A circular clarifier has a diameter of 60.0 ft and a side water depth of 12.0 ft. If the plant flow rate is 1.80 MGD, what is the hydraulic detention time in hours?

Formula Used: Detention Time (hrs) = Volume (gallons) ÷ Hourly Flow Rate (gal/hr)

Step-by-Step Mathematical Derivation:

1. Calculate circular surface area: 0.7854 × (60 ft)² = 2,827.43 sq ft.
2. Calculate volume in cubic feet: 2,827.43 sq ft × 12.0 ft = 33,929.2 cu ft.
3. Convert volume to gallons: 33,929.2 cu ft × 7.48 gal/cu ft = 253,790 gallons.
4. Convert daily flow to hourly flow: 1,800,000 gpd ÷ 24 hrs/day = 75,000 gal/hr.
5. Detention Time = 253,790 gal ÷ 75,000 gal/hr = 3.38 hours.

⚠️ Common Exam Trap: Remember that diameter must be squared in 0.7854 × D² (or π × r²). Do not accidentally multiply diameter by 2.