A soap bubble is blown slowly at the mouth of a tube of internal radius

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Fluid statics and the continuum picture · Fluid statics and the continuum picture

Fluids and Continuum Physics, Ch Surface tension, capillarity and wetting

Problem

A soap bubble is blown slowly at the mouth of a tube of internal radius a=4.0 mma = 4.0\ \mathrm{mm}. At every stage the film is a spherical cap of radius RR whose edge is pinned to the circular rim of radius aa, and the film has two faces of surface tension γ=0.025 N m−1\gamma = 0.025\ \mathrm{N\,m^{-1}}. The weight of the film is ignored, and the blowing is slow enough that the cap is in equilibrium at each stage, so the Young-Laplace result for a spherical soap film applies throughout. Take ρ=1000 kg m−3\rho = 1000\ \mathrm{kg\,m^{-3}} for water and g=9.8 m s−2g = 9.8\ \mathrm{m\,s^{-2}}. ((a)) Explain why the cap radius must satisfy R≥aR \ge a, with R=aR = a exactly when the cap is a hemisphere, and describe how RR changes as the cap grows from nearly flat to nearly a whole sphere. ((b)) Hence derive an expression for the largest gauge pressure the blower must supply, and evaluate it. ((c)) The blower's lungs are connected to a water manometer. Find the height difference of water this maximum pressure corresponds to.

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