Mechanical Properties of Fluids
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Question : 22
Total: 31
A manometer reads the pressure of a gas in an enclosure as shown in figure. (a). When a pump removes some of the gas, the manometer reads as in figure (b). The liquid used in the manometers is mercury and the atmospheric pressure is 76 cm of mercury.
(a) Give the absolute and gauge pressure of the gas in the enclosure for cases (a) and (b), in units of cm of mercury.
(b) How would the levels change in case (b) if 13.6 cm of water (immiscible with mercury) are poured into the right limb of the manometer? (ignore the small change in the volume of the gas).
(a) Give the absolute and gauge pressure of the gas in the enclosure for cases (a) and (b), in units of cm of mercury.
(b) How would the levels change in case (b) if 13.6 cm of water (immiscible with mercury) are poured into the right limb of the manometer? (ignore the small change in the volume of the gas).
Solution:
Here, atmospheric pressure, P = 76
(a) In figure (a) pressure head,h = + 20 c m
∴ Absolute pressure= P + h = 76 + 20 = 96
Gauge pressure= h = 20
In figure (b) pressure head,h = – 18
Absolute pressure= P + h = 76 + ( – 18 ) = 58
Gauge pressure= h = – 18
(b) Here 13.6 cm of water added in right limb is equivalent to
= 1
i.e.h ′ = 1
Now pressure atA
P a = P + h ′ = 76 + 1 = 77 c m
Let the difference in mercury levels in the two limbs beh 1 b ,
P b = 58 + h 1
As,P a = P b ′
∴ 77 = 58 + h 1 h 1 = 77 − 58 = 19
(a) In figure (a) pressure head,
∴ Absolute pressure
Gauge pressure
In figure (b) pressure head,
Absolute pressure
Gauge pressure
(b) Here 13.6 cm of water added in right limb is equivalent to
i.e.
Now pressure at
Let the difference in mercury levels in the two limbs be
As,
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