To drink up

from The Collaborative International Dictionary of English v.0.48
Drink \Drink\, v. t.
   1. To swallow (a liquid); to receive, as a fluid, into the
      stomach; to imbibe; as, to drink milk or water.
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            There lies she with the blessed gods in bliss,
            There drinks the nectar with ambrosia mixed.
                                                  --Spenser.
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            The bowl of punch which was brewed and drunk in Mrs.
            Betty's room.                         --Thackeray.
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   2. To take in (a liquid), in any manner; to suck up; to
      absorb; to imbibe.
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            And let the purple violets drink the stream.
                                                  --Dryden.
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   3. To take in; to receive within one, through the senses; to
      inhale; to hear; to see.
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            To drink the cooler air,              --Tennyson.
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            My ears have not yet drunk a hundred words
            Of that tongue's utterance.           --Shak.
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            Let me . . . drink delicious poison from thy eye.
                                                  --Pope.
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   4. To smoke, as tobacco. [Obs.]
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            And some men now live ninety years and past,
            Who never drank to tobacco first nor last. --Taylor
                                                  (1630.)
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   {To drink down}, to act on by drinking; to reduce or subdue;
      as, to drink down unkindness. --Shak.

   {To drink in}, to take into one's self by drinking, or as by
      drinking; to receive and appropriate as in satisfaction of
      thirst. "Song was the form of literature which he [Burns]
      had drunk in from his cradle." --J. C. Shairp.

   {To drink off} or {To drink up}, to drink completely,
      especially at one draught; as, to drink off a cup of
      cordial.

   {To drink the health of}, or {To drink to the health of}, to
      drink while expressing good wishes for the health or
      welfare of.
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