My name is Alexander FufaeV and here I will explain the following topic:

How Does a Barometer Work?

Formula

What do the formula symbols mean?

Pressure

Unit
Air pressure (or the pressure of another fluid) at height $$h$$ above the sea surface. According to this barometric formula, air pressure decreases exponentially with height.

Pressure at the bottom

Unit
Air pressure at sea level $$h = 0$$.

Scale height

Unit
Scale height is a constant that depends, for example, on the temperature of the air and the gravitational acceleration. The scale height is approximately $$H=8\,\mathrm{km}$$ on Earth.

Height

Unit
Height measured from the sea surface.
Explanation

Video

A simple barometer works by using the barometer formula, which relates the height $$h$$ above the ground to the air pressure $$\mathit{\Pi}$$ prevailing at that height:

Formula anchor

Here $$H ~=~ 8005 \, \mathrm{m}$$ and the mean air pressure at sea level is $$\mathit{\Pi}_0 = 101 \, \mathrm{kPa} = 1 \, \mathrm{bar}$$. The formula states that the air pressure decreases exponentially with increasing height $$h$$.

So an barometer measures the air pressure $$\mathit{\Pi}$$ and calculates from it the height at which this air pressure prevails:

Formula anchor