He was trying to 'drown his fears'. [=to get drunk so that he wouldn't be afraid]
I'm being 'drowned in' paperwork. [=I'm being overwhelmed by paperwork]
Noise from the passing airplane 'drowned out' our conversation.
(..) so I was wondering if you could take them off my hands. Well, I don't know. It's a huge imposition. And I'll have to get them taken in. I mean, they'll drown me. But I suppose I could help you out. I will have Roy pick them up this afternoon. Thanks, Em. I appreciate it. Good luck. (..)2006 The Devil Wears Prada