smollett said:
Chocolate fireguard said:
Power = flow rate (m3/sec) x head (m) x gravity (9.8) / Efficiency constant (0.6)
Hardest part is estimating your flow volume. On larger streams you can get a figure by measuring the cross-sectional area of part of the channel and measuring the rate of flow using a stick timed over a set distance. Some simple math will give you a reasonable estimation of the flow rate.
The formula assumes the water has fallen freely for 100m and has therefore converted all of the gravitational potential energy (GPE) to kinetic energy (KE). The water would be travelling at around 45m/s or 100mph. The 6kW is a reasonable estimat of the electrical power you might get from converting all of the KE (MULTIPLY by 0.6). On any hillside the majority of the GPE will in fact be converted to heat, via friction, leaving little for KE. The crucial thing is that the KE of a mass is proportional to the SQUARE of its speed so if the water were still moving at 15m/s (still over 30mph and probably faster than any stream I have seen) this is one third of the assumed speed and so the KE is one ninth of 6kW. A more realistic 5m/s for the average speed means the KE is reduced by a factor of 81 and we struggle to light half a dozen low-energy bulbs. The obvious solution is more buckets per second but even a healthy stream of 1 cubic metre per second still only gives 7.5kW. It might be worth pointing out that it is not possible to take ALL of the KE from the water as that would mean stopping it completely and the turbine would soon be full! But things work for us here and reducing the speed from 5m/s to 1m/s means we have captured 96% of the KE.
Things may be better though. The stream will reach its 5m/s or whatever very soon after setting off downhill so it may be feasible to set up several mini generatore along the way so long as they are far enough apart to allow the water to reach "terminal" speed between one and the next.
Velocity is not the most important component and anyhow can easily be obtained (not that you want it) by reducing the diameter of the pipe. Try putting water round a bend in a pipe at 45m/s and see what happens! You will get tremendous vibrations and cavition at the bend which will make it fail. Anything over 4m/s and you have to be very careful. Pressure is the most important factor. Once you know the pressure you can choose the pipe diameter to keep velocity low. You don't want a high velocity because then you get large losses in the pipe which will reduce efficiency (see Darcy Weissbach equation). You increase the velocity at the turbine by reducing diameter just before it. THe most efficient way is to use one machine, not a series of them. Gilkes in kendal specialise in high head turbines.
Using ram pumps to fill a reservoir to generate from would be incredibly inefficient. You would need thousands of them to generate a tiny amount of power. I doubt you would recoup the energy required to build and install the system in the first place.
[/quote]Smollett, you might want to reread my post of Dec 27 and Hoehlenforscher`s to which I was replying. I was not saying you must have high speed water in pipes, merely that if you want to generate hydroelectrical power at 6kW using a machine with efficiency 60% and have 0.01m^3/s of water coming in then it MUST be travelling at 45m/s. If you want to deliver the water from 100m above then it MUST (at least on planet earth) have fallen freely (2 words I used in the post). Free fall is a situation where the only force acting is gravity so pipes, with the inevitable friction, are out. So for that matter is a 100m fall through anything but a vacuum!
My suggestion about using a series of generators was to point it out as a way of increasing the power you could get from a stream flowing a long way downhill but never exceeding, say, 5m/s. I was not recommending it as an alternative to a proper generator in a situation where one could sensibly be used.
Those comments apart, everything you have posted since is spot on.
