How Does a Cartesian Diver Work? A Simple Science Explanation

If you squeeze a plastic bottle containing a small floating object, the object sinks. When you release the bottle, it floats back up. That is the basic answer to how does a cartesian diver work: squeezing increases the pressure inside the bottle, which compresses the air pocket inside the diver. This makes the diver heavier relative to the water, so it sinks. Releasing the pressure lets the air expand, and the diver becomes buoyant again.

The experiment demonstrates two core physics principles: the compressibility of air versus the incompressibility of water, and Archimedes’ principle of buoyancy.

The Core Physics: Pressure, Volume, and Buoyancy

To understand the mechanism, you need to look at three things: the air inside the diver, the water around it, and the pressure you apply.

What happens when you squeeze the bottle

When you squeeze the sides of a sealed plastic bottle, you reduce the volume of air inside the bottle. Because the air has nowhere to escape, its pressure increases. This pressure is transmitted equally throughout the bottle, including to the water and the diver inside it. This is a direct application of Pascal’s law, which states that pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid.

How the diver responds

The diver (often an eyedropper or a small open-bottomed tube) contains a pocket of air. Water is nearly incompressible, but air is highly compressible. The increased pressure from the squeeze pushes more water into the open bottom of the diver, compressing the air bubble inside. As the air bubble shrinks, the diver’s total volume decreases. According to Archimedes’ principle, an object floats when it displaces a volume of water equal to its own weight. When the diver’s volume shrinks, it displaces less water. Its weight stays the same, so it becomes denser than the surrounding water and sinks.

What happens when you release the bottle

When you let go of the bottle, the pressure inside returns to normal. The compressed air inside the diver expands back to its original size, pushing the extra water out. The diver’s volume increases again, it displaces more water, and it becomes positively buoyant. It rises back to the top of the bottle.

Building a Simple Cartesian Diver at Home

You can make a working cartesian diver with common household items. The most common version uses a clear plastic soda bottle and an eyedropper.

What you need

• A clear, empty 1- or 2-liter plastic soda bottle with a tight-fitting cap.
• A glass or plastic eyedropper (the kind with a rubber bulb at the top).
• Water.

Step-by-step setup

1. Fill the eyedropper about halfway with water. The goal is to have just enough air in the bulb that the dropper barely floats at the surface of a glass of water. If it sinks, remove some water. If it floats too high, add a little more water.
2. Fill the plastic bottle completely to the brim with water.
3. Drop the eyedropper (tip pointing down) into the bottle. It should float near the top.
4. Screw the cap on tightly. There should be no air bubbles trapped in the bottle.

How to operate it

Squeeze the sides of the bottle firmly. The eyedropper should sink. Release your grip, and it should rise. If the diver does not sink, the eyedropper contains too much air (it is too buoyant). If it sinks without squeezing, it contains too little air (it is too heavy). Adjust the water level inside the dropper until it responds correctly.

Why the Diver Does Not Stay in the Middle

You might wonder if you can squeeze just hard enough to make the diver float in the middle of the bottle, suspended. In theory, this would require the diver’s density to exactly match the water’s density. In practice, this is an unstable equilibrium. Any tiny change in depth changes the water pressure on the diver’s air bubble. If the diver drifts upward by even a millimeter, the water pressure decreases slightly, the air bubble expands a little, and the diver becomes more buoyant. It then rises faster. The same effect works in reverse: a slight downward drift compresses the air, making the diver denser, and it sinks faster. The diver will either float to the top or sink to the bottom, but it will not stay put.

Practical Uses and History

The cartesian diver is not just a toy. The principle is used in some types of pressure gauges and depth indicators. A device called a “Cartesian manometer” uses the same mechanism to measure the pressure of a liquid or gas Wikipedia.

The experiment was first described in 1648 by the Italian physicist Raffaello Magiotti. It is named after the French philosopher and mathematician René Descartes, who is credited with inventing the toy. Plastic versions of the diver were given away as free toys in American cereal boxes in the 1950s, and a version modeled after Tony the Tiger was produced in the 1980s Wikipedia.

Key Takeaways

• A cartesian diver works by changing its volume in response to external pressure, which changes its buoyancy.
• Squeezing the bottle increases pressure, compresses the air inside the diver, and makes it sink.
• Releasing the bottle reduces pressure, allows the air to expand, and makes the diver float.
• The experiment demonstrates Pascal’s law, the compressibility of air, and Archimedes’ principle of buoyancy.
• The diver cannot stay suspended at a fixed depth because the equilibrium is unstable.