gmalivuk wrote:Ah, right. Still, I don't think steam would bubble out of the surface of the ocean, for the same reason it already doesn't above thermal vents. (The pressure is too high for it to be gaseous, plus the water around it would carry away heat pretty effectively.)

gmalivuk would be correct for a small hole, and mere ocean depths, but this hole must be huge and very deep (and I presume, very hot).

Ignoring the materials behavior for the moment. To fill Death Valley and make up for evaporation requires a vast amount of water flow, and the pipe is 13,000 kilometers long. Assume "fill" means 2 meters below sea level (end-to-end hydrostatic pressure difference) and the water flow must make up for 3 meters per year of evaporation over 500,000 hectares. The pipe must move 1.5e10 cubic meters of sea water per year, about 500 cubic meters per second, with a pressure difference of 2000 Pascals.

How big does the pipe need to be? Start with zero viscosity and zero friction, and assume no heat flow into the pipe. The water drops 2 meters, establishing a velocity of 6.3 meters per second, so the pipe cannot be less than 80 square meters in area.

Now, assume laminar flow and zero velocity at the walls. Assume an isothermal, incompressable, Newtonian fluid, with the viscosity of liquid water at STP, μ = 1e-3 Pa-s (all terribly optimistic assumptions). Assume half the pressure difference establishes the dynamic flow, and half fights viscosity. Use the Hagen-Poiseuille equation, volume flow rate Q = π R⁴ Δp /8 μ L, or R⁴ = 8 μ L Q / π Δp . Given L = 1.3e7 m, Δp = 1000 Pa, μ = 1e-3, and Q = 500 m³/s, then R must be at least 11 meters, a pipe area of 400 square meters. Ideally, the water moves at 1.2 m/s, traversing the pipe in four months.

BTW, the hydrostatic pressure at the center of the Earth for this magic incompressable water is 0.5 ρ g₀ Re or 30 gigaPascals, 50 million times the triple-point pressure, up in dotted line territory way the hell beyond any graphs or measurements I know about. Add heat flow from the Earth's core ( about 6000K, pressure around 300 GPa ) and things will get frisky. I don't know what the hell you call it, but solid, liquid, or vapor water It Ain't.

If we wanted to deliver something approximating water to the other side, the bore would have to be much bigger to accomodate the dynamics and minimize surface to volume ratios on the way through the Earth's core. My W.A.G. is that a 100 km³ bolus of water will fall down the hole, vaporize to incandescence, and come blowing back out the hole perhaps once per day.

In any case, we are talking volcano-scale bore sizes, and much higher temperatures and bigger heat fluxes than a typical volcano, dwarfing a mere undersea vent. Can a supervolcanic explosion smash through 5 kilometers of seawater and send a vast jet of superheated steam skyward? Perhaps someone else can take over from here, and give this a properly devastating What-If conclusion.

Added note: If Ken Jennings was on a boat above the pipe when a steam explosion occured, would he become the hottest game show contestant of all time? Or did they have game shows in Nagasaki in 1945?