Energy produced by an infinite waterfall
Sep. 4th, 2014 06:06 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
jackA friend asked on twitter, if you could place two connected portals anywhere on earth (but not in space), what would you do with them. Personally, linking Cambridge and Liv's campus flat would be nicest! Geopolitically, probably linking two disparate regions might be most useful.
But of course, the question turned to free energy. Suppose the portal is 1mx2m, laid horizontally, one at ground level and one 100km up at the edge of space, and you diverted sufficiently much water into the lower one to get an endless waterfall. How much energy would you get out?
I'm not sure I have these equations right any more, but under those assumptions (and that the density of water and the gravitational constant for the whole height are rounded to the nearest power of ten and that the square root of 2 is 1.5), and assuming that extracting the energy from the falling water slows it to rest again, I tried to calculate the speed and the energy. I think freefall from that height (assuming you can somehow construct an airtight tube) lands at 1500m/s. And that translates to 3x10^12 Watts = 3TW. Can anyone confirm if I have that right?
It's hard to tell from wikipedia, but it looks like that world energy consumption was 15 TW the last time someone worked it out and updated that page. So this device would make a worthwhile dent in it, but not obsolete everything else.
Of course, that assumes there are sensible engineering solutions to "build an airtight tube to the edge of space" and "slow water from mach 5 safely without wasting any energy" which there probably aren't.
You could dig the tunnel _down_ instead, but you'd have to actually dig it, although you could put one portal down there and dig up through the other one, until the rock fell freely. And you'd have to be careful not to go down too far because if your experiment starts spewing pressurised magma you've invented your own personal volcano, and you have to hope that it solidifies and buries it well enough to withstand ten atmospheres of pressure.
Of course, if you did the above experiment with rock instead of water, the energy involved would be 10 times greater, although presumably the engineering challenge would still be the limiting factor.
However, leaving the practical impossibilities aside, something bothered me about the physics. It seems like, if you don't slow the falling substance completely but let it go through the portal already at high speed, you get correspondingly more energy out. I guess because the limiting factor for energy is that each atom going through a portal to 100km up creates a certain amount of potential energy, so you get the more energy the more you cause that to happen. It seems dodgy that the energy production could just keep on growing in that case, but I guess the assumptions violated physics, so there's no reason not to expect that to violate a wide number of other principles. Have I actually got that right?
But of course, the question turned to free energy. Suppose the portal is 1mx2m, laid horizontally, one at ground level and one 100km up at the edge of space, and you diverted sufficiently much water into the lower one to get an endless waterfall. How much energy would you get out?
I'm not sure I have these equations right any more, but under those assumptions (and that the density of water and the gravitational constant for the whole height are rounded to the nearest power of ten and that the square root of 2 is 1.5), and assuming that extracting the energy from the falling water slows it to rest again, I tried to calculate the speed and the energy. I think freefall from that height (assuming you can somehow construct an airtight tube) lands at 1500m/s. And that translates to 3x10^12 Watts = 3TW. Can anyone confirm if I have that right?
It's hard to tell from wikipedia, but it looks like that world energy consumption was 15 TW the last time someone worked it out and updated that page. So this device would make a worthwhile dent in it, but not obsolete everything else.
Of course, that assumes there are sensible engineering solutions to "build an airtight tube to the edge of space" and "slow water from mach 5 safely without wasting any energy" which there probably aren't.
You could dig the tunnel _down_ instead, but you'd have to actually dig it, although you could put one portal down there and dig up through the other one, until the rock fell freely. And you'd have to be careful not to go down too far because if your experiment starts spewing pressurised magma you've invented your own personal volcano, and you have to hope that it solidifies and buries it well enough to withstand ten atmospheres of pressure.
Of course, if you did the above experiment with rock instead of water, the energy involved would be 10 times greater, although presumably the engineering challenge would still be the limiting factor.
However, leaving the practical impossibilities aside, something bothered me about the physics. It seems like, if you don't slow the falling substance completely but let it go through the portal already at high speed, you get correspondingly more energy out. I guess because the limiting factor for energy is that each atom going through a portal to 100km up creates a certain amount of potential energy, so you get the more energy the more you cause that to happen. It seems dodgy that the energy production could just keep on growing in that case, but I guess the assumptions violated physics, so there's no reason not to expect that to violate a wide number of other principles. Have I actually got that right?
no subject
Date: 2014-09-09 04:45 pm (UTC)My answer to the question was similar, but to drop a solid steel bar through the portals. If the portals are 2m^2 and we drop the bar at a very modest 10 m/s we get out 160MW.
It's trivial to extract this energy; electric railway locomotives have all the engineering we need. The Class 91 is an obsolete design now, but each bogie's 4 driving wheels can move nearly 250kW from one steel surface to another (an electric motor pretty well runs in reverse as a generator, the frictional considerations are the same, etc). We can also obviously drop the bar at the Class 91's c. 60 m/s top speed, generating just under a gigawatt from 16,000 steel wheels pressed against the bar. (Sanity check; each wheel then has just over 300 cm^2 of bar surface to itself). The bar is safely held by the infrastructure of wheels, electric generators, and the supporting framework for same; it can be sped up or slowed down by adjusting the load.
Obviously one could do much better with custom designed equipment, but this is clearly possible because it uses existing - 1980s - technology.
It's counterintuitive that the speed of the bar makes one get more free energy out, but it does make sense. Cyclists (who are also nerds) are familiar with this effect because, although power to overcome air resistance varies with the cube of speed, power input from gravity varies with speed. Another way of looking at it is that our figure for work done by gravity on the bar (which is where that 160MW comes from) should match our figure for potential energy created by teleporting stuff. 2m^2 (cross-section) * 10 m/s (speed of bar) * 8000 kg/m^3 (density of steel) * 100m (height teleported) * 10 J/kg/m (energy imparted to mass by being teleported up against gravity) is indeed 160MW. Now it's clear why a faster moving bar works better; more mass is being teleported every second.
I don't know what the air resistance losses are - although I hope they're low for a polished steel cylinder - but in principle we could run the mechanism in a low-pressure environment.