A second approximation for the velocity of a large gas bubble rising in an infinite liquid

A second approximation for the velocity of a large gas bubble in an infinite liquid is derived from a linear perturbation of the first approximation. Previously known experimental results are in excellent agreement with the resulting velocity, \[ U = 0.652(g\overline{a})^{\frac{1}{2}}, \] where $\overline{a}$ is the apparent radius of curvature of the front part of the bubble, and g the acceleration due to gravity. The shape of this second approximation is seen to be indistinguishable from spherical over a large region near the front stagnation point.