First, the amount of air you plan to move to cool your hoods is somewhere between excessive and outrageous, lol- you'll do just fine with a 6" fan, one that matches the 6" openings in the hoods themselves. I would have two intakes (these, to maintain a sealed room, should draw their air from out side the room), each passing across two hoods, then use a Y connector to connect them. Place your fan at that junction so it PULLS the air through the hoods, then use insulated 6" ducting from there, through/over the bathroom door and to the window to exhaust it. The insulation will keep the heat in the duct where it belongs, and the insulated duct tubing will effectively muffle the fan noise. IF that air is cool enough- and it may not be- then you can use it to cool your AC unit.
Remember that your AC unit is really two air circulation systems in one box; the front pulls air in, cools it by running it across the condensor coils, then blows it back out into the room. The back pulls cool air from somewhere OTHER than where you want to cool- like outside- and heats that by blowing air through the compressor coils, then out. Therefore, you need to effectively handle 4 different air streams to effectively use your AC unit in the room.
I'm a big fan- and exponent here on the Farm of- larger scale water chilling systems. The reasons boil down to flexibility and running costs for cooling. I have just one big chiller, but it cools my entire setup; from clone, veg and bloom rooms to all the RDWC systems I have. That's 3 rooms, 3 systems and a total of 12kW of lighting, all cooled with a chiller that runs less than half the time while pulling only 8.5 amps@220. The advantage of water cooling is that you can place your 'ac' chiller unit wherever you want, and then run cold water from it to all the places you need cooled, and then back. These can be nice long runs, as water's thermal density ensures it will still arrive cool and ready to work.
So, if you need your bloom room cooled, you place an Ice Box or two in there with a fan blowing through each one, and connect that fan to your temerature controller. If you need an RDWC system cooled, you run the water through a 15-20' coil of 3/8" copper tubing and place that coil down into the water in your epicenter or head bucket where it will see constant water circulation.
Your friend's water chilled setup with the endless loop vented hoods thing might be effective, but I bet I can same him a small fortune by routing all that hot air outside and cooling the room with the chiller instead... Or at the very least, I can have that heat go to heating his house and watch his heating bill drop to nothing, lol. The best part? Water chillers do not transport smell. Period.
