If a barometer is made up of water in place of mercury, calculate the height of water column for measuring 1 atm pressure.

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Borys Shumyatskiy | College Teacher | (Level 3) Associate Educator

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There are several almost identical definitions of 1atm. Because you mentioned mercury, I suggest to use the definition "1 atm = the pressure of the mercury column with the height of 760 mm".

As you probably know, the pressure of a liquid column is

P = ρ*g*h

where ρ is a liquid's density, h is a column's height and g is the acceleration of gravity (does not depend on liquid).

When we substitute mercury with water, the density decreases from 13.534 g/cm^3 to 1 g/cm^3, i.e. decreases 13.534 times. To preserve the same pressure, we have to increase the height with the same ratio.

Summarising, we obtain the height

760mm * 13.534 = 10285.84 mm, or 1028.584 cm, or 10.28584 m. (actually, 10m is accurate enough for many practical purposes.)

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