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WPI Class I Wastewater Treatment
Formula & Reference Sheet — BC (EOCP) · AB (AWWOA) · SK (SAHO) · MB (MWWA)
Flow & Hydraulics
Flow Rate
Q = A × V
QFlow rate (m³/s or m³/d)
ACross-sectional area (m²)
VVelocity (m/s)
Example:A = 0.5 m², V = 0.3 m/s → Q = 0.15 m³/s
1 m³/s = 86,400 m³/d
Hydraulic Retention Time (HRT)
HRT = V ÷ Q
HRTHydraulic retention time (hours or days)
VTank volume (m³)
QFlow rate (m³/d)
Example:V = 2000 m³, Q = 5000 m³/d → HRT = 0.4 d = 9.6 h
Pump Head
TDH = Static Head + Friction Head + Minor Losses
TDHTotal dynamic head (m)
Static HeadElevation difference (m)
Friction HeadHead loss due to pipe friction (m)
Use Hazen-Williams or Darcy-Weisbach for friction head calculations.
Pump Power
P = (Q × ρ × g × TDH) ÷ η
PPower (W or kW)
QFlow rate (m³/s)
ρDensity of water (1000 kg/m³)
gGravitational acceleration (9.81 m/s²)
TDHTotal dynamic head (m)
ηPump efficiency (decimal)
Example:Q = 0.05 m³/s, TDH = 20 m, η = 0.75 → P = 13.1 kW
Manning's Equation (Gravity Sewers)
V = (1/n) × R^(2/3) × S^(1/2)
VFlow velocity (m/s)
nManning's roughness coefficient (0.013 for concrete)
RHydraulic radius (m) = Area / Wetted Perimeter
SSlope of the hydraulic grade line (m/m)
Minimum velocity for self-cleaning: 0.6 m/s (2 fps) at design flow.
Primary Treatment
Surface Overflow Rate (SOR)
SOR = Q ÷ A
SORSurface overflow rate (m³/m²·d)
QFlow rate (m³/d)
ASurface area of clarifier (m²)
Example:Q = 5000 m³/d, A = 400 m² → SOR = 12.5 m³/m²·d
Typical primary clarifier SOR: 24–48 m³/m²·d
Weir Overflow Rate (WOR)
WOR = Q ÷ L
WORWeir overflow rate (m³/m·d)
QFlow rate (m³/d)
LTotal weir length (m)
Typical WOR: < 250 m³/m·d for primary clarifiers
BOD Removal Efficiency
E = (BOD_in − BOD_out) ÷ BOD_in × 100%
ERemoval efficiency (%)
BOD_inInfluent BOD (mg/L)
BOD_outEffluent BOD (mg/L)
Example:BOD_in = 250 mg/L, BOD_out = 20 mg/L → E = 92%
Secondary Treatment (Activated Sludge)
Food-to-Microorganism Ratio (F/M)
F/M = (Q × BOD) ÷ (V × MLVSS)
F/MFood-to-microorganism ratio (kg BOD/kg MLVSS·d)
QFlow rate (m³/d)
BODInfluent BOD (mg/L or kg/m³)
VAeration tank volume (m³)
MLVSSMixed liquor volatile suspended solids (mg/L)
Example:Q = 5000 m³/d, BOD = 200 mg/L, V = 2000 m³, MLVSS = 2500 mg/L → F/M = 0.2 kg/kg·d
Typical F/M: 0.05–0.15 for extended aeration; 0.2–0.6 for conventional AS
Sludge Retention Time (SRT / SludgeAge)
SRT = (V × MLSS) ÷ (Q_w × SS_w)
SRTSludge retention time (days)
VAeration tank volume (m³)
MLSSMixed liquor suspended solids (mg/L)
Q_wWaste activated sludge flow rate (m³/d)
SS_wWAS suspended solids concentration (mg/L)
Example:V = 2000 m³, MLSS = 3000 mg/L, Q_w = 200 m³/d, SS_w = 8000 mg/L → SRT = 3.75 d
Nitrification requires SRT > 10 days at 15°C
Sludge Volume Index (SVI)
SVI = (SV₃₀ × 1000) ÷ MLSS
SVISludge volume index (mL/g)
SV₃₀Settled sludge volume after 30 min (mL/L)
MLSSMixed liquor suspended solids (mg/L)
Example:SV₃₀ = 250 mL/L, MLSS = 2500 mg/L → SVI = 100 mL/g
Good settling: SVI < 120 mL/g. Bulking: SVI > 200 mL/g
Return Activated Sludge (RAS) Rate
RAS% = SVI × MLSS ÷ (1000 − SVI × MLSS/1000) × 100
RAS%Return sludge ratio (% of influent flow)
SVISludge volume index (mL/g)
MLSSTarget MLSS (mg/L)
Simplified: RAS% ≈ MLSS / (RAS SS − MLSS) × 100. Typical RAS: 25–100% of Q.
Oxygen Demand (Theoretical)
O₂ = Q × (BOD_in − BOD_out) × 1.42 × (ΔX/ΔT)
O₂Oxygen required (kg/d)
QFlow rate (m³/d)
BODBOD concentration (mg/L = g/m³)
1.42O₂ equivalent of cell mass (kg O₂/kg VSS)
Simplified: O₂ demand ≈ 1.0–1.5 kg O₂ per kg BOD removed
Disinfection
Chlorine Dose
Dose = Demand + Residual
DoseChlorine added (mg/L)
DemandChlorine consumed by wastewater (mg/L)
ResidualChlorine remaining after contact time (mg/L)
Example:Demand = 6 mg/L, Residual = 2 mg/L → Dose = 8 mg/L
CT Value
CT = C × T
CTDisinfection CT value (mg·min/L)
CDisinfectant concentration (mg/L)
TContact time (minutes)
Example:C = 2 mg/L, T = 30 min → CT = 60 mg·min/L
Required CT for 4-log Giardia inactivation at 15°C: ~170 mg·min/L for free chlorine
Chlorine Feed Rate
Feed Rate = Q × Dose ÷ 1000
Feed RateChlorine feed rate (kg/d)
QFlow rate (m³/d)
DoseChlorine dose (mg/L = g/m³)
Example:Q = 5000 m³/d, Dose = 8 mg/L → Feed Rate = 40 kg/d
UV Dose
UV Dose = Irradiance × Exposure Time
UV DoseUV dose (mJ/cm²)
IrradianceUV intensity (mW/cm²)
Exposure TimeContact time (seconds)
Minimum UV dose for 4-log virus inactivation: 186 mJ/cm²
Solids Handling
Sludge Production
P = Q × (TSS_in − TSS_out) ÷ 1000
PSludge production (kg/d)
QFlow rate (m³/d)
TSS_inInfluent TSS (mg/L)
TSS_outEffluent TSS (mg/L)
Example:Q = 5000 m³/d, TSS_in = 250 mg/L, TSS_out = 20 mg/L → P = 1150 kg/d
Sludge Volume
V_sludge = P ÷ (ρ × %solids)
V_sludgeSludge volume (m³/d)
PSludge mass (kg/d)
ρSludge density (~1000 kg/m³ for liquid sludge)
%solidsSolids content (decimal)
Example:P = 1000 kg/d, %solids = 0.02 (2%) → V = 50 m³/d
Volatile Solids Reduction
VSR = (VS_in − VS_out) ÷ VS_in × 100%
VSRVolatile solids reduction (%)
VS_inVolatile solids fed to digester (kg/d)
VS_outVolatile solids leaving digester (kg/d)
Target VSR for anaerobic digestion: ≥ 38% (Class B biosolids requirement)
Digester Loading Rate
Loading = VS_fed ÷ V_digester
LoadingVolatile solids loading rate (kg VS/m³·d)
VS_fedVolatile solids fed (kg/d)
V_digesterDigester volume (m³)
Typical mesophilic digester loading: 1.6–4.8 kg VS/m³·d
Nutrient Removal
Nitrification Oxygen Demand
O₂_nitrification = 4.57 × ΔNH₃
O₂_nitrificationOxygen required for nitrification (mg/L)
4.57Stoichiometric O₂ demand per mg NH₃-N oxidized
ΔNH₃Ammonia removed (mg/L as N)
Example:ΔNH₃ = 30 mg/L → O₂ = 137 mg/L
Denitrification Alkalinity Recovery
Alkalinity recovered = 3.57 × ΔNO₃
Alkalinity recoveredAlkalinity produced (mg/L as CaCO₃)
3.57Alkalinity recovered per mg NO₃-N denitrified
ΔNO₃Nitrate removed (mg/L as N)
Phosphorus Removal — Alum Dose
Alum dose ≈ 9.6 × P_removed
Alum doseAlum required (mg/L as Al₂(SO₄)₃)
P_removedPhosphorus to be removed (mg/L as P)
Molar ratio Al:P ≈ 1.5–2.0 for reliable removal to < 1 mg/L
Phosphorus Removal — Ferric Chloride Dose
FeCl₃ dose ≈ 5.2 × P_removed
FeCl₃ doseFerric chloride required (mg/L)
P_removedPhosphorus to be removed (mg/L as P)
Molar ratio Fe:P ≈ 1.5–2.0 for reliable removal
Laboratory Calculations
BOD Calculation
BOD = (DO_initial − DO_final) × Dilution Factor
BODBiochemical oxygen demand (mg/L)
DO_initialInitial dissolved oxygen (mg/L)
DO_finalFinal dissolved oxygen after 5 days (mg/L)
Dilution FactorSample volume / Total volume
Example:DO_i = 8.5, DO_f = 3.5, DF = 10 → BOD = (8.5−3.5) × 10 = 50 mg/L
TSS Calculation
TSS = (W_filter+residue − W_filter) ÷ V_sample × 10⁶
TSSTotal suspended solids (mg/L)
WWeight of filter + residue after drying (g)
V_sampleVolume of sample filtered (mL)
Example:W_residue = 0.025 g, V = 500 mL → TSS = 50 mg/L
Dilution Factor
DF = V_total ÷ V_sample
DFDilution factor (dimensionless)
V_totalTotal volume of diluted sample (mL)
V_sampleVolume of original sample (mL)
Example:1 mL sample in 300 mL total → DF = 300
Percent Solids
%TS = (Dry weight ÷ Wet weight) × 100
%TSPercent total solids (%)
Dry weightWeight after drying at 105°C (g)
Wet weightWeight of wet sample (g)
Example:Dry = 25 g, Wet = 1000 g → %TS = 2.5%
Quick Reference — Typical Operating Ranges
| Parameter | Typical Range | Units | Notes |
|---|---|---|---|
| Primary clarifier SOR | 24–48 | m³/m²·d | Average flow conditions |
| Secondary clarifier SOR | 16–32 | m³/m²·d | Average flow conditions |
| Aeration tank HRT | 4–8 | hours | Conventional activated sludge |
| MLSS (conventional AS) | 1500–3000 | mg/L | |
| MLSS (extended aeration) | 3000–6000 | mg/L | |
| SRT (nitrification) | > 10 | days | At 15°C |
| SVI (good settling) | < 120 | mL/g | |
| SVI (bulking) | > 200 | mL/g | |
| F/M (conventional AS) | 0.2–0.6 | kg BOD/kg MLVSS·d | |
| F/M (extended aeration) | 0.05–0.15 | kg BOD/kg MLVSS·d | |
| RAS rate | 25–100 | % of Q | |
| DO in aeration tank | 1.5–3.0 | mg/L | |
| Digester SRT (mesophilic) | 15–30 | days | |
| VS reduction (digestion) | > 38 | % | Class B requirement |
| Chlorine residual (effluent) | 0.5–1.0 | mg/L | After 30-min contact |
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