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file: GATE CH 2020 (with Solutions).pdf

pages: 27–28

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AU-/text{tube} /text{manometer} /text{contains} two /text{manometric} /text{fluids} /text{of} /text{densities} 1000 kg m^{-3} /text{and} 600 kg m^{-3} . /text{When} /text{both} /text{the} /text{limbs} are /text{open} /text{to} /text{atmosphere} , the difference between the two levels is 10 cm at equilibrium, as shown in the figure. PQ 10 cm

The rest of the manometer is filled with air of negligible density. The acceleration due to gravity is

9.81ms^{-2} /text{and} /text{atmospheric} /text{pressure} /text{is} 100 kPa . /mathrm{How} /text{much} /text{absolute} /text{pressure} (/text{in} kPa) has /text{to} be /text{applied} /text{on} /text{the} /text{limb} ‘ P ’ /text{to} /text{raise} /text{the} /text{fluid} /text{in} /text{the} /text{limb} ‘ Q ’ /text{by} /text{another} 20 cm ?

.

P_1 = P_2

P_{atm}+/delta{}_1gh = P_{atm}+/delta{}_2g(.1+h)

1010 /times h = 600 /times 9.01(0.1+h)

h = 0.149m /approx 15cm

.

cm = 0.1m

P_1' = P_2'

P_a_b_s+/delta{}_1gh^1 = P_{atm}+/delta{}_2g(h^1+0.2)

Pₐ_bₛ=100.104 KPa Hence, the correct option is (A).

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Source PDF: GATE CH 2020 (with Solutions).pdf

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