, as with a glass bottle, the cork sealing the bottle would be pressed inwards or drawn outwards.

Inside an oval bottle
A reverse diver
A double action diver

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 an 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.

Pascal's law is a principle in fluid mechanics that states that pressure at a point has infinite direction, and thus a pressure change at any point in a confined incompressible fluid is transmitted throughout the fluid such that the same change occurs everywhere. The law was established by French mathematician Blaise Pascal in 1647–48.

In fluid mechanics, displacement occurs when an object is immersed in a fluid, pushing it out of the way and taking its place. The volume of the fluid displaced can then be measured, and from this, the volume of the immersed object can be deduced.

Archimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the center of mass of the displaced fluid. Archimedes' principle is a law of physics fundamental to fluid mechanics. It was formulated by Archimedes of Syracuse.

It might be thought that if the weight of displaced water exactly matched the weight of the diver, it would neither rise nor sink, but float in the middle of the container; however, this does not occur in practice. Assuming such a state were to exist at some point, any departure of the diver from its current depth, however small, will alter the pressure exerted on the bubble in the diver due to the change in the weight of the water above it in the vessel. It is an unstable equilibrium. If the diver rises, by even the most minuscule amount, the pressure on the bubble will decrease, it will expand, it will displace more water, and the diver will become more positively buoyant, rising still more quickly. Conversely, should the diver drop by the smallest amount, the pressure will increase, the bubble contract, additional water enter, the diver will become less buoyant, and the rate of the drop will accelerate as the pressure from the water rises still further. This positive reinforcement will amplify any departure from equilibrium, even that due to random thermal fluctuations in the system. A range of constant applied pressures exists that will allow the diver either to float at the surface, or sink to the bottom, but to have it float within the body of the liquid for an extended period would require continuous manipulation of the applied pressure.

In classical mechanics, a particle is in mechanical equilibrium if the net force on that particle is zero. By extension, a physical system made up of many parts is in mechanical equilibrium if the net force on each of its individual parts is zero.

Divers inside an oval plastic bottle acquire new interesting properties. Indeed, an oval bottle can increase in volume when it is compressed, and if this happens, the drowned diver can ascend.