Can't run more than 7 water purifiers.

At Lazarus, I decided to see how many purifiers I could feed from one pump. Turns out the answer is four. So, naturally, I set up an array of sixteen purifiers to feed twelve fresh water tanks. However, I soon discovered that the overall flow-rate never exceeded 7,000, and only a few of the purifiers were actually running. After paring them down, I found that seven seems to be the limit.