Math Problem Statement

A sewage treatment plant discharges a pollutant with a concentration of 10 mg/L. The plant's total discharge is 0.3 MGD (millions of gallons per day). Determine the rate of pollutant released in pounds per day. Give your answer accurate to at least two decimal places.

Solution

The problem asks us to determine the rate of pollutant released in pounds per day, given a concentration of 10 mg/L and a discharge of 0.3 million gallons per day (MGD).

Step-by-step solution:

  1. Convert the discharge from MGD to liters per day: 1 gallon=3.78541 liters1 \text{ gallon} = 3.78541 \text{ liters} So, 0.3 MGD0.3 \text{ MGD} (million gallons per day) is: 0.3×106 gallons/day×3.78541 liters/gallon=1,135,623 liters/day0.3 \times 10^6 \text{ gallons/day} \times 3.78541 \text{ liters/gallon} = 1,135,623 \text{ liters/day}

  2. Determine the mass of the pollutant in milligrams per day: Since the concentration is 10 mg/L10 \text{ mg/L}, the mass of pollutant released per day is: 10 mg/L×1,135,623 L/day=11,356,230 mg/day10 \text{ mg/L} \times 1,135,623 \text{ L/day} = 11,356,230 \text{ mg/day}

  3. Convert milligrams to pounds: To convert milligrams to pounds, use the conversion factor: 1 pound=453,592.37 mg1 \text{ pound} = 453,592.37 \text{ mg} So: 11,356,230 mg/day453,592.37 mg/pound25.04 pounds/day\frac{11,356,230 \text{ mg/day}}{453,592.37 \text{ mg/pound}} \approx 25.04 \text{ pounds/day}

Final Answer:

The rate of pollutant released is approximately 25.04 pounds per day.

Would you like any more details or explanations on this? Here are some related questions:

  1. How do you convert different units of volume, such as gallons to liters?
  2. Why is it important to use correct conversion factors in environmental calculations?
  3. How can this method be adapted for different pollutants or discharge rates?
  4. What factors might affect the concentration of pollutants in sewage treatment plants?
  5. How do regulatory agencies use calculations like this to monitor pollution levels?

Tip: Always double-check unit conversions to ensure consistency throughout environmental calculations.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Unit Conversion
Rate Calculation
Pollutant Discharge

Formulas

1 gallon = 3.78541 liters
Total pollutant released = Concentration (mg/L) × Discharge (liters/day)
1 pound = 453,592.37 milligrams

Theorems

-

Suitable Grade Level

Grades 11-12