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PRACTICE / Excess pressure in drops and bubbles

Separate depth from curvature

Two separate spherical gas bubbles of equal radius 0.80 mm are at depths 0.10 m and 0.25 m in the same liquid. Each is momentarily in mechanical equilibrium with its surroundings. Liquid density is 1000 kg/m³, g = 10 m/s² and surface tension is the same at both interfaces. Neglect motion and pressure variation over each small bubble.

How much higher is the deeper bubble’s absolute gas pressure?

Organize the givens & assumptions
  • Equal bubble radii
  • Depths 0.10 m and 0.25 m
  • ρ = 1000 kg/m³
  • g = 10 m/s²
  • Same surface gas pressure

Static or initially equilibrated interfaces, constant uniform surface tension, negligible gravity-induced shape distortion where spherical or cylindrical curvature is specified, and negligible evaporation. Capillary heights use the narrow-tube model with equal gas pressures and a large reservoir.

  1. A0 Pa0\ \mathrm{Pa}
  2. B1500 Pa1500\ \mathrm{Pa}
  3. C2500 Pa2500\ \mathrm{Pa}
  4. D1000 Pa1000\ \mathrm{Pa}

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