In this work, a novel homotopy analysis method for the solution of two-fluid models is presented. A fully developed bubbly through a pipe is considered. Different physical and mathematical properties of the two-fluid model were identified. The problem was solved in the central region of the pipe where the wall forces were neglected, which implies that void fractions and velocity profiles are not affected by the wall. The system of equations was reduced to a single equation without parameters with an intrinsic length scale L. Away from the wall of the pipe, the flat void fraction depends on the applied pressure gradient, the density of different phases and gravity. It was also found that the effective specific weight of the fluid column was cancelled by the pressure gradient.