How efficient would pumping water uphill be using hydropower?

Question

How efficient would hydropower be at pumping water upward? Waterwheels are the cornerstone of unmanned power and are basically gravity powered (solar too if you count the water cycle,) which is very weird. Down is easy and up is hard.

Over the course of history there have been many inventions to pump water upward; the pump being the most obvious example and the Archimedes screw being one of my favourites. However I wanted to get a little original.

Here's my version:

Water spins a waterwheel which in turn spins millstones over water-filled bellows. The subsequent pressure sends water upward through tubes. Springs in the bellows expand them in between rotations to suck in water and the stones pass over them again. To prevent backflow between the stones rotations a series of valves like those of veins open and close across segments of the tubes. The valves consist of three petals that are pushed up (open) when water rises and pressed down (closed) when water drops down. To sum it up: water spins rocks and water goes up. Simple enough.

However, as I'm sure you are aware, I am no engineer and probably got something wrong along the way. Putting aside the considerable infrastructure and construction costs, how efficient would this method actually be? At least compared to other methods. I should also clarify that by "up" I actually mean uphill not necessarily vertically.

I expect it to be slower but require no energy (not manned energy anyway.) Starting up the stones will take some time and energy but once the momentum gets going the rest is easy. Feel free to propose improvements to my baby if you come up with a good idea (but don't replace her as it would hurt her feelings.)

Answer 1

It'll be not very efficient

There are many ways to pump water upwards. The screw is one of them and has lasted a long time. It is very effective for such a low tech solution. So effective that it is still used in many, many modern pumping stations.

The reason we can determine your solution isn't efficient is the cost of transferring energy. Each time you transfer energy, you can safely assume some of the energy isn't used for your intended purpose. The water against the water wheel will not just move the wheel, but add stress to the structure and friction generates heat. That means that part is 'lost'. Any system has loss, so we need to check the efficiency and amount of transfer points.

First of all, water transfers energy into the water wheel. Assuming a Pelton wheel, there's not much you can do to make it more efficient. Good point. Then you transfer that energy to some big spinning rocks. This isn’t such a bad idea. Flywheels operate on this exact principle. It is being used as energy storage devices in busses and even on the electrical grid. The problem is that it is an extra transfer. Is it needed? If not, remove it. You have frictional powers on the shaft and with the air, let alone the starting cost of getting it to spin. Although we now have incredibly efficient flywheels, it probably isn't as efficient if you use the old millstones as technology. It was surprisingly advanced before factories took over the work, but compared to modern technology it'll just be a waste.

The transfer mechanism to the bellows is not well specified. You can expect some to enormous energy losses here, depending on the way. As the bellows seem to compress due to the rotation of a millstone, I expect high amounts of friction. The bellows itself aren't too strange mind you. It's similar to a way you can pump water. If you time it right, you can have an equal pressure on the water system. The bellows do need to suck in water, as well as spill it. Another two points of energy loss.

The whole thing can be water powered, using a stream of water to pump other water upwards. The efficiency is highly dependent on the technology used. Although each has a basis in real world technology, it's inefficient compared to many real world solutions. You're using multiple real world technologies chained for little reason. Each technology represents energy transfer to something else, giving a loss. It does happen in the real world for some reasons, like temporary storing the power in a flywheel to give off a stable amount of energy. Still it is better to use the waterwheel to directly power some pumps. Or just grab some big efficient screws and not think too much about it.

I wouldn't let such ideas go though. Creativity can only be commended.

Answer 2

Far more efficient and easier to build than water wheel, gears, cam wheels, bladders, and so forth is a "pulse pump" or "ram pump" -- these can be made as soon as rigid tubing is available, using the same technology you'd use to make a hand or windmill driven reciprocating down-well pump.

Water running downhill in a pipe sequentially activates a pair of flap valves -- one in line with the flow, and another vertically upward. The closure of the inline valve cause the momentum of the water in the inlet pipe to force water past the vertical valve, until the momentum is spent and the vertical valve closes -- and the still water no longer keeps the inline valve shut, so the flow starts again.

These pumps can raise a small fraction of the flow to heights well above the head of the inlet pipe, or much more flow to more modest heights, and are technology that was accessible at least as far back as the classical Helenic period (in terms of materials and tools being available -- bronze and lead piping could be used).

Answer 3

There's nothing in your question about the technology level you're asking about, so let's assume modern real-world technology. A system where a downhill flow of water is used to power a pump could be about 70-80% efficient, meaning either the uphill flow rate could be 70-80% of the downhill flow rate at the same vertical separation, or the flow rates could be equal but the pump reaches 70-80% of the vertical separation compared to the downhill flow, or some other numerical combination of flow rate and vertical separation which works out to 70-80% efficiency.

This figure comes from Wikipedia's page about pumped-storage hydroelectricity, which states:

The round-trip energy efficiency of PSH varies between 70%–80%,^[4][5][6][7] with some sources claiming up to 87%.^[8]

A pumped-storage hydroelectric facility can operate as either a generator (producing energy from the downhill flow of water) or a pump (consuming energy to pump water uphill). Its purpose is to balance the load on an electrical grid, basically a giant battery that can be charged while supply exceeds demand, or drawn down when demand exceeds supply. The system I described in my first paragraph is simply equivalent to two such facilities connected to each other, one always operating as a generator, the other always operating as a pump, so the efficiency would be the same.

If you can think of a way to do significantly better than this, then you would make more money by actually building it in the real world, rather than writing a story about it.

Answer 4

I expect it to be slower but require no energy (not manned energy anyway). Starting up the stones will take some time and energy but once the momentum gets going the rest is easy

"The rest" (the energy expended to keep the stones turning) is, minus the losses, equal to the gravitational potential energy accumulated by the water that goes up. So, the less energy expended to keep the stones turning, the less water is being pumped up (assuming a 30% pumping efficiency, each liter/second of flow rate going up one meter costs about 30W; so, 10L/s at 20m head require about 6 kW).

Your main difficulty is water pressure: the bellows must pressurize the water enough to send it upward against the counterpressure of the water already in the pipes that is keeping the valves closed. You can supply that pressure with the millstones, but will the gaskets hold? And the pipes? So, the maximum height attainable will be limited (every 10 meters adds one atmosphere of pressure).

Then, efficiency. Millstones, however well balanced and installed, are going to produce a considerable friction. The incoming running water will have to overcome that friction. This is more than possible - after all, watermills do exist, and they can reach about 60% conversion efficiency. The bellows can theoretically be very efficient, but this relies on the material being flexible yet unyielding (it mustn't stretch, as that energy gets wasted). With the appropriate characteristics of the bellow material, we might be looking at a 90%-95% pumping efficiency, which translates to around 40% overall. With slowly flowing water and an overshoot waterwheel, conversion efficiency would likely double.

As an alternative (also with slowly flowing water), you might consider a waterwheel powering a vertical water cableway: four or five buckets going down can send three buckets up at whatever height (slower and slower the higher you go), and the friction is concentrated in the top bullwheel. The wheel and the cableway can be scaled somewhat by thickening them (the buckets become troughs).

Answer 5

Noria. A typical flat board undershot wheel uses about 20 percent of the energy, though it can be improved to ~50% with some experimentation.

Answer 6

Thermodynamic considerations tell you that you will end up pumping up less water than you are dropping down, because of all the losses in the process, and you can basically forget about going as up as you are going down.

My gut feeling says you'd be lucky to get a 30% overall yield.

Answer 7

Using an Archimedes Screw is one way they did it in ancient times... You would just need to use some of the remaining water to turn the screw...

In terms of water efficiency, you need to consider energy efficiency, then consider the energy the remaining water will produce. The later depends on the weight of the water you want to lift W, times the vertical distance D you are lifting to, times some energy efficiency alpha, with alpha>1 and depending on the technology. This energy you will get from either the kinetic energy of the water you have (e.g. wheel on a riverbed) or by dropping the water to some large distance (and then using wheel(s) at the end / along the way, (think how its done in Hoover Dam) times some efficiency alpha, with alpha<1 depending on your technology.

For the first method you depend on the mass of the water you release being significantly more than the one you lift. The second method is far far better in terms of energy released per gallon lost.

There is a nice trick to simplify things: Using the low of conservation of energy, if you want to lift some mass,drop equal mass to the same height (plus energy losses), or drop half the mass to double the height, or drop double the mass to half the height, or even drop one tenth of that mass to ten times the height and so on.

Btw, the fact that you are pumping water or sand, or whatever makes little difference to energy conservation, only to the technology used and the losses incurred...