Need help with math

[Tombones]

I am not good with math, so any math majors out there willing to help?
I need a formula to determine alkalinity if I make a 20 gallon water change to my 100 gallon reef tank.
Reef tank 7 DKH
New water 7.8 DKH
I want to see how high alkalinity will be after the change. I am using a new salt and I want to see if I will need to lower the alkalinity before I use it.
Thanks for your help.

 

[redfishbluefish]

I would not adjust the DKH down on the new water. First off 7 is on the low end of alkalinity and the 20 gallon water change will only raise alk up to 7.16. If you have any hard corals, coralline algae or clams, this will be consumed quickly.

 

[Sarah24!]

I would not adjust the DKH down on the new water. First off 7 is on the low end of alkalinity and the 20 gallon water change will only raise alk up to 7.16. If you have any hard corals, coralline algae or clams, this will be consumed quickly.

Hello,

I totally agree with him on this, if you are actually trying to mathematically do this, it will be something you do constantly every day. You will never have a solid are consistent number because it will vary based on how fast the corals are consuming it. Somedays they may consume more, others none at all, and it needs to be synced with your calcium which should be 440, and alk at a min 8. I would still stay under ten but have seen a few so it.

The better way possibly is to set s three week schedule so Tuesday Thursday Saturday, at night, at the same time every time say 8pm. Test your alk and see where it is at, then adjust from there. Dosing would be much easier than trying to figure the loss and gain reducing from old to new water then the time of overall balance in the system.

What changes are always good, but normally to reduce nitrates and nitrites etc and phosphates. It also replenishing the natural sea water nutrients which are just as important.
There are much easier ways to do this than what your trying to do, you basically would never stop doing math because the variable would change from day to day to within hours. I have had my tank go from a solid 8 alk tk a 6 in a day because corals were hungry. At the same time I have had to stable at 8 for a few weeks with out doing anything. Just depends on when they feed and what they are doing as a life form.

 

[chipmunkofdoom2]

You can calculate the overall increase in any tank parameter if you know the percentage of the change, the concentration of the new water, and the concentration in your tank. The formula can be written like so:

Cd = Pn(Cn - Ct)

Cd = difference in concentration
Pn = Percentage of new water (water change %)
Cn = Concentration of new water
Ct = Concentration of tank water

You're doing a 20% change. Your tank is 7dKh, the new water is 7.8 dKh. So:

Cf = 0.20 * (7.8 - 7)
Cf = 0.20 * 0.8
Cf = 0.16 dKh

So the water change you describe above will increase the alkalinity of your tank by 0.16 dKh. Not a big deal at all.

 

[chipmunkofdoom2]

To add to my previous post, this also works if your salt mix happens to have a lower value of a parameter. This formula will tell you the decrease that a water change will cause. Let's say you overdosed calcium and want to determine how much a water change will decrease your Ca. You know your tank is at 500 ppm Ca. You know your water change has about 420 ppm Ca. Let's say you want to do a 25% change:

Cf = 0.25 * (420 - 500)
Cf = 0.25 * - 80
Cf = -20 ppm

So in the hypothetical scenario above, the water change would change your calcium by -20 ppm. In other words, it will reduce your calcium by 20 ppm.

 

[Tombones]

Redfish,
I agree, 7.16 is not so bad. On the internet Tropic Marin states alk 9- 10 DKH but I am getting 7.8 when I sample test. I want the formula you used so if it reads higher I can determine if I want to adjust the water before I use it.
Thanks again.

 

[Tombones]

Thanks Chipmunk!

 

[redfishbluefish]

With math, there are typically multiple ways to solve a problem. What I did, since you have 100 gallons and wish to change 20 gallons.....80% will be "old" water while 20% will be "new" water. So

(7 x 0.8) + (7.8 x 0.2) = 7.16 dKH

 

[chipmunkofdoom2]

With math, there are typically multiple ways to solve a problem. What I did, since you have 100 gallons and wish to change 20 gallons.....80% will be "old" water while 20% will be "new" water. So

(7 x 0.8) + (7.8 x 0.2) = 7.16 dKH

That's actually exactly the formula I started out with. Just in case anyone wants to check my math:

Cf = (Ct x Pt) + (Cn x Pn)

Where Cf = final concentration, Ct = tank concentration, Pt = percentage of tank water, Cn = concentration of new water, and Pn = percentage of the new water. I wanted to figure out the exact change, which can be expressed as follows:

Cd = Cf - Ct

Where Cd is the concentration difference (in our case, 0.16 dKh), Cf is the final concentration (7.16 dKh), Ct is the initial tank concentration (7 dKh in our case). Since Cf can be expressed as the equation above, you can substitute that in when solving for Cd (concentration difference):

Cd = [(CnPn) + (CtPt)] - Ct

I refined the equation further. Pn and Pt (the water change amount and the tank water left) are related: if you take out 25%, 75% will be left from the tank. If you take out 50%, 50% will be left from the tank. So Pt (the percentage of tank water left) can be defined as 1 - Pn, or 100% - the percentage of the water change:

Cd = [(CnPn) + (Ct x [1 - Pn])] - Ct

When simplified, you get:

Cd = CnPn + Ct - CtPn - Ct

The two Ct terms cancel out, and you can factor a Pn out of two of the terms, and that's how I got my equation:

Cd = Pn(Cn - Ct)

Cd = difference in concentration
Pn = Percentage of new water (water change %)
Cn = Concentration of new water
Ct = Concentration of tank water

It's worth saying that both of these formulas work just fine. It all depends how you want to see the output!

 

[Halal Hotdog]

With math, there are typically multiple ways to solve a problem. What I did, since you have 100 gallons and wish to change 20 gallons.....80% will be "old" water while 20% will be "new" water. So

(7 x 0.8) + (7.8 x 0.2) = 7.16 dKH

Yup super easy to calculate if you break it down to percentages of the whole. Haha chipmunkofdoom2 you took it to a crazy level.

 

[KStatefan]

Engineer? chipmunkofdoom2

 

[chipmunkofdoom2]

LOL @Halal Hotdog

@KStatefan no not an engineer, I'm a programmer by trade but I studied computer science. I had to take a lot of math.

I wanted to simplify it to the level I did because I suspected it would help with mental math. The increase or decrease of a tank parameter is basically the difference times the change. If your salt mix has alkalinity 2 dKh higher than your tank, a 25% change will increase your tank's alkalinity by 0.5 dKh (2 * 0.25, or a quarter of two). If your salt mix has Mg 100 ppm higher than your tank and you do a 20% change, your Mg will increase by 20 ppm (100 ppm * 0.20). And so on.

 

[Sarah24!]

Hello,

Well this is the moment in time it all comes down algebra lol. (Funny line in the movie the red planet)

 

[hotashes]

Loving the calculations here gang. Numbers

A.

 

[redfishbluefish]

I had my wife double check my math, and it all looks good.

 

[KStatefan]

Math is cool

 

[hotashes]

Math is cool

Numbers keep the world spinning

A.

 

[JimWelsh]

Yup super easy to calculate if you break it down to percentages of the whole. Haha chipmunkofdoom2 you took it to a crazy level.

Yeah, this isn't "math major" stuff. It's "paid attention in middle school" stuff. No chalkboard necessary.

 

[hotashes]

Yeah, this isn't "math major" stuff. It's "paid attention in middle school" stuff. No chalkboard necessary.

Calculator or notepad at least lol

A.

 

[Stigigemla]

To make it a bit heavier. What woud it be if I slowly add 20% kH 9 water to my tanks of 1000 gallons and kH 8 and just let the panik owerflow lead the water to the drain.
I know if I empty 20% and then refill kH will go to 8.2 but the corals at the top will die. So a continous water change is the only way to go.