The equation for working out battery life is approximately amphours x volts = Watt hours, so 1ah x 12.6v = 12.6 Watt hours, then knock off about 15% for amp inefficiencies so call it 10 Watt hours, but music program is approximately 1/7 of the maximum output, so if you have a 10 Watt peak amplifier a 1ah 12.6v battery will run it at full blast for approximately 7 hours.
In real world conditions most amps are probably more lossy than that and other factors come into play, but it's a good rule of thumb to start from.
Your amp doesn't need to be 8 ohm impedence unless you buy 8ohm drivers. All aps you can buy will be able to run 8 or 4 ohms. If you're only running one driver per cabinet, try and buy a 4ohm variant, if running two buy 8ohms and run 2 off each amp channel.
https://www.bluearan.co.uk/index.php?id=FTP4FE32CF" rel="nofollow - https://www.bluearan.co.uk/index.php?id=FTP4FE32CF <-- 4fe32 4ohm version
If you're planning to run a single driver in a single cabinet in mono, you should get a mono amp as stereo amps don't really like having just one channel plugged in (it can be a cause of component failure)
For a basic low budget project like this you'd probably be fine with any of the TA2020 or equivalent Class D amps available on eBay, some will come with an enclosure with volume/power switch/led etc built in, some just as a bare board. I quite like the ones which are bare boards but also have a volume pot built in which double functions as an on/off switch, that would probably be perfect for what you're trying to do and you can get them for less than £10, that will drive 2x Faital drivers at 20w each which is just about the right amount of power for them.
Lastly I think you're going to find the baby milk tins will be the weak link in the chain unless they're a whole lot sturdier than they look, or unless you take significant steps to reinforce them from the inside. You may end up spending £60-70 on the other components, but they won't sound much like a £70 investment if you mount them in a cardboard tube.
You could spend £10 on a metre of chopped strand mat fibreglass and a pot of resin and hardener and line the inside and perhaps the outside too with a few windings of that before painting, that could make all the difference, and maybe even something to brace it too. You shouldn't need to compromise on weight and cost much to add quite a lot of stiffness. Something will be a lot better than nothing.
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