Question

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).

Answer 1

(1) Atmospheric pressure (Po) = 76cm of Mercury .
in fig (a)
Pressure head ( h1) = 20 cm of Hg
So, absolute pressure of the gas (P) = Po + h1.d.g
= 76 cm of Hg + 20cm of Hg
= 96cm of Hg

Guage pressure = absolute pleasure- atmospheric pressure
= 96cm of Hg - 76cm of Hg
= 20cm of Hg

In fig (b)
Head pressure (h2) = 18cm of Hg
So, absolute pleasure of the gas ( P') = Po + h2.d.g
= 76cm of Hg + (-18cm of Hg )
= 58cm of Hg

Guage pressure = absolute pleasure - atmospheric pressure
= 58 cm of Hg - 76cm of Hg
= -18cm of Hg

(ii) 13.6 cm of water poured into the right limb is equivalent to
P1 = P2
h1.d1.g = h2.d2.g
h2 = h1.d1/d2
= 13.6 × 1/13.6
= 1 cm of Hg

Answer 2

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