  Based on the Wigner function in local equilibrium, we derive hydrodynamical
quantities for a system of polarized spin-1/2 particles: the particle number
current density, the energy-momentum tensor, the spin tensor, and the dipole
moment tensor. Comparing with ideal hydrodynamics without spin, additional
terms at first and second order in the Knudsen number $\text{Kn}$ and the
average spin polarization $\chi_s$ have been derived. The Wigner function can
be expressed in terms of matrix-valued distributions, whose equilibrium forms
are characterized by thermodynamical parameters in quantum statistics. The
equations of motions for these parameters are derived by conservation laws at
the leading and next-to-leading order $\text{Kn}$ and $\chi_s$.
