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I'd rather stab myself with a spork.
Don't you mean "runcible spoon", Trebuchet? :laugh:
I had a professor once who insisted that if there was a fluid head difference (potential energy gradient) between two ends of a uniform level pipeline, no matter what the continent-spanning length of it might be, a fluid could be induced to flow from one end all the way to the other. He said that all head losses (losses of flow energy) were velocity dependent, so at some point the flow velocity would fall below the point where friction, viscosity and other velocity-dependent losses were strong enough to prevent the flow. Similar flows were already observable in ocean bottom currents which - though it might take thousands of years - trickled from the pole to the equator propelled by nothing more than a slight head difference.
In short, Errorist, his claim was that your claim was theoretically possible, provided you don't care how fast the flow is moving.
Unfortunately, the expected flow velocity is hardly fast enough to keep the water at a stable temperature all the way from the poles. It would heat up to within a few degrees of equatorial temperatures along the way if you ran your line along the surface. You'd need pumps just to get the water to the equator in your lifetime, much less while it still had a chill on it.
It will pump water, but you can forget this as a heat exchange mechanism.
The applicable equation is Bernoulli's Equation adjusted for external work and potential losses, also called the Fluid Energy Equation. It goes like this:
P1 + rho1 * a1 * h1 + alpha * rho1 * v1 ^ 2 + W =
= P2 + rho2 * a2 * h2 + alpha * rho2 * v2 ^ 2 + Q
where
P1 & P2 are the pressures on each end of the pipeline,
rho1 & rho2 are the fluid densities on each end,
a1 & a2 are the local accelerations (gravity + centripetal force) on each end,
h1 & h2 are the elevations on each end,
v1 & v2 are the flow velocities on each end,
W is the total pumping work added to the fluid over the entire pipe,
Q is the total loss in potential energy over the entire pipe,
and
alpha is a constant correction factor for non-uniform flow across the pipe's cross section.
The basic idea is that the energy on one end of the pipe is the same as the energy on the other end of the pipe. This equation can be found in any Fluid Mechanics textbook, as well as equations for computing W and Q.
If you plug appropriate values into this equation, assuming W = 0 and Q = C L v^2 (where L is the pipe length and C is some system-dependent constant describing the energy losses per unit length), you see that v has to be very small before any of the other terms become larger than Q, because L is so freaking huge. And nothing will move until the other terms sum to more than Q. Without a lot of big pumps, you're probably looking at a flow velocity of a few millimeters per second. It might outrace a snail - maybe, with a really big pipe.
"We go big, or we don't go." - GCNRevenger
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BTW, Errorist, Graeme Skinner is quite correct. Judging from what I've seen of your posts, this sort of simple theoretical model is probably well within your capababilities. You really should try to work out the math for yourself first. That will allow you to defend yourself better against those who try to shoot you down for fun.
The world resists your theories, but remember: Math is Power! :laugh:
Bernoulli's Equation holds true whether you're raging against the establishment or not, but you need to learn it first.
"We go big, or we don't go." - GCNRevenger
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Does angular momentum have an effect in that formula somewhere? Also, if the water is flung outwardly would that not be cetrifugal force instead of centripital force?
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Does angular momentum have an effect in that formula somewhere? Also, if the water is flung outwardly would that not be cetrifugal force instead of centripital force?
The http://iparrizar.stcloudstate.edu/~juan … df]formula for the local acceleration is g-wr
where r is the radius and w is the http://hyperphysics.phy-astr.gsu.edu/hb … ml]angular velocity in http://www.themathpage.com/aTrig/arc-length.htm]radians per second and http://csep10.phys.utk.edu/astr161/lect … rav.html]g is the acceleration due to gravity.
Dig into the [url=http://child-civilization.blogspot.com/2006/12/political-grab-bag.html]political grab bag[/url] at [url=http://child-civilization.blogspot.com/]Child Civilization[/url]
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P1 at the noth pole is actually 13 miles below sea level when compared at P2 and the equator.That is a very high water fall isn't it?
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Not really over the distance your talking about (around 6000 miles give or take a mile or two).
Graeme
There was a young lady named Bright.
Whose speed was far faster than light;
She set out one day
in a relative way
And returned on the previous night.
--Arthur Buller--
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Wow, if the surface of the Artic Ocean is 13 miles below the surface of the ocean at the Equator would that mean gravity at those two points is also different? How would that work into the formula?
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The formula John Creighton gave for the local acceleration is correct. Just be sure to compensate for latitude when you do the calculation.
(That equation is: a = g - w r sin(latitude) )
Angular momentum, per se, does not figure into the equation, but inertial accelerations do. Centripetal/Centrifugal acceleration is what causes the variation in local acceleration, and consequently the head difference that pumps the water. Coriolis force is a cause of additional drag and energy loss.
With the difference in sea level, there should be a difference in gravitational acceleration, but it will increase toward the equator, and reduces the head difference that's moving the water (making the flow even slower).
Regarding the idea of using this to propel water to space:
You'll notice the interchangeable use of "energy" and "head" when describing the fluid energy equation. By dividing each term in the equation by the specific weight of water, you can convert every term to a distance value, or head (pressure head, elevation head, velocity head, pump head, etc.). This is the height of the column of water corresponding to that much potential energy (or alternately, the depth at which the pressure would correspond). It's also the height to which the water would rise at that point if you just opened a nozzle and let it fly. It will never go higher than that under its own power.
The elevation difference is only a few kilometers, and it won't spurt very high moving at one millimeter per second.
This effect will never allow you to pump anything to orbital heights, because the head doesn't correspond to an orbital height. Any "pipeline to space" idea will need to use something else.
"We go big, or we don't go." - GCNRevenger
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What if you angled the pipeline backward toward the equator opposite of Earths rotation to compensate for the coriolis force?
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What if you angled the pipeline backward toward the equator opposite of Earths rotation to compensate for the coriolis force?
The water would no longer be pushed sideways into the pipe wall (lower C value in the equation), but the angled pipeline would require a longer length of pipe to reach the equator(bigger L value).
The energy savings of not fighting the Coriolis Force would be cancelled out by having to pipe the water farther.
"We go big, or we don't go." - GCNRevenger
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Hmm...
It occurs to me that this would be a useless contrivance on Earth, but NOT on Mars.
Mars has a lower gravity, but an equivalent angular velocity to Earth, making the "pumping" action due to the pole/equator head difference more pronounced. Mars has water in its polar regions which might prove useful in its rather water poor tropics. And while water would prove a problem to pipe all that way without freezing, methane gas would not. (This concept would work for a gas pipeline as well as liquid. Let methane carry the hydrogen and convert it to water on arrival.)
Maybe Percival Lowell had the right idea after all. It just needs some Martians to make it work.
However, this "Pipelines of Mars" discussion might be better suited for the Terraforming forum.
"We go big, or we don't go." - GCNRevenger
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http://www.newmars.com/forums/viewtopic.php?t=307]The Pipelines of Mars
I took the liberty of starting a companion thread in the Terraforming forum.
"We go big, or we don't go." - GCNRevenger
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Looks neat CM.Hey, what if you placed the outlet of the pipe at the equator to let the gulfstream to flow past the opening and the opening at the pole to face against the flow of the Artic current? That should create a difference in pressure. Say the current at both locations is 5mph.
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