  We give an exact description of the steady flow of a black string into a
planar horizon. The event horizon is out of equilibrium and provides a simple,
exact instance of a `flowing black funnel' in any dimension D>=5. It is also an
approximation to a smooth intersection between a black string and a black hole,
in the limit in which the black hole is much larger than the black string
thickness. The construction extends easily to more general flows, in particular
charged flows.
