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?

Re: Calculating nutrient solution concentration

Quote:

Originally Posted by

**Pimpernickel** 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

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

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.