Part number for AC belt tension pulley
 

Which one of these is the tension pulley on for the AC belt? I see two pulleys -- one idler and one tension pulley for the main serpentine belt -- but I can't see which one for used for the AC belt?
Edit: I think it's #13. I am not sure why it costs so much though.
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According to other threads, it is Dayco 89133

You are correct in assuming it's #13...and you should check ..., realoem, pelicanparts among other sites that have very good prices... I just replaced my tensioner that drives the water pump, alternator, powersteering etc for $48.95... And that's not expensive at all...

OP, you need to know if you have hydraulic or mechanical tensioner. #13 shows mechanical tensioner with pulley...but that's no longer a bmw part...it's shifted to all hydraulic now.

I just replaced my pulley...and although many are mechanical tensioners and take the 89133 pulley, some are hydraulic. You need to look and know what you have...or just order both and return the one you don't need.

See threads with 'pulleys' in the title...you'll learn all you need to know.

Of course, do the belts...and of course, do all three pulleys...since when one is gone, the others are close behind.

OEM part # 11281433571

My main belt tension pulley is hydraulic but I think the one on the AC belt has always been mechanical I think. I notice the cost does vary from vendor to vendor. Tischer has it for $99 while ECS Tunnings about $67. I'll be doing my water heater and will replace the pulleys on the main belt, but I think I'll wait on this one. When I spin it, it seems pretty quiet - no noise. Worse comes to worse, I'll be driving without the AC :-).

Here's my part list:
Mechanical Catalog - 2004 - BMW - M3
cooling system, thermostat M3 $44.39 $8.88 $35.51 $0.00 $35.51 Delete From Cart
Collision Catalog - 2004 - BMW - M3
cooling system, cooling, water pump, water pump assy M3 $499.42 $99.88 $399.54 $0.00 $399.54 Delete From Cart
Collision Catalog - 2004 - BMW - M3
cooling system, cooling, water pump, water pump assy gasket M3 $8.84 $1.77 $7.07 $0.00 $7.07 Delete From Cart
Collision Catalog - 2004 - BMW - M3
cooling system, cooling, water pump, thermostat gasket M3 $4.74 $0.95 $3.79 $0.00 $3.79 Delete From Cart
OEM Catalog
O-RING $1.87 $0.37 $1.50 $0.00 $3.00 Delete From Cart
OEM Catalog
O-RING $2.16 $0.43 $1.73 $0.00 $1.73 Delete From Cart
Collision Catalog - 2004 - BMW - M3
cooling system, cooling, belts & pulleys, tension pulley HYDRAULIC TENSIONER, adjust $50.59 $10.12 $40.47 $0.00 $40.47 Delete From Cart
Collision Catalog - 2006 - BMW - M3
cooling system, cooling, belts & pulleys, tension pulley HYDRAULIC TENSIONER, idler $49.63 $9.93 $39.70 $0.00 $39.70 Delete From Cart

ECS tuning is cheaper because the part is not OE

PS: E46 M3 always use mechnical AC tensioner. It's only the Non-m that it changes

Does turning the fan nut mess up the engine timing? It took me a few tryiniesg - having to turn the nut may be two or three times to be able to get the fan nut off.
Initially I was trying to hold down the screw then tried to turn the 32mm wrench but couldn't find a good way to pivot. Finally I had to do a couple of whack on the wrench
and surprisingly the nut came off pretty easily.

When you turn the water pump, the entire engine also turn right? So does it anyway mess up the engine timing?