I ran a bilge pump to circulate water in my wife's greenhouse. The pump has about a 5A running current and about a 15A startup surge. I used a small 12V lead-acid battery with about a 1A constant-current charger. I built a voltage cutin/cutout circuit that watches the battery voltage, turns on the pump when the battery voltage reaches ~14V, and shuts the pump off when the battery voltage drops to ~12.4V. Since the 1A charger cannot keep up with the pump, it means that the pump runs about 20% of the time, and it cycles on/off about 5 times per hour.
If you run the bilge pump continuously, it will not last long...