There is evidence for coronal plasma flows to break down into fragments and to be laminar. We investigate this effect by modeling flows confined along magnetic channels. We consider a full MHD model of a solar atmosphere box with a dipole magnetic field. We compare the propagation of a cylindrical flow perfectly aligned to the field to that of another one with a slight misalignment. We assume a flow speed of 200 km/s, and an ambient magnetic field of 30 G. We find that while the aligned flow maintains its cylindrical symmetry while it travels along the magnetic tube, the misaligned one is rapidly squashed on one side, becoming laminar and eventually fragmented because of the interaction and backreaction of the magnetic field. This model could explain an observation of erupted fragments that fall back as thin and elongated strands and end up onto the solar surface in a hedge-like configuration, made by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory. The initial alignment of plasma flow plays an important role in determining the possible laminar structure and fragmentation of flows while they travel along magnetic channels.