You will definitely use less chlorine on cloudy days. And, I agree with you that 1.5 gallons (6 quarts) would raise your chlorine by about 6ppm if it were 10% sodium hypo. It is pretty typical for many of the bottles of liquid chlorine to not be the strength they are advertised. That will be especially true if they sit on a shelf for awhile in a hot store. That is one reason we like Walmart's generic bleach. They have a fast turnover and the bottles are in an air conditioned store which further slows the break down.
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