What size capacitor do I need to reliably close a 1" US Solid motorized ball valve?
I'm not exactly sure what I was doing wrong with my math before, but my calculations were way off. On re-calculating, assuming the worst case of drawing 2 watts for 5 seconds, the valve would need about 300 mF. Having actually gotten the valve and measured the current draw through it, it was actually drawing 30-40mA at 13V for about 5 seconds to close, and could continue to operate down to about 5V. I selected a 15V power supply, and assuming it could go down to 9V and would draw 40mA at 13V for 5 seconds, I calculated needing a 36 mF capacitor.

To be on the safe side, I ordered a 68,000 μF 16V electrolytic capacitor. This, when charged to 12.5V, could take the valve from fully open to fully closed, back to fully open again, and about 90% of the way to fully closed before quitting.