  It can be observed that the differential operators of fluid mechanics can be
defined in terms of the complete derivative on the finite - dimensional affine
space. It follows from the fact that all norms on the finite - dimensional
vector space are equivalent and from the definition of the complete derivative
on the normed affine spaces (see: L.Schwartz, Analyse Mathematique, Hermann,
1967). In particular, it is shown that the "substantial derivative" of the
standard formulation is a directional derivative along the "non - relativistic
four - velocity".
