This article refers to the elevator paradox as it relates to the physics of a hydrometer. For the elevator paradox as it relates to the elevator

Elevator

An elevator is a type of vertical transport equipment that efficiently moves people or goods between floors of a building, vessel or other structures...

 as a transportation device, see elevator paradox

Elevator paradox

The elevator paradox is a paradox first noted by Marvin Stern and George Gamow, physicists who had offices on different floors of a multi-story building...

.

The elevator paradox relates to a hydrometer

Hydrometer

A hydrometer is an instrument used to measure the specific gravity of liquids; that is, the ratio of the density of the liquid to the density of water....

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

Elevation

The elevation of a geographic location is its height above a fixed reference point, most commonly a reference geoid, a mathematical model of the Earth's sea level as an equipotential gravitational surface ....

s, changes the atmospheric pressure

Atmospheric pressure

Atmospheric pressure is the force per unit area exerted into a surface by the weight of air above that surface in the atmosphere of Earth . In most circumstances atmospheric pressure is closely approximated by the hydrostatic pressure caused by the weight of air above the measurement point...

. In this classic demonstration, the floating hydrometer remains at an equilibrium

Mechanical equilibrium

A standard definition of static equilibrium is:This is a strict definition, and often the term "static equilibrium" is used in a more relaxed manner interchangeably with "mechanical equilibrium", as defined next....

 position. Essentially, a hydrometer measures specific gravity

Specific gravity

Specific gravity is the ratio of the density of a substance to the density of a reference substance. Apparent specific gravity is the ratio of the weight of a volume of the substance to the weight of an equal volume of the reference substance. The reference substance is nearly always water for...

 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

Cartesian diver

A Cartesian diver or Cartesian devil is a classic science experiment, named for René Descartes, which demonstrates the principle of buoyancy and the ideal gas law.-Experiment description:...

, 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 SCUBA

Scuba set

A scuba set is an independent breathing set that provides a scuba diver with the breathing gas necessary to breathe underwater during scuba diving. It is much used for sport diving and some sorts of work diving....

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.