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Chamber with two compartments: absolute pressures, gauge C

Short answer

Absolute pressures: compartment 1 = 396.06 kPa, compartment 2 = 276.06 kPa. Gauge C reads 180 kPa. Atmospheric pressure is 96.06 kPa.

A large chamber is separated into compartments 1 and 2, as shown in Figure P.8, which are kept at different pressure. Pressure gauge A reads 300 kPa and pressure gauge B reads 120 kPa. If the local barometer reads 720 mm Hg, determine the absolute pressure existing in the compartments and the reading of gauge C. Take ρ = 13600 kg/m³ and g = 9.81 m/s². [Figure P.8: a chamber with compartments 1 and 2 in a row; gauge A on the left end (compartment 1), gauge B on the partition between 1 and 2, gauge C on the right end (compartment 2).]

Given: P_A = 300 kPa, P_B = 120 kPa, barometer = 720 mm Hg, ρ = 13600 kg/m³, g = 9.81 m/s².

Assumption: Gauge A reads compartment 1 above atmosphere, gauge B reads P₁ − P₂ across the partition, gauge C reads compartment 2 above atmosphere.

Step 1: Atmospheric pressure P_atm = 13600 × 9.81 × 0.720 = 96 060 Pa = 96.06 kPa

Step 2: Compartment 1 P₁ = P_atm + P_A = 96.06 + 300 = 396.06 kPa (abs)

Step 3: Compartment 2 P₂ = P₁ − P_B = 396.06 − 120 = 276.06 kPa (abs)

Step 4: Gauge C P_C = P₂ − P_atm = 276.06 − 96.06 = 180 kPa

Answer: P₁ = 396.06 kPa, P₂ = 276.06 kPa (abs); gauge C reads 180 kPa.

✓ Answer checked by Claude Opus 5.5 (high effort)

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