  Bohm developed the Bohmian mechanics (BM), in which the Schr\"odinger
equation is transformed into two differential equations: A continuity equation
and an equation of motion similar to the Newtonian equation of motion. This
transformation can be executed both for single-particle systems and for
many-particle systems. Later, Kuzmenkov and Maksimov used basic quantum
mechanics for the derivation of many-particle quantum hydrodynamics (MPQHD)
including one differential equation for the mass balance and two differential
equations for the momentum balance, and we extended their analysis in a prework
[K. Renziehausen, I. Barth, Prog. Theor. Exp. Phys. 2018, 013A05 (2018)] for
the case that the particle ensemble consists of different particle sorts. The
purpose of this paper is to show how the differential equations of MPQHD can be
derived for such a particle ensemble with the differential equations of BM as a
starting point. Moreover, our discussion clarifies that the differential
equations of MPQHD are more suitable for an analysis of many-particle systems
than the differential equations of BM because the differential equations of
MPQHD depend on a single position vector only while the differential equations
of BM depend on the complete set of all particle coordinates.
