Should I let pump run after adding Muriatic Acid

You want to make sure the pump is running for at least 1/2 hour, preferably even an hour, during and right after after adding most chemicals.

Running the pump longer than 1/2 hour is just fine, particularly if you would normally have it running anyway. There isn't any reason to turn off the pump early, just because you added muriatic acid. Just about the only situation that requires turning off the pump is a floc treatment.
 
If you poured it into the stream of a return or prediluted it and poiured it around the pool then about 30 minutes should be good. If you dumped it in undiluted I would start brushing to mix it up.

However, there is no reason at all to shorten your pump run time because you added acid for either pH or TA!
 
Thanks Guys. I did use the liquid type and poured it in the returns. How long should I wait before the kids jump in? They're out of school and the temperature should get in the upper 70's. Too cold for me to get in but good enough to have a few beers by the pool side.
 
30 minuutes should suffice. If you want to double check then test the pH in the area you poured in the acid and at the opposite end of the pool. If they are the same everything is mixed. If they are not give it a bit more time or brush the pool to 'stir it up'.
 
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