Significance of large multiply-processed water volumes

Equation (17) shows how much of the tank water $V_0$ has passed through an aquarium device with flow rate $F_0$. This may be useful information, particularly when assessing how long to run an ultra-violet sterilizer. When $\alpha t \approx 6.90$, we showed in the previous section that 99.9 % of the water will have flowed through the device at least once. Formula (17) allows us to demonstrate that most of the water has been through many times more than once! Again, assuming that $\alpha t = 6.90$, formula (17) shows that 99.2 % of the water has passed through the device at least two times, and that 96.8 % of the water has passed through at least three times! See the plot below.

Formula (17) may in fact be useful in determining safe reduced run times for ultra-violet sterilization devices. Turn-over time does not tell the whole story: by the time 99.9 percent of water has passed through a sterilizer, the vast majority of water-- over 99.2 % -- has passed through the sterilizer at least 2 times. Therefore, it may be that flow rates through the device can safely be increased (thereby reducing total dosage delivered with a single pass through the device) without reducing overall ultra violet dosage below a safe level. This because most of the water actually circulates through the device twice or three times.

Escobal [1] defines turn-over time as the time it takes to process 99.99 % of tank water. This requires that run time increase from about 7 times $V_0/F_0$ to more than 9 times $V_0/F_0$. In light of the fact that so much of the water has been processed two and three times by the time even 99.9 % of the water has been processed, it seems reasonable to lower the standard a bit. Even so, less than 1 pint of water out for every 100 gallons never gets processed. On the other hand, with the 99.9 % standard, over 96.8 % of tank water -- all but 3.2 gallons of a 100 gallon tank -- is processed three times or more.