  In the first part of this paper, the many-particle quantum hydrodynamics
(MPQHD) equations for a system containing many particles of different sorts are
derived exactly from the many-particle Schr\"odinger equation. It includes the
derivation of the many-particle continuity equations (MPCE), many-particle
Ehrenfest equations of motion (MPEEM), and many-particle quantum Cauchy
equations (MPQCE) for any of the different particle sorts and for the total
particle ensemble. The new point in our analysis is that we consider a set of
arbitrary particles of different sorts in the system. In MPQCEs, there appears
a quantity called pressure tensor. In the second part of this paper, we analyze
two versions of this tensor in depth -- the Wyatt pressure tensor and the
Kuzmenkov pressure tensor. There are different versions because there is a
gauge freedom for the pressure tensor similar to that for potentials. We find
that the interpretation of all quantities contributing to the Wyatt pressure
tensor is understandable but for the Kuzmenkov tensor, it is difficult.
Furthermore, the transformation from Cartesian coordinates to cylindrical
coordinates for the Wyatt tensor can be done in a clear way, but for the
Kuzmenkov tensor, it is rather cumbersome.
