{{about, the elevator paradox in the hydrometer, the elevator paradox in the transportation device, Elevator paradox The elevator paradox relates to a

hydrometer A hydrometer or lactometer is an instrument used for measuring density or relative density of liquids based on the concept of buoyancy. They are typically calibrated and graduated with one or more scales such as specific gravity. A hydrometer ...

placed on an "elevator" or vertical conveyor that, by moving to different

elevation The elevation of a geographic location is its height above or below a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface (see Geodetic datum § Vert ...

s, changes the atmospheric pressure. In this classic demonstration, the floating hydrometer remains at an equilibrium position. Essentially, a hydrometer measures

specific gravity Relative density, or specific gravity, is the ratio of the density (mass of a unit volume) of a substance to the density of a given reference material. Specific gravity for liquids is nearly always measured with respect to water (molecule), wa ...

of liquids independent of barometric pressure. This is because the change in air pressure is applied to the entire hydrometer flask. The submerged portion of the flask receives a transmitted force through the liquid, thus no portion of the apparatus receives a net force resulting from a change in air pressure. This is a paradox if the buoyancy of the hydrometer is said to depend on the weight of the liquid that it displaces. At a higher barometric pressure, the liquid occupies a slightly smaller volume, and thus more dense might be considered to have a higher specific gravity. However, the hydrometer also displaces air, and the weight of the liquid and the air are affected equally by elevation.

Cartesian divers

A Cartesian diver, on the other hand, has an internal space that, unlike a hydrometer, is not rigid, and thus can change its displacement as increasing external air pressure compresses the air in the diver. If the diver, instead of being placed in the classic plastic bottle, were floated in a flask on an elevator, the diver would respond to a change in air pressure. Similarly, a non-rigid container like a toy balloon will be affected, as will the rib cage of a human

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diver, and such systems will vary in buoyancy. A glass hydrometer is rigid under normal pressure, for all practical purposes.

The hydrometer in an accelerating frame of reference

The upward or downward acceleration of the elevator, as long as the net force is directed downward, will not change the equilibrium point of the hydrometer either. The force due to acceleration acts on the hydrometer exactly as it would on an equal mass of water or other liquid. Experimental physics Physical paradoxes