Add 70 gallons 15-30-15 to the 50-gallon stock solution for a final concentration of 400 ppm N at the hose end. The final solution contains 58.33% fertilizer.
Here is how to calculate the amount of 15-30-15 fertilizer needed:
1. Define the variables:
- Stock solution concentration of nitrogen (N): 50 ppm
- Desired concentration of N at the end of the hose: 400 ppm
- Fertilizer concentration of N: 15%
- Dilution ratio of the Commander injector: 1:128
- Volume of the stock solution: 50 gallons
- Volume of 15-30-15 fertilizer needed: X (unknown)
2. Calculate the total volume of the final solution:
- Final volume = Volume of stock solution + Volume of fertilizer
- Final volume = 50 gallons + X
3. Calculate the concentration of N in the final solution:
- Total N = Stock solution N + Fertilizer N
- Total N = 50 ppm * 50 gallons + X * 0.15 * 1000 ppm/gallon
- Total N = 2500 ppm + 150X ppm
4. Equate the desired concentration to the total concentration and solve for X:
- 400 ppm = (2500 ppm + 150X ppm) / (50 gallons + X)
- 400 ppm * (50 gallons + X) = 2500 ppm + 150X ppm
- 20000 ppm + 400X ppm = 2500 ppm + 150X ppm
- 250X ppm = 17500 ppm
- X = 17500 ppm / 250 ppm/gallon
- X = 70 gallons
5. Calculate the percentage of 15-30-15 fertilizer in the final solution:
- Percentage of fertilizer = Volume of fertilizer / Total volume * 100%
- Percentage of fertilizer = 70 gallons / (50 gallons + 70 gallons) * 100%
- Percentage of fertilizer = 58.33%
Therefore, you need to add 70 gallons of 15-30-15 fertilizer to a 50-gallon stock solution to achieve a final concentration of 400 ppm N at the end of the hose using a 1:128 Commander injector. This will result in a final solution that is 58.33% 15-30-15 fertilizer.