A mercury barometer reads 745.0 mm on the roof of a building and 760.0 mm on the ground. Assuming a constant value of 1.29 kg/m3 for the density of air, determine the height of the building

The height of the building is 158.140 meters.

Explanation:

A barometer is system that helps measuring atmospheric pressure. Manometric pressure is the difference between total and atmospheric pressures. Manometric pressure difference is directly proportional to fluid density and height difference. That is:

Where:

- Manometric pressure difference, measured in kilopascals.

- Fluid density, measured in kilograms per cubic meter.

- Height difference, measured in meters.

Now, an equivalent height difference with a different fluid can be found by eliminating manometric pressure and proportionality constant:

Where:

- Height difference of the air column, measured in meters.

- Height difference of the mercury column, measured in meters.

- Density of air, measured in kilograms per cubic meter.

- Density of mercury, measured in kilograms per cubic meter.

If , and , the height difference of the air column is:

The height of the building is 158.140 meters.

this is poiselle's equation from fluid mechanic in physics. mech eng

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