[newrobert (OP)]

Hmmm,
Say you are raising the water 100 feet.
Then, optimally, with 1 foot drop, you should be able to raise 1% of the water 100 feet.
For 5 feet of drop, you should be able to raise 5% of the water.

However, I'd anticipate your water wheels to be far from optimal.  I don't have the efficiency numbers, but if the wheel is, say 20% efficient, then you would get the equivalent of 0.2% of the water flow being raised 100 feet per foot of drop.

Sorry man, I am not technical person, so please bear with me.   []

Now I can understand something but I think since wheel should be made according to requirement using latest techniques to extract maximum force from dropping water that's why I assume it must should be at least 80%+. Because wheel does not have to lift water itself, wheel have to covert force to piston. If wheel lift water itself then there are chances of leaking water while lifting, incomplete water buckets, etc.

So if I assume 80% wheel efficiency and I want to calculate first wheel and last wheel in row.

Wheel efficiency = 80%+
Water lifting at: 200 feet
First wheel = Drop 1 feet (since pool is at 20' height so vertical distance is less between top pool-wheel)
Last wheel = Drop 20 feet (since pool is at 20' height so vertical distance is higher between top pool-wheel)

Now how much water both wheel can lift. Depending on your calculation I will calculate each wheel (20 in a row) myself.

Thank you for helping me.

Robert

[CliffordK]

If you have a total of 20 foot drop.
And are raising the water 200 feet.

Then the maximum amount of water you could pump is 10% of the water no matter whether you have one wheel or a dozen wheels, nor whether they are arranged in series or parallel (drop/(total height to raise water)).  I believe that is raising the water from the lower pool.  You could only use the waterwheel to raise water from the upper pool, but then you would subtract the water pumped from the total water powering the wheel, and I believe end up with the same answer.

You then multiply in the efficiency of the wheel and the efficiency of your pump. 

The series wheel arrangement may have some impact on the overall system efficiency. 

I think 80% efficiency would be optimistic for your wheel. 

However, say you have a 90% efficient pump, and an 80% efficient wheel (or chain of wheels), then the overall system efficiency is 0.9*0.8 = 0.72, or 72% efficiency, which you can then multiply by the portion of water being pumped (10%), to get 7.2% of the water being pumped.

Your problem is that the 20 foot drop costs you essentially 10% more energy to raise the water up 220 feet rather than 200 feet.  Your super-efficient water wheel gains you 7.2%, and you're still down 3% energy.

So, say a pump that took 100% of x amount of energy to pump the water 200 feet, now with the addition of the additional drop, and super-efficient water wheels now requires 103% of the original energy consumption to make up for the additional losses (or more).

[syhprum]

I think we should distinguish between perpetual motion which is pretty common on a human time scale i.e  planets going around a star, sub atomic particles orbiting and jittering and machines that can extract useful power indefinitely from such motion.
satellites can draw power from the motion of planets via a sling shot technique but it is only a transfer of energy not its generation.