Backyard Aquaponics
A place to discuss aquaponics

My head a little clearer this morning...
The 420 Watts (In Jaymie's unit) is the Power Factor adjusted value (Power factor of computer equipment is around 70%) and nothing to do with battery capacity, in fact on the APC website they don't specify the battery capacity anywhere.
So that was a bad example.

My estimate of 72 hours for your system is wrong too, more like 50 hours (70%)
It will depend on the power factor of your pump.

So to re-answer your question "How long will it last?"

I have no idea, plug it in and try it

Unfortunately I'm not sure if there is an easy way to explain power factor.
So if you are really in the mood for thinking .. ask DuiNui

I don't feel like thinking about it enough to explain it in an easy to understand way, sorry

In an AC circuit there is an "apparent" power and a "real" power. The apparent power is proportional to the current times the voltage. The real power (or the actual work being done), is the apparent power times the power factor. The power factor is related to the phase shift between between the voltage and the current. Theoretically a resistive load like a heating element will have no phase shift and the power factor will be 1. Inductive loads such as transformers and motors will cause a phase shift between the current and voltage that will cause the apparent power to be greater than the actual work being done. The adjustment from the apparent power to the real power is the power factor which is the cosine of the phase angle between the current and the voltage.
Think of it as a freshly poured glass of beer. The volume of the full glass is the apparent power. The real power is the liquid in the glass doing all the work, and the power factor determines how much of a head you have on the glass.
At least that's my understanding anyway. My background is not electrical.

I haven't done this stuff since school, I try to stay away from AC stuff, it's nasty and makes my head hurt.

As you're thinking about doing an ultra low power thing BW, you might want to look into power factor correction.
This site explains it quite nicely.
http://www.allaboutcircuits.com/vol_2/chpt_11/4.html

Basically you want to put a cap across your pump power to try to cancel out the effects of an inductive load (the motor), make sure the cap is rated for mains

But with a 200Ah battery and an 8W pump, it's probably not worth the trouble tbh.

@IMelting: Now you have to explain phasors and why inductive loads cause the current to lag with respect to the voltage, and how a capacitor does the opposite

Woah. Thanks power factor people. A lot to learn about everything.