I'm going to take a wild stab at this: Darth Vader requires minimal nutrition and fluids, drained by a mechanized "flushing" system.

I've been a lifelong fan and have found no evidence of anything that suggests Vader, eats, drinks, leaks, toots or pinches loafs. I'm suspecting he's pretty burned up under the cod piece and under the backside of his leather trousers.

I read a recent comic book where Vader declines an invitation to eat with some aliens. He reflects that he denies the invitation to eat "like a living (thing)."

I guess that he has a system of nutrition handled by a droid that must give him some sort of feeding tube. Perhaps the hypothetical machine empties some sort of catheter that accumulates his minimal waste from day to day. This could be a first-thing-in-the-morning activity, or perhaps a last-thing-at-night deal. Maybe he does this while he gets a "breather" from his helmet, as we saw him doing in TESB before he was so rudely interrupted with his helmet off. For a FABULOUS description of what goes through Vader's mind while he breathes without a helmet, go and read "Shadows of the Empire" immediately!

Let's face it: he's still part human. He has to have at least water to go with that beautiful breathing of his, even if his arms and legs don't need blood and oxygen. Nothing wrong with a steady diet of Blue Milk, Jawa Juice or Luke's personal fave ... hot chocolate. And no, smart alecs, there is no freaking "Starbucks" inside the Death Star cafeteria!