Field Equations for Flows of Newtonian Fluids

Abstract

The equations of motion for a general (Newtonian) fluid will now be established. In doing so the fluid will be considered to be a continuum. In a continuum the smallest volume element considered dV is still homogeneous, i.e. the dimensions of dV are still very large compared to the average distance between the molecules in the fluid. In gases the assumption of a continuum is valid if the Knudsen number Kn = l ₀/l is very small, where h is the mean free path and l ₀ a characteristic length of the flow field, see S.A. Schaaf (1958).