Water Treatment — Coagulation, Sedimentation, Filtration & Chlorination | EngineeringHulk


Water Treatment — Coagulation, Sedimentation, Filtration & Chlorination

Unit operations of a conventional water treatment plant — coagulation, flocculation, sedimentation, filtration, disinfection, and softening — with CPHEEO design parameters and GATE CE worked examples

Last Updated: April 2026

Key Takeaways

  • Conventional surface water treatment train: Screening → Aeration → Coagulation/Flocculation → Sedimentation → Filtration → Disinfection.
  • Coagulant dose (alum): jar test determines optimum dose; alum reacts with alkalinity: Al₂(SO₄)₃ + 3Ca(HCO₃)₂ → 2Al(OH)₃↓ + 3CaSO₄ + 6CO₂.
  • Sedimentation: overflow rate (surface loading) = Q/A (m³/m²/day); detention time = V/Q; particle settles if vs ≥ overflow rate.
  • Stokes’ law: vs = (ρs – ρw)gd²/(18μ) — settling velocity for discrete (non-flocculent) particles.
  • Rapid sand filter: filtration rate 4–5 m³/m²/h; backwashed every 24–48 hours; removes turbidity to < 1 NTU.
  • Chlorine demand = chlorine applied – residual chlorine; breakpoint chlorination destroys all ammonia-N.
  • Lime-soda softening: removes hardness; Ca(OH)₂ + CO₂ → CaCO₃↓ + H₂O; Na₂CO₃ + CaSO₄ → CaCO₃↓ + Na₂SO₄.

1. Conventional Water Treatment Train

A conventional surface water treatment plant processes turbid, coloured river or reservoir water through a series of unit operations to produce potable water meeting IS 10500 standards.

StepUnit OperationPurposeRemoves
1Intake screening (bar/fine screens)Remove large floating debrisLeaves, twigs, fish, plastics
2AerationAdd oxygen; remove CO₂, H₂S, taste/odourDissolved gases, volatile organics, iron/manganese (oxidation)
3CoagulationDestabilise colloidal particles by charge neutralisationInitiates removal of colloids, colour, turbidity
4FlocculationGently agitate to form large settleable flocsColloids aggregated into floc
5Sedimentation (clarifier)Remove floc by gravity settling60–70% turbidity; 40–60% colour; SS; some bacteria
6FiltrationRemove remaining fine suspended matterResidual turbidity to < 1 NTU; most bacteria removed
7Disinfection (chlorination)Kill pathogens; provide residual protection in distributionBacteria, viruses, protozoa (Giardia — requires filtration too)
8*Softening (if required)Remove hardnessCa²⁺, Mg²⁺
9*Fluoridation / DefluoridationAdjust fluoride to 0.6–1.0 mg/LExcess fluoride; or add fluoride to deficient water

* Optional steps — applied when source water requires specific treatment

2. Screening and Aeration

2.1 Screening

Bar screens (coarse: 50–100 mm spacing) remove large debris. Fine screens (2–10 mm) protect pumps and treatment units. Screens are cleaned manually or automatically. Screenings (solids removed) are disposed to landfill or incinerated.

2.2 Aeration

Aeration adds dissolved oxygen to water and strips out dissolved gases (CO₂, H₂S, CH₄) and volatile organic compounds (VOCs) responsible for taste and odour. Methods:

  • Cascade aerator: Water flows over a series of steps — simple, low-cost, widely used in India
  • Spray nozzle aerator: Fine droplets maximise air-water contact
  • Diffused air aerator: Compressed air diffused through porous media in a tank
  • Mechanical aerator: Surface agitation by paddle or turbine impeller

Aeration oxidises Fe²⁺ → Fe³⁺ (ferric iron, then removed as Fe(OH)₃ precipitate in sedimentation) and Mn²⁺ → MnO₂. Very important for iron-rich groundwater sources in India.

3. Coagulation and Flocculation

3.1 Why Coagulation is Needed

Colloidal particles (0.001–1 μm) in water carry a negative surface charge (zeta potential), causing electrostatic repulsion that keeps them stably dispersed. These particles are too small to settle by gravity alone (settling time = years) and pass through filters. Coagulation neutralises the surface charge, allowing particles to come together.

3.2 Common Coagulants

CoagulantChemicalOptimal pHReaction with Water Alkalinity
Alum (most common in India)Al₂(SO₄)₃·18H₂O6.5–8.0Al₂(SO₄)₃ + 3Ca(HCO₃)₂ → 2Al(OH)₃↓ + 3CaSO₄ + 6CO₂
Ferrous sulphate (copperas)FeSO₄·7H₂O> 8.5 (with lime)Requires lime addition; forms Fe(OH)₃ floc at high pH
Ferric chlorideFeCl₃3.5–6.5; 8–11FeCl₃ + 3H₂O → Fe(OH)₃↓ + 3HCl; works over wide pH range
Polyaluminium chloride (PAC)Aln(OH)mCl3n–m5.0–8.5More efficient than alum; less sludge; used in large modern WTPs

3.3 Alum Dosing — Chemical Reaction

Al₂(SO₄)₃ + 3Ca(HCO₃)₂ → 2Al(OH)₃↓ + 3CaSO₄ + 6CO₂

Molecular weights: Al₂(SO₄)₃ = 342; Ca(HCO₃)₂ = 162 (combined = 3 × 162 = 486); CaCO₃ = 100

For every 1 mg/L alum dose: destroys 342/(3×162) × 162 = 0.47 mg/L alkalinity as Ca(HCO₃)₂

or equivalently: destroys ~0.50 mg/L alkalinity as CaCO₃ per mg/L alum

If natural alkalinity is insufficient: add lime Ca(OH)₂ or soda ash Na₂CO₃ to maintain alkalinity for effective coagulation (minimum 50 mg/L as CaCO₃ after coagulant addition)

3.4 Jar Test

The jar test is the standard laboratory procedure to determine the optimum coagulant dose and type for a given water source. Six jars of raw water are treated with increasing doses of coagulant, subjected to rapid mixing (1 min at ~100 rpm) then slow mixing (flocculation at ~30 rpm for 15–20 min), then allowed to settle. The dose that gives the best settled water quality (lowest turbidity and colour) at minimum cost is the optimum dose.

3.5 Flocculation

After rapid mixing (coagulation), the water is gently agitated in a flocculation basin for 20–40 minutes at G (velocity gradient) = 10–30 s⁻¹. This allows the destabilised particles to collide and form large, dense flocs (0.1–1 mm) that settle efficiently.

Velocity gradient: G = √(P/(μV)) = √(ρghy/(μT))

where P = power input (W); μ = dynamic viscosity (Pa·s); V = tank volume (m³)

Rapid mix: G = 300–700 s⁻¹; detention time = 1–2 min

Flocculation: G = 10–75 s⁻¹; detention time = 20–40 min

Gt = 10⁴–10⁵ (Camp number; product of G and detention time; optimal floc formation range)

4. Sedimentation — Design Parameters

Sedimentation (clarification) uses gravity to separate the floc formed in coagulation/flocculation from the water. It is the most space-intensive unit operation in a water treatment plant.

4.1 Key Design Parameters

Overflow rate (surface loading rate):

v₀ = Q/A = Q/(L × W)    [m³/m²/day or m/day]

where Q = flow rate; A = plan area of tank; L = length; W = width

CPHEEO: 12,000–24,000 L/m²/day = 12–24 m³/m²/day = 0.5–1.0 m/h

Detention time:

t = V/Q = (L × W × H)/Q

CPHEEO: 2–4 hours for conventional sedimentation; 1.5–2 hours with tube settlers

Weir loading rate:

= Q/length of effluent weir

CPHEEO: ≤ 186 m³/m/day (150,000 L/m/day)

4.2 Sedimentation Tank Types

TypeFlow PatternDepth (m)Use
Rectangular horizontal flowHorizontal; inlet end to outlet end2.5–5.0Most common for water treatment in India
Circular radial flow (hopper bottom)Radially inward; sludge to centre3.0–4.5Medium-size WTPs; continuous sludge withdrawal
Upflow clarifier (sludge blanket)Upward; floc-blanket filter4.0–6.0High-rate; turbid tropical waters
Tube/plate settlerNear-horizontal in inclined tubesShallowUpgradation of existing tanks; high-rate

4.3 Ideal Sedimentation Theory

In an ideal horizontal flow sedimentation tank, a particle settles completely if:

vs ≥ v₀ = Q/A

where vs = particle settling velocity; v₀ = overflow rate

Particles with vs < v₀ are partially removed; fraction removed = vs/v₀

The overflow rate is independent of tank depth — increasing depth does NOT improve removal efficiency in ideal theory (it only increases detention time).

However, in practice, deeper tanks reduce short-circuiting and turbulence effects.

5. Stokes’ Law and Particle Settling

Stokes’ law (discrete, non-flocculent particle settling):

vs = (ρs – ρw) g d² / (18μ)

where:

  • vs = settling velocity (m/s)
  • ρs = density of particle (kg/m³); ρw = density of water = 1000 kg/m³
  • g = 9.81 m/s²
  • d = particle diameter (m)
  • μ = dynamic viscosity of water (Pa·s); at 20°C: μ = 1.002 × 10⁻³ Pa·s

Validity: Stokes’ law valid for Rep = ρwvsd/μ < 1 (laminar settling; very small particles)

For larger particles (Rep > 1): use intermediate or Newton’s law (drag coefficient varies)

5.1 Particle Size Categories

CategorySizeSettling BehaviourRemoval Method
Gravel> 2 mmSettles rapidly (seconds)Simple settling; grit chambers
Sand/silt0.02–2 mmSettles in hours (Stokes’ law)Sedimentation tank
Fine silt/clay0.001–0.02 mmSettles in days–monthsCoagulation + sedimentation
Colloids0.001–1 μmNever settles (Brownian motion)Coagulation essential
Dissolved< 0.001 μmCannot settleChemical/biological treatment

6. Filtration — Types and Design

Filtration removes residual suspended solids (turbidity, colour, bacteria) after sedimentation, producing clean water suitable for disinfection. The filter bed consists of granular media (sand, anthracite) that physically strains and adsorbs particles.

6.1 Slow Sand Filter (SSF)

Filtration rate: 0.1–0.4 m³/m²/h (0.1–0.4 m/h)

Sand size: 0.15–0.35 mm (effective size); uniformity coefficient ≤ 2

Sand depth: 0.9–1.5 m; gravel support: 0.3–0.5 m

Cleaning: scraping off top 2–3 cm of contaminated sand; no backwash (biological action in schmutzdecke layer is important)

Schmutzdecke: biological mat on top surface — responsible for biological purification; removes Giardia and Cryptosporidium cysts effectively

BOD removal: 60–90%; Bacteria removal: 99.9%; Turbidity: effective at < 10 NTU incoming

Suitable for: small communities, groundwater, relatively clean surface water

6.2 Rapid Sand Filter (RSF)

Filtration rate: 4–5 m³/m²/h (upto 6 m/h) = 120–150 m³/m²/day

Sand effective size: 0.45–0.70 mm; uniformity coefficient ≤ 1.5

Sand depth: 0.6–0.9 m; gravel support: 0.3–0.6 m

Cleaning: backwashing with treated water (upflow) at 12–15 m³/m²/h for 5–15 minutes

Backwash water rate: 30–40 L/s·m² = 0.3–0.4 m/s (must expand and fluidise the bed)

Run time between backwashes: 24–48 hours (governed by head loss build-up)

Requires pre-treatment (coagulation + sedimentation) as it is not a biological filter

Turbidity removal to < 0.5–1 NTU from < 5 NTU incoming (after sedimentation)

6.3 Comparison: SSF vs RSF

FeatureSlow Sand Filter (SSF)Rapid Sand Filter (RSF)
Filtration rate0.1–0.4 m/h (slow)4–6 m/h (fast)
Sand size0.15–0.35 mm (fine)0.45–0.70 mm (coarse)
Pre-treatment requiredNo (treats turbid water up to 10 NTU)Yes (coagulation + sedimentation essential)
Cleaning methodScraping (no backwash)Backwash (upflow hydraulic cleaning)
Biological activityImportant (schmutzdecke)No (purely physical/chemical)
Land requirementVery large (50–100× more than RSF)Small
Capital costLowModerate–high
Skilled operationMinimalModerate
Best applicationSmall rural WTPs, developing countriesAll sizes of modern WTPs

6.4 Dual Media Filter

A dual media filter uses a layer of anthracite (coarser, lighter: 0.8–1.2 mm, sp. gr. 1.4–1.6) above a sand layer (finer, denser: 0.4–0.55 mm, sp. gr. 2.65). The coarser anthracite traps larger flocs; the finer sand provides final polishing. After backwash, the lighter anthracite naturally stratifies on top. Dual media filters run at higher filtration rates (7–10 m/h) with longer run times between backwashes — used in modern high-rate WTPs.

7. Disinfection — Chlorination

Disinfection kills pathogenic microorganisms in treated water to prevent waterborne disease. Chlorination is the most widely used method in India and worldwide due to its low cost, effectiveness, and ability to provide a residual in the distribution system.

7.1 Chemistry of Chlorination

Chlorine gas dissolves in water:

Cl₂ + H₂O → HOCl + HCl (hypochlorous acid + hydrochloric acid)

HOCl → H⁺ + OCl⁻ (hypochlorite ion)

Hypochlorous acid (HOCl) is the active disinfectant — 40–80× more effective than OCl⁻.

At pH 7.5: ≈50% HOCl, 50% OCl⁻

At pH < 6: almost all HOCl (maximum disinfection); at pH > 9: almost all OCl⁻ (minimal disinfection)

→ Lower pH → more effective chlorination → disinfection works best at low pH

7.2 Chlorine Demand and Residual

Chlorine demand = Chlorine applied – Residual chlorine

Chlorine reacts with: organic matter, iron, manganese, H₂S, NH₃, bacteria

IS 10500 residual chlorine: 0.2 mg/L (minimum) to 1.0 mg/L (maximum) at consumer end

For distribution mains in India: 0.2–0.5 mg/L free residual chlorine

7.3 Breakpoint Chlorination

When chlorine is added to water containing ammonia (NH₄-N), it forms chloramines:

Stage 1: Cl₂ + NH₃ → NH₂Cl (monochloramine) + HCl    [combined chlorine residual rises]

Stage 2: Additional Cl₂ converts NH₂Cl → NCl₃ → N₂    [residual drops — the “breakpoint”]

Stage 3: Beyond breakpoint → free chlorine residual (HOCl/OCl⁻) builds up

Breakpoint: Molar ratio Cl₂/NH₃ ≈ 7.6:1 (by weight: ~10 mg Cl₂ per mg NH₃-N)

Beyond breakpoint: free residual chlorine available — more effective for disinfection

IS 10500 requires free residual (not combined residual) in piped water supply

7.4 CT Concept for Disinfection

CT = Concentration × Time (mg/L × minutes)

Required CT for Giardia cyst inactivation: CT = 150 (Cl₂ at pH 7, 10°C)

Required CT for viruses: CT = 6–12 (Cl₂ at pH 7–8, 10°C)

Higher CT required at higher pH (less HOCl) and lower temperature (slower kill rate)

7.5 Alternative Disinfectants

DisinfectantAdvantageDisadvantageUse
Chlorine gas (Cl₂)Cheap; residual; effectiveToxic gas; handling hazard; DBP formationLarge WTPs in India
Sodium hypochlorite (NaOCl)Safer than gas; liquidDegrades on storage; more expensiveSmall/medium WTPs
Calcium hypochlorite (bleaching powder)Stable solid; easy transportLower Cl₂ content (30–35%); scalingRural schemes; village tanks
ChloramineMore stable residual in distributionLess effective; slower killLarge distribution systems
Ozone (O₃)No DBPs; excellent for taste/odour; Cryptosporidium killNo residual; costly; on-site generationHigh-quality treatment; bottled water
UV radiationNo chemicals; no DBPs; effective vs Giardia/CryptosporidiumNo residual; needs turbidity < 1 NTUPoint-of-use; small-scale; bottled water

8. Water Softening — Lime-Soda Process

Softening removes calcium and magnesium hardness from water by precipitating them as insoluble carbonates and hydroxides.

8.1 Chemical Reactions

Remove free CO₂ (prerequisite for softening):

Ca(OH)₂ + CO₂ → CaCO₃↓ + H₂O    (1 mole lime per mole CO₂)

Remove temporary hardness (bicarbonates):

Ca(HCO₃)₂ + Ca(OH)₂ → 2CaCO₃↓ + 2H₂O    (lime only)

Mg(HCO₃)₂ + 2Ca(OH)₂ → 2CaCO₃↓ + Mg(OH)₂↓ + 2H₂O    (two moles lime)

Remove permanent hardness (non-carbonate):

CaSO₄ + Na₂CO₃ → CaCO₃↓ + Na₂SO₄    (soda ash for permanent Ca hardness)

MgSO₄ + Ca(OH)₂ → Mg(OH)₂↓ + CaSO₄    (first step; then Ca hardness added)

MgSO₄ + Ca(OH)₂ + Na₂CO₃ → Mg(OH)₂↓ + CaCO₃↓ + Na₂SO₄    (combined)

8.2 Residual Hardness after Lime-Soda Softening

Theoretical softening cannot reduce hardness to zero — CaCO₃ and Mg(OH)₂ have finite solubility. Minimum achievable hardness ≈ 30–40 mg/L as CaCO₃. Recarbonation (adding CO₂) is needed to reduce pH from ~11 back to 8–9 before distribution.

8.3 Ion Exchange Softening

Zeolite (synthetic cation exchange resin) replaces Ca²⁺ and Mg²⁺ with Na⁺:

Ca²⁺ + Na₂Z → CaZ + 2Na⁺ (Z = zeolite exchanger)

Regeneration with NaCl brine: CaZ + 2NaCl → Na₂Z + CaCl₂

Produces softened water (near-zero hardness); increases Na⁺ in water

Used for: industrial boiler feed, hospitals, domestic water softeners

9. Fluoridation and Defluoridation

9.1 Fluoridation

In areas where natural fluoride is below 0.6 mg/L, fluoride is added to water to prevent dental caries (the Kissimmee/Grand Rapids studies showed 60% reduction in caries at 1 mg/L F⁻). Fluoridation chemicals: sodium fluoride (NaF), sodium silicofluoride (Na₂SiF₆), hydrofluosilicic acid (H₂SiF₆). Target: 0.8–1.0 mg/L in Indian conditions (lower target than WHO 1.5 mg/L due to higher water intake in hot climate).

9.2 Defluoridation

In endemic fluorosis areas (parts of Andhra Pradesh, Rajasthan, Karnataka, UP with natural fluoride 2–10 mg/L), excess fluoride must be removed:

  • Nalgonda technique: Alum (Al₂(SO₄)₃) + lime → Al(OH)₃ floc adsorbs F⁻ → coagulation + sedimentation. Simple, low-cost; suitable for India. Removes F⁻ from 5 mg/L to < 1.5 mg/L.
  • Activated alumina: Fixed bed column; removes F⁻ by ion exchange/adsorption. Effective to < 0.5 mg/L. Regeneration with NaOH + H₂SO₄.
  • Reverse osmosis (RO): Removes all dissolved solids including F⁻; expensive; used for community-scale systems with high TDS + high F⁻.

10. Worked Examples (GATE CE Level)

Example 1 — Sedimentation Tank Design (GATE CE 2022 type)

Problem: Design a sedimentation tank for a water treatment plant with a design flow of 8 MLD (million litres per day). The overflow rate = 20 m³/m²/day; detention time = 3 hours. Find (a) the plan area, (b) the tank volume, and (c) the tank depth.

Given: Q = 8 MLD = 8 × 10⁶ L/day = 8000 m³/day; overflow rate = 20 m³/m²/day; t = 3 h

(a) Plan area:

A = Q/overflow rate = 8000/20 = 400 m²

For a rectangular tank: e.g., L × W = 40 m × 10 m = 400 m²

(b) Tank volume:

V = Q × t = 8000 m³/day × (3/24) day = 8000 × 0.125 = 1000 m³

(c) Tank depth (side water depth):

H = V/A = 1000/400 = 2.5 m

Add 0.5–1.0 m freeboard → total depth = 3.0–3.5 m

Check overflow rate method:

v₀ = Q/A = 8000/400 = 20 m³/m²/day ✓

Alternatively: v₀ = H/t = 2.5 m/(3 h) = 2.5/3 m/h = 0.833 m/h = 20 m³/m²/day ✓

Answer: A = 400 m²; V = 1000 m³; H = 2.5 m (plus freeboard)

Example 2 — Stokes’ Law Settling Velocity (GATE CE 2021 type)

Problem: Compute the settling velocity of a discrete sand particle (d = 0.1 mm, ρs = 2650 kg/m³) in water at 20°C (μ = 1.002 × 10⁻³ Pa·s, ρw = 1000 kg/m³). Verify whether Stokes’ law applies.

Given: d = 0.1 mm = 0.0001 m; ρs = 2650 kg/m³; ρw = 1000 kg/m³; μ = 1.002 × 10⁻³ Pa·s

Stokes’ settling velocity:

vs = (ρs – ρw) g d² / (18μ)

= (2650 – 1000) × 9.81 × (0.0001)² / (18 × 1.002 × 10⁻³)

= 1650 × 9.81 × 10⁻⁸ / (1.8036 × 10⁻²)

= 16,186.5 × 10⁻⁸ / 0.018036

= 1.6187 × 10⁻⁴ / 0.018036

= 8.976 × 10⁻³ m/s = 8.98 mm/s

Verify Stokes’ law (Rep < 1):

Rep = ρw vs d / μ = 1000 × 8.976 × 10⁻³ × 0.0001 / (1.002 × 10⁻³)

= 8.976 × 10⁻⁴ / 1.002 × 10⁻³ = 0.896 < 1 ✓

Stokes’ law is applicable.

Answer: vs = 8.98 mm/s; Rep = 0.896 < 1 → Stokes’ law valid.

Example 3 — Particle Removal in Sedimentation Tank (GATE CE type)

Problem: A sedimentation tank has an overflow rate of 25 m³/m²/day. What percentage of particles with settling velocity 15 m³/m²/day is removed? What is the minimum settling velocity of particles that are completely removed?

Given: v₀ = 25 m/day (overflow rate); vs = 15 m/day

Fraction removed (vs < v₀):

Removal = vs/v₀ = 15/25 = 0.60 = 60%

(Particles with settling velocity less than v₀ are only partially removed — the fraction removed equals vs/v₀)

Minimum settling velocity for 100% removal:

vs,min = v₀ = 25 m/day

All particles with vs ≥ v₀ = 25 m/day are completely removed.

Answer: 60% of these particles removed; minimum vs for complete removal = 25 m/day.

Example 4 — Chlorine Demand (GATE CE type)

Problem: A water supply of 5 MLD requires a chlorine dose of 4 mg/L for breakpoint chlorination. The residual chlorine after 30 minutes contact time is 0.3 mg/L. Find (a) the chlorine demand, (b) the daily chlorine requirement in kg, and (c) verify whether the residual meets IS 10500 requirements.

Given: Q = 5 MLD = 5 × 10⁶ L/day; Cl₂ dose = 4 mg/L; residual = 0.3 mg/L

(a) Chlorine demand:

Chlorine demand = dose – residual = 4 – 0.3 = 3.7 mg/L

(b) Daily chlorine requirement:

= 4 mg/L × 5 × 10⁶ L/day × (1 g/1000 mg) × (1 kg/1000 g)

= 4 × 5,000,000/1,000,000 kg = 20 kg/day

(c) IS 10500 check:

Residual = 0.3 mg/L; IS 10500 requires 0.2–1.0 mg/L free residual

0.3 mg/L is between 0.2 and 1.0 mg/L → Meets IS 10500 ✓

Answer: Demand = 3.7 mg/L; Daily requirement = 20 kg/day; Residual 0.3 mg/L meets IS 10500.

Example 5 — Hardness Removal by Lime Softening (GATE CE type)

Problem: Water has Ca²⁺ = 100 mg/L and HCO₃⁻ = 300 mg/L. How much lime Ca(OH)₂ is needed to remove the temporary (carbonate) hardness? Molecular weights: Ca = 40, O = 16, H = 1, C = 12.

Reaction: Ca(HCO₃)₂ + Ca(OH)₂ → 2CaCO₃↓ + 2H₂O

MW: Ca(HCO₃)₂ = 162; Ca(OH)₂ = 74; CaCO₃ = 100

Moles of Ca(HCO₃)₂ in water:

Ca²⁺ as Ca(HCO₃)₂: Ca = 40 in Ca(HCO₃)₂ = 162

Ca(HCO₃)₂ concentration = 100 mg/L × (162/40) = 405 mg/L

Lime required:

Ca(OH)₂/Ca(HCO₃)₂ = 74/162 (molar ratio 1:1)

Lime dose = 405 × (74/162) = 405 × 0.4568 = 185 mg/L Ca(OH)₂

Alternative (milliequivalent method):
Ca²⁺: 100 mg/L; equivalent weight = 20; meq/L = 100/20 = 5
Lime equivalent weight = 74/2 = 37; lime needed = 5 × 37 = 185 mg/L ✓

Answer: Lime required = 185 mg/L Ca(OH)₂

Example 6 — Rapid Sand Filter Area (GATE CE type)

Problem: A water treatment plant serves a population of 100,000 at a per capita demand of 135 LPCD. Design the rapid sand filtration unit (filtration rate = 5 m³/m²/h). How many filter beds of 6 m × 10 m are required?

Design flow: Q = 100,000 × 135 L/day = 13,500,000 L/day = 13,500 m³/day = 562.5 m³/hour

Total filter area required:

A = Q/filtration rate = 562.5 m³/h ÷ 5 m³/m²/h = 112.5 m²

Area of each filter bed: 6 × 10 = 60 m²

Number of filter beds required (working):

N = 112.5/60 = 1.875 → 2 beds minimum

Add 1 standby unit for backwashing: provide 3 filter beds total (2 working + 1 on backwash or standby)

Total area with 2 working beds = 2 × 60 = 120 m² > 112.5 m² ✓

Answer: Required area = 112.5 m²; 2 working beds of 6 m × 10 m (+ 1 standby = 3 beds total)

11. Common Mistakes

Mistake 1 — Confusing Overflow Rate with Flow Velocity in the Tank

Error: Treating overflow rate (Q/A, surface loading) as the horizontal flow velocity through the tank instead of the theoretical settling velocity threshold.
Root Cause: Both are measured in m/h or m³/m²/h, creating confusion. Overflow rate = Q/plan area = the settling velocity at which a particle is just completely removed. Horizontal flow velocity = Q/(W × H) = the speed of water moving through the tank.
Fix: Overflow rate = Q/(L × W) determines which particles settle. Horizontal velocity = Q/(W × H) determines scouring risk. A particle with vs ≥ overflow rate settles completely regardless of tank depth. Depth affects only detention time.

Mistake 2 — Applying Rapid Sand Filter Rates to Slow Sand Filters

Error: Designing a slow sand filter at 4–5 m/h (RSF rate) instead of 0.1–0.4 m/h (SSF rate), giving a unit 10–50× too small.
Root Cause: Both are called “sand filters” but operate on completely different principles at vastly different rates. RSF uses coarser sand, rapid hydraulics, and backwashing. SSF uses fine sand, slow flow, and biological schmutzdecke action.
Fix: SSF: 0.1–0.4 m/h; RSF: 4–6 m/h. These differ by a factor of 10–50. The slow rate for SSF is essential for the biological activity in the schmutzdecke to develop and function.

Mistake 3 — Not Checking Whether Stokes’ Law Applies

Error: Computing settling velocity with Stokes’ law for large sand particles without checking Rep < 1.
Root Cause: Stokes’ law is valid only for laminar settling (creeping flow, Rep < 1). For Rep = 1–1000 (intermediate regime), the intermediate law applies: vs = 0.153 g⁰·⁷¹(ρs–ρw)⁰·⁷¹d¹·¹⁴/(ρw⁰·²⁹ μ⁰·⁴³). For Rep > 1000 (Newton’s law): vs = 1.74√(g d (ρs–ρw)/ρw).
Fix: After computing vs using Stokes, always calculate Rep = ρwvsd/μ. If Rep < 1 → Stokes’ valid. If Rep = 1–1000 → use intermediate law. For GATE CE, most particles given are in the Stokes’ regime (d < 0.1 mm typically) but always verify.

Mistake 4 — Confusing Chlorine Demand with Chlorine Dose

Error: Using chlorine demand (3.7 mg/L) as the daily requirement instead of chlorine dose (4 mg/L).
Root Cause: Chlorine dose = total chlorine applied; chlorine demand = chlorine consumed by reactions; residual = what remains. Daily kg requirement = dose × volume, not demand × volume.
Fix: Daily Cl₂ required = dose (mg/L) × Q (L/day) / 10⁶ (kg). The demand tells you how much is consumed and helps size the chemical storage, but the dose governs the chemical procurement.

Mistake 5 — Using Tank Volume Instead of Plan Area for Overflow Rate

Error: Computing overflow rate = Q/V (flow divided by volume) instead of Q/A (flow divided by plan area).
Root Cause: Volume and plan area are both properties of the tank, and both appear in sedimentation design. Q/V = 1/detention time (not overflow rate). Q/A = overflow rate = critical settling velocity.
Fix: Overflow rate (surface loading) = Q/A [m³/m²/day]; Detention time = V/Q [hours]. Both are needed to fully characterise the tank. A is plan area (L × W); V is volume (L × W × H).

12. Frequently Asked Questions

Q1. Why does increasing the depth of a sedimentation tank not improve particle removal efficiency in ideal theory?

In ideal sedimentation theory (Camp’s model), a particle entering the tank at any depth will settle completely if its settling velocity vs ≥ v₀ (overflow rate = Q/A). A particle entering at the maximum depth H settles to the bottom in exactly the detention time t = H/v₀. A particle entering at half the depth (H/2) settles out in half the detention time. Thus, regardless of the depth at which a particle enters, if vs ≥ v₀ it always settles before reaching the outlet — the fraction removed depends only on the ratio vs/v₀, not on tank depth. This is why the overflow rate (Q/A) is the governing design parameter for particle removal, not detention time. In practice, however, deeper tanks perform better than ideal theory predicts because: deeper tanks are less susceptible to wind-induced turbulence, thermal stratification, and inlet/outlet short-circuiting. The depth must be sufficient (typically 2.5–4 m) to prevent scouring of settled sludge by the horizontal flow velocity, and to provide adequate sludge storage volume.

Q2. What is the significance of the schmutzdecke in slow sand filtration, and why is it destroyed by backwashing?

The schmutzdecke (German: “dirt layer”) is a biological community — bacteria, protozoa, algae, diatoms, rotifers — that develops on the surface of a slow sand filter bed over 2–4 weeks of operation. It is responsible for 50–90% of the pathogen removal achieved by slow sand filtration, including the removal of Giardia and Cryptosporidium cysts (which are resistant to chlorination) through biological predation and physical straining. The schmutzdecke works effectively only at very low hydraulic velocities (0.1–0.4 m/h) — at higher velocities, the biological community is disrupted. If a slow sand filter were backwashed like a rapid sand filter (with high-velocity upflow), the schmutzdecke would be completely destroyed and the filter would need 2–4 weeks to mature biologically before it could effectively remove pathogens again. This is why SSF cleaning involves scraping only the top 2–3 cm of sand (removing the clogged schmutzdecke), washing it separately, and returning it after the new schmutzdecke has regrown. This limitation means SSF cannot handle highly turbid waters (>10 NTU) without separate pre-treatment, and explains why RSF, despite requiring coagulation, is preferred for treating turbid Indian river water.

Q3. What are disinfection byproducts (DBPs) and why are they a concern in chlorinated water?

Disinfection byproducts (DBPs) are compounds formed when chlorine reacts with natural organic matter (humic and fulvic acids from decomposing vegetation) in water. The most significant DBPs are trihalomethanes (THMs) — chloroform (CHCl₃), bromodichloromethane (CHBrCl₂), dibromochloromethane (CHBr₂Cl), and bromoform (CHBr₃) — and haloacetic acids (HAAs). THMs are formed when HOCl reacts with natural organic matter at elevated pH and temperature. They are classified as potential human carcinogens (Group 2B); at the low concentrations in drinking water, the cancer risk is estimated at 1–3 cases per 100,000 population over a lifetime. WHO and US EPA regulate THMs at 80 μg/L (total); IS 10500 is being revised to include DBP limits. Strategies to minimise DBP formation: remove organic precursors before chlorination (enhanced coagulation, activated carbon adsorption), reduce chlorine dose, lower pH during chlorination, use alternative disinfectants (ozone + low-dose chloramine). The fundamental trade-off — chlorination protects millions from acute waterborne disease versus DBPs that pose a small chronic cancer risk — consistently favours chlorination in the public health calculus, especially in countries like India where waterborne disease remains a major cause of childhood mortality.

Q4. Why is the Nalgonda technique for defluoridation widely promoted in India despite its limitations?

The Nalgonda technique was developed by NEERI (National Environmental Engineering Research Institute, Nagpur) and is named after the fluorosis-endemic district in Telangana where it was first deployed. It uses alum (readily available, cheap) and lime (also cheap) to coagulate and precipitate fluoride along with the Al(OH)₃ floc, followed by settling and filtration. It can reduce fluoride from 5 mg/L to below 1.5 mg/L in a simple jar-and-bucket process requiring no electricity or skilled operation — making it suitable for rural communities in India where sophisticated membrane systems or activated alumina units are impractical. Its main limitations are: (1) residual aluminium in treated water (0.1–0.5 mg/L Al³⁺) — a concern for Alzheimer’s risk though evidence is debated; (2) high sludge generation; (3) inconsistent removal below 1 mg/L at high initial fluoride levels. More effective technologies (activated alumina, RO) are increasingly available through the Jal Jeevan Mission’s piped water supply infrastructure, gradually replacing Nalgonda technique for community water supply — but it remains the most accessible emergency/household-level intervention for acute fluorosis prevention in remote areas.


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