Annoying engine whining noise

Could be the belt tension loose, tensioner or driven components such AC compressor but the water pump is run by the timing chain which if the tension is too tight the engine will whine. Here are some guides to help you see how the water pump job is done (below). I would recheck the timing chain tension.

Please let us know what happens.

Cheers

Considering u don't have to touch the serpentine belt for the water pump exchange I'm doubting that it's any of those also it's coming from behind the motor where the water pump is located I'm hearing that the timing chain may b too tight or need to readjusted that this may be causing the whining

The image attached shows that the serpentine belt must be removed to remove the water pump. Can you please upload a video of the noise so we can hear it?

No it doesn't the water pump on a 04 Saab 93 turbo is located at the back of the motor the timing chain runs through it and must be readjusted after the water pump replace I have contacted a actual Saab tech and got the same answer the serpentine belt runs the alternator and ac also the is a belt tensioner and the harmonic balancer as shown once we readjusted the tension on the timing chain the noise went away thanks 2Carpros you guys are great.

The picture above is for Step 23 of the water pump removal process for a 2004 Saab 9-3 turbo as listed in our Mitchell1 online reference.
"23. Mark the direction of rotation, relieve the multigroove belt and remove it using 83 96 095 Belt Circuit Relieving Tool. B207"

7 figures later, Fig 59, attached, shows that removing the serp belt shouldn't be required.

WARNING! Everyone BEWARE when replacing the water pump!

Even when using the required special tool the timing chain still whines!

The balance shaft timing chain must be reset or it will make noise.
We just found this out through experience and want to pass this along to others so they will not walk blindly in to this job.

Note: Mechanics & shops make sure you add extra time to remove timing cover and reset the balance shaft chain tensioner. As this is not included in any labor guides.