An open tube manometer is a device to measure the pressure of a gas in a vessel. It consists of a U-shaped tube containing a liquid (say, mercury) of density p, as shown in below figure.
One end of the tube is connected to the vessel while the other end is open to the atmosphere. The pressure p at point A is the (unknown) pressure of the gas in the vessel. The pressure on the mercury column in the open tube is the atmospheric pressure p0
A point B, at the same horizontal level as A, is at a depth h from the surface of mercury in the open tube. Therefore, the pressure at B is p0 + ρgh.
The pressures at points A and B at the same liquid level being the same, equating the unknown pressure p (at A) to the pressure at B.
p = p0 + ρgh
The pressure p is called the absolute pressure, and the difference in pressure p – p0 is called the gauge pressure.
