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Originally posted by mhc_70
My theory. All objects have work stored within. You put them in motion, use complex mechanics to invoke the forces of nature to increase the force of their motion. Force= mass x velocity2. That means if you double either one , you quadruple the force, double both and you increase the force 8x, fact, not my theory.
Originally posted by Pilgrum
reply to post by mhc_70
In E=m.C^2, C (light speed) is the only factor squared
Q.g.h is an adaptation of M.g.h which is the expression for gravitational potential energy (mass x gravity x height) but efficiency must be considered and for a typical hydro application an overall figure of about 80% or even a little higher is the norm when conduit friction (head loss), machine losses (mostly heat), runner cavitation, transformer and conductor losses are all factored in. Cascaded schemes are dictated by topography where using the total head at a single point isn't practical but they suffer in overall efficiency compared to using the total head on a single turbine. As the turbines peak in efficiency at approx 70-90% of rated output, better efficiency over a wide range of outputs is achieved by using multiple turbines in parallel.
Originally posted by Pilgrum
reply to post by mhc_70
Sorry if I was drifting off a little there
I'm just working on your 'hydro' example given above to put some actual quantities to it like energy available compared to energy actually obtained. The energy is initially gravitational potential energy which gets converted to kinetic by falling, then mechanical (spins a turbine) and finally electrical energy at the terminals of an alternator.
[edit on 3/6/2009 by Pilgrum]
Originally posted by Pilgrum
reply to post by mhc_70
The key to the 'potential energy' is the term 'potential'. It can only be used if the mass or part thereof in m.g.h is allowed to fall where it becomes kinetic energy. Basically potential energy is a form of energy storage.
In your example of a pond with 1000' head and no inflows, how much potential energy does it have once all the water is drained out (falling 1000')? Where does the potential energy go?
When I speak of efficiency it's in terms of the overall energy conversion and in practise a portion of that initial potential energy is always lost in the conversion process(es) most commonly as wasted heat.
Originally posted by mhc_70
Niether system has a 1000' head, both have a 100' head. System A the water exits the headgate and free falls 1000'. System B the the water exits the headgate and impacts the turbine and then begins to fill the next reservoir. The volume of water is the same, the decrease in PE, in both systems, is due to lower elevation, not the work it performed on the turbines.
Originally posted by Pilgrum
I see you're acknowledging the reduction in PE caused by the reduction in height and if you consider the principle of conservation of energy you should realise that the lost potential energy didn't just disappear, it had to be converted to another form of energy and that is kinetic energy. The potential energy can be restored by simply raising the water back to its original height but that requires input of energy in some other form doesn't it? Consequently storing energy - potential energy which can be re-used.
The amount of energy recovered from your hypothetical system is paltry in comparison to the losses because of the highly inefficient setup.
I'll put some actual numbers to it (using metric because it's more convenient for conversion to actual kW available)
The 'magic' formula for hydro applications is P=Q.g.h (kW)
1000' head = 304.8m
100' = 30.48m
g=9.8m/sec^2
and let's suppose you can release water from the top pond at 1 m^3/sec until the pond is empty.
First - the most efficient arrangement would be as I suggested earlier
IE a turbine fed by a penstock at the bottom of the 1000' drop.
That output figure amounts to 1 x 9.8 x 304.8 = 2987kW or nearly 3 megawatts.
Not mysteriously by any means, that is the minimum amount of energy you'd need to supply to lift that water back up to the top pond (by pumping) if the pump system was 100% efficient (they never are). The act of pumping is a good example as it's the whole system in reverse IE using electrical energy, converted to mechanical energy, then kinetic energy and finally potential energy once the water is back in the top pond.
Next - let's see how much energy is recovered when the water falls, say, just 1m to the turbine, then free-falling the rest of the drop with the same constant flow of 1m^3/sec:
P = Q.g.h = 1 x 9.8 x 1 = 9.8kW
10 such drops with turbines at each outlet with the same 1m effective head on each turbine would, at best, generate only 98kW.
So what happens to the lost 2987kW-98kW = almost 2.9MW gone?
It's because your system is only making use of 10m of the available 304.8m of head and the missing 2.9MW is simply being wasted with your comparative efficiency of merely 3.3% which is woeful.
Once the water reaches the lowest level its potential energy has been exhausted no matter how it gets there but the energy has not been destroyed, it was simply converted on the way down. The variance in the examples reflects only the efficiency of the systems.
Now there is a way to extract the full potential of the fall with the turbine located somewhere other than the bottom and that involves utilising what we call 'suction head' and I could explain it for you if you're interested. It is subject to some stringent mechanical limitations though. I work with these systems every day.
[edit on 4/6/2009 by Pilgrum]
The modern hydrodynamic turbulent water circulation will be eliminated as good as possible. On the other hand we developed the world wide first so called gravitation water vortex power plant which uses the rotation energy of a single gigantic water vortex. It is a milestone in the hydrodyamic development because in the past we needed energy to aerate water - now we have a water aeration process which produce electric energy. Already in the first operation year the invention of the Austrian engineer Franz Zotlöterer produced 50.000kWh - electric energy for 14 average european households. The prototype plant supply the public electricity network with current. You can find the gravitation water vortex power plant on the millstream in Obergrafendorf (10km southwest from St.Pölten in Austria in Central Europa). It is public and can be reached on the cycle track along the pielach river:
Presently used falling height 1,3m
Presently used flow rate 1m³/s
Diameter of the rotation tank 5,5m
Hydraulical power 13kW
Elektrical power 8kW
Effectiveness of the turbine 80% at 3/3, 83% at 2/3 and 76% at 1/3 of the maximum flow rate
Turbine speed 25rpm
Investment minus financial support around 40.000€
Joyful working capacity of 50.000kWh in the first year of operating - since February 2006 the actually total production of electricity is over 120.000kWh