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Search and buy some Meguiars APC (All Purpose Cleaner) and dilute with 10 parts water...amazing stuff. Light hose wont hurt anything....I wash under the hood of every car I've ever owned, and in my 52 years thats quite a few!
Then I use things like their Rubber/Vinyl Cleaner Conditioner on black plastic parts, hoses, etc that I want darker and shinier.
If it's just dust you're wanting to clean, then I would recommend spraying detail spray on a cloth(preferably microfiber) and just start wiping. This is how I clean about every few weeks so it stays that way.
If it's more grime and grease you want to remove, then JETNinja is on the right track. Just make sure you plastic wrap open electrical devices such as the alternator etc...Shower caps work nicely. If you google Adams Polishes they have how-to videos that are extremely helpful in this area.
I have never never used a hose or power washer under the hood of my car. There are some sensors/connections which may be effected (if even only temporarily).
I've read a few threads here since '06 about the gremlins caused by the practice. Maybe others get lucky, but I remember weird things happening with cars w/ much less electronics than a C5/Z06. Your car, your choice. It seems like a lazy way to tackle an easy job.
If it's just dusty, as suggested above, wipe it down with your favorite cleaning agent. Diluted WINDEX or SIMPLE GREEN is what I used when I first got the car. If it was really bad, I used aerosol non chlorinated brake cleaner. It dissolved the grease and evaporated. Once you get the bad areas cleaned you shouldn't have to do it again unless you have a leak. That should be addressed.
Then I use 303 PROTECTANT on the rubber hoses and plastic surfaces.
I sometimes, take a air hose and lightly spray the dust out. Afterwards, I will take some detailing spray (mentioned above) or a micro fiber cloth that I have used just before detailing the car (so it is damp) and just wipe down what needs wiped down. I the will take some Mother's BACK to BLACK and apply it on the radiator shroud and other areas that are black to give it a little shine. I have never used water on mine, never will!
I would never use a pressure spray or even hose power stream, just light fan of water to soften then rinse. Some peeps are silly, these cars are fine in Rain with 80mph drops getting forced in there, a light spray isn't going to hurt anything. Just use some common sense. Things like my CAI and even the ECU are much less protected on my 95 M3 yet never a problem in over 100k of driving..
I would never use a pressure spray or even hose power stream, just light fan of water to soften then rinse. Some peeps are silly, these cars are fine in Rain with 80mph drops getting forced in there, a light spray isn't going to hurt anything. Just use some common sense. Things like my CAI and even the ECU are much less protected on my 95 M3 yet never a problem in over 100k of driving..
I have done it before, but I did it with the car running and was very careful in not getting to much water on the electrical components.
had my car 4 years now and its 01ZO6. I will use purple power or simple green and spray the areas i want the grim away from. Then VERY LIGHTLY i will gentle spray off the residue. I cover my alternator before doing all of this. Once clean i quickly start the car and let if run nearly 10min. Ill leave the hood open most of the day when the sun is nice and bright outside. Ill take some armoral and clean up a few parts i want shiney. Good as new and no problems.