No it shouldnt. That means your bearings are going out on it.
Water leak at weep hole at bottom of water pump? Shaft loose? Bearing noise or wobble when engine is running?
Just about the only thing that will fail on that pump is the shaft seal or the shaft bearing. So, if the pump shaft (not the base seal) leaks water, the pump needs to be replaced or rebuilt. If you disconnect all the belts to the pump, it should turn freely, feel balanced, and you should not be able to wobble the shaft. If the car has really been abused and there was a lot of gunk in the coolant, then you might take the pump off and make sure that the impeller has not been banged up too much.
It should spin freely, but not wobble.It should spin freely, but not wobble.
Only replace the water pump if you have a visible external leak, the water pump bearings are bad, or the shaft is broken.
That would be a long shaft water pump.
The water pump is driven by the oil pump shaft - there is a tab on the end of the oil pump shaft and there is a groove on the water pump which sits into that shaft. All shafts end up being driven by the motor.
Failed water pump bearing.
The bearing in the water pump has failed and the water pump will need replaced.
Leaking around water pump mounting or shaft Play in shaft
Pull the radiator shroud, remove the serpentine belt, remove the fan from the water pump shaft, then remove the water pump.
Leaking?Wobble in pulley?
Water pump shaft loose? Water pump leaking? Water circulating in coolant system?