Measuring pressure

A device to measure pressure is called a manometer. A device which measures atmospheric pressure is called a barometer. The simplest design for these is a column of mercury in a beaker:

When the atmospheric pressure is increase, force is applied on the mercury, pushing it up the column. Mechanical equilibrium is reached when this force is balanced by both increased pressure inside the column, and weight of the mercury inside the column.

If the column contains a vacuum, then the increased atmospheric pressure is balanced purely by the weight of the mercury.

Pressure is force divided by area. The weight of the lifted mercury is mg, so the pressure on the base of the column is this weight divided by cross-sectional area. This has to match the increase in atmospheric pressure for the system to be at equilibrium:

Pressure = mg / A

Since mass is volume*density:

Notice that pressure is independent of the cross-sectional area of the cylinder.

A more advanced solution is to use a curved tube:

The change in pressure is directly proportional to the difference in height of the two columns. A different of 1 mm corresponds to 1 mm Hg, also known as one torr.

The reason mercury is used is because of its low vapor pressure. Using a liquid like water would mean having to account for more vapor pressure in the sealed part of the tube - but it can be done.