Manometer Calculator

A manometer measures pressure by balancing it against the weight of a liquid column. The fundamental relation is ΔP = ρgΔh, where ρ is the manometer fluid density, g ≈ 9.81 m/s², and Δh is the vertical height difference between the two liquid levels (always use vertical height, not slant length unless corrected).

U-tube manometer: two legs connected at the bottom; the difference in liquid levels between high-pressure and low-pressure sides gives ΔP = ρgΔh. If one leg is open to atmosphere, the other side measures gauge pressure P_gauge = ρgh relative to air.

Mercury (ρ ≈ 13,600 kg/m³) is used for compact high-range instruments: 760 mm Hg column height ≈ 1 standard atmosphere (101.3 kPa). Water (ρ = 1000 kg/m³) gives 10.3 m of water per atmosphere — excellent sensitivity for small ΔP in labs but impractical for very high pressures.

Inclined manometer: tube tilted at angle θ so a small vertical rise h = L sin θ produces a longer readable displacement L along the tube — multiplies sensitivity by 1/sin θ. Differential manometers measure small ΔP between two systems without referencing atmosphere.

Important corrections: use manometer fluid ρ at operating temperature; for gas-filled legs, gas density is usually negligible compared to liquid; capillary rise in narrow tubes can affect small Δh readings; for two immiscible fluids in one manometer, use interface analysis.

Conversions: 1 mmHg ≈ 133.3 Pa; 1 in H₂O ≈ 249 Pa; 1 bar = 10⁵ Pa. Blood pressure in mmHg is historically a manometric scale. Digital transducers have largely replaced manometers in industry, but manometers remain the calibration standard.