How Does an Open-End Manometer Tell You a Gas's Pressure?
Fluid Statics: Reading Gas Pressure with an Open-End Manometer
Take the horizontal equal-pressure level through the lower meniscus. Every point on it lies in one connected body of fluid at one depth, so pressure there is identical in both limbs. Gas limb contributes pg. Open limb contributes p₀ plus the column of height h standing above that level. Equate: pg = p₀ + ρgh. The gas column itself is ignored — gas density is roughly 10⁻⁴ of the liquid’s.
h carries a sign. Define h = (open-limb level) − (gas-limb level). h > 0 means the open limb stands higher, so the gas is above atmospheric: positive gauge pressure. h < 0 means the gas limb stands higher and pg < p₀. Set pg = 101.3 kPa and h = 0 — equal levels are the signature of zero gauge pressure, not of zero pressure.
Rearranged, h = Δp / ρg, so h ∝ 1/ρ. Switching mercury to water multiplies every reading by 13.6. At Δp = 28.7 kPa mercury rises 21.5 cm; water needs 2.93 m. That is why dense mercury, not water, fills a laboratory manometer.
The Equal-Pressure Level, and Why h Carries a Sign
Drag the gas pressure slider and watch both limbs move. The gas limb falls exactly as far as the open limb rises, so the height difference h is always split evenly between them.
The equation comes from a single horizontal line. Take the level of the lower meniscus — the dashed line in the simulation. Every point on it lies in one connected body of fluid at one depth, so the pressure there is identical in both limbs. On the gas side that pressure is p_g. On the open side it is p₀ plus the column of height h standing above that level. Setting the two equal gives p_g = p₀ + ρgh. The gas column itself is ignored, since its density is roughly 10⁻⁴ of the liquid's.
h is signed: h = (open-limb level) − (gas-limb level). Positive h means the open limb stands higher and the gas is above atmospheric — positive gauge pressure. Negative h means the reverse. Set p_g to exactly 101.3 kPa and the two levels sit dead flat. Equal levels signal zero gauge pressure, not zero pressure.
Now switch the manometer fluid. Because h = Δp/ρg, the column length scales as 1/ρ. The simulation opens with oil at 850 kg/m³; mercury is exactly 16 times denser, so its column is 16 times shorter for the same Δp — 21.5 cm against 3.44 m at Δp = 28.7 kPa. That ratio is why a laboratory manometer is filled with mercury. Watch the scale marker beside the tube change as you switch: the drawing rescales, the physics doesn't.
