Manometers measure pressure.
It is basically a glass tube closed at one end, the other end open to the atmosphere. The closed end contains a gas, separated from the atmosphere by liquid in a 'U' bend, shown in blue above. The gas in the bulb exerts a pressure,
and pushes the liquid around the U bend until forces on the surfaces of the two surfaces of the liquid are useful.
The gas in the bulb 4 exerts a pressure
We calculate the force exerted on the surface using the equation
so the force exerted on the left hand liquid surface 3 by the gas is
This force must be balance by an equal and opposite force exerted at 2 by the atmosphere and the liquid. The atmosphere exerts a pressure equally in all directions, of about
so using (1) again, the pressure exerted by the atmosphere is
To find the force at 2 we must add to this the force exerted at 2 by the column of liquid between 1 and 2. The pressure exerted by a column of liquid of height
is
where
is the density and
so the force exerted by this column of liquid is
using (1) again.
Equating forces at 3 and 2 gives
If the mass and temperature of gas in the glass bulb is kept constant, a manometer can be used to measure atmospheric pressure. If the gas is pumped out so that there is a vacuum in the bulb then
The liquid in the U bend will move towards the bulb end and the pressure exerted by the liquid will be useful to atmospheric pressure.