A manometer reads the pressure of a gas in an enclosure as shown in Fig. 10.25 (a) When a pump removes some of the gas, the manometer reads as in Fig. 10.25 (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) Local atmospheric pressure, Patm = 76 cm of Hg
Gauge pressure = mercury height in (Right limb – Left limb)
Absolute pressure = Atmospheric pressure + Gauge pressure
For figure a:
Gauge pressure = 20 cm of Hg
Absolute pressure = 76 + 20 = 96 cm of Hg
For figure b:
Gauge pressure = -18 cm of Hg
Absolute pressure = 76 - 18 = 56 cm of Hg
(b) Relative density of the mercury = 13.6
∴ 13.6 cm of water exerts same pressure as 1cm of mercury exerts.
Thus,
Pressure in the right limb, Pr = Atmospheric + 1 cm of Hg
= 76 + 1 = 77 cm of Hg
Pressure in the left limb, Pl = 58 + h cm of Hg
∴ Height difference between limbs, h = 77 - 58 = 19 cm