42 formulas across 6 modules — activated sludge, BNR, biosolids, collection systems, lab analysis, and safety. Each with worked examples and exam tips.

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SVI

SV₃₀ × 1000 ÷ MLSS

mL/g

SRT

V × MLSS ÷ (Qw × WAS + Qe × TSS_e)

days

F:M

BOD × Q ÷ (V × MLVSS)

kg/kg·d

RAS ratio

SV₃₀ ÷ (1000 − SV₃₀)

O₂ (nitrif.)

4.57 × ΔNH₄

kg/kg N

VSR

(VS_in − VS_out) ÷ VS_in × 100

Manning's Q

(1/n) × A × R^(2/3) × S^(1/2)

m³/s

BOD₅

(DO_i − DO_f) × dilution

mg/L

H₂S IDLH

50 ppm

Cl₂ TLV-C

0.5 ppm

🔬

Activated Sludge Process

6 formulas

Sludge Volume Index (SVI)

SVI = (SV₃₀ × 1000) ÷ MLSS

Units: mL/g

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Solids Retention Time (SRT / MCRT)

SRT = (V × MLSS) ÷ (Qw × WAS + Qe × TSS_e)

Units: days

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Food-to-Microorganism Ratio (F:M)

F:M = (BOD_in × Q) ÷ (V × MLVSS)

Units: kg BOD / kg MLVSS · d

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Mixed Liquor Suspended Solids (MLSS)

MLSS = (SRT × BOD_in × Q × Y) ÷ (V × (1 + kd × SRT))

Units: mg/L

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Volumetric Oxygen Demand

O₂ demand = Q × (BOD_in − BOD_out) × 1.5 ÷ 1000

Units: kg O₂/d

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Return Activated Sludge (RAS) Rate

RAS ratio = SV₃₀ ÷ (1000 − SV₃₀)

Units: dimensionless (expressed as % of influent flow)

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🌿

Nutrient Removal (BNR)

5 formulas

Nitrification Rate (Nitrifier Growth)

μ_n = μ_max × NH₄ ÷ (Ks + NH₄) × (DO ÷ (Ko + DO))

Units: d⁻¹

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Oxygen Demand for Nitrification

O₂ (nitrification) = 4.57 × ΔNH₄

Units: kg O₂/kg NH₄-N oxidized

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Denitrification — NO₃ Removal

NO₃ removed = (Q_r × NO₃_r) ÷ (Q_in + Q_r)

Units: mg/L

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Phosphorus Removal — Chemical Precipitation

Alum dose = 9.6 × TP_removed

Units: mg alum / mg P removed

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Total Kjeldahl Nitrogen (TKN)

TKN = Organic-N + NH₄-N

Units: mg/L as N

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🪣

Biosolids & Sludge

6 formulas

Sludge Production Rate

P_x = Y_obs × Q × (BOD_in − BOD_out) ÷ 1000

Units: kg VSS/d

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Waste Sludge Flow Rate (Qw)

Qw = (V × MLSS) ÷ (SRT × WAS_conc)

Units: m³/d

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Solids Loading to Digester

Solids load = Q_sludge × C_sludge ÷ 1000

Units: kg TS/d

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Volatile Solids Reduction (VSR) — Digestion

VSR = (VS_in − VS_out) ÷ VS_in × 100

Units: %

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Biogas Production (Anaerobic Digestion)

Biogas = 0.75 × VS_destroyed

Units: m³ biogas / kg VS destroyed

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Digester Hydraulic Retention Time

HRT = V_digester ÷ Q_feed

Units: days

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🌊

Primary & Secondary Treatment

6 formulas

Hydraulic Detention Time (HDT)

HDT = V ÷ Q

Units: hours (convert Q to m³/h)

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Surface Overflow Rate (SOR)

SOR = Q ÷ A

Units: m³/m²·d (m/d)

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Weir Overflow Rate (WOR)

WOR = Q ÷ L_weir

Units: m³/m·d

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Secondary Clarifier Solids Loading Rate

SLR = (Q + Q_r) × MLSS ÷ A

Units: kg TSS/m²·d

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BOD Removal Efficiency

E = (BOD_in − BOD_out) ÷ BOD_in × 100

Units: %

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Effluent Limits Reference (O. Reg. 347)

Class 2: BOD ≤ 25 mg/L, TSS ≤ 25 mg/L | Class 3: BOD ≤ 15 mg/L, TSS ≤ 15 mg/L

Units: mg/L

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🧪

Disinfection

4 formulas

Chlorine Dose

Dose = Demand + Residual

Units: mg/L

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Chlorine Feed Rate

Feed rate = Q × Dose ÷ 1000

Units: kg/d

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CT Value (Disinfection Efficacy)

CT = C × t

Units: mg/L·min

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UV Dose (Disinfection)

UV Dose = Irradiance × Exposure Time

Units: mJ/cm²

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🌊

Collection Systems

6 formulas

Manning's Equation (Gravity Sewer)

Q = (1/n) × A × R^(2/3) × S^(1/2)

Units: m³/s

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Hazen-Williams (Pressure Main)

V = 0.8492 × C × R^0.63 × S^0.54

Units: m/s

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Inflow & Infiltration (I/I) Rate

I/I = (Q_wet − Q_dry) ÷ L_sewer

Units: L/s·km or m³/d·km

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Peaking Factor

PF = Q_peak ÷ Q_average

Units: dimensionless

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Lift Station Wet Well Volume

V_ww = Q_avg × t_cycle ÷ 4

Units: m³

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Force Main Velocity

V = Q ÷ A

Units: m/s

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🧪

Laboratory Analysis

5 formulas

BOD₅ Calculation

BOD₅ = (DO_initial − DO_final) × dilution factor

Units: mg/L

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Total Suspended Solids (TSS)

TSS = (W_filter+dry − W_filter) ÷ V_sample × 1000

Units: mg/L

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Settleable Solids (Imhoff Cone)

SS = volume settled after 1 hour

Units: mL/L

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Dissolved Oxygen — Winkler Titration

DO = V_thiosulfate × N_thiosulfate × 8000 ÷ V_sample

Units: mg/L

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Turbidity — Nephelometric (NTU)

Turbidity (NTU) = I_scattered ÷ I_incident × calibration factor

Units: NTU

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🦺

Safety & Confined Space

4 formulas

Hydrogen Sulfide (H₂S) — Key Thresholds

H₂S: TLV-TWA = 1 ppm | STEL = 5 ppm | IDLH = 50 ppm

Units: ppm (parts per million by volume)

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Chlorine Gas — Key Thresholds

Cl₂: TLV-C = 0.5 ppm | IDLH = 10 ppm

Units: ppm

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Confined Space Atmospheric Testing Order

Test sequence: O₂ → Flammable gases → Toxic gases (H₂S, CO)

Units: N/A — procedural

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LOTO — Lockout/Tagout Energy Verification

Zero-energy state: V = 0, P = 0, T = ambient, springs released

Units: N/A — procedural

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