Abstract Air bubbles of various sizes moving up in still water are carefully treated experimentally and then theoretically. Their terminal velocities are determined in relation to their sizes, and the changes of their shapes during their motion are investigated. The mass of water carried up with a moving bubble and the resistance to its motion are determined, and the most probable equation of motion is proposed. It is also proved that there are two different kinds of motion of a bubble in water exactly analogous to the stream-line and the turbulent flows of a viscous fluid, which passes from the one to the other distinctly at the critical radius of the bubble.
Otogorô Miyagi (1925) studied this question.