Environmental Engineering, Water/Wastewater Clarification & Hydraulics
Clarifier Surface Overflow Rate (SOR) & Weir Loading Formula
Calculate Circular Clarifier Settling Plan Area (ft²), Camp-Hazen Surface Overflow Rate SOR (GPD/ft²), Hydraulic Detention Time HRT (hrs), and Peripheral Weir Overflow Rate (GPD/ft).
Camp-Hazen law: discrete particle capture depends on Surface Area (Q / A)—not tank depth!
Under Camp-Hazen Ideal Sedimentation Theory, a discrete floc particle with Stokes settling velocity v_s settles to the scraper floor before reaching the effluent launder if and only if v_s >= Q / A—the Surface Overflow Rate (SOR = Flow_GPD / Plan_Area_ft2, typically 600–1,000 GPD/ft² at average flow and <= 1,600 GPD/ft² at peak wet-weather flow)! Increasing Sidewater Depth H raises Hydraulic Detention Time (HRT_hrs = Area * H * 7.48 * 24 / Flow_GPD) to buffer sludge blankets, yet leaves theoretical discrete SOR completely unchanged, while Peripheral Weir Overflow Rate (WOR = Flow_GPD / (PI() * D_ft)) checks launder updraft velocity (< 20,000 GPD/ft)!
Verify on an 80-ft Diameter Municipal Clarifier—Plant_Flow = 4.00 MGD (4,000,000 GPD, B2), Tank_Diameter = 80.0 ft (B3 -> Settling Plan Area = PI() * 80^2 / 4 = 5,026.55 ft² in E2), and Sidewater_Depth = 12.0 ft (B4): Surface Overflow Rate equals 4,000,000 / 5,026.55 = 795.77 GPD/ft² (E3), Hydraulic Detention Time is 2.71 hours (E4), and Single-Launder Weir Overflow Rate is 4,000,000 / (PI() * 80) = 15,915.49 GPD/ft (E5)!
| Ten-States Clarifier Sizing KPI (4.00 MGD, D = 80 ft, SWD = 12 ft) | Formula | Verified Output |
|---|---|---|
| Clarifier Plan Area (ft²) | PI() * (Diameter_ft ^ 2) / 4 | 5,026.55 ft² |
| Surface Overflow Rate SOR (GPD/ft²) | (Flow_MGD * 10^6) / Plan_Area_ft2 | 795.77 GPD/ft² (1,591.55 @ 8 MGD) |
| Hydraulic Detention Time HRT (hrs) | Plan_Area * Depth_ft * 7.48 * 24 / Flow_GPD | 2.71 hrs (1.35 hrs @ 8 MGD) |
| Peripheral Weir Loading (GPD/ft) | (Flow_MGD * 10^6) / (PI() * Diameter_ft) | 15,915.49 GPD/ft |
Camp-Hazen Surface Overflow Rate & Detention Formula
Validate Flow_MGD > 0, Diameter_ft >= 10, and Sidewater_Depth_ft >= 7!
=LET(qm_g, B2, dm_f, B3, sw_d, B4, IF(OR(qm_g <= 0, dm_f < 10, sw_d < 7), "Invalid Clarifier Input", LET(ar_f, PI() * (dm_f ^ 2) / 4, ROUND((qm_g * 1000000) / ar_f, 2))))2x Peak Wet-Weather Storm-Flow Check (Set Flow = 8.00 MGD)
Double Plant_Flow B2 from 4.00 MGD to a 2.0x storm peak of 8.00 MGD: Surface Overflow Rate E3 doubles to 1,591.55 GPD/ft² (just inside the 1,600 GPD/ft² peak Ten-States limit), while Detention Time E4 halves to 1.35 hrs (actually 2.7072 / 2 = 1.35 hrs)!
=IF(ISTEXT(E3), E3, ROUND((B2 * 1000000) / (PI() * B3), 2))Try the example
Use the original values or change them to test your understanding.