I know it's a very old post but I'll answer just in case I'm not the only one in the world still driving a Y3-Sonata V6.
I just did timing belt and water pump on mine last weekend so I'm a little more familiar with the cooling system now.
The old Sigma V6 installed in the Y3 has a water tube going all the way from the right end (where the hose attaches it to the radiator) to the left where it's plugged into the water pump back, sealed by an O-ring.
If water runs out both ends it's likely that the O-Ring failed. Or the tube is corroded.
The water pump itself has a leak 'channel' that allows water to run out in case the pulley seal fails. Water will then drip out at the water pump bottom near the front cylinder bank right above the oil filter but not on the other engine's end.
Originally Posted by rachelj
remove the "v6 3000" casing to get a closer look.
will not be a good approach. You'll have to remove upper and lower part of the intake to get free view of the V-area from the top. Better invest in a 20$ USB snake-cam.
Unlike the Delta engine (Sonata EF and others) the back housing of the water pump is not part of the crankcase casting but a separate part.
Also Hyundai wins a 'moron prize' from me for placing one of the pump mounting screws INSIDE the power steering pump bracket as well as for the 6th screw holding back and front case together being installed from the back of the pump.