Class 3 Water Treatment Formula Sheet

Variables

• pH = measured pH of water

• pHs = pH at which water is saturated with CaCO₃

• pHs = (pK₂ − pKs) + p[Ca²⁺] + p[HCO₃⁻]

• LSI > 0: scale-forming (CaCO₃ deposits)

• LSI < 0: corrosive (dissolves CaCO₃ scale)

• LSI = 0: balanced

📊 Worked Example

pH = 7.8, pHs = 8.2 → LSI = 7.8 − 8.2 = −0.4 (slightly corrosive)

💡 Exam Tip

Class 3 exams test pHs calculation from temperature, calcium, and alkalinity. Know that LSI < −0.5 requires corrosion control treatment.

Variables

• Applied Dose = chlorine added (mg/L)

• Residual = free or total chlorine remaining after contact time (mg/L)

• Demand = consumed by organics, ammonia, metals, etc.

📊 Worked Example

Applied 3.5 mg/L, residual 1.2 mg/L → Demand = 3.5 − 1.2 = 2.3 mg/L

💡 Exam Tip

Breakpoint chlorination requires ~10× the ammonia-N concentration to reach the breakpoint and achieve free chlorine residual.

Variables

• C = disinfectant residual concentration (mg/L)

• T = contact time (minutes) — typically T₁₀ (10th percentile)

• CT required depends on pathogen, disinfectant, pH, temperature

• Higher CT = more disinfection credit

📊 Worked Example

C = 1.5 mg/L free Cl₂, T₁₀ = 30 min → CT = 45 mg·min/L

💡 Exam Tip

For Giardia: 3-log inactivation requires CT ≈ 73 mg·min/L at 15°C, pH 7. For Cryptosporidium: chlorine is ineffective; UV or ozone required.

Variables

• Volume of coagulant stock = mL added to jar

• Concentration of stock = mg/mL (or g/L)

• Volume of sample = typically 1,000 mL (1 L)

📊 Worked Example

Add 1.5 mL of 10,000 mg/L alum to 1,000 mL sample → Dose = (1.5 × 10,000) / 1,000 = 15 mg/L

💡 Exam Tip

Jar test results must be scaled to plant flow for actual chemical feed rate. Optimal pH for alum coagulation is 6.5–7.5.

Variables

• Flow = plant flow rate in megalitres per day (ML/day)

• Dose = chemical dose in mg/L

• 1 ML/day × 1 mg/L = 1 kg/day

📊 Worked Example

Flow = 25 ML/day, alum dose = 18 mg/L → Feed Rate = 25 × 18 = 450 kg/day

💡 Exam Tip

This is the most common Class 3 calculation. Memorize: ML/day × mg/L = kg/day. Convert m³/s to ML/day: × 86.4

Variables

• Target = desired fluoride concentration (mg/L), typically 0.7 mg/L

• Current = existing fluoride in source water (mg/L)

• Plant Flow = ML/day

• Fluoride concentration = mg/L in stock solution

• Purity = fraction (e.g., 0.98 for 98% pure NaF)

📊 Worked Example

Target 0.7 mg/L, current 0.1 mg/L, flow 10 ML/day, 10,000 mg/L NaF stock, 98% purity → Volume = (0.7−0.1) × 10,000,000 / (10,000 × 0.98) = 612 L/day

💡 Exam Tip

Fluoride calculations appear frequently at Class 3. Know the three fluoride chemicals: NaF (sodium fluoride), Na₂SiF₆ (sodium fluorosilicate), H₂SiF₆ (fluorosilicic acid).

Variables

• CO₂ removal: CO₂ (mg/L) × 2.27 = lime dose (mg/L as CaCO₃)

• Carbonate hardness removal: 1 mg/L CaCO₃ hardness requires 1 mg/L lime (as CaCO₃)

• Mg removal: 1 mg/L Mg hardness requires 1 mg/L lime (as CaCO₃) extra

• Actual lime = lime dose (as CaCO₃) × 0.74 (converts to Ca(OH)₂)

📊 Worked Example

CO₂ = 20 mg/L, carbonate hardness = 150 mg/L as CaCO₃ → Lime = (20 × 2.27 + 150) × 0.74 = 145 mg/L Ca(OH)₂

💡 Exam Tip

Soda ash (Na₂CO₃) is needed for non-carbonate hardness removal: 1 mg/L NCH requires 1.06 mg/L soda ash (as CaCO₃).

Variables

• Flow = total flow through the filter (m³/h)

• Filter Area = plan area of filter media (m²)

• Typical design rate: 5–15 m/h for rapid sand filters

• Maximum rate: 15–20 m/h (check turbidity at high rates)

📊 Worked Example

Flow = 500 m³/h, filter area = 50 m² → Loading Rate = 500/50 = 10 m/h

💡 Exam Tip

Filter loading rate affects turbidity removal. Rates above 15 m/h may cause turbidity breakthrough. Reduce rate when source water turbidity is high.

Variables

• Backwash Flow = flow rate during backwash (m³/h)

• Filter Area = plan area of filter (m²)

• Typical backwash rate: 36–60 m/h (10–15 gal/min/ft²)

• Target: 20–30% bed expansion

📊 Worked Example

Backwash flow = 2,000 m³/h, filter area = 50 m² → Backwash Rate = 2,000/50 = 40 m/h

💡 Exam Tip

Insufficient backwash rate leaves mud balls in the media. Excessive rate washes out fine media. Backwash water volume = 2–5% of filtered water production.

Variables

• UV Intensity = measured at the sensor (mW/cm²)

• Contact Time = hydraulic residence time in UV reactor (s)

• Dose ≥ 40 mJ/cm² for 4-log Cryptosporidium inactivation

• Dose ≥ 186 mJ/cm² for 4-log Giardia inactivation (UV less effective)

• Dose ≥ 40 mJ/cm² for 4-log virus inactivation (with 254 nm)

📊 Worked Example

Intensity = 20 mW/cm², contact time = 5 s → UV Dose = 20 × 5 = 100 mJ/cm²

💡 Exam Tip

UV dose is reduced by turbidity and UVT (UV transmittance). Always use validated dose-response curves. UV does not provide residual disinfection.

Variables

• Ozone Residual = dissolved ozone concentration (mg/L)

• Contact Time = T₁₀ in ozone contactor (min)

• CT for 3-log Giardia inactivation: 0.5–1.0 mg·min/L at pH 7, 15°C

• CT for 3-log Cryptosporidium: 5–10 mg·min/L

• Ozone decomposes rapidly; residual must be measured at contactor outlet

📊 Worked Example

Ozone residual = 0.4 mg/L, T₁₀ = 4 min → CT = 0.4 × 4 = 1.6 mg·min/L

💡 Exam Tip

Ozone CT is much lower than chlorine CT for Giardia/Crypto. Ozone also oxidizes taste/odour compounds and NOM. Bromate formation is a concern with bromide-containing source water.

Variables

• Influent Turbidity = raw water or settled water turbidity (NTU)

• Effluent Turbidity = filtered water turbidity (NTU)

• 2-log removal = 99% removal

• 3-log removal = 99.9% removal

📊 Worked Example

Influent = 50 NTU, Effluent = 0.05 NTU → Log Removal = log(50/0.05) = log(1000) = 3.0 log

💡 Exam Tip

Ontario requires filtered water turbidity ≤ 0.3 NTU (95th percentile) and ≤ 1.0 NTU at all times. Individual filter turbidity ≤ 0.1 NTU is the operational target.

Variables

• Free chlorine = HOCl + OCl⁻ (measured with DPD #1)

• Total chlorine = free + combined (measured with DPD #3)

• Combined chlorine = chloramines (NH₂Cl, NHCl₂, NCl₃)

• Ontario minimum free Cl₂ residual: 0.2 mg/L at all points in distribution

📊 Worked Example

DPD #1 = 1.5 mg/L (free), DPD #3 = 2.1 mg/L (total) → Combined = 2.1 − 1.5 = 0.6 mg/L

💡 Exam Tip

At Class 3, know the breakpoint chlorination curve: combined chlorine peaks at ~7.6:1 Cl₂:NH₃-N ratio, then drops to zero at the breakpoint (~10:1 ratio).

Variables

• Mass of residue = mass of dish + dried residue (mg)

• Mass of dish = tare weight (mg)

• Sample Volume = volume filtered (mL)

• Multiply by 1,000,000 to convert g/mL to mg/L

📊 Worked Example

Dish = 50.0000 g, Dish + residue = 50.0250 g, Sample = 100 mL → TDS = (25 mg) × 1,000,000 / 100 = 250 mg/L

💡 Exam Tip

TDS by evaporation (gravimetric) is the reference method. Conductivity-based TDS meters use a conversion factor (typically 0.5–0.7 × conductivity in μS/cm).

Variables

• Ca (mg/L) = calcium concentration

• Mg (mg/L) = magnesium concentration

• 2.497 = conversion factor for Ca (MW CaCO₃/MW Ca × 0.5 = 100/40.08 × 1 = 2.497)

• 4.118 = conversion factor for Mg (100/24.31 × 1 = 4.118)

📊 Worked Example

Ca = 80 mg/L, Mg = 20 mg/L → Hardness = (2.497 × 80) + (4.118 × 20) = 199.8 + 82.4 = 282 mg/L as CaCO₃

💡 Exam Tip

Hardness classification: 0–75 mg/L = soft, 75–150 = moderately hard, 150–300 = hard, >300 = very hard. Ontario aesthetic objective: ≤200 mg/L as CaCO₃.

Variables

• Volume of H₂SO₄ = mL of acid used to reach pH 4.5 endpoint

• Normality = normality of H₂SO₄ titrant (typically 0.02 N)

• 50,000 = conversion factor (equivalent weight of CaCO₃ × 1,000)

• Sample Volume = mL of sample

📊 Worked Example

H₂SO₄ = 8.5 mL, N = 0.02, Sample = 100 mL → Alkalinity = (8.5 × 0.02 × 50,000) / 100 = 85 mg/L as CaCO₃

💡 Exam Tip

Alkalinity is the buffering capacity of water. Low alkalinity (<50 mg/L) makes pH control difficult during coagulation. Alkalinity is consumed by coagulant addition.

Variables

• UV₂₅₄ = UV absorbance at 254 nm (measured in cm⁻¹, then × 100 to convert to m⁻¹)

• DOC = dissolved organic carbon (mg/L)

• SUVA > 4: high aromatic NOM, amenable to coagulation, high THM formation potential

• SUVA 2–4: mixed NOM character

• SUVA < 2: low aromatic NOM, NOT amenable to coagulation, high HAA formation potential

📊 Worked Example

UV₂₅₄ = 0.15 cm⁻¹ = 15 m⁻¹, DOC = 5 mg/L → SUVA = 15/5 = 3.0 L/mg·m (mixed NOM)

💡 Exam Tip

SUVA > 4 indicates enhanced coagulation will be effective for NOM removal and DBP control. SUVA < 2 requires alternative treatment (GAC, NF).

Variables

• TOC_in = TOC of raw or settled water (mg/L)

• TOC_out = TOC of filtered water (mg/L)

• Enhanced coagulation target: depends on raw water TOC and SUVA

• Typical target: 25–50% TOC removal by coagulation

📊 Worked Example

TOC_in = 8 mg/L, TOC_out = 5 mg/L → % Removal = (8−5)/8 × 100 = 37.5%

💡 Exam Tip

Ontario requires enhanced coagulation for systems with TOC > 2 mg/L and SUVA > 2. Target TOC removal depends on raw water TOC (see EPA Enhanced Coagulation guidance table).

Variables

• Water Power (kW) = Flow (m³/s) × Head (m) × ρg / 1,000

• ρg = 9,810 N/m³ (specific weight of water)

• Shaft Power (kW) = power input to pump shaft

• Overall efficiency = pump efficiency × motor efficiency

📊 Worked Example

Flow = 0.1 m³/s, Head = 30 m → Water Power = 0.1 × 30 × 9,810 / 1,000 = 29.4 kW. If shaft power = 35 kW → Efficiency = 29.4/35 × 100 = 84%

💡 Exam Tip

Pump efficiency typically 70–85% for centrifugal pumps. Efficiency decreases significantly when operating far from the design point (BEP).

Variables

• N = pump speed (rpm)

• Q = flow rate (gpm or m³/s)

• H = total head (ft or m)

• Low Ns (500–1,500): radial flow, high head, low flow

• High Ns (>5,000): axial flow, low head, high flow

📊 Worked Example

N = 1,750 rpm, Q = 500 gpm, H = 100 ft → Ns = 1,750 × 500^0.5 / 100^0.75 = 1,750 × 22.4 / 31.6 = 1,240 (radial flow pump)

💡 Exam Tip

Specific speed determines pump type. Water treatment plants typically use radial flow (centrifugal) pumps with Ns 500–3,000.

Variables

• Pa = absolute pressure at suction (m of water)

• Pv = vapour pressure of water at operating temperature (m)

• Zs = elevation of water surface above pump centreline (m, negative if below)

• hf = friction losses in suction piping (m)

• NPSHa must exceed NPSHr (required) to prevent cavitation

📊 Worked Example

Pa = 10.3 m, Pv = 0.17 m (15°C), Zs = −2 m, hf = 0.5 m → NPSHa = 10.3 − 0.17 − 2 − 0.5 = 7.6 m

💡 Exam Tip

Cavitation occurs when NPSHa < NPSHr. Signs: noise, vibration, pitting of impeller. Prevent by: reducing suction lift, increasing suction pipe diameter, reducing flow velocity.

Variables

• Q = flow rate (m³/s or gpm)

• H = total head (m or ft)

• P = power (kW or hp)

• N = pump speed (rpm)

• Subscripts 1 and 2 = original and new operating conditions

📊 Worked Example

Reduce speed from 1,750 to 1,400 rpm (ratio = 0.8): Q₂ = 0.8 × Q₁, H₂ = 0.64 × H₁, P₂ = 0.51 × P₁ (49% power reduction!)

💡 Exam Tip

VFDs (variable frequency drives) use affinity laws. Reducing speed to 80% reduces power by 49% — huge energy savings for variable demand systems.

Variables

• Permeate Flow = filtered water production rate (L/h)

• Membrane Area = total active membrane area (m²)

• Typical flux: MF/UF = 20–80 LMH, NF/RO = 10–30 LMH

• Higher flux = faster fouling, more frequent cleaning

📊 Worked Example

Permeate flow = 1,000 L/h, membrane area = 50 m² → Flux = 1,000/50 = 20 LMH

💡 Exam Tip

Transmembrane pressure (TMP) increases as membranes foul. When TMP reaches the cleaning threshold, chemical cleaning (CIP) is required. Track TMP vs. flux to monitor fouling.

Variables

• Permeate Flow = product water flow rate

• Feed Flow = total inlet flow rate

• Concentrate Flow = Feed − Permeate

• Typical recovery: RO = 75–85%, NF = 80–90%, UF/MF = 90–95%

📊 Worked Example

Feed = 100 m³/h, Permeate = 80 m³/h → Recovery = 80/100 × 100 = 80%

💡 Exam Tip

Higher recovery = less concentrate waste but higher salt concentration in concentrate. Scaling risk increases at high recovery. Antiscalant dosing may be required.

Variables

• Stroke Length = % of maximum stroke (0–100%)

• Stroke Rate = strokes per minute

• Displacement = volume per stroke at 100% stroke length (mL)

• Calibrate by measuring actual output over a timed period

📊 Worked Example

Stroke length = 75%, rate = 60 spm, displacement = 5 mL → Output = 0.75 × 60 × 5 × 60 / 1,000 = 13.5 L/h

💡 Exam Tip

Always calibrate chemical metering pumps by measuring actual output — do not rely on dial settings alone. Calibrate after any maintenance or chemical change.

Variables

• River Flow = upstream river flow (m³/s or ML/day)

• Effluent Flow = wastewater discharge flow (m³/s or ML/day)

• Diluted concentration = Source concentration / (Dilution Ratio + 1)

📊 Worked Example

River flow = 15 m³/s, effluent = 0.3 m³/s → Dilution = 15/0.3 = 50:1. If effluent has 10 mg/L of a contaminant, diluted concentration = 10/51 = 0.2 mg/L

💡 Exam Tip

Even at 50:1 dilution, pharmaceuticals and pathogens may be present at concentrations of concern. Source water monitoring is essential.

Variables

• Volume = reservoir storage volume (ML or m³)

• Flow = average daily withdrawal rate (ML/day)

• Long HRT (>30 days): algal bloom risk, thermal stratification

• Short HRT (<7 days): less treatment time, higher turbidity risk

📊 Worked Example

Volume = 5,000 ML, Flow = 50 ML/day → HRT = 5,000/50 = 100 days

💡 Exam Tip

Long HRT allows algae to bloom and taste/odour compounds to accumulate. Short HRT means contamination events clear faster but treatment must respond quickly.

Variables

• Chl-a = chlorophyll-a concentration (μg/L)

• TSI < 40: oligotrophic (clear, low nutrients)

• TSI 40–50: mesotrophic

• TSI 50–70: eutrophic (algal blooms possible)

• TSI > 70: hypereutrophic (severe algal blooms)

📊 Worked Example

Chl-a = 20 μg/L → TSI = 9.81 × ln(20) + 30.6 = 9.81 × 3.0 + 30.6 = 60 (eutrophic)

💡 Exam Tip

TSI > 50 indicates elevated algal bloom risk. Cyanobacteria blooms and taste/odour problems are common in eutrophic reservoirs.

Variables

• Secchi Depth = depth at which a Secchi disk disappears from view (m)

• Relationship is approximate and varies with particle type

• Deeper Secchi depth = clearer water = lower turbidity

📊 Worked Example

Secchi depth = 2 m → Turbidity ≈ 40/2 = 20 NTU (approximate)

💡 Exam Tip

Secchi depth is a quick field measurement of water clarity. It is NOT a substitute for turbidimeter measurement for regulatory compliance.

Variables

• Concentration = total phosphorus in tributary (mg/L)

• Flow = annual tributary flow (m³/year)

• Divide by 1,000 to convert mg to g, then g to kg

• Compare to reservoir critical loading to assess eutrophication risk

📊 Worked Example

TP = 0.05 mg/L, Flow = 10,000,000 m³/year → P Load = 0.05 × 10,000,000 / 1,000 = 500 kg/year

💡 Exam Tip

Phosphorus loading drives eutrophication. Reducing P loading from agricultural runoff, wastewater, and urban stormwater is the key to controlling algal blooms.

Variables

• Weight Loss = decrease in cylinder weight (kg)

• Time = elapsed time (h)

• Maximum withdrawal rate: 1-tonne cylinder = 18 kg/h at 20°C

• Exceeding max rate causes cylinder frosting and reduced output

📊 Worked Example

Cylinder weight decreased from 450 kg to 430 kg over 2 hours → Leak Rate = 20/2 = 10 kg/h

💡 Exam Tip

Chlorine cylinders should be weighed daily to monitor consumption and detect leaks. Keep cylinders in a ventilated, locked room with a chlorine gas detector.

Variables

• Inventory = current stock on hand (kg)

• Daily Usage = average daily consumption (kg/day)

• Minimum stock: typically 30 days supply

• Critical stock: 7 days supply triggers emergency order

📊 Worked Example

Inventory = 2,000 kg alum, Daily Usage = 450 kg/day → Days of Supply = 2,000/450 = 4.4 days (CRITICAL — order immediately)

💡 Exam Tip

Class 3 operators are responsible for chemical inventory management. Maintain minimum 30-day supply of critical chemicals (chlorine, coagulant, fluoride).

Variables

• C₁ = concentration of stock solution

• V₁ = volume of stock solution to use

• C₂ = desired concentration of diluted solution

• V₂ = total volume of diluted solution

📊 Worked Example

Make 100 L of 1% NaOCl from 12.5% stock: V₁ = (1% × 100 L) / 12.5% = 8 L of stock + 92 L water

💡 Exam Tip

Always add acid to water (never water to acid) when diluting concentrated acids. For bleach dilution, use cool water to reduce chlorine loss.

Variables

• Volume Produced = total water treated and pumped to distribution (m³)

• Volume Billed = total metered water sold to customers (m³)

• Difference includes: real losses (leaks), apparent losses (meter error, theft)

• Target: < 10% water loss for well-maintained systems

📊 Worked Example

Produced = 10,000 m³/day, Billed = 8,500 m³/day → Loss = (10,000−8,500)/10,000 × 100 = 15% (above target)

💡 Exam Tip

Water loss > 15% indicates significant leakage or metering problems. Pressure management, leak detection, and meter replacement are key strategies.

Variables

• Total Energy = electricity consumed by all plant equipment (kWh)

• Volume Treated = total water treated (m³)

• Typical range: 0.2–0.5 kWh/m³ for conventional treatment

• Membrane systems: 0.5–1.5 kWh/m³

• RO desalination: 3–5 kWh/m³

📊 Worked Example

Energy = 5,000 kWh/day, Volume = 25,000 m³/day → Energy = 5,000/25,000 = 0.20 kWh/m³

💡 Exam Tip

Energy is typically 30–40% of water treatment operating costs. VFDs, off-peak pumping, and process optimization are key energy reduction strategies.