Answer: 4T/r (two surfaces: inner and outer).
- A 4T/r (two surfaces: inner and outer)
- B 2T/r, as for a single liquid drop with one surface
- C T/r, treating the film as having only one surface
- D 8T/r, double-counting both surfaces twice over
Correct answer: A. 4T/r (two surfaces: inner and outer)
Explanation: A soap bubble has two surfaces (inside and outside). Each surface contributes 2T/r, giving total excess pressure = 4T/r. For a single liquid droplet, it is 2T/r.
Since the same volume of fluid must pass every cross-section per second (continuity), the fluid speeds up where the pipe narrows; Bernoulli's equation then says this faster-moving fluid has lower pressure - the principle behind a venturi meter and an aircraft wing's lift.
Concept context
Pressure, buoyancy, Bernoulli equation, viscosity, and surface tension.