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Two-compartment vessel gauges: reading of gauge C

Short answer

Gauge C reads 2 bar. Atmospheric pressure is 1.014 bar; absolute pressure in the compartment with gauge A is 5.014 bar, and in the other compartment 3.014 bar, giving gauge C = 3.014 - 1.014 = 2 bar.

A vessel shown has two compartments as shown in figure below at different pressures. The pressure gauge A reads 4 bar and B reads 2 bar. The barometer reads 760mm of Hg. Calculate the reading of gauge C. [Take ρ = 13600 kg/m³ and g = 9.81 m/s²] [Figure: a vessel with two compartments; gauge C on the left end, gauge B on the partition region, gauge A on the right end.]

Given: gauge A = 4 bar, gauge B = 2 bar, barometer = 760 mm Hg, ρ = 13600 kg/m³.

Assumption: Gauge A reads one compartment above atmosphere, gauge B reads the pressure difference across the partition, and gauge C reads the other compartment above atmosphere (the arrangement in the standard two-compartment problem).

Step 1: Atmospheric pressure P_atm = 13600 × 9.81 × 0.760 = 101 396 Pa = 1.014 bar

Step 2: Compartment with gauge A P_a = P_atm + 4 = 1.014 + 4 = 5.014 bar (abs)

Step 3: Other compartment (gauge B reads the difference) P_c = P_a − P_B = 5.014 − 2 = 3.014 bar (abs)

Step 4: Gauge C reading P_C = P_c − P_atm = 3.014 − 1.014 = 2 bar (gauge)

Equivalently, C = A − B = 4 − 2 = 2 bar.

Answer: Gauge C reads 2 bar (absolute pressure there = 3.014 bar).

Note: if the figure shows the compartment with gauge C at the higher pressure (gauge B reading it above the compartment with gauge A), then C = A + B = 6 bar (absolute 7.014 bar).

✓ Answer checked by Claude Opus 5.5 (high effort)

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