The simplest practical application of the hydrostatic formula is the barometer, which measures atmospheric pressure. 

A tube is filled with mercury and inverted while submerged in a reservoir. This causes a near vacuum in the closed upper end because mercury has an extremely small vapor pressure at room temperatures (0.16 Pa at 20°C). 

A barometer measures local absolute atmospheric pressure: (a) the height of a mercury column is proportional to patm; (b) a modern portable barometer, with digital readout, uses the resonating silicon element. (Courtesy of Paul Lupke, Druck Inc.)

Since atmospheric pressure forces a mercury column to rise a distance h into the tube, the upper mercury surface is at zero pressure.

At sea-level standard, with pa 101,350 Pa and M 133,100 N/m3 from Table 2.1, the barometric height is h 101,350/133,100 0.761 m or 761 mm. 

In the United States the weather service reports this as an atmospheric “pressure’’ of 29.96 inHg (inches of mercury). 

Mercury is used because it is the heaviest common liquid. A water barometer would be 34 ft high.

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