U-tube manometer contains water or mercury in a U-shaped tube, and is usually used to measure gas pressure. One end of the U tube is exposed to the unknown pressure field (P) and the other end is connected to a reference pressure source (usually atmospheric pressure) (Pref), shown in the schematic below.
If fluid C is the atmosphere, fluid B is the liquid in the U tube (e.g. water or mercury), and fluid A is a gas, then we can assume that ρB >> ρA, ρC. The pressure contributed by the weight of gas within the U tube can therefore be neglected. The gage pressure of the gas can be approximated by,