Mercury Barometer

Several simple instruments for the measurement of pressure make use
of a column of liquid. A mercury barometer consisting of a tube of
glass, about 1m long, closed at the upper end and open at the lower
end. The tube is filled with mercury, except for a small empty space at
the top. The bottom of the tube is immersed in an open bowl filled with
mercury. The atmospheric pressure action on the exposed airfare of
mercury in the bowl prevents the mercury from flowing out of the
tube. At the level of the exposed surface, the pressure exerted by the
column of mercury is ρgh where ρ = 1.36 × 104 kg/m3 is the density of
mercury and h the height of the mercury column. For equilibrium, this
pressure must match the atmospheric pressure -

P0= ρhg

This equation permits a simple determination of the atmospheric
pressure from a measurement of the height of the mercury column.
In view of the direct correspondence of the atmospheric pressure and
the height of the mercury column, the pressure is often quoted in terms
of this height, usually expressed in millimeters of mercury (mm-Hg).
The average value of the atmospheric pressure at sea level is 760 mm-
Hg, which by definition is one atmosphere (atm). Hence,
1 atm = 760 mm-Hg = P × g × 0.760 m
= 1.36 × 104kg/m3 × 9.81m/s2 × 0.760 m
= 1.01 × 105 N/m2
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