Rising bubble
Classical Mechanics
Level
5
A small spherical gas bubble of diameter \(d=4~\mu \mbox{m}\) forms at the bottom of a pond. When the bubble rises to the surface its diameter is \(n=1.1\) times bigger. What is the depth in meters of the pond?
Details and assumptions
The atmospheric pressure is \(p_{A}=10^{5}~\mbox{Pa}\), the acceleration of gravity is \(g=9.8~\text{m}/{\text{s}^{2}}\) and water's surface tension and density are \(\sigma=73\times 10^{-3}~\text{N}/\text{m}\) and \(\rho=1\times 10^{3}~\text{kg}/\text{m}^3\), respectively. The gas expansion is assumed to be isothermal.
by
David Mattingly