We consider motions to the nonhomogeneous Navier-Stokes problem in
cylindrical domains in $R^3$, with large inflow and outflow. With
"nonhomogeneous" we mean a density dependent system. The inflow and
outflow are prescribed on the parts of the boundary which are
perpendicular to the $x_3$-axis. We prove the existence of global strong
solutions without smallness restrictions on velocity and flux but under
assumptions that inflow and outflow are close to homogeneous and $x_3$
derivatives of external force and initial velocity are sufficiently
small. The key step is to verify that 3-rd coordinate of velocity
remains positive.