In theory, if you poured water down this sort of well from both ends, it would experience less and less gravity as it fell: the mass of Earth’s rocks pulling it from below would diminish, and be counterbalanced by the increasing mass of rock behind it. At the exact centre, the pull of gravity from all sides is balanced out, creating a situation of effective weightlessness, but the diminishing downward force lasts all the way to the centre. Normally a falling object dropped down the well would ‘yo-yo’ from one side of Earth to the other before eventually settling in the middle.
But if two streams of water hit each other in the centre, they’d stop each other dead and coalesce into a single floating mass – a bit like the way water behaves on spacecraft. That’s if you could somehow stop it from evaporating in the tremendous heat, of course!
Answered by Giles Sparrow