1 The manometer

• A manometer measures the difference between the pressure of a gas in a container and the atmospheric pressure.
• It is a U-shaped tube containing a liquid of known density (usually mercury, or water/oil for small pressures).
• One arm is connected to the gas container; the other is open to the air.

• Gas pressure greater than atmospheric:

  • the liquid is lower in the arm connected to the gas.
  • Using two points at the same level in the same liquid:

  P = P_a + ρ g h

• Gas pressure less than atmospheric: the liquid in the open arm is lower:

  P = P_a − ρ g h

The pressure difference (gauge pressure) is ΔP = P − P_a = ρ g h (positive or negative).

Choice of manometer liquid.

• Mercury for large pressures (dense, so the height difference is small); a light liquid (water, oil) for small pressure differences, which gives a large and readable height difference.
• The liquid must not react with or dissolve the gas and should have a low vapour pressure.

Example 1. A mercury manometer connected to a gas container shows the mercury in the open arm 24 cm higher than in the arm connected to the container. The gas pressure P = 76 + 24 = 100 cm Hg = 100/76 = 1.316 atm = 1.316 × 1.013 × 10⁵ = 1.333 × 10⁵ N/m².

Example 2. If the mercury in the open arm were 18 cm lower, then P = 76 − 18 = 58 cm Hg (below atmospheric: a partial vacuum).

Example 3 (water manometer). A water manometer shows a height difference of 40 cm. ΔP = ρgh = 1000 × 9.8 × 0.4 = 3920 N/m².

Example 4 (mercury, SI). In a manometer h = 25 cm of mercury, ρ = 13 600, g = 9.8: ΔP = 13 600 × 9.8 × 0.25 = 3.332 × 10⁴ N/m²; the absolute gas pressure = 1.013 × 10⁵ + 0.333 × 10⁵ = 1.346 × 10⁵ N/m².