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:

Solids Loading Rate (SLR)=Flow Rate (Q)×MLSS Concentration (C)Clarifier Area (A)\text{Solids Loading Rate (SLR)} = \frac{\text{Flow Rate (Q)} \times \text{MLSS Concentration (C)}}{\text{Clarifier Area (A)}}

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:

Q=3,900,000gallons/day×0.1337cubic feetgallon=521,430cubic feet/dayQ = 3,900,000 \, \text{gallons/day} \times 0.1337 \, \frac{\text{cubic feet}}{\text{gallon}} = 521,430 \, \text{cubic feet/day}

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:

MLSS (lb/gal)=2940mg/L×8.34×106lbmg/L=0.0245lb/gal\text{MLSS (lb/gal)} = 2940 \, \text{mg/L} \times 8.34 \times 10^{-6} \, \frac{\text{lb}}{\text{mg/L}} = 0.0245 \, \text{lb/gal}

Now, to get pounds per cubic foot:

MLSS (lb/ft3)=0.0245lb/gal×10.1337galft3=0.183lb/ft3\text{MLSS (lb/ft}^3\text{)} = 0.0245 \, \text{lb/gal} \times \frac{1}{0.1337} \, \frac{\text{gal}}{\text{ft}^3} = 0.183 \, \text{lb/ft}^3

Step 3: Calculate the area of the clarifier

The diameter of the clarifier is given as 75 feet, so the radius rr is half of that:

r=752=37.5ftr = \frac{75}{2} = 37.5 \, \text{ft}

The area AA of the clarifier is then:

A=πr2=π(37.5)24417sq ftA = \pi r^2 = \pi (37.5)^2 \approx 4417 \, \text{sq ft}

Step 4: Calculate the solids loading rate

Now, we can substitute all the known values into the formula for the solids loading rate:

SLR=521,430cubic feet/day×0.183lb/ft34417sq ft21.42lb/day/sq ft\text{SLR} = \frac{521,430 \, \text{cubic feet/day} \times 0.183 \, \text{lb/ft}^3}{4417 \, \text{sq ft}} \approx 21.42 \, \text{lb/day/sq ft}

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:

  1. How does changing the MLSS concentration affect the solids loading rate?
  2. What factors could influence the area of the secondary clarifier in a wastewater treatment plant?
  3. How do you convert between different units of flow rate (e.g., from gallons to cubic feet)?
  4. Why is the unit conversion from mg/L to lbs/ft³ necessary in wastewater treatment calculations?
  5. 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.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

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