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Can home based hydro-electric power work? Calculate for yourself!

I've been sick at home this weekend noodling over whatever can distract me from feeling sick and did an interesting Virtual proof of concept. I invite you to do the math with me and tell me if my thinking is wrong or not but I think it is possible for many of us to have our own hydro electric power scheme!

Why would I want one? It's not about generating power... its about storing it... even if you have a 4kWh solar panel setup you can still only run it during the day. The point of using stored water is that it can be used like a battery. But unlike a battery a water tank and water turbine has no dangerous chemicals and is much easier to maintain than a bank of batteries. Tesla recently announced a solution in this field but even at 15-20k I still worry about having all those batteries stored in the garage... so here goes the math.

Hydro power (watts) = the mass of the stored water (kg or litres) x the water flow (litres per second) x the distance the water drops (metres) x gravity (9.8 metres per second squared) x the efficiency of the turbine (larger turbines are 90% efficient)

(see http://www.engineeringtoolbox.com/hydropower-d_1359.html )

To put this in perspective an average Australian home uses 18.1 kilowatt hours of electricity.
One kilowatt hour is equal to 1,000 watts being used up over an hour. To put this in every day terms 18.1 kilowatt hours is the same amount of energy as running 10 old 100 watt light bulbs for 18.1 hours a day.. that's how much we use on average each day.

So to supply the same amount of electricity from a hydro scheme we would need a minimum of 18,100 watts of power delivered over 24 hours which is 750 watts per hour. So here goes the calculation.

If we have 1000 litres of water (1,000kg) and drop it 1 metre at a rate of 1 litre a second with gravity and a 90% efficiency then we would generate 1000L*1M*1 Lpsec*9.8*0.9 watts or 8,820 watts!

OK so we need 18,100 watts over 24 hours so we need the power/ water to run 24 hours and the 2.5 times the power we are generating above. The water above would last 1000 seconds.. and there are 24X60x60 seconds in a day... 86,400! mmmmmmm

So if we increase the stored water to 10,000 litres and reduce the flow from 1 litre per second to 210 milliliters of  water per second then the figures look like this:

energy in watts (target 18,100) = 10,000*0.21*1*9.8*0.9 = 17,640

And the water would flow at the rate of 210ml per second which is 13.2 hours ooops.. we need 24 hours so back to the drawing board.

To make 10,000 litres last 24 hours the flow rate is a maximum of 115ml per second so if we make the drop 3 metres we should have it... lets do the calc.

energy = 10,000 * 0.115*3*9.8*0.9

Wow that 30,429 watts so lets dial back to 2m drop

energy = 10,000 * 0.115*2*9.8*0.9
ok we now have 20,286 watts

So that's it... I think!
a 10,000 litre tank with a hose that allows a 115ml flow per second dropping 2 metres with a turbine that is 90% efficient should supply the power for a normal household for 1 day.

So how do we get the water into the tank in the first place?
Solar, wind turbine or wind pump (see http://en.wikipedia.org/wiki/Windpump) Amazingly some windpumps can consistently pump 6400 litres of water per hour in a 24km/h wind so even a medium breeze for 3-4 hours a day may keep the tank topped up...!

Maybe the killer idea is to run the power mains to a pump to keep the main tank filled and only use mains when solar, wind or windpumps don't cover the lost power.... mmm am I not calculating this right?

Tell me what you think... maybe Im not thinking this through properly... Please comment below or on Facebook.




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