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Mercury manometer: absolute pressure of stream

Short answer

Gauge pressure equals mercury column height; absolute pressure adds atmospheric pressure. At 97.5 mm, P_abs = 760 + 97.5 = 857.5 mm Hg (114.4 kPa); at 80 mm, it becomes 840 mm Hg (112.1 kPa).

A mercury manometer is used to measure the pressure in steam pipe. The level of the mercury in the manometer is 97.5 mm. Find the absolute pressure of steam inside the pipe. If the reading of the manometer drops to 80 mm, what is the new pressure of steam? [Take sp.gr. of Hg = 13.6, Patm = 760 mm of Hg and g = 9.81 m/s²]

Given: mercury column difference h₁ = 97.5 mm (steam pressure above atmosphere), later h₂ = 80 mm, SG of Hg = 13.6, P_atm = 760 mm Hg, g = 9.81 m/s².

ρ_Hg = 13.6 × 1000 = 13 600 kg/m³.

Step 1: Atmospheric pressure P_atm = ρ g h = 13600 × 9.81 × 0.760 = 101 396 Pa = 101.40 kPa

Step 2: Gauge pressure for 97.5 mm P_gauge = 13600 × 9.81 × 0.0975 = 13 008 Pa = 13.01 kPa

Absolute pressure P = P_atm + P_gauge = 101.40 + 13.01 = 114.40 kPa
(in mm Hg: 760 + 97.5 = 857.5 mm Hg)

Step 3: When the reading drops to 80 mm P_gauge = 13600 × 9.81 × 0.080 = 10 673 Pa = 10.67 kPa

P = 101.40 + 10.67 = 112.07 kPa
(840 mm Hg)

Answer: Absolute steam pressure = 114.4 kPa initially and 112.1 kPa after the reading falls to 80 mm.

✓ Answer checked by Claude Opus 5.5 (high effort)

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