  The kinematics of the extra-planar neutral and ionised gas in disc galaxies
shows a systematic decline of the rotational velocity with height from the
plane (vertical gradient). This feature is not expected for a barotropic gas,
whilst it is well reproduced by baroclinic fluid homogeneous models. The
problem with the latter is that they require gas temperatures (above $10^5$ K)
much higher than the temperatures of the cold and warm components of the
extra-planar gas layer. In this paper, we attempt to overcome this problem by
describing the extra-planar gas as a system of gas clouds obeying the Jeans
equations. In particular, we consider models having the observed extra-planar
gas distribution and gravitational potential of the disc galaxy NGC 891: for
each model we construct pseudo-data cubes and we compare them with the HI data
cube of NGC 891. In all cases the rotational velocity gradients are in
qualitative agreement with the observations, but the synthetic and the observed
data cubes of NGC 891 show systematic differences that cannot be accommodated
by any of the explored models. We conclude that the extra-planar gas in disc
galaxies cannot be satisfactorily described by a stationary Jeans-like system
of gas clouds.

Astrophysics of Galaxies