# Rising bubble

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.

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