30-03-2005 02:13									#61
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And which is susceptible to math errors...

	30-03-2005 02:13									#62
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quote: Originally posted by KrazyHorse Whyy? It's not like the earth's spin is accelerating...

Rotation is acceleration.

	30-03-2005 02:15									#63
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quote: Originally posted by chegitz guevara Rotation is acceleration.

Truth is whatever serves the party. PRAVDA!

	30-03-2005 02:17									#64
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quote: Originally posted by TCO I'm struggling to understand your thought process. Where did 8m/second come from? I tend to think in terms of volumetric flow rates versus velocities for a system with changing cross-sectional area. What's the velocity of water "accross the lake" behind Hoover dam?

I mean the velocity of water through the narrowest area of the channel feeding the lake...

This can be at most 8 m/s (if fed entirely by the gravitational drop). There's no way to make it go faster.

Therefore the limitting factor is the cross-sectional area of the narrowest point.

	30-03-2005 02:17									#65
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quote: Originally posted by chegitz guevara Rotation is acceleration.

Centripetal acceleration and tangential acceleration are at right angles. Vectors at right angles do not affect each other.

	30-03-2005 02:19									#66
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quote: Originally posted by TCO also, just because the step change is only 18 feet does not mean the supply (and exhaust) channels are limited to this depth. They could be deeper, which will minimize head loss from friction with the channel walls.

I understand you can minimise frictional loss (the relevant fact here is that velocity profiles go to zero at boundaries, I suppose)

	30-03-2005 02:21									#67
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quote: Originally posted by KrazyHorse Centripetal acceleration and tangential acceleration are at right angles. Vectors at right angles do not affect each other.

You can't push a rope and F=MA.

What my USNA physics prof said when asked to boil down the year's teaching before finals...

	30-03-2005 02:22									#68
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GP, do you plan to dam the entire country of panama?

	30-03-2005 02:23									#69
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or will there still be an artificial river feeding the dam?

	30-03-2005 02:30									#70
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quote: Originally posted by KrazyHorse I mean the velocity of water through the narrowest area of the channel feeding the lake... This can be at most 8 m/s (if fed entirely by the gravitational drop). There's no way to make it go faster. Therefore the limitting factor is the cross-sectional area of the narrowest point.

You're losing me. We're not planning on giving up any appreciable portion of that 18 feet drop in the channel. The drop will happen at the dam. The volumetric flow rate times the pressure drop (proportional to head loss) determines the power. W'~(V')(deltap). Yes, as we start sizing the turbines bigger and bigger (to increase flow rate), we start to reach a point where head loss along the channel becomes appreciable. The wider and deeper the channel, the better of course. Use those earth-moving nukes. I saw the crater from one of those that we used in the 50s or 60s on a secret Nevada base.*


*I have no clue the volume of the earth need to move and how many bombs you need. Probably still a huge problem and not worth it. Still those bombs that have been optimized for earth clearing leave an impressive-looking crater. Almost like a small caldera...

	30-03-2005 02:37									#71
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quote: Originally posted by KrazyHorse or will there still be an artificial river feeding the dam?

I don't understand you. It's just a channel cut through the country. A thin extension of the Pacific ocean into the land (or of the Atlantic into the land). I'm assuming that we use the dam as a bridge for traffice. So we would want to be on one of the coasts.

[segue] I guess this discussion would have some similarity in terms of type of analysis to looking at tidal energy collection schemes.

	30-03-2005 02:46									#72
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quote: Originally posted by TCO You're losing me. We're not planning on giving up any appreciable portion of that 18 feet drop in the channel. The drop will happen at the dam. The volumetric flow rate times the pressure drop (proportional to head loss) determines the power. W'~(V')(deltap). Yes, as we start sizing the turbines bigger and bigger (to increase flow rate), we start to reach a point where head loss along the channel becomes appreciable. The wider and deeper the channel, the better of course. Use those earth-moving nukes. I saw the crater from one of those that we used in the 50s or 60s on a secret Nevada base.*

I understand that you want to run the water slow enough that you don't lose any energy, GP

My original estimate is the best of all possible worlds. The maximal volumetric flow rate F, assuming no loss from walls is proportional to the cross-sectional area A of the thinnest part of the channel and the velocity of the water v at that point.

The maximum v can be is 8 m/s without an outside driving force. I understand that you do not plan to run the channel at this speed (this would involve using all of your potential energy right away to speed up the water), but for the purposes of providing an estimate of the maximum available power it will do.

The current cross-sectional area of the panama canal is around 1000 m^2

Therefore if we did not increase the cross-sectional area of the Canal we would have 8000 m^3/s flow rate = 8*10^6 kg/s flow rate. Now, remember all that energy we used to accelerate the water to its ridiculous flow rate of 8 m/s? We're going to use it again. Why? Because I'm only providing an estimate of the maximum.

So, 8*10^6 kg/s * 6m * 10 m/s^2 = 4.8*10^8 J/s = 480 MW

	30-03-2005 02:50									#73
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No...no...no. We're not going to use the cross-sectional area of the current canal. That is sized for transport. I want something like the cross-sectional area of the lake behind Hoover dam. The thinnest part of the channel is not going to be the constraint to flow, it's going to be the nozzles going into the turbines.

	30-03-2005 02:51									#74
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I'm not interested in using the current cut (which isn't even at sea level) for this project. This is something we think about from scratch. Perhaps even relooking at Nicaragua as a site. (We need to get some extra value from Ollie's spendings down there...)

	30-03-2005 03:14									#75
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Ok...I finally understand what you are doing. You are looking at this as a sort of graviational drop chamber and thus see a velocity limit based on acceleration due to gravity. I don't think that's a normal (or valid, but I need to think about it) way to work the problem.

Really, you don't need to even think about gravity, Kitty. We are talking about fluid flow through a system based on pressure differences. Imagine two tanks with a connection pipe and some pressure difference. (you could do this thing in space with zero g). It's the fluid's friction with the walls (and with itself) that causes the velocity to be limited. There are some freaky things that happen near the sound barrier too of course.

I do want to think about the open channel aspects of this though. And see whether they enable your "drop tube" type thinking.

	30-03-2005 03:22									#76
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The pressure difference is due to gravity drop.

	30-03-2005 03:25									#77
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let d be the density of water, h be the difference in height, g be the acceleration due to gravity and P be the pressure difference. with no drag due to turbulence or friction with walls,

P = ghd

	30-03-2005 03:43									#78
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Yeah...I already got that, you are trying to think about this like dropping balls off of a window.

Yes the gravity causes the pressure head difference. but that does not dictate velocity limiters on the fluid as it moves in a pipe between the two tanks (oceans). The acceleration happens at the mouth of the pipe and in the "near-mouth" region. Water is incompressible so the speed as it moves within the pipe is constant. (if area of pipe is constant). So why think about graviational acceleration anyway? I mean if this were in space and you had the same pressure difference, for instance? Surely you agree that it is the head loss (pressure drop from friction) that limits flow rate?

I do need to think about open channel though.

	30-03-2005 03:57									#79
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quote: I like it better than the laser launching system which requires a beam that stays on target (and does not spread) over 1000 bounces and planetary distances or whatever...)

Actually, I was going to make a thread about this, but I'll ask here.

Assuming a high power solid state laser (1 MW - 10 MW range), what would the diameter of the beam be at interplanetary distances? Assume a power satellite in GEO (i.e., no atmospheric impact).

	30-03-2005 03:59									#80
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I think the 50% power contained area would expand to miles wide (this is using FHA analysis).

	30-03-2005 04:00									#81
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A power collector miles wide? Wow. Possible using short-term conceivable technology, but not at high efficiency.

Thanks for order of magnitude calculation. Very useful in comparing with space nuclear reactors.

I guess we would seek to combine multiple lasers.

	30-03-2005 04:48									#82
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Besides the rotational force there are also gravitational forces that give differences.

http://www.npagroup.co.uk/imagery/rs_intro/global.htm

quote: The strength of the earth's gravitational field at its surface varies according to the ocean depth and the density of local rocks. Dense rocks and shallow ocean, such as along the Mid-Atlantic Ridge (shown in red in the image), creates a higher local gravitational force which causes a greater 'pull' on the surrounding ocean water and thus results in a higher local sea level. Satellites orbiting in very precisely determined orbits are able to measure the sea level to an accuracy of a few centimetres by using Radar Altimeters which transmit microwave pulses and time their return. This measurement of the results of gravitational variations gives us a better picture and understanding of the geological structure of the sea floor. From the time variation of the returned signal Altimeters can also build up a model of ocean wave heights, which relate to surface wind speed. Radar Altimeters therefore also provide valuable data useful in meteorological forecasting.

Apparently it isn't only at "left side" of continents there are buildups. Midatlantic is at a higher level than at the European and American coast.

	30-03-2005 06:23									#83
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Which all goes to show, there are many small scale phenomenon going on, just like with tides in general, which depend a lot on local geography...
If we are talking about a couple meters, the general "
sea level is sea level" is not true...

	30-03-2005 14:02									#84
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quote: Originally posted by BlackCat Besides the rotational force there are also gravitational forces that give differences.

Again, this does not make a difference as far as the difference in "height" is concerned.

Variations in local gravity might make the surface of the ocean further away from the earth's centre at some points rather than others, but they will maintain the surface of the ocean as an equipotential. You can't slide down the tidal bulge, or the equatorial bulge or the variations in local gravity. Without dynamic forces (winds, currents, vibrations, etc.) the surface of the earth would be exactly an equipotential.

	30-03-2005 14:04									#85
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I just spent the last 13 hours of my life doing this

http://www.pha.jhu.edu/~mmcevoy/hw7.pdf

Great.

	30-03-2005 14:06									#86
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quote: Originally posted by TCO I think the 50% power contained area would expand to miles wide (this is using FHA analysis).

WTF is FHA analysis?

	30-03-2005 19:01									#87
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Fourier Harmonic Analysis is my guess?

	30-03-2005 19:28									#88
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quote: Originally posted by KrazyHorse WTF is FHA analysis?

consulting term. "from Henry's ass"

	31-03-2005 01:35									#89
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quote: Originally posted by Lul Thyme Fourier Harmonic Analysis is my guess?

I thought that, but he added in another "analysis

Like PIN number...

	31-03-2005 02:27									#90
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quote: Originally posted by TCO I don't understand you. It's just a channel cut through the country. A thin extension of the Pacific ocean into the land (or of the Atlantic into the land). I'm assuming that we use the dam as a bridge for traffice. So we would want to be on one of the coasts.

No, the Panama Canal is NOT just a channel. As I said before, the water in the canal is fresh water provided by the Chagres river, which while short has a very heavy volume due to the heavy tropical rainfall. The bulk of the Canal is at a higher elevation than BOTH oceans, which is why locks have to raise ships on both sides to get them into the Canal. In theory then you could place a damn on BOTH sides, with power generated by the waters of the Chagres of the artificial Gatun lake falling into both oceans.