To determine the pressure in a fluid at a given depth with the air-filled cartesian diver, we can employ Boyle's law, which states that the pressure in an ideal gas (held at constant temperature) is inversely proportional to its volume. At a fluid's surface, the pressure of the fluid is the same as the pressure of the atmosphere just above it, which we'll denote as LaTeX: P_{atm}P a t m. If the volume of air, which can be treated as an ideal gas here, in the cartesian diver decreases by 19% as it is lowered to a specific depth in the fluid, the pressure of the fluid at this depth, in terms of atmospheric pressure, is

The pressure at this depth is .

Explanation:

According to the statement, the uncompressed fluid stands at atmospheric pressure. By Boyle's Law we have the following expression:

(1)

Where:

- Initial and final volume.

- Initial and final pressure.

If we know that , then the pressure ratio is:

If , then the final pressure of the gas is:

The pressure at this depth is .

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