h a l f b a k e r yRecalculations place it at 0.4999.
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Create a circular funnel shaped reservoir at least 1km in diameter. Have the tributary river entering along an edge so as to encourage rotation.
In the thinner part of the funnel, there would be a turbine, which would be more efficient as the water is already rotating rather than just pushing. Ther
could also be other turbines throughout the lake but I don't know if the turbulence they would create would reduce the power available to the main turbine more than it would add to the overall output.
The rotation means that you could use cyclonic filtering of debris rather than a traditional grill.
People would love to see the lake and the phenomenon which is rare in nature. You could have a platform in the centre where people could stand below the normal water level and watch it spiral around them. You could create a new extreme sport of surfing the spiral with anyone that falls being filtered out and dumped on the platform.
An alternative version of this would be a dish shaped lake with the incoming river still entering at the edge and the outgoing river exiting at the edge, with turbines throughout the lake, possibly similar to wind turbines. This version would generate very little power but would have less environmental impact.
I'll try to do some coriolis force calculations later unless someone else generously adds them for me :o)
Solar Tower Vortex Generator
Solar Tower Vortex Generator
This was my take on using extra spinning energy to improve the yield of a turbine driven generator. As everyone knows, the only way to counter the 2nd law of thermodynamics, is by spinning. [zen_tom, Sep 20 2007]
coriolis effect myths
http://www.ems.psu....ad/BadCoriolis.html
[the dog's breakfast, Sep 20 2007]
also, is it worth it if she throws up?
http://www.xkcd.com/162/
[bleh, Sep 25 2007]
[link]
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So the tributary enters along a tangent to the circular lake - I've got that, but can you explain a bit more why the Coriolis effect will cause the water in the lake to rotate? |
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I think he forgot to mention the drain at the bottom. |
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Does the effect vary with the size of the opening at the bottom? Can you provide a link or more information? |
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The only clue I could find about the amount of force was a snippet from Wikipedia which said that in the ocean a circle of 1km radius rotates at 10cm/s. |
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<Edit>My calculation differs from this. Earth circumference = 40,000km; rotational speed at equator = 40,000km per day = 463m/s; at pole = 0; distance from equator to pole = 10,000km; speed gradient = 463m/s / 10,000km = 4.63cm/s/km. The calculation is close (9.26cm/s) if we look at the difference in speeds between opposite edges.</edit> |
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The spinning effect at the funnel is independent of the coriolis effect, the speed of rotation increases in inverse proportion to the radius of the circle, like pulling your arms and legs in on a rotating chair. |
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Basically, coriolis forces provide the power, the funnel focuses it. |
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[ldischler] Indeed I did. The idea is that this replaces a traditional dam and turbine arrangement, where the 'used' water exits at the bottom. |
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[the dog's breakfast] I assume so. There must be an ideal opening size for a given shape of funnel. Basically the hole would be as big as the flow rate of the river allowed. |
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//but can you explain a bit more why the Coriolis effect will cause the water in the lake to rotate// |
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I'm not sure I can help, beyond saying that the Coriolis force is blamed on causing water to go down the plugholes in an anti-clockwise direction in the Northern Hemisphere, and clockwise in the Southern Hemisphere (of course, everyone knows that at the equator, the water just goes straight down the plughole without any messing about - this is because gravity is caused by spinning) In this instance, the lake at the head of a dammed river is very much like a great big bathtub. |
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I'd argue against the idea that Coriolis forces provide the power, they don't - it's the mass of the water in a gravitational field that provides the power, all the Coriolis forces do is provide the butterfly-wing nudge in the appropriate direction. |
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Gravity is an EFFECT of spinning. Everything relies on spinning. <takes deep breath> WHEEEEEEE! |
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//water goes down the plugholes in an anti-clockwise direction in the Northern Hemisphere, and clockwise in the Southern Hemisphere// |
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And on the equator it just stays where it is. |
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I'm not sure if the size of the lake would have any relationship to the power in the vortex. Maybe it's like saying that the pressure in the ocean depends on how wide the ocean is (Mmmm... must experiment with different bathtubs). |
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I stand by these so called coriolis effect "myths" since, far from being completely wrong, in the absence of other incidental forces, they are entirely correct. |
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Plus, for a great big, standing lake, I suppose they would have greater time to manifest themselves in actual motion. |
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Anyway I suppose, in terms of the idea, it's not that important - the spinning motion (however it starts off) will self perpetuate. |
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The idea, as written, proposes that the force of the river be used to add to the Coriolis effects caused by the rotating Earth, which are a hell of a lot smaller than most folks believe. |
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Sorry, I'm raving. <swallowing meds> Coriolis effects are one of those bad-science beliefs that get right up my nose. Thanks, [dog's] for the Bad Coriolis link. |
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If the round lake is intended to capture the energy of the rotating Earth, with the river as a trivial addition to the rotation, the math is complicated. The differences in speed arise from the relative distances to the AXIS of the rotating Earth. (The goofball demonstrating Coriolis effects at the Equator is in the worst possible place.) I'm not gonna do the math, I'm going to go drink some lunch. |
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[Edited to take out the crazy] |
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Doesn't matter if this idea is practical or not. It's hella interesting. + |
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The placement of the rivers is to aid the effect, rather than having them perpendicular to rotation and causing turbulence. |
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Remember this idea is only to make a hydro plant more efficient (and other cool stuff). |
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The secondary idea of just having a big dish of water that rotates would only get power from coriolis forces. |
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Sure, it's all fun and games until you suck enough angular momentum from the Earth that days become noticeably longer. |
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Anyone want to compute how many kWh we get out of the Earth before days are, say, 25 hours? |
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OK. The moment of inertia of the Earth
is given by: |
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taking the mass as 6x10^24 kg and the
radius as 6.4 x 10^6 m, we get: |
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However, this assumes a sphere of
uniform density, whereas a lot of the
Earth's mass is in its core. I don't know
how to compute for this, but a
reasonable approximation will be to
assume: |
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The rotational energy of a sphere is
given by: |
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where w is the angular velocity. |
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At the moment, with a 24 hour day, we
have: |
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w = 2 x Pi / (24 x 60 x 60)
=7.2 x 10^-5 rads/s |
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Hence, at present, the earth's rotational
energy is 2.59 x 10^22 Joules. |
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With a 25 hour day, w becomes: |
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w= 2 x Pi / (25 x 60 x 60)
=7.0 x 10^-5 rads/s |
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and hence its rotational energy is
reduces to 2.45 x 10^22 Joules. |
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Hence, by slowing the earth to a 25
hour day, we could recover 0.14 x
10^22J. |
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I think I'm having my own moment of
inertia. Could we have all that in Ergs
please (preferably not scrambled)? |
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"This is 3.9 x 10^14 kWh." |
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Thanks! I don't even know where my college physics book *is* at this point. |
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At 10% efficiency and $0.1/kHw that gives $4e12. Sounds like a winning proposition to me. I have long wished for a 25 hour day anyway. |
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//Could we have all that in Ergs please//
OK, it's 3.9 x 10^24 erg-hours. (1
Joule=10^7 ergs - I had to Google it.) |
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<EDIT> Sorry. As [Ling] pointed out, this
is
nonsense. It's 1.4 x 10^28 ergs, period. |
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Note that "erg" is energy.
"Watt" is power. Power over 1 hour supplies energy, hence "Watt-hour" or kWh. |
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So kWh can be converted to ergs & there is no such thing as erg-hours. |
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/which would be more efficient as the water is already rotating rather than just pushing/ |
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Anything to back that up, [marklar]? |
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[regehr] I thought about this the other day. However, the turbine is placed vertically and resists the spin of the water. The turbine is of course anchored to the ground, so the rotational force is transfered back into the Earth, with only efficiency losses being taken from the spin. |
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[Texticle] Nope, only logic. If a force is rotating the lake and you focus that force, you should get extra power from it, in addition to its weight. If you assume a lake with no drain, a turbine in it would turn. |
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Edit: And before anyone else does it, I'm suggesting bathtub turbines and sink turbines and turbines anywhere else you get small useless spinning water that isn't worth harnessing (yes I know these are not caused by coriolis forces). So, household whirlpool generators are now redundant. |
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//So kWh can be converted to ergs & there
is no such thing as erg-hours.// Oooops
- of course you are correct. Edited -
thanks. |
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So basically this is a gigantic constantly flushing toilet? With a platform in the center like the old Tidy Bowl Man commerials? Oh, hell yes this gets a bun! (even if coriolis forces have nothing to do with it.) |
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Um, one question, how does one get TO this platform? Parachute? Zipline? Not to mention getting back off again. |
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I haven't seen anything yet that shows why the water in the lake will rotate or form a vortex. |
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Well, assuming constant angular momentum, the water will spin faster as it accelerates down the funnel tube, because the closer something gets toward it's axis of rotation the faster it will spin in order to maintain a constant angular momentum L=(R)x(P).... the trade-off is that it gains linear momentum, and therefore you get the coriolis force. |
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Of course, the force from the dynamic pressure of the incoming stream of water would need to be strong enough to overcome the counter forces due to viscoscity and friction in order to maintain a zero-torque condition (constant angular momentum). |
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.... and thus, the super-donut! |
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Oh for the love of monkeys, coriolis forces and a vortex are completely seperate things. If you drain a bath on the moon you will still get a vortex. |
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There is no point me explaining why coriolis forces cause the lake to rotate or why a vortex forms due to turbulence, as Wikipedia does a much better job than I can. |
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As I stated before, the main source of energy is the potential energy of the height of the water. The secondary energy is kinetic energy from the rotation of the lake due to coriolis forces plus a bit from the direction of the incoming river. This energy is focussed by the vortex. |
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So maybe "Lake Vortex" would be a better title or subtitle for this idea. |
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//So, household whirlpool generators are
now redundant.// |
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actually I mentioned these in my 'Method
of Power for Shampoo Bottle Centrifuge' |
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Big juicy [+] for you. I really like the idea. |
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We now return you to your regularly-scheduled "why-the-toilet-spins" arguments.
[+] |
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EDIT: As an aside, getting to the platform should be easy enough. Simply walk across a bridge from either side of the lake, and down a flight of stairs to the suspended platform. |
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Getting to the platform is quite easy. Rope
bridge. They naturally sag in the middle (a
hyperbolic sine curve I believe). The
surface of the water will be forming a
parabola so you could get pretty close to
the bottom depending on the slack in the
ropes (and the speed of rotation). |
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Just to divert attention from the why-the-toilet-spins arguments: |
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A rope bridge forms a catenary curve. |
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The lake would only form a parabola--more properly a paraboloid--if the entire bed was rotating (or completely frictionless) AND there was no drainage in the middle. |
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A catenary is a hyperbolic cosine not a
sine. my bust. |
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I was considering the level curve in the
plane of the bridge when I said parabola
rather than paraboloid. |
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A pointy thing with wet people in the middle. |
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