Has this particular disk been used previously with your iMac and shown up in the Finder / Disk Utility, or is it the first time you're tried to use it with your mac?
If the former, restart the mac with the disk still connected. If it now shows up, you should think about backing up any data on that disk to another one ASAP as it may be failing.
Sounds like its failed already. Depending on how DIY proficient you are, you could try
1. connecting the disk with a different cable - oftentimes, its the cable that's at fault
2.ripping the disk out of the enclosure and putting it in a different enclosure (you can buy empty disk cases from most electronic hardware stores for a few bucks) to test whether its the disk itself that's failed or just the bus board (sometimes its just the electronics inside the disk case that's at fault).
Alternatively, take the disk along to either a Genius store or any computer electronics repair shop (cheaper...) and have them test it for you and/or try to recover any data that's on it.