How long to turn a profit pumping water from one lake to another and generating pwr during the day?

Question

You have two storage locations each capable of holding 25,000 m3 of water. One lies 100 m above the other. You'll pump water to the higher one during the nighttime and allow it to flow through your generation facility during the daytime. Using the data in the following table and the First Law of Thermodynamics, determine how long it will be before your business will turn a profit. Assume all such activities will happen once a day, i.e., you will pump the water up once at night and allow it to drain during the day.

Efficiency of Pumps80%
Efficiency of Generator80%
Cost of Energy during Day$0.08 / kWh
Cost of Energy at Night$0.03/ kWh
Initial Cost of Equipment$100,000
Maintenance Cost for Equipment$50 / day

Efficiency is defined as the ratio of the amount of useful work you can get out divided by the energy that must be put in.

Answer 1

If my calculations are correct I come up with 7000 kwatt-hours of energy to pump the water up and the same number would be given back with perfect efficiency. This would cost $210 at night and give back $560 during the day for a difference of $350 profit each day. Subtract maintenance and this becomes $300 per day. So it would take about 300 days to recover the initial costs at perfect efficiency.

You can figure this out for a less than perfect efficiency. Sounds like an interesting project.

Answer 2

OK, the way to set this up is as follows.
- how much money do I spend per night?
(cost of maintenance + cost of lifting the water)
- how much money do I make per day?
(price of selling the energy generated)
- Assuming I make more during the day than I spend during the night, how long until I pay back the investment?

Now, what does it cost to lift the water? Maybe this has something to do with the volume, the height, the density of water, and the efficiency of the pump.
Similarly, the amount of energy I can recover has to do with the stored energy and the efficiency of the generator.

You need to figure out the rest yourself.

In a more realistic problem, you would also have to consider the cost of capital (that $100k wasn't an interest-free loan).

Answer 3

Spend all your money pumping back up,The Maintenance cost is not right.Pumps will have to be serviced,replaced,and what are you going to run them on and i did say them.You are going to let the water free fall then you have to pump it back up the hill What is the flow rate,if you turn a 6in line to flow down that means you have to have 12 in pump pushing back to be ready to go the next day,what are you going to power the pumps with,gas, diesel,Elect,You are not taking everything into account.If it was that easy every body would have two ponds a pump A generator but it is not.

Answer 4

I'm not a mathematician, just a redneck. Even I know that it takes more energy to pump the water up hill than you can be generated.