The velocity of gas bubble rise in a tube

The solutions of the Laplace equation involving the diverging infinite series are used in the classical works at the analysis of the problem of the gravitational rise of a gas bubble in a tube filled with ideal fluid (the Taylor bubble). In the present work, an approximate method is proposed for a correct analysis of the above problem. The ideal fluid flow around a body of revolution in a tube is constructed by the method of the superposition of elementary solutions. The satisfaction of the free surface condition in the critical point neighborhood and the passage of the main parameter to the limit lead to the sought expression for the dimensionless velocity of the gas bubble — Froude number.