Underground Rivers - University of New Mexico

If we don't want to pour
water to China -- Saudi
Arabia may be a better
market -- we can drill a
tunnel accordingly and the
journey will still take 42
minutes. Rather than as free
fall, however, our frictionless
water will flow along the side
of the tunnel nearest the
earth's center.
Chapter 26 -- Subterranean Water Bodies
We ourselves may, of course, not wish to jump into
the trans-global shaft, even with theoretical
assurance that we can exit at zero velocity in the
Orient.
We'd prefer to sail through the earth on an
underground river. For safety's sake, we'd also
prefer that the river velocity and wave characteristics
not change throughout the journey. To maintain the
current's downward speed as the pull of gravity
dwindles, we'll thus need a steeper and steeper
channel. When we head upward to the exit, we'll
correspondingly want the channel slope to flatten as
gravity returns.
A channel in which radial slope varies inversely with
the radius will do the trick, other than at the center
where the equations explode. The boatride before
and after this singularity should go reasonably well.
Regarding the principal of material conservation --
we've two gravity-flowing channels and nowhere for
the inflow to accumulate -- we employ the Greek
philospophers' concept of the Great Abbyss.
Flow accelerating Flow decelerating
The nearer we are to the earth's center, the less an object weighs. In
some adventure fiction, vegetation at the earth's cernter grows
gargantuan under the lesser gravitational pull. At the center, an
object has no weight whatsoever.
Illustration from Verne's Journey to the Center of the Earth
Burroughs addresses the gravitational question in At the Earth's Core (1914). Perry, inventor of
the subterranean prospecting machine speaks,
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