Quote ="Ferocious Aardvark"I have often wondered about this. For example, having some idea of the tremendous weight that water has, and having watched rivers eg the Aire in spate at Saltaire, I often think of just how much power there must be passing by per second. So multiply that by the UK, and whichever way you look at it, it must surely be a monumental untapped (sorry!) resource.
But how much motive power is there? I am no scientist, nor mathematician but somebody must have worked it out, in order to say there isn't enough motive power. I am not disputing that answer, but the fact there isn't enough ain't the point, why don't we tap into this free resource more than we do?
Anyway some of you who do maths may be able to help. On the back of my fag packet it says that average rainfall is broadly speaking 1 litre; the approx area of the UK is 250,000 sq km; I have no clue what the average height above sea level is, but if it was for the sake of argument 10m, then on average, wouldn't the annual motive power nominally available be the amount it would take to raise that volume of water to that height? And what would that figure be?'"
OK, so I'll have a punt at this. You can challenge all of my assumptions as you like.
OK, so 1 litre of water falls on each square cm per year (I think that's your statement). That gives us a pulsating 2.5x10^15 litres of rainfall in the UK per year. (2,500,000,000,000,000 litres).
Nicely enough, that's the same number of kilos of rainfall. OK, so if we with 100% efficiency extract 10m of potential energy from this water (PE = mass x g x height) we get 2.45x10^17 J of energy (per year).
There are 31.5 million seconds in a year, so the power output is 2.45^17 divided by 31.5^6. Which is about 8000MW, or the output of 2-3 coal fired power stations.
Clearly we won't a) get our hands on all the water or b) get 100% efficiency from our mythical PE recovery engine.
I think the key point is that you need the big drop to get the power output through a tubine that would even approach this sort of efficiency.