What relay should I buy for this scenario?
I used this one, but that's only for reference. You first must determine what voltage and amps your pump needs and what voltage is available to power the relay, and whether AC or DC for both. I developed the schematic you saw in my thread before I ordered any parts, so I could match up watts and volts and amps.
You should work on your schematic first, post it, then I can help with the parts list.
Do I need a box to house the relay? Anything else to buy?
Mine is all enclosed. Most relays have open contacts, so they should be housed somehow for both safety and to ward off the elements (corrosion, water, etc).
I think 1.92 ounces per minute model would provide enough granular control. Don’t you? For example, with the timer set to run the pump for 4 minutes a day, the pump would deliver 7.68 oz. When set to 3 minutes per day, the pump would deliver 5.76 oz. The next smaller pump delivers 1.02 oz per minute.
The Econ T pump with built in timer can be set to run in one minute increments several times a day. So, it can run for 1 min at 9am, 1 min at noon, 1 min at 3pm and so forth.
I pretty much have the same non-answer on this, too, because the amount of acid you'l need to dispense each day will depend on (1) the strength of acid you use, (2) the size of your pool, and (3) how much acid it requires to maintain your target pH. So what works for me won't necessarily work for you.
But for reference, I mentioned I pump acid for 2 minutes - 3 times a week. That's 6 minutes total. I dilute my 31% acid 1:1 with water, so it's half-strength.* So I wouldn't be able to use that Stenner timer for more runs than once a day (and I'd have to skip one day a week). I'd prefer to run 15 seconds, four times a day, six days a week (total 6 minutes per week), but neither my timer nor the Stenner can do that.
I can't say whether your example schedule of 1 minute, three or four times a day, seven days a week, for 28 minutes total per week, is going to be just right, or way too much. Do you have any records for reference? How many ounces of which acid have you been adding each week? That's the place to start.
But as I said, I think the smaller 1.02 per minute pump would be the better choice. It would give you the most control. If you needed to run it 6, 7, 8 times a day, to dispense the acid you need, that's fine, that's actually better, that just means your pH will be more stable throughout the day. But if you go with the bigger pump, and find it's dispensing too much at even 1 minute per day, then you'll have to start shaving days, and your pH will be less stable.
Anyway, let's start with how much acid you've been using, and how old is your pool finish. Some finishes use a lot of acid when new, and then taper as they get older. So if your finish is newish, you might end up needing way less acid eventually. Mine didn't do that, it's been sucking down acid since day one and six years later (has more to do with my fill water than my finish). Either way, you want the finer control, not the fastest dispensing.
* Diluting 31% by 1:1 with water is Pentair's recommendation. That's easier on all the parts and tubes and on the injector, so that's the way to go. Plus, at half strength, because you can't fit more than 4 gallons in the tank, that's 2 gallons of 31% total. So if your system goes haywire and drains the entire tank into your pool (which Murphy's Law states will only happen the day after you fill the tank!), that'll put just 2 gallons of acid into your pool. That won't hurt anything but your pH level, and that'll recover quick enough. Guys that want to save some filling effort and hook up 15 gallon tanks, or bigger, to a Stenner are just asking for a disaster (and a potential very dangerous one at that). There's a story here about that happening with a large chlorine tank, and some kids got hurt. You can just imagine jumping into a pool that's got an extra 15 gallons of 31% in it! Yikes. Then there's the issue of how much acid is safe to store in a single tank in a residential backyard. Four gallons is safe-ish. 15 or more is a toxic spill waiting to happen. More reasons I love my little 4 gallon Pentair system. Yes, I have to fill it a little more often, but the peace of mind is worth it.