paddy wrote:You seem to know a bit about it Stew could you please explain this part.
Now, there's an invitiation. I can try to explain a bit about my understanding of it. But you may find yourself with the irresistable urge to drift away before you get to the end. I know very little about waterwheels (and, some may point out, not a great deal about physics), so have made a few assumptions:
There is an immutable rule in physics that says you cannot get more energy out of a system than you put into it[1]. I like to think of this as a form of economics; energy is an actual thing, even though we can't see it in literal terms. But we can store it and use it. And like in any other type of economics, you can only expend it if you actually have it to spend. You cannot put 10 biscuits into a tin, and then get 20 out of it. Similarly, you cannot put 10 units of energy into a system and get 20 units out of it - if you put 10 units in, that is all there is to get out again.
Energy can be made to do work which can be expressed in lots of different forms - not only in electricity in wires and batteries, but in water flowing through a hosepipe, and in the turning of a waterwheel. But the amount of work that the waterwheel can do is dependent upon the amount of work that the water can do in turning the wheel in the first place - if there is not much work being done by the water in turning the wheel, then the wheel will, in turn, not be able to do much work. In effect, all we are doing is converting that energy from one form to another. We are not adding to it.
So, OK, we have a big wheel which is turning very fast. Ideally, it will be a well balanced wheel, on bearings that are pretty low friction. This means that it will turn easily. Because it is well balanced, it will start to turn even when a small amount of water is in one of the buckets. The low friction bearings will offer little resistance to this turning, and if we apply no more water, it will still keep turning for a long while. But if we go on adding more and more water, it will go on getting faster, because there is very little to stop it. In terms of physics, this is covered by the rule that says a body will keep on accellerating for as long as we apply a force to it (Newton's second law of dynamics). The only thing that can stop it getting faster and faster is the friction in the bearings, and the resistance of the air around it. The effect of these two resistances will increase as the wheel gets faster, and eventually it will get fast enough for them to exactly oppose the input effort of the water. Given enough time, even a fairly heavy wheel may get up to quite a fast speed.
But if we were to connect a dynamo to it, and generate some electricity, we are adding some more resistance to it, so the wheel must start to slow down, and the resistance of the
three opposing forces (friction, air resistance, and the dynamo) must equal the effort that the water is putting in to the wheel. What is interesting to learn about any sort of generator, is that the more work you ask it to do, the harder work it is to turn it. And remember, that the wheel cannot do more work than the water applies to the wheel in the first place.
In reality, a waterwheel is more complicated than this, in energy conservation terms. Not all the water will be able to turn the wheel efficiently; some of it will be spilled, some of it will be tipped out of the bucket before it has travelled from top to bottom. There are other ways that energy is lost beside friction and air resistance. All of this lost energy can only come from the input source (the hosepipe), leaving less than 100% for the dynamo to convert into electricity. And the dynamo itself will not be 100% efficient either (nothing is).
But what we can say, with absolute certainty, is that the
output of the wheel cannot exceed the amount of work we
apply to it. Since this input is only coming from a single hosepipe, and we know the rate of flow of the water (2 gallons a minute), and we know the height that water is falling as it turns the wheel (8' diameter), we can use some basic formulae to work out a maximum figure that the output cannot exceed. The speed of the free wheel (without the load of the dynamo applied to it) may be impressive to watch, but it doesn't represent the amount of work that we can get out of that wheel.
In this case, 2 gallons a minute is falling through about 8'. It's not doing anything else. 2 gallons weighs 20 lbs, so, as a rate of work, this is equivalent to about 5 ozs falling 8' per second (in metric measure, this multiplies out to a rate of work - power - of about 3.6 W). There is no other effort being applied to the wheel, so we will not be able to get any more work than this out of it.
But enough of the physics. I reckon there is an interesting project in your waterwheel idea. The only real way you are going to see if you can make something viable is to do a bit of experimentation. Maybe make a small version of the wheel, and see how it goes in different parts of the river.
[1] Periodically, someone will claim to have invented a way round this, and that they are getting more energy out of a system than they put in. I've looked at many of them with increasing disgust. They are never able to say where this additional energy is coming from. This is the basis of the perpetual motion machine (there are one or two example of this in some old posts on this forum). They will defend their invention stoutly, some will offer to demonstrate it, and yet, for some reason, we never see
any of them in proper applications. Often, the inventor asks for people to 'invest' in the development of their invention, and people always lose their money. I am, of course, an unrepentant Newtonian in my (limited) understanding of physics. Others may choose to put their faith elsewhere.
