The author develops the general solution for the axial two-phase viscous flow in a long circular pipe. The interface between the two phases is taken to be either circular-cylindrical or an arc-segment of a cylindrical surface; possibly of zero curvature. The expressions for the velocity distributions obtained may be of use in calculating the amount of water that should be added to oil pipelines, in order to reduce pumping costs. The mathematical problem is that of potential and, hence, this work is also the solution of various analogous problems in the fields of elasticity, heat transfer, mechanics, or electricity.

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