Math Problem Statement
clarifier 75ft diameter recieves flow of 3.9 million gallons per day if the MLSS concentration in the aeration tank is 2940 mg/L what is the solids loading rate on the secondary clarifier in lbs/day/sq ft?
Solution
To calculate the solids loading rate on the secondary clarifier, we can use the following formula:
Where:
- Q is the flow rate (in gallons per day)
- C is the mixed liquor suspended solids (MLSS) concentration (in mg/L)
- A is the area of the clarifier (in square feet)
Step 1: Convert the given flow rate to cubic feet per day (cfd)
The flow rate given is 3.9 million gallons per day. We know that:
- 1 gallon = 0.1337 cubic feet
So, the flow rate in cubic feet per day will be:
Step 2: Convert the MLSS concentration to pounds per cubic foot
The MLSS concentration is given as 2940 mg/L. To convert this to pounds per cubic foot, we use the following conversion factor:
- 1 mg/L = 8.34 × 10^-6 pounds per gallon (lb/gal)
- 1 gallon = 0.1337 cubic feet
Thus, we first convert to pounds per gallon, and then to pounds per cubic foot:
Now, to get pounds per cubic foot:
Step 3: Calculate the area of the clarifier
The diameter of the clarifier is given as 75 feet, so the radius is half of that:
The area of the clarifier is then:
Step 4: Calculate the solids loading rate
Now, we can substitute all the known values into the formula for the solids loading rate:
Final Answer:
The solids loading rate on the secondary clarifier is approximately 21.42 lbs/day/sq ft.
Would you like further clarification on any part of the process? Here are some related questions that might be useful:
- How does changing the MLSS concentration affect the solids loading rate?
- What factors could influence the area of the secondary clarifier in a wastewater treatment plant?
- How do you convert between different units of flow rate (e.g., from gallons to cubic feet)?
- Why is the unit conversion from mg/L to lbs/ft³ necessary in wastewater treatment calculations?
- How can the solids loading rate affect the performance of the secondary clarifier?
Tip: When calculating the solids loading rate, always ensure that the units are consistent throughout the formula to avoid errors in the final result.
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Math Problem Analysis
Mathematical Concepts
Unit Conversion
Flow Rate Calculations
Area of Circle
Concentration and Density
Formulas
Solids Loading Rate (SLR) = (Flow Rate (Q) × MLSS Concentration (C)) / Clarifier Area (A)
Flow Rate in cubic feet/day = Flow Rate in gallons/day × 0.1337
MLSS (lb/ft³) = MLSS (lb/gal) × 1 / 0.1337
Area of Clarifier (A) = π × radius²
Theorems
Pi Theorem for Area of Circle
Suitable Grade Level
Grades 11-12
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