摘要: This paper is concerned with the flow of an incompressible heavy liquid past a gas bubble in infinitely long vertical tube. Attention confined to plane flow, and it assumed that extends downwards without limit, so motion steady. A co-ordinate system attached chosen, falling around bubble, instead rising liquid. It supposed irrotational, whence can be described terms complex potential C = 0 + i3f which analytic function variable z x iy physical plane. The considered at rest, state constant pressure. tube represented as infinite strip - -h < Ih width h. (z) normalized transforms region flowing this conformally on 1 /i 1, free boundary mapping slit along positive axis. If origin placed vertex Bernoulli's equation shows requirement pressure takes form
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