Can 吃 be used for liquids?
Well you can 吃酒，or 吃喜酒 at a wedding, but that involves eating and drinking.

zdic has: (4) 饮;喝 [drink]。如:吃血(饮血酒);吃茶(喝茶)

A song about human nature.

一个和尚挑水吃 When you're alone you have to help yourself.
两个和尚抬水吃  2 people can cooperate
三个和尚没水吃呀  when there are 3 people, each thinks, 'Why should I do it? Let them do it.'
三个和尚没水吃
没水吃呀 

Edit: thinking about oil, which is a liquid，I was just reading an article about 副食品:

食用油大战，使人们吃上了精炼洁净的瓶装油。