Comment by thaumasiotes | Hacker News Reader

Comment by thaumasiotes | Hacker News Reader

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> Gravitational potential energy is not something that can be depleted in the way you're talking about. If Idaho is at 3,000 ft above sea level, whether or not they build a hydro dam doesn't impact the ability of Washington or Oregon to build hydro dams at lower elevations.

Gravitational potential energy is depleted when anything's elevation lowers. In rivers as in everything else, it is converted to other forms of energy. In rivers, that is kinetic energy. This is depleted in the normal way by harvesting it as "hydroelectric power".

Building a hydroelectric dam at 3,000 feet won't impact the ability of Oregon to build one at 0 feet and get 3,000 feet worth of river energy. But rivers flowing through Idaho started out with more than 0 energy (they're flowing!), which would also have been available for Oregon to use.

Idaho's gain is Oregon's loss. They can't drain Oregon to literally 0 energy extractible from the river, but they can come close.

Idaho is not sending the water into Oregon at any lower elevation because they added a dam and a hydro-plant upstream!

Hydro plants don’t harvest the ambient kinetic energy because the terminal velocity of the water is quite low! You can’t build a hydro plant at 0ft elevation, even if that water just flowed down a 10,000ft mountain.

A hydro plant takes a specific localized elevation drop and turns that drop into power by harvesting the gravitational mass of the water to rotate turbines installed along the way.

The water at the top entrance to the hydro plant is sitting perfectly still in a reservoir built to feed the plant.

If you tried to put a turbine at the bottom of a fast flowing river it wouldn’t work. You need the weight (mass) of millions of tons of water pushing directly down on your turbines to generate the necessary power.

Now here’s a fun thought. All that potential energy in the water at the top of the mountain, that potential energy got into the water when it evaporated from the surface and raised up into the atmosphere. So really it’s all just another form of solar power.

most power is solar power (hydro, wind, solar, oil, natural gas, coal).

Which hypothetical river contains more energy when it reaches Oregon?

- A river that came from 8,000 feet

- A river that came from 3,000 feet

Oregon potentially has access to energy that Idaho cannot extract from the river, by virtue of Idaho's higher elevation. But any and all energy that Idaho does extract from the river is energy that would otherwise have been available downstream. Again, all gains to Idaho are losses to Oregon. The reverse is not true: Oregon enjoys some minor gains which are not losses to Idaho.

I’m about ready to give up :-)

The potential energy in the water at the top of the mountain gets eaten away as it flows downstream whether there is a hydro dam or not, due to the massive friction of the water flowing downstream.

This is what I mean by terminal velocity of the river. The water does not just keep speeding up and speeding up as it flows downstream.

At first the water starts to flow faster, and indeed it is converting potential energy into kinetic energy. But as the water starts to flow, the kinetic energy starts getting sucked out through massive amounts of friction in the flow. Ever hear a river roaring? That’s the audio track of massive amounts of kinetic energy draining out into the surrounding earth. (A frictionless river would flow silently)

As the water keeps speeding up as it flows downstream it reaches a point where the friction is costing as much energy as the elevation drop is adding. Terminal velocity. At that point, every foot of elevation drop keeps the river flowing but does not increase net kinetic energy in the river.

Take one kilogram of water and pour it down a chute at the top of a 100 foot high drop.

Take another kilogram of water and pout it down a 200ft high chute. A 1,000ft high chute.

At the bottom of the chutes we measure the speed of the water. You will find the water is flowing at exactly the same speed in all three cases. Why?

For a typical hydroelectric dam, kinetic energy is not particularly important (although smaller kinetic hydroelectric plants do exist). The relevant factors are pressure (determined by the hydraulic head) and volumetric flow.

In ideal conditions, if you have two sections of identical pipe, and a turbine in the middle, water flowing through the pipe will not change velocity (incompressible fluid, and none is gained or lost), yet the turbine can harvest one Joule per cubic metre per Pascal of pressure.

This is the predominant principle by which a dam works; it creates a large pressure differential, and then drives a turbine at a relatively much slower velocity than the maximum possible by converting all the GPE to KE.

To adapt this to your chutes idea. Water will not pour down the longer chute significantly quicker than the shorter one, yet if you fill them, the longer chutes will have a proportionately larger pressure at the bottom. Thus a flow of 1m^3/s will deliver proportionately more energy across a turbine which reduces the pressure to ambient.

> But any and all energy that Idaho does extract from the river is energy that would otherwise have been available downstream.

This is false. Huge portions of that kinetic energy are going to be lost to transfer, heat, and sound if it is not captured by Idaho.

> Which hypothetical river contains more energy when it reaches Oregon?

Assume a spherical cow...

In order for any of your claims to be true, your 'rivers' would have to be straight, frictionless channels.

To know the actual impact on flow you would have to measure it. It is possible the flow will be reduced. But this is irrelevant for energy generation, since it is the gravitational potential that is being harvested[0]. Any kinetic energy coming into the system from upstream is dissipated when it reaches the reservoir.

[0] - Yes, step 1 is to convert the gravitational potential energy into kinetic energy, so you can be pedantic and say you are actually harvesting kinetic energy. However, this is not the kinetic energy in the pre-existing flow.

In your world, a river would be flowing at a speed of 132 m/s (= 295 mph) after coming from 3000 ft [1]. Now compare this to rivers in the real world and you will see that you're overlooking a factor which reduces the speed of the flow by two orders of magnitude.

[1] Potential energy of 1 kg water at 3000 ft: 1 kg * 900 m * 9.81 m/s² = 8829 J. Kinetic energy: 8829 J = 0.5 * 1 kg * v² ==> v = 132.88 m/s

That's not how physics works... Are you claiming that the dam somehow changes the elevation of the Idaho/Oregon border?

This is not how it works. The dam in Oregon (or anywhere) doesn’t work on kinetic energy from the flow. In fact it often is stopping the flow (dissipating the kinetic energy) entirely.

The elevation drop that matters is from the top of the dam to the bottom of the damn.

Doesn’t matter a whit whether the water that falls that 500’ has previously come from 1000’ or 10,000’.

> The elevation drop that matters is from the top of the dam to the bottom of the dam.

> Doesn’t matter a whit whether the water that falls that 500’ has previously come from 1000’ or 10,000’.

Depends what you're counting. As you say, stopping the river entirely dissipates its accumulated flow. If you're downstream, then such a dam would lose you much more energy in the case where the water had originally come down 10,000' than in the case where it had originally come down 1,000'. The energy harvested usefully is the same, but the energy wasted is very different. And the total, the energy removed, is also very different.

I'll note, though, that a dam that completely stops the flow of the river is producing zero energy. (And also, about to cause a flood somewhere.) You only get energy by letting water through, and slowing it while it goes.

I'm gonna guess that there's no significant impact on the kinetic energy of the river very far downstream. There's constant resistance and it's at a relatively low speed. Think of how quickly the river wouldn't be a river anymore if gravity suddenly ceased - it's virtually all potential energy being converted and lost to the surrounding environment and turbulence constantly. I would bet a lot of money that if you measured the kinetic energy in Oregon, you would find no statistical significance before and after a dam is built in Idaho.

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