As I am setting up my automated water change system I was wondering- how much "fresh" water do we waste by doing the water exchange continuously? We start removing the new water right away, right?
The answer wasn't obvious to me so I did some calculations. Skip to the end if you don't care how the results were derived.
Let's say we do 10% water change in 1 month (1 week, 1 year- the interval is not important).
1. If we do 1 water change, we are left with 90% old water, 10% fresh water.
2. If we do 2 water changes 5% each, we are left with 0.95*0.95- 90.25% old water, 9.75% fresh water.
3. If we do 3 water changes 3.33% each, we are left with 0.9667^3- 90.32% old water, 9.68% fresh water
x. If we do x changes totaling 10%, we will be left with (1-0.1/x)^x old water
Continuous water change will result in the following amount of old water after 1 month (or week, year, etc): see image
The final result is 90.484% old water, 9.516% fresh salt water vs 90%-10% with a single change.
Continuous water change does not waste much replacement water. Once you get to 50% water changes, the wasted amount of fresh water becomes more meaningful (you are left with 60% old water and 40% fresh water if done continuously).
The answer wasn't obvious to me so I did some calculations. Skip to the end if you don't care how the results were derived.
Let's say we do 10% water change in 1 month (1 week, 1 year- the interval is not important).
1. If we do 1 water change, we are left with 90% old water, 10% fresh water.
2. If we do 2 water changes 5% each, we are left with 0.95*0.95- 90.25% old water, 9.75% fresh water.
3. If we do 3 water changes 3.33% each, we are left with 0.9667^3- 90.32% old water, 9.68% fresh water
x. If we do x changes totaling 10%, we will be left with (1-0.1/x)^x old water
Continuous water change will result in the following amount of old water after 1 month (or week, year, etc): see image
The final result is 90.484% old water, 9.516% fresh salt water vs 90%-10% with a single change.
Continuous water change does not waste much replacement water. Once you get to 50% water changes, the wasted amount of fresh water becomes more meaningful (you are left with 60% old water and 40% fresh water if done continuously).