Atmospheric Pressure, Barometers & Manometers

Above you stands a column of air hundreds of kilometres tall. Its weight presses on everything: on this page, on your skin, on the surface of every lake. We just don’t notice, because the push is the same from all sides.

The weight of the air#

The atmosphere extends to roughly 200 km above the Earth. The force per unit area it exerts on any surface (always perpendicular to that surface) is the atmospheric pressure. At the top of the atmosphere it is zero; going down, it builds up as $\int\rho g\,dz$. Air is so light that over everyday height differences the pressure hardly changes: we can speak of “the” atmospheric pressure of a town without worrying whether we measure it at street level or on a rooftop.

Torricelli’s barometer#

Fill a glass tube about a metre long with mercury, close the open end with a thumb, turn it upside down into a dish of mercury and remove the thumb. The mercury falls a little and stops, leaving a vacuum at the top of the tube.

At the top of the column (A) the pressure is zero (vacuum). A point B inside the tube at the level of the dish’s surface is at the same height as the open surface C, where the pressure is atmospheric, so $P_B = P_0$. If B is a height H below A,

Atmospheric pressure is often quoted as the height of this mercury column. At sea level it is about 76 cm:

If the tube were shorter than 76 cm, the mercury would not fall at all; the glass would press down on it to make up the difference.

The manometer#

To measure the pressure of a gas in a closed vessel, connect it to one arm of a U-tube containing liquid, leaving the other arm open to the air. Points at the same level in the liquid have the same pressure, so