I think we’re looking at this backwards. The real question is not whether the oceans would entirely drain into the hole; it’s how wide to make the hole to accommodate all the ocean water.
Okay, Wikipedia says that the volume of the ocean is 1.34 x 10[sup]9[/sup] cubic kilometres. The earth has a mean diameter of 1.2746 x 10[sup]4[/sup] km.
So the hole will be 12,746 km long.
If it’s a cylinder, the cross-sectional area will be:
pi * radius[sup]2[/sup]
or
pi * (diameter/2)[sup]2[/sup]
The volume will be:
length * pi * (diameter/2)[sup]2[/sup]
Rearranging for diameter:
volume = (length * pi * (diameter/2)[sup]2[/sup])
volume / (length * pi) = (diameter/2)[sup]2[/sup]
sqrt (volume / (length * pi)) = (diameter/2)
2 * sqrt (volume / (length * pi)) = diameter
We put in the known length (km) and volume (km[sup]3[/sup]),and we solve for the diameter in kilometres:
diameter = 2 * sqrt (1.34 x 10[sup]9[/sup] / (1.2746 x 10[sup]4[/sup] * 3.14))
diameter = 366 km
Hmm. Wider than I thought.
The elimination of all ocean life should’t stand in the way of a good thought experiment, though. We’d better get digging. Maybe we can save a few bucks if we start digging at the Marianas Trench.
What happens when water becomes supercritical, again?