Which Is Higher? Atlantic Ocean Or Pacific Ocean?

[TCO]

And which is susceptible to math errors...

[chequita guevara]

Originally posted by KrazyHorse
Whyy? It's not like the earth's spin is accelerating...

Rotation is acceleration.

[TCO]

Originally posted by chegitz guevara


Rotation is acceleration.

Truth is whatever serves the party. PRAVDA!

[KrazyHorse]

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.

[KrazyHorse]

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.

[KrazyHorse]

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)

[TCO]

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...

[KrazyHorse]

GP, do you plan to dam the entire country of panama?

[KrazyHorse]

or will there still be an artificial river feeding the dam?

[TCO]

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...

[TCO]

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.

[KrazyHorse]

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

[TCO]

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.

[TCO]

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...)

[TCO]

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.