Open End U‑Tube Manometer

Open-End U-Tube Manometer

An open-end U-tube manometer compares the vessel’s gas pressure p_g with atmospheric pressure p₀ using a liquid column (mercury, ρ ≈ 13 593 kg/m³). The vertical separation h between the free surfaces converts pressure difference to height: Δp = p_g − p₀ = ρgh.

Gauge pressure = pressure relative to atmosphere → Δp = p_g − p₀

Sign convention (used in this simulation)
Take L2 = 0 (left, gas side). Define h = level(L1) − level(L2), measured vertically.
Then p_g − p₀ = ρgh:
• h > 0 ⇒ p_g > p₀ (positive gauge)
• h = 0 ⇒ p_g = p₀
• h < 0 ⇒ p_g < p₀ (negative gauge)

How to use the simulation
• Move the Gas Pressure (p_g) slider. Higher p_g makes gas particles move faster.
• Watch the levels: the right arm is open to atmosphere (p₀). Thin tick lines mark each surface; the double-headed arrow is h.
• Read the numbers: p_g (kPa), p₀ = 101.3 kPa, and h (cm). For mercury, 1 kPa ≈ 0.75 cm Hg.
• Explore: set p_g ≈ 101.3 kPa → h ≈ 0; raise p_g by ~8.7 kPa → h ≈ 6.5 cm; lower p_g below p₀ → the left (gas) arm rises.

Quick example
Given p₀ = 101.3 kPa and p_g = 110.0 kPa:
Δp = 8.7 kPa = 8700 Pa; h = Δp/(ρg) = 8700/(13 593×9.81) m ≈ 0.065 m = 6.5 cm.

Key takeaways
• Gauge vs absolute: slider sets p_g (absolute); gauge = Δp = p_g − p₀.
• Linear scaling: for fixed ρ and g, h ∝ Δp.
• Density matters: smaller ρ (e.g., water) → larger h for the same Δp.
• Measure h vertically (not along the bend). Signs follow the convention above.