The basic barometer can be used to measure the height of a...

The basic barometer can be used to measure the height of a building. If the barometric readings at the top and at the bottom of a building are 675 and $695 \mathrm{mmHg}$, respectively, determine the height of the building. Take the densities of air and mercury to be $1.18 \mathrm{kg} / \mathrm{m}^{3}$ and $13,600 \mathrm{kg} / \mathrm{m}^{3}$ respectively.

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Key Concepts

Hydrostatic Equation

This concept relates the pressure difference in a fluid column to the product of the fluid's density, gravitational acceleration, and the height difference. It is expressed as ?P = ?gh and is fundamental in determining height differences when pressure measurements are known.

Atmospheric Pressure Difference

This involves measuring the change in atmospheric pressure between two points, which can be used to estimate the elevation difference between those points. In problems like this, the pressure difference measured by a barometer at different heights provides the necessary data to compute the height of a structure.

Barometer

A barometer is an instrument used to measure atmospheric pressure. In the context of using it to measure building heights, the barometer takes readings at different elevations and the difference in these readings, when interpreted with the relevant physical laws, can be used to determine the height difference between the two measurement points.

Fluid Density

The density of the fluid, in this case mercury, is a key factor in converting a difference in measured pressure (expressed in terms of a fluid column height) into a height value. Knowing the density allows the application of the hydrostatic equation, as it directly relates the pressure exerted by a column of fluid to its height.

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