Water Changes - the mathematical bit!

[csdax]

I've been wondering for ages about water changes, and whether it's best to change a little often or a lot, less frequently; it's also a question that seems to get asked on this type of forum, so I guess I'm not alone in wondering about it.

Being addicted to Microsoft Excel, I finally decided to do some number-crunching, to figure this out. I assumed that any given 'pollutant' goes up the same amount every day, and set my computer to comparing:

10% change every day
20% change every 2 days
30% change every 3 days
40% change every 4 days
50% change every 5 days​

Basically, I've found that there is not a huge amount of difference between the different options. It doesn't matter how much of a pollutant you have in your tank, any of the above will gradually bring it to the same level.

If there's a sudden spike in a particular pollutant, all the above approaches will work just as quickly to bring the level back to 'normal'.

Mathematical argument for 'larger, less frequent' changes:
- keeps the average pollutant level slightly lower than the smaller more frequent changes

Mathematical argument against 'larger, less frequent' changes:
- If a spike occurs at the wrong time (i.e. the day after the change) it will be more time before the level is brought back down. If you look at the attached graph, the first spike happens the day after a 50% change: the second spike happens the day before a 50% change.

The main thing I've learned from this is that yes - 30% every week is practically the same as 60% every 2 weeks (mathematically speaking!)

Obviously, there's more to it than the math, but I've wondered about this for ages, so I thought I'd post my findings for anyone else who's interested!

 

[Roan Art]

You're overlooking a lot of variables and the major one being how important it is to keep your tank water as close to your source water as possible.

I realize you are being pressured into not spending as much time on maintenance as you would like, but trying to find ways to cut back on water changes isn't a good long-term choice for your fishes' health.

Here's an article on Water Change Math by RTR:

http://www.thepufferforum.com/articles/water/waterchangemath.html

Roan

 

[joephys]

Oh you opened up one of my favorite subject.

A = concentration of nitrates
t = time between water change.

dA/dt = the rate of change in nitrates per day. (this is a calculus thing, if you don't know calculus don't worry about it)

lets say your fish produce waste at a rate that is 2 nitrates per day. (you would need to measure it out for your tank to get the actual number)

lets also say you do a x% water changes every t. First lets say 10% per day, which means you remove 10% of the nitrates every water change, so

dA/dt = -.10A+2

When the rate of change equals zero, then the consentration can't change so its in equalibrium. This is an important property of differential equations, which this is.

-.10A+2=0
.10A=2
A=20

your long term concentration of nitrates will be about 20 ppm

Now lets look at 50% water changes once a week. t= 1 week now, so the ammount of nitrate added between water changes is 2x7=14.

dA/dt = -.50A+14

-.50A+15=0
.50A=15
A=30
The long term concentration of nitrates in this instance is 30 ppm. So daily 10% water changes result in lower nitrate levels.

The issue mentioned above is true though. While nitrates are lower, but the old water is in the tank longer as shown in the article mentioned above since you remove less and less old water with each water change.

I know the math is more than what is necessary, but what can I say, I'm a geek.

 

[RTR]

A 10% daily change for 5 days serially is not equal to a 50% change on day 5. Over time the differences become highly significant. But auotomated daily water changes are wonderful IME - you just need to throw in a bit of vacuuming and glass cleaning.

If the tank is not subject to some anormalous incident, there should be no spikes in any pollutant - fish, bacteria, and overall tank bioactivity is normally quite stable. It an anomaly occurs of whatever type, the routine is off the boards anyway.

 

[YoFishboy]

Here's how I do the math:

50% weekly water changes=Happier, more colorful and active fish that often spawn immediately after the water change and don't get sick and do not require me to spend money on meds which also = a happier me!

It's the new math! :sim:

 

[Emg]

There are more reasons for not doing more frequent water changes, than just not "feeling" like doing the maintenance. Don't automatically assume that the frequency of water changes has to do with a person's laziness. Some folks just have very busy lives and fit them in when they can...and that does't mean that they shouldn't be able to enjoy the hobby....just that they need to perhaps stock thier tanks lighter and make any other adjustments to filtration and the like than those of us who are able to perform more frequent WCs.

I guess I just don't like to 'assume' the worst in others, especially when I don't know them. :huh:

Thanks for sharing the info Csdax !

 

[Roan Art]

There are more reasons for not doing more frequent water changes, than just not "feeling" like doing the maintenance. Don't automatically assume that the frequency of water changes has to do with a person's laziness. Some folks just have very busy lives and fit them in when they can...and that does't mean that they shouldn't be able to enjoy the hobby....just that they need to perhaps stock thier tanks lighter and make any other adjustments to filtration and the like than those of us who are able to perform more frequent WCs.

I guess I just don't like to 'assume' the worst in others, especially when I don't know them. :huh:

Well, I reread everyone's responses to Caroline's post and I honestly don't see where this is coming from.

No one said anything about her not "feeling" like doing the maintenance. No one said anything that would give an indication that they liked "to 'assume' the worst in others". In fact, no one said anything detrimental at all.

The only thing that was said was by me, and it was a reference to another thread where she told us that her husband was pressuring her into spending less time with her maintenance and, ergo, she wanted to know if she could get away with doing less water changing.

Personally, I don't care for being ripped on for no apparent reason.

Roan

 

[csdax]

I realize you are being pressured into not spending as much time on maintenance as you would like, but trying to find ways to cut back on water changes isn't a good long-term choice for your fishes' health.

I'm really not sure where in my post you read anything about cutting back on water changes!

josephys - I'm glad to see I'm not the only geek on here. To put my stuff into the same terms as your model, my comparison was 50% every 5 days, rather than every week, so we have:

dA/dt = -0.5A + 10
So when our stable condition occurs, at dA/dt = 0 :
A = 20​

That was what I set out to find out - whether 10 x 1g changes is the same as a 1 x 10 g change - I have my answer: both will give me the same overall rate of water change and will bring my nitrates to the same stable level!
(btw - I have no probs with the calculus; it's adding where I'm more likely to mess up! :duh: )

For non-geeks: I'm NOT advocating any changes in your water change routine! This was just a little mathematical investigation that my brain forces me into, occasionally, and I thought I'd share!

 

[Roan Art]

I'm really not sure where in my post you read anything about cutting back on water changes!

Someone had posted recently that their SO was pressuring them into spending less time on maintenance. I thought it was you. Obviously it was not. My apologies.

Roan

 

[csdax]

Someone had posted recently that their SO was pressuring them into spending less time on maintenance. I thought it was you. Obviously it was not. My apologies.

Roan

lol. No problem. Reading so many posts on this site can get confusing, I know! :thud: