  The idea to describe quantum systems within a hydrodynamic framework (quantum
hydrodynamics, QHD) goes back to Madelung and Bohm. While such a description is
formally exact for a single particle, more recently the concept has been
applied to many-particle systems by Manfredi and Haas [Phys. Rev. B {\bf 64},
075316 (2001)] and received high popularity in parts of the quantum plasma
community. Thereby, often the applicability limits of these equations are
ignored, giving rise to unphysical predictions. Here we demonstrate that
modified QHD equations for plasmas can be derived from Thomas-Fermi theory
including gradient corrections. This puts QHD on firm grounds. At the same time
this derivation yields a different prefactor, $\gamma=(D-2/3D)$, in front of
the quantum (Bohm) potential which depends on the system dimensionality $D$.
Our approach allows one to identify the limitations of QHD and to outline
systematic improvements.
