Hi, and welcome to the forum!!
Looks like your studying from last season has paid off--if you got your pool to go from green to blue cloudy, then you're more than halfway there!
The bleach killed off the algae, but the cloudiness in the pool is dead algae that needs to be filtered out. Is your filter pressure rising at all, and do you have a sand or DE filter? If it's a sand filter, many people on this forum, including the other three mods, find that adding a small amount of DE (just enough to make your pressure rise by 1 psi) to their sand filter helps to filter out much of the smaller stuff. If you have a sand filter, you might give this a try.
Otherwise, your numbers aren't looking too bad--your TA and CH are fine where they are. You do need to get some chlorine into the pool. With a CYA of 0, you can safely keep it at 1-4 ppm, but keep in mind that you're going to need to be consistent about adding chlorine until you have the CYA because the sun is going to consume much of your chlorine. I think you should make sure that all the algae is dead, though--if you add chlorine to the pool at night, measure for a Cl level, and then test it again in the morning before the sun is on the pool, you should have less than a 1 ppm chlorine loss if the algae is indeed dead. In that case, then 1-4 ppm would be okay until you get some CYA in there. If you have more than a 1 ppm loss, then you need to take the chlorine back up, preferably with bleach, to 15 ppm and hold it there until you do not have more than 1 ppm chlorine loss overnight.
Your pH is high at 8.0. Use muriatic acid to drop it to 7.6. You can go lower, but the standard advice I've seen around here from the SWCG experts is that 7.6 is better than lower, because it won't rise as quickly as it will if you drop it lower. There is going to be some rise just due to the way the SWCG works, but pH of 7.6 seems to be the optimum.
You need to get some CYA into the water--most SWCG instruction manuals recommend 80 or so ppm to make the cell at its most efficient, so you might want to check your manual for the manufacturer's recommended level. You can get it at WalMart, home depot, or some Lowe's. It's often labeled as "conditioner" or "balancer", but if you look at the ingredient label, the ingredient that you want is cyanuric or isocyanuric acid. Follow label directions to get to the level you want, but I would only add about 1/2 of the dose at first--if you overdose with CYA, the only way to lower it is to drain/refill water, so it's much better to sneak up on your desired level than to overshoot and have to drain water. Don't broadcast it in the pool, as some labels will instruct you to--instead, either pour it very slowly into the skimmer, where it will sit in the filter and dissolve, or put it in a tube sock or old nylon hose and suspend it in front of your return. If you put it in the skimmer, don't backwash your filter for 5-6 days, because it takes that long for the CYA to completely dissolve. I wouldn't test for it before 4-5 days either, because it will just waste your CYA reagent. After about 6 days, test, then you can add additional CYA as needed. Keep in mind that you're going to have to keep an eye on your chlorine level until you have some CYA to help protect your chlorine from the sunlight. Now that you've cleared up an algae bloom, you don't want to have to do it all over again!!
Hope this helps, and if you have other questions, feel free to post them. Again, welcome to the group!!
Janet
Bookmarks