Drag reduction in heavy oil transport systems is a key for high-efficiency oil transfer and, thus, for energy conservation. In this paper, we investigated the influence of viscosity, velocity, and velocity-gradient fields on drag resistance in fluid flow with variable viscosity in terms of the field synergy. The theoretical analysis indicates that the drag during varying viscosity fluid flow processes depends upon not only the synergy between the velocity and its gradient over the entire flow domain but also the viscosity and velocity gradient at the boundary. That is, for a given flow rate or inlet velocity, simultaneously reducing the fluid flow field synergy number over the entire flow domain and decreasing the fluid viscosity and the velocity gradient at the boundary will lead to a smaller flow resistance. In addition, starting from the basic governing equation and via the calculus of variations, we derived Euler’s equation, essentially the momentum equation with a special additional volume force, usi...