The advice at TFP wasn't for any of that pool store advice (algaecide) nor for the borax, baking soda, etc. In fact, I only find two posts from dcsharpe over at TFP that are not related to this problem.
In general at TFP, it is first and foremost to get a good test kit because without knowing the true CYA level it will be very hard to know exactly what to do. Nevertheless, adding unstabilized chlorine is usually recommended (usually chlorinating liquid or bleach unless the CH is low) and IF the CYA was known to be zero (say from a far more rapid chlorine loss during the day compared to night) then some CYA could be added either by pure CYA or (faster) by Dichlor. The standard recommendations of 24/7 filtration and brushing the pool are also usually stated.
Those are the good points, though without the proper test kit things are still somewhat of a shot in the dark. Now the bad points. For reasons I do not understand, there is this thought at TFP that chlorine alone (with filtration and brushing) will always clear a pool. Well, they do check to see that a filter is working properly (though not always looking at the pump/filter combo) and sometimes suggest adding DE to a sand filter. However, in my opinion, if there isn't visible progress, especially after a week, then one needs to look at other issues such as what Ben is describing or even the possibility of using a clarifier even though they don't always work. There are other threads with some folks who ended up on their own using a clarifier where in one day the pool was cleared and I did that once in my own pool after a phosphate remover experiment (a freebie from someone at Orenda who came over -- no, I'm not a phosphate remover promoter) when I wanted to quickly clear the pool overnight for my wife to swim in the next day. Now maybe a better filter/media/flow rate would have worked, but if one doesn't have that then a clarifier can at least consolidate particles so they are bigger and get caught in the less-than-ideal filter. Of course, if one already has calcium carbonate saturation for a plaster pool, then one can use additional techniques of creating precipitation in the filter by raising pH via the skimmer (a technique sometimes done to capture metal oxides), but for vinyl pools the CH is typically too low for that.
There is also the issue with above-ground pools that the bottom circulation is typically awful because there are no floor drains, pop-ups, low-positioned returns, etc. Circulation is critical to get cloudy water to the filter so pointing a return diagonally downward can stir things up as can regular brushing. The symptom for this is where the surface water looks OK but one cannot see the bottom clearly.
Anyway, those are my thoughts, but I pretty much stayed out of the recent threads with persistant cloudiness since I've put in my 2 cents before and been overridden on this particular issue, especially when it comes to using a clarifier (as a last resort or when speed is desired and cost is not a concern).
Bookmarks