  The nonhomogeneous Navier-Stokes equations are considered in a cylindrical
domain in ${\mathbb R}^3$, parallel to the $x_3$-axis with large inflow and
outflow on the top and the bottom. Moreover, on the lateral part of the
cylinder the slip boundary conditions are assumed. The global existence of
regular solutions is proved under assumptions that inflow and outflow are close
to homogeneous and norms of derivative with respect to $x_3$ of the external
force and initial velocity are sufficiently small. The key point of this paper
is to verify that $x_3$-coordinate of velocity remains positive.
