A Modified Navier-Stokes Equation for Incompressible Fluid Flow

In the actual flow process, due to the unsteady feature of the flow, the rotation of fluid element and variation in the changes of shear rate and other factors, thus the shear force impacted on the fluid should not just follow the Newton's law of viscosity. Based on this, the additional viscous forces related with variation in time and the history effects, the additional part with spatial variation and the relevant part due to the rotational motion have been proposed. An analogy method has been used to derive the shear rate related forces. This paper presents the corresponding expressions for the four additional forces. The action characteristic of the four additional part have been analyzed, the former two parts show influence on the unsteady movement of fluid element and the other two parts have impact on the lateral motion of the surrounding fluid. On the basis of the above considerations, a modified Navier-Stokes equation containing the additional force related with velocity has been given. The magnitude of the additional forces has been compared, the impact of which on the flow process has been analyzed.