The second law of thermodynamics basically explains that perpetual motion devices will not work.
Using a battery back up for the pump will work until the battery is exhausted as it will require more energy to pump the water than you will get back into the battery.
However not to be a party pooper lemme try to help.
I suggest forgoing an electric pump and attach this to your water wheel to pump water.
Here is a pick of a real one
Add that to the side of the water wheel (of smaller diameter than the pump), so that the turning of the wheel replaces that axle crank.
Using a battery back up for the pump will work until the battery is exhausted as it will require more energy to pump the water than you will get back into the battery.
However not to be a party pooper lemme try to help.
I suggest forgoing an electric pump and attach this to your water wheel to pump water.
Here is a pick of a real one
Add that to the side of the water wheel (of smaller diameter than the pump), so that the turning of the wheel replaces that axle crank.