This type of manometer as the name suggests has an inverted U-shaped tube. It is used to measure differences in low pressure between two points, where the high level of accuracy is desired.It is filled with liquid on the ends. The space between liquids is filled with air.This air can be expelled or admitted into the apparatus using a tap.This is done to adjust the pressure difference to obtain an accurate reading.
The equation for the same (source:http://www.msubbu.in/ln/fm/Unit-I/InvertedUtubeMano.htm)
Equating the pressure at the level XX'(pressure at the same level in a continuous body of static fluid is equal),
On the left-hand side:
Px = P1 – rg(h+a)
On the right-hand side:
Px‘ = P2 – (rga + rmgh)
Since Px = Px’
P1 – rg(h+a) = P2 – (rga + rmgh)
P1 – P2 = (r – rm)gh
If the manometric fluid is chosen in such a way that rm << r then,
P1 – P2 = rgh.
4. Micro Manometer:
Micromanometer is a great tool used in fluid statics. It is a modified form of a simple manometer. It has one limb which is larger in cross-section. It is a device which is used to measure very minute pressure differences with high accuracy.
The equation of hydrostatic equilibrium at PQ can be written as
where and are the densities of working fluid, gauge liquid, and manometric liquid respectively.
From continuity of gauge liquid,
If a is very small compared to A
With a suitable choice for the manometric and gauge liquids so that their densities are close a reasonable value of y may be achieved for a small pressure difference.