You are considering buying some land that use to be part of a sheep farm. The property is too far away from the grid so you have to have your own remote area power supply. This would take the form of solar for hot water and wind and solar panels for electricity. You would also need a way of storing the energy for times when the sun was not shining and the wind was not blowing. Someone suggested that pumped hydro might work but before you rush off and purchase the equipment you do some back of envelope calculations to see if the idea has merit. Assume you were to purchase
• two 30,000 litre water tanks and put one on a frame 6m higher than the other
• a small pump which is 85% efficient
• a small turbine which is 90% efficient when providing a maximum output of 300 watts.
a) What percentage of the input energy needed to pump the water up to the top tank could you recover from the turbine as the water ran back to the bottom tank?
b) What is the maximum amount of energy your water tank system could store?
c) With what velocity would the water be flowing in to the turbine at the moment just before the top tank became empty?
d) If you could get the turbine to output 42W at 12V to light three fluorescent globes how long would they be lit for?