Abstract: This macroscopic approach is based on the conception of fluid elements which represent (mass)-points and (point)-masses at the same time. As individual point the fluid element owns a momentum and as collective domain a potential of energy. This dualistic view has the advantage that the basic equations of fluid mechanics can be simplified. If the system is reduced to a balance of momentum and energy the continuity equation does not explicitly become part of it. Then, the number of dynamic variables in the classical equations will be reduced to four: the momentum vector and a quantity of energy leading to a kinematic representation in the end. In case of incompressible flows agreement is reached with the Navier–Stokes equations. Computational results concern unsteady three-dimensional flows, particularly showing the formation of Taylor vortices in a turning cylinder and of spiral vortices behind a backwards-facing step in a channel flow. As a remarkable result of this approach a deeper insight into the phenomenon of turbulence could be achieved.