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:
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 .
Step 2: Calculate the weir overflow rate
Now, divide the flow rate by the area:
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:
- How does the weir overflow rate affect the efficiency of a clarifier?
- How would the weir overflow rate change if the diameter were increased?
- What other factors impact the design of a clarifier?
- How do you determine the required number of weirs in a clarifier?
- 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
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