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Math Help - Calculating nutrient solution concentration

  1. #1
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    Calculating nutrient solution concentration

    I grow plants in a hydroponic system. It holds 78 gallons of nutrient solution at a 450ppm(parts per million) concentration. Currently each day 7 gallons of 0ppm water are added from a top-off reservoir to replace water removed through transpiration. At the end of each day my solution is reduced to 400ppm and I have to add nutrients directly to my system to return it to 450.

    How do I calculate the concentration required in the top-off reservoir to keep my system at a steady 450ppm?
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  2. #2
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    Re: Calculating nutrient solution concentration

    Quote Originally Posted by Pimpernickel View Post
    I grow plants in a hydroponic system. It holds 78 gallons of nutrient solution at a 450ppm(parts per million) concentration. Currently each day 7 gallons of 0ppm water are added from a top-off reservoir to replace water removed through transpiration. At the end of each day my solution is reduced to 400ppm and I have to add nutrients directly to my system to return it to 450.

    How do I calculate the concentration required in the top-off reservoir to keep my system at a steady 450ppm?
    let y = nutrient concentration of the remaining 71 gal at the end of the day

    7(0) + 71y = 78(400)


    let x = amount of nutrients in ppm added to the 7 gal top-off

    7x + 71y = 78(450)

    7x + 78(400) = 78(450)

    7x = 78(50)

    x = 557.1 ppm
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  3. #3
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    Re: Calculating nutrient solution concentration

    My calculation
    71 gal * 400 ppm/10^6 = 0.0284 gal nutrient left at end of day
    7 gal make up water at x ppm nutrient = 7x/10^6 gal nutrient
    78 gal * 450ppm/10^6 = 0.0351 gal nutrient required by system

    7x/10^6 = 0.0351 -0.0284=0.0067
    x= 957 ppm conc of nutrient in make up water
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  4. #4
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    Re: Calculating nutrient solution concentration

    I guess it all comes down to how one interprets the problem ...

    ... if the concentration is 400 ppm before adding the 7 gal of pure water, then bjhopper's calculation is correct.

    ... if the concentration is 400 ppm after adding the 7 gal of pure water, then my calculation is correct.
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