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Three pressure gauges on two compartments

Short answer

Atmospheric pressure = 13600 × 9.81 × 0.75 = 100.06 kPa. Absolute pressure in compartment 1 = 100.06 + 300 = 400.06 kPa. Compartment 2 = 400.06 - 200 = 200.06 kPa absolute. Gauge C reads 200.06 - 100.06 = 100 kPa.

Three pressure gauges are connected to a container consisting of two compartments as shown in figure below. If the local barometer reads 750 mm of Hg and pressure gauges A and B reads 300 kPa and 200 kPa respectively. Determine the absolute pressure in each compartment and reading of pressure gauge C. [Take ρHg = 13600 kg/m³ and g = 9.81 m/s²] [Figure: a container with two compartments 1 and 2; gauge A is connected to compartment 1, gauge B is connected between compartments 1 and 2, gauge C is connected to compartment 2.]

Given: barometer = 750 mm Hg, P_A = 300 kPa (gauge, compartment 1), P_B = 200 kPa (difference between compartments 1 and 2), ρ_Hg = 13600 kg/m³.

Assumption: Gauge A reads compartment 1 above atmosphere, gauge B reads the pressure difference P₁ − P₂, and gauge C reads compartment 2 above atmosphere.

Step 1: Atmospheric pressure P_atm = ρ g h = 13600 × 9.81 × 0.750 = 100 062 Pa = 100.06 kPa

Step 2: Compartment 1 P₁ = P_atm + P_A = 100.06 + 300 = 400.06 kPa (abs)

Step 3: Compartment 2 P₂ = P₁ − P_B = 400.06 − 200 = 200.06 kPa (abs)

Step 4: Gauge C P_C = P₂ − P_atm = 200.06 − 100.06 = 100 kPa (gauge)

Answer: P₁ = 400.06 kPa, P₂ = 200.06 kPa (absolute); gauge C reads 100 kPa.

✓ Answer checked by Claude Opus 5.5 (high effort)

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