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

How Does a Barometer Work?

Formula

Formula: Barometric Formula
Pressure-Height Graph of a Fluid (Air)
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
fufaev.org Pressure-Height Graph of a Fluid (Air)
Exponential decrease of pressure with height.

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