The best and most realistic approach is to use a fluid simulator to create a mesh sequence which you use in Vue with this script -> http://www.cornucopia3d.com/forum/viewtopic.php?t=5089
Currently the choice of fluid simulators is either RealFlow (ask Forester) or Blender (ask me).

A second approach would be to use animated textures on alpha planes (this method won't be able to do the overflow though).
The realism of the stream from the faucet would be limited to a small range of camera angles (as is usual with alpha planes).