Manometers and Barometers

A barometer is a tube of mercury, closed at the top, sealed and then inverted into a dish of mercury, with a vacuum at the closed top. Atmospheric pressure pushes down on the mercury in the dish, and that pressure has to support the column of mercury in the tube. The column stops rising at whatever height makes the mercury's weight per area equal atmospheric pressure. At sea level that works out to about 76 cm of mercury, so if you know the density of mercury you can convert that height directly into pressure using P = rho g h.

A manometer does the same trick but compares two pressures instead of one. A U-shaped tube holds mercury, one end connects to a gas tank, the other end is open to the atmosphere. If the gas pressure is higher than atmospheric, it pushes the mercury down on its side and up on the open side, and the height difference between the two surfaces tells you exactly how much higher the gas pressure is. Add that extra pressure, rho g h, to atmospheric pressure, and you get the absolute gas pressure. When a storm rolls in, atmospheric pressure drops, so the barometer's mercury column shrinks since there is less pressure available to hold it up.

This connects directly to the general fluid pressure relationship P = P0 + rho g h used throughout the fluids unit: pressure increases with depth in a fluid because of the weight of fluid above. Manometers and barometers are just that same idea read backwards, using a measured height to find an unknown pressure instead of the other way around.