just looked in the Cooling section of the K3 manual here
http://www.sv650.org/sv_manuals.htm
and on page 6-14 it shows that pipe coming from behind the engine cover, running under the coolant pump, then going
downwards and sitting in a small clip just beside/below the starter motor. I don't know what that pipe is or where it comes from, but that's where it goes to.
(PS - it looks like it comes from a short stub in the bottom of the pump which is almost certainly a drain pipe for draining the system. The bolt just above it is the drain bolt IIRC
)
(PPS - looking further down that section, it actually looks more like it's a "weep" pipe to avoid any coolant seepage past the face seal from getting to the bearings. Seems a bit OTT if it is, it's more usual just to have a small hole
)