  The Weyssenhoff fluid is a perfect fluid with spin where the spin of the
matter fields is the source of torsion in an Einstein-Cartan framework. Obukhov
and Korotky showed that this fluid can be described as an effective fluid with
spin in general relativity. A dynamical analysis of such a fluid is performed
in a gauge invariant manner using the 1+3 covariant approach. This yields the
propagation and constraint equations for the set of dynamical variables. A
verification of these equations is performed for the special case of
irrotational flow with zero peculiar acceleration by evolving the constraints.
