Unflood Areas Within Fortress

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Well in my wisdom I've managed to flood a rather large section of my fortress by accident whilst digging a moat. I've managed to isolate the area, however, I'd quite like to unflood this area and repair the damage, is this possible?
It's flooded with water from a river, in my haste I forgot that water can leak diagonally
Update: The accepted answer worked, however, I lost so many dwarves they couldn't fight off an elven invasion that followed shortly after. Sad times.
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Deaths Door walkthrough part 7 - Flooded fortress - All collectible locations available 1st visit
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