The inverted U-tube differential manometer is reciprocal of the U-tube differential manometer at a different level. This type of manometer is used to measure the accuracy of small differences if pressure is increased. Inverted U-tube manometer, Fig.1 is used for measuring pressure differences in liquids. The space above the liquid in the manometer is filled with air. To adjust the level of the liquid in the manometer, a tap at the top is provided that admits or expels the air. The pressure at the same level in a continuous body of static fluid is equal.
The pressure at level XX’ is equated as follows:
For the left arm of the manometer:
Px = P1 − ρ g (h + a) … (1)
where Px is pressure in the left arm at point X, P1 is pressure in the left arm fluid, ρ is the density of the air and g is the gravitational force.
For the right arm of the manometer:
Px = P2 − (ρ g a + ρm g h) …. (2)
where, ρm is the density of mercury.
Px = Px’ …. (3)
P1 – ρ g (h + a) = P2 − (ρ g a + ρm g h)
P1 – P2 = (ρ – ρm) g h …. (4)
If the manometric fluid is chosen in such a way that ρm << ρ then,
P1 – P2 = ρ g h …. (5)
For an inverted U-tube manometer, the manometric fluid is usually air.
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