Question

A 60 ft diameter circular clarifier has a weir overflow rate of 15 gpm/ft. What is the daily flow in MGD?

Short answer

4.0674 MGD

Step-by-step solution

Calculate the Circumference of the Clarifier

To find the circumference of a circular clarifier with a diameter of 60 ft, use the formula for the circumference of a circle: \( C = \pi d \) where \( d \) is the diameter. Therefore, \( C = \pi \times 60 \approx 188.5 \text{ ft} \)

Determine the Total Flow Rate in gpm

Multiply the weir overflow rate by the circumference to find the total flow rate in gallons per minute (gpm): \( 15 \text{ gpm/ft} \times 188.5 \text{ ft} = 2827.5 \text{ gpm} \)

Convert the Flow Rate to MGD

Convert the total flow rate from gpm to million gallons per day (MGD). There are 1,440 minutes in a day, so: \( 2827.5 \text{ gpm} \times 1440 \text{ min/day} = 4067400 \text{ gallons/day} \)Then, convert gallons per day to million gallons per day:\( 4067400 \text{ gallons/day} \div 1000000 = 4.0674 \text{ MGD} \)

Key concepts

Circular Clarifier Circumference

Understanding the circumference of a circular clarifier is essential for calculating flow rates. The circumference is the distance around the outer edge of the clarifier. For a circular object, we use the formula for the circumference of a circle, which is expressed as: \( C = \pi \times d \), where \( d \) represents the diameter.

In this exercise, the diameter (\