Question

Solve the following chemical dosage problems. Be sure to account for the differences in chemical percent concentrations. Ferric chloride is used as the coagulant of choice at a $5.75$ MGD rated capacity treatment plant. If the plant operated at the rated capacity for $75\mathrm{\%}$ of the year and operated at $60\mathrm{\%}$ of rated capacity for $25\mathrm{\%}$ of the year, how many pounds of the coagulant was needed to maintain a dosage of $45\mathrm{mg}/\mathrm{L}$ ?

Short answer

56,148.29 lbs

Step-by-step solution

- Calculate the annual water volume treated at rated capacity

First, find out the annual water volume treated when the plant is operating at its rated capacity of 5.75 MGD (Million Gallons per Day). Multiply this by 365 days to get the yearly capacity: $$5.75\text{ MGD}\times 365\text{ days}=2098.75\text{ Million Gallons}$$

- Adjust for operational percentage

Calculate the volume of water treated when the plant operates at 75% of its rated capacity for 75% of the year: $$2098.75\text{ MG}\times 0.75\times 0.75=1180.359375\text{ MG}$$ Next, calculate the volume of water treated when the plant operates at 60% of its rated capacity for 25% of the year: $$2098.75\text{ MG}\times 0.60\times 0.25=314.8125\text{ MG}$$

- Sum the treated volumes

Add the two volumes calculated to determine the total annual volume of water treated: $$1180.359375\text{ MG}+314.8125\text{ MG}=1495.171875\text{ MG}$$

- Calculate the dosage required in pounds

Convert the total volume treated to liters (1 MG = 3,785,411.78 liters): $$1495.171875\text{ MG}\times 3785411.78\text{ liters/MG}=566,078,437.25\text{ liters}$$ Then, use the dosage formula to find the total mass of the coagulant in milligrams: $$566,078,437.25\text{ liters}\times 45\text{ mg/L}=25,473,529,676.25\text{ mg}$$ Convert milligrams to pounds (1 lb = 453,592.37 mg): $$25,473,529,676.25\text{ mg}\times \frac{1\text{ lb}}{453,592.37\text{ mg}}=56,148.29\text{ lbs}$$

Key concepts

coagulant dosage

Coagulant dosage plays a crucial role in water treatment. It involves determining the right amount of chemical coagulants needed to purify water effectively. In the given problem, ferric chloride is used as the coagulant. To calculate the coagulant dosage, you must first know the total volume of water to be treated and the desired coagulant concentration. The standard unit for concentration is mg/L (milligrams per liter). This ensures the water meets the necessary purity and quality standards. Knowing the correct dosage also helps in cost management and prevents overuse of chemicals, which can be harmful.

water treatment

Water treatment is the process of making water safe to drink and use in daily life. It removes harmful contaminants and chemicals. Coagulation is a key step in water treatment, where coagulants like ferric chloride are added to remove suspended particles. These tiny particles clump together and form larger particles, which can then be removed easily. The effectiveness of water treatment depends on the right balance of chemical dosages and the volume of water treated. Regular monitoring and accurate dosage calculations ensure safe, clean water.

volume conversion

Volume conversion is crucial when dealing with different measurement units in water treatment. The problem example involves converting volumes from million gallons (MG) to liters (L). This is important because dosages are often given in mg/L. To convert million gallons to liters, you use the conversion factor: 1 MG = 3,785,411.78 liters. Accurate volume conversion ensures proper dosage calculation and maintains the effectiveness of the treatment process. Without precise conversions, the chemical dosages may fail to purify the water correctly.

percent concentration

Percent concentration is used to specify the amount of a substance (like a coagulant) in a solution. In the example, the water treatment plant operates at different capacities (75% and 60%). This affects the total volume of water treated and, consequently, the amount of coagulant needed. Calculating the correct percent concentration ensures that the water gets the exact amount of coagulant required for effective treatment. Understanding and applying percent concentration helps in adjusting dosages based on varying operational levels of the treatment plant.