Math Problem Statement

Calculate the weir overflow rate gallons per day per foot (gpd/ft) for a circular clarifier with a diameter of 60 feet, a depth of 12 feet and a flow rate of 800,000 gallons per day solve using .785 x diameter squared

Solution

To calculate the weir overflow rate in gallons per day per foot (gpd/ft), we use the formula:

Weir Overflow Rate=Flow Rate0.785×(Diameter)2\text{Weir Overflow Rate} = \frac{\text{Flow Rate}}{0.785 \times (\text{Diameter})^2}

Given:

  • Flow Rate = 800,000 gallons per day (gpd)
  • Diameter = 60 feet

Step 1: Calculate the area of the clarifier

First, calculate the area using the formula A=0.785×(Diameter)2A = 0.785 \times (\text{Diameter})^2.

A=0.785×(60)2A = 0.785 \times (60)^2 A=0.785×3600A = 0.785 \times 3600 A=2826square feetA = 2826 \, \text{square feet}

Step 2: Calculate the weir overflow rate

Now, divide the flow rate by the area:

Weir Overflow Rate=800,0002826\text{Weir Overflow Rate} = \frac{800,000}{2826} Weir Overflow Rate283.9gpd/ft\text{Weir Overflow Rate} \approx 283.9 \, \text{gpd/ft}

Final Answer:

The weir overflow rate is approximately 283.9 gallons per day per foot (gpd/ft).


Would you like more details or clarifications on any step? Here are some related questions:

  1. How does the weir overflow rate affect the efficiency of a clarifier?
  2. How would the weir overflow rate change if the diameter were increased?
  3. What other factors impact the design of a clarifier?
  4. How do you determine the required number of weirs in a clarifier?
  5. How does the depth of the clarifier factor into its overall performance?

Tip: To optimize clarifier efficiency, it is important to maintain an appropriate weir overflow rate to prevent clogging or overflow.

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Math Problem Analysis

Mathematical Concepts

Area Calculation
Flow Rate
Units Conversion

Formulas

Weir Overflow Rate = Flow Rate / (0.785 × Diameter^2)

Theorems

Area of a Circle (A = 0.785 × Diameter^2)

Suitable Grade Level

Grades 9-11