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At minimum you will need the car battery. This should power the pump for about 15 minuets if that.
The inverter is designed to run off of a system that is connected to a generator/alternator. The average inverter will drain a car battery in about 15 minuets running a small appliance from the inverter. If you hook up a microwave to it you will be lucky to warm a cup of coffee.
The pump size is adiquate for what you want to do. At 22.5 seconds it will put out 2-1/16 gallons. The size of the apperature that it is pumping it through will be a factor though. At 25 - 30 feet output at that flow rate a 3/8" nozzle would be pushing it. A 1/4" nozzle would restrict the pump (causing more strain on the inverter/battery) and you will not get the GPM mentioned above.
Best suggestion is to rent a small generator from your local rental yard to power the pump.
The inverter and just a battery will not cut it. Figure a 20 minuet parade march you would be out of battery at the half way mark.
With a small generator you will probably run out of water first.
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Steve, I am most intrigued with your plans. Please let me know how it turns out.