In this paper the structure is investigated of three-dimensional flows of rheological complex media (water-oil mixtures) in pipes and channels with long and short sections of constant and variable cross-sections. This is operating units of equipment for the oil and gas industry and power engineering. The steady and unsteady modes flows are modeling of oil-water environments in the internal systems. The ability analyzed of a low-viscosity two-phase structure of the movement to regroup in the peripheral region of the pipe wall with a higher shear stress. We study the pattern of change: coefficient of friction reducing its relatively high viscosity of the nucleus by forming a water ring, local hydrodynamic parameters for complex mixtures flow. The mechanisms are obtained of the influence of flow regimes on the phase boundary. Marked parts modeling of flow profile with immiscible phases within the system full equations of two-phase flow dynamics with allowance for the effects of interfacial interaction. The particular boundary conditions discussed for these flows. The reliability calculation estimated by comparison with the existing data of similar flows (for example, A.Wegmann and P.R. Rohr's results).