Environmental Engineering-I (CE-602) - Unit 3 Short Notes

UNIT 3: Water Supply and Wastewater Engineering

1.0 Population Forecasting for Water Supply

1.1 Arithmetic Increase Method

Assumes constant rate of population increase.

• Formula: $$\displaystyle P_n = P_0 + n \cdot \bar{x} $$

  • $$\displaystyle P_n $$ = Population after $n$ decades

  • $$\displaystyle P_0 $$ = Present population

  • $\bar{x}$ = Average increase per decade

• Use: Mature cities with stable growth.

• Limitation: Underestimates future growth.

1.2 Incremental Increase Method

Averages the incremental increases, not total.

• Formula: $$\displaystyle P_n = P_0 + n \cdot \bar{x}_i $$

  • $$\displaystyle \bar{x}_i $$ = Average of incremental increases per decade

• Use: Growing towns where growth rate is accelerating.

• More accurate than arithmetic for rapidly developing areas.

1.3 Logistic Growth Method

Models growth with a saturation limit ($$\displaystyle P_s $$). Follows S-curve.

• Logistic Equation: $$\displaystyle P_t = \frac{P_s}{1 + e^{a + b t}} $$

  • $$\displaystyle P_t $$ = Population at time $t$

  • $$\displaystyle P_s $$ = Saturation population

  • $a, b$ = Coefficients

  • $t$ = Time (decades from origin)

1.3.1 Saturation Population ($$\displaystyle P_s $$)

• Maximum population the region can sustain based on resources.

• Determination: From curve fitting using past data. As $t \to \infty$, $$\displaystyle P_t \to P_s $$.

1.3.2 Coefficients ($a, b$)

• Solve using two known population points $$\displaystyle (t_1, P_1) $$ and $$\displaystyle (t_2, P_2) $$:

$$ \ln\left(\frac{P_s - P_1}{P_1}\right) = a + b t_1 $$

$$ \ln\left(\frac{P_s - P_2}{P_2}\right) = a + b t_2 $$

• Subtract to find $b$, then back-substitute for $a$.

1.3.3 Predicting Future Population

• Once $$\displaystyle P_s, a, b $$ are known, plug $$\displaystyle t_{future} $$ into logistic equation.

• Exam Tip: Past papers often give three population points over two equal time intervals to find $$\displaystyle P_s $$ first using:

$$ P_s = \frac{2P_0 P_1 P_2 - P_1^2(P_0 + P_2)}{P_0 P_2 - P_1^2} $$

2.0 Water Demand Analysis

2.1 Factors Affecting Per Capita Water Demand

2.2 Types of Water Demands

1. Domestic: Drinking, cooking, bathing, washing (≈ 50-60% of total).

2. Industrial: Process water, cooling (varies with industry type).

3. Institutional/Public: Schools, hospitals, parks, street washing.

4. Fire Demand: Not daily, but must be available on peak days.

5. Losses & Theft: Leakage, unauthorized connections (15-30% in old systems).

2.3 Fire Demand Estimation

Fire demand is intermittent but high rate for short duration.

2.3.1 Kuichling's Formula

$$ Q = 3182 \sqrt{P} \quad \text{(where } Q \text{ in lit/min, } P \text{ in 1000s)} $$

• For $$\displaystyle P > 50,000 $$: $$\displaystyle Q = 6360 \sqrt{P-50} + 3182 \sqrt{50} $$

• Most common in Indian practice.

2.3.2 Boston's Formula

$$ Q = 150 \sqrt{P} \quad \text{(where } Q \text{ in lit/min, } P \text{ in 1000s)} $$

• Gives lower value than Kuichling's.

2.3.3 National Board of Fire Underwriters Formula

• For residential areas:

$$ Q = 4600 \sqrt{P} \quad (P < 200,000) $$

$$ Q = 21000 \sqrt[3]{P-200} + 4600 \sqrt{200} \quad (P > 200,000) $$

• For business areas: Add 50% to above.

2.3.4 Factors Influencing Fire Demand

• Population density (main factor)

• Type of construction (wooden vs. RCC)

• Availability of firefighting facilities

• Street width (narrow streets → higher demand)

• Water main pressure

• Fire hazard class of area

[!TIP]

Fire demand is NOT added to average daily demand. It is considered for peak hourly demand or maximum daily demand design.

3.0 Water Sources and Intake Structures

3.1 Sources of Water

3.1.1 Surface Water (Rivers, Lakes, Reservoirs)

3.1.2 Groundwater (Wells, Springs, Infiltration Galleries)

3.1.3 Selection Criteria

• Quantity reliability: Must meet demand in dry years.

• Quality: Compliance with drinking water standards.

• Cost: Source development + treatment + transmission.

• Topography: Gravity flow possible? Elevation difference.

• Environmental impact: Dam displacement, ecosystem.

3.2 Intake Structures

3.2.1 Types

• Canal Intake: From a canal (gravity or pumping).

• River Intake: From river (with screens, pumps).

• Lake Intake: Floating or shore type.

3.2.2 Working of Canal Intake

1. Gravity type: Canal water enters intake chamber through screen (removes debris).

2. Pumps located in pump house draw water from chamber.

3. Valves control flow.

4. Settling basin may precede pumps for silt removal.

• Key components: Screen, intake pipe, pump well, gate valves.

3.2.3 Factors Governing Selection

• Source type (river, lake, canal)

• Water level fluctuations

• Silt content

• Flow velocity (to avoid sedimentation)

• Accessibility for maintenance

• Proximity to treatment plant

• Flood/erosion protection

3.3 Pumping Stations

3.3.1 Types & Locations

• Low-lift pumps: From source to treatment plant.

• High-lift pumps: From treatment plant to distribution mains.

• Booster pumps: In distribution system to maintain pressure.

• Location: Near source (low-lift), near clear water reservoir (high-lift), or in zones (booster).

3.3.2 Pump Calculations

• Static Lift ($$\displaystyle H_s $$): Vertical distance from source water level to pump centerline.

• Friction Head Loss ($$\displaystyle H_f $$): From Darcy-Weisbach or Hazen-Williams.

• Total Dynamic Head (TDH): $$\displaystyle H_{total} = H_s + H_f + H_v $$ (velocity head, usually negligible).

• Water Horsepower (WHP): $$\displaystyle WHP = \frac{Q \cdot H_{total}}{75} $$ (for $Q$ in m³/s, $H$ in m) or $$\displaystyle \frac{Q \cdot H}{3960} $$ (for $Q$ in gpm, $H$ in ft).

• Brake Horsepower (BHP): $$\displaystyle BHP = \frac{WHP}{\eta_p} $$ ($$\displaystyle \eta_p $$ = pump efficiency).

• Motor Power: $$\displaystyle BHP_{motor} = \frac{BHP}{\eta_m} $$ ($$\displaystyle \eta_m $$ = motor efficiency).

[!TIP]

Always use peak hourly demand for pump sizing, not average.

4.0 Water Quality and Standards

4.1 Characteristics of Water

4.2 Water Quality Standards

4.3 Common Impurities

• Turbidity: Clay, silt, organic matter → shields pathogens from disinfectant.

• Colour: Humic acids (decaying vegetation).

• Taste & Odour: Algae, industrial waste, dissolved gases (H₂S).

• Hardness: Ca²⁺, Mg²⁺ → scaling, soap wastage.

• Iron & Manganese: Staining, taste, bacterial growth.

• Nitrates: >45 mg/L → methemoglobinemia ("blue baby").

• Fluorides: 0.5–1.5 mg/L beneficial; >1.5 → fluorosis.

• Arsenic/Lead: Toxic, carcinogenic.

4.4 Waterborne Diseases

[!TIP]

Coliforms are indicator organisms, not necessarily pathogenic. Their presence suggests fecal contamination and possible pathogens.

4.5 Microbiological Parameters

4.5.1 Coliform Index & E. coli

• Total Coliforms: Group of bacteria (incl. E. coli, Klebsiella). Presence indicates possible fecal pollution.

• Fecal Coliforms / E. coli: Specific to intestines of warm-blooded animals. Definitive indicator of fecal contamination.

• Standard: Zero coliforms / 100 mL in any sample (BIS/WHO).

4.5.2 Most Probable Number (MPN) Test

• Purpose: Estimate coliform density by probability.

• Procedure: Inoculate multiple tubes (e.g., 3 sets of 5, 10, 1 mL dilutions) with lactose broth. Observe gas production (positive).

• Interpretation: Use MPN table based on number of positive tubes in each dilution.

• Example: 3/5, 2/10, 0/1 positive → MPN index = 7 per 100 mL.

• Limitation: Gives statistical estimate, not exact count.

5.0 Water Treatment Processes

5.1 Coagulation and Flocculation

5.1.1 Purpose & Theory

• Purpose: Destabilize colloidal particles (silt, clay, organic matter) so they aggregate.

• Theory: Colloids have negative charge → repel. Coagulant (metal salt) neutralizes charge (Schulze-Hardy rule). Particles then collide and form flocs.

• Coagulation: Rapid mixing (seconds) to disperse coagulant.

• Flocculation: Slow mixing (15–30 min) to promote floc growth.

5.1.2 Common Coagulants

5.1.3 Chemical Reactions

• Aluminium Sulfate:

$$ Al_2(SO_4)_3 \cdot 14H_2O + 6Ca(HCO_3)_2 \rightarrow 2Al(OH)_3\downarrow + 3CaSO_4 + 6CO_2 + 14H_2O $$

(If alkalinity sufficient)

$$ Al_2(SO_4)_3 + 3Ca(OH)_2 \rightarrow 2Al(OH)_3\downarrow + 3CaSO_4 $$

(If lime added)

• Chlorinated Copperas (FeCl₃):

$$ FeCl_3 + 3H_2O \rightarrow Fe(OH)_3\downarrow + 3HCl $$

(Acid produced → consumes alkalinity)

5.1.4 Factors Affecting Coagulation

• pH: Critical for coagulant hydrolysis and floc formation.

• Temperature: Lower temp → slower reaction, weaker floc.

• Turbidity: Higher turbidity → more coagulant needed.

• Alkalinity: Needed for reaction; low alkalinity → add lime/soda.

• Mixing intensity & time: Rapid mix (50–100 s⁻¹, 30–60 sec); flocculation (20–60 s⁻¹, 15–30 min).

• Coagulant dose: Determined by jar test.

5.2 Sedimentation

5.2.1 Theory (Stokes' Law)

For discrete settling (laminar flow, Re < 0.2):

$$ v_s = \frac{g(\rho_p - \rho) d^2}{18\mu} $$

• $$\displaystyle v_s $$ = Terminal settling velocity (m/s)

• $g$ = Acceleration due to gravity (9.81 m/s²)

• $$\displaystyle \rho_p $$ = Particle density (kg/m³)

• $\rho$ = Water density (1000 kg/m³)

• $d$ = Particle diameter (m)

• $\mu$ = Dynamic viscosity (N·s/m²)

Assumptions: Spherical particle, still water, no wall effect, no particle interaction.

5.2.2 Factors Affecting Sedimentation

• Particle size, shape, density

• Temperature (affects $\mu$)

• Flow velocity (turbulence resets settling)

• Detention time

• Depth of tank (affects settling path length)

5.2.3 Types of Sedimentation Tanks

1. Horizontal Flow (Rectangular): Flow from inlet to outlet. Common.

2. Radial Flow (Circular): Flow from center to periphery. Space-saving.

3. Upflow (Hopper Bottom): Used with coagulation; sludge collection by hopper.

4. Inclined Plate/Tube Settlers: Lamella clarifiers – increase area.

5.2.4 Design Parameters

• Overflow Rate = Critical velocity for smallest particle to settle.

[!TIP]

Design based on overflow rate, not detention time. Detention time is secondary.

5.3 Filtration

5.3.1 Theory of Filtration Mechanisms

1. Straining: Physical interception of particles larger than pore space.

2. Sedimentation: Particles settle in pores due to low velocity.

3. Inertial Impaction: Particles deviate from streamlines and hit media.

4. Diffusion: Brownian motion of very small particles (<1 µm) to media.

5. Electrostatic Attraction: Opposite charges between particle and media.

6. Biological Action (slow sand): Schmutzdecke (biological layer) removes organic matter.

5.3.2 Slow Sand Filters

• Construction: Concrete basin, ** graded sand media** (0.3–0.5 m depth), underdrain system, no gravel support.

• Working: Gravity flow, low rate (0.1–0.2 m³/m²/hr). Ripening period (5–10 days) when effluent quality improves.

• Cleaning: Scraping top 1–2 cm sand when head loss ~0.5–1 m. No backwash.

• Sketch:

  DiagramCANVAS: Slow sand filter cross-section: raw water inlet, sand bed (graded), underdrain system with perforated pipes, effluent collection, scraping mechanism.

5.3.3 Rapid Sand Filters

• Construction: Concrete basin, dual/triple media (anthracite, sand, gravel), underdrain with nozzles or wash troughs.

• Working: Gravity or pressure, high rate (5–15 m³/m²/hr). Requires pretreatment (coagulation + sedimentation).

• Backwashing: Reverse flow with air + water (air scour 2–3 min, then water 5–10 min) to expand bed 50–60%.

• Sketch:

  DiagramCANVAS: Rapid sand filter cross-section: raw water inlet, layered media (anthracite top, sand middle, gravel bottom), underdrain system with nozzles, wash water inlet, effluent outlet, wash troughs at top.

5.3.4 Comparison: Slow vs. Rapid Sand Filters

5.3.5 Design of Rapid Sand Filters

• Filter Area ($A$): $$\displaystyle A = \frac{Q_{design}}{f} $$

  • $$\displaystyle Q_{design} $$ = Design flow (m³/day)

  • $f$ = Rate of filtration (m³/m²/day) – typically 10,000–15,000 m³/m²/day.

• Number of units: Usually 2–6, with one standby.

• Dimensions: L:B = 1:1 to 1.5:1; depth = 2–3 m.

5.3.6 Filter Media & Backwash Calculations

• Effective size ($$\displaystyle D_{10} $$): Size where 10% of media by weight is finer.

• Uniformity coefficient ($$\displaystyle C_u $$): $$\displaystyle C_u = \frac{D_{60}}{D_{10}} $$; should be < 1.7 for sand.

• Backwash Velocity ($$\displaystyle v_b $$):

$$ v_b = \frac{g(\rho_p - \rho)d^2}{18\mu} \cdot \phi^3 \cdot \frac{1}{\phi_e} \quad \text{(modified Stokes)} $$

• $\phi$ = Shape factor (~0.85 for sand)

• $$\displaystyle \phi_e $$ = Porosity of expanded bed (~0.7)

• Expanded Depth ($$\displaystyle H_e $$):

$$ H_e = H \cdot \frac{1 - n}{1 - n_e} $$

• $H$ = Original bed depth

• $n$ = Original porosity (~0.4)

• $$\displaystyle n_e $$ = Expanded porosity (~0.7)

5.4 Disinfection

5.4.1 Methods

5.4.2 Break Point Chlorination

• Theory: Add chlorine in excess to oxidize all reducing agents (organic matter, ammonia, H₂S) first, then establish free chlorine residual.

• Chlorine Demand Curve:

  1. Initial: Chlorine consumed by reducing substances (no residual).

  2. Break Point: Ammonia oxidized to nitrogen; chlorine residual begins.

  3. After Break Point: Free chlorine residual ($HOCl$, $$\displaystyle OCl^- $$) increases linearly with dose.

• Goal: Dose beyond break point to ensure free chlorine residual (0.2–0.5 mg/L after 30 min contact).

• Chlorine Forms:

  • $$\displaystyle Cl_2 + H_2O \rightleftharpoons HOCl + HCl $$

  • $$\displaystyle HOCl \rightleftharpoons H^+ + OCl^- $$ (HOCl more effective, dominant at pH < 7.5)

[!TIP]

Break point dose = Chlorine to oxidize organic matter + ammonia (to nitrogen) + desired residual.

5.5 Water Softening

5.5.1 Soda Lime Process

• Chemical: $$\displaystyle Ca(OH)_2 + Na_2CO_3 $$ (soda ash) → removes Ca²⁺, Mg²⁺.

• Reaction: $$\displaystyle Ca(HCO_3)_2 + Ca(OH)_2 \rightarrow 2CaCO_3\downarrow + 2H_2O $$

  $$\displaystyle Mg(HCO_3)_2 + 2Ca(OH)_2 \rightarrow Mg(OH)_2\downarrow + 2CaCO_3\downarrow + 2H_2O $$

  (For non-bicarbonate hardness, add soda ash).

• Advantages: Cheap chemicals, simple.

• Disadvantages: Produces large sludge, not suitable for very hard water, requires skilled operation.

5.5.2 Ion Exchange Method

• Resin: Cation exchange resin (Na⁺ form) exchanges Na⁺ for Ca²⁺, Mg²⁺.

$$ 2R-Na + Ca^{2+} \rightarrow R_2-Ca + 2Na^+ $$

• Regeneration: With concentrated NaCl solution.

• Advantages: Very soft water (< 1 mg/L hardness), no sludge, automatic.

• Disadvantages: High capital/operational cost, resin fouling by iron/organics, adds sodium to water (problem for hypertensive patients).

6.0 Water Distribution Systems

6.1 Types of Distribution Networks

6.2 Layouts of Distribution Systems

• Dead-end (Tree): Simple, used in radial systems. High head loss at ends.

• Gridiron (Loop): Interconnected loops. Uniform pressure, but costly.

• Circular (Ring): Main ring around area. Best reliability.

• Hybrid: Combination (e.g., ring main with radial branches).

[!TIP]

Grid systems are preferred for cities for reliability. Dead-end used for outskirts.

6.3 Storage Reservoirs

6.3.1 Storage vs. Service Reservoirs

6.3.2 Balancing Reservoirs

• Purpose: Meet hourly demand fluctuations; maintain constant pump rate.

• Location: At distribution system extremities (elevated) or central points.

• Elevated Service Reservoirs: Provide gravity pressure; no pumping during distribution.

6.3.3 Storage Capacity by Mass Curve Method (24-hr pumping)

• Assumption: Pumping at constant rate (average daily demand), consumption varies hourly.

• Mass Curve: Cumulative inflow (straight line) vs. cumulative outflow (curve).

• Storage Required = Maximum vertical gap between curves.

• Procedure:

  1. Plot hourly demand → cumulative demand (mass curve).

  2. Draw line with slope = average hourly demand (constant pumping).

  3. Vertical difference = required storage.

  4. Capacity = Max surplus (positive gap) + emergency reserve (25% of avg. daily demand).

[!TIP]

Storage = Maximum cumulative deficit from mass curve.

6.4 Distribution System Design Considerations

• Pressure: 2–3 kg/cm² (20–30 m) at consumer end; 4–6 kg/cm² at mains.

• Velocity: 0.6–1.8 m/s (to avoid scouring/silting).

• Loops: Prefer loops for continuity.

• Pipe sizing: Based on Hardy Cross method (iterative) or formula method (e.g., $$\displaystyle Q = C V^{1.85} D^{2.63} $$).

• Materials: CI, DI, PVC, HDPE – consider pressure, corrosion, cost.

• Future expansion: Provide extra capacity.

6.5 Pumping Stations in Distribution

• Types: Low-lift, high-lift, booster.

• Energy Requirements:

  • Energy per m³: $$\displaystyle E = \frac{g H_{total}}{367 \eta} $$ (kWh/m³) for $H$ in meters.

  • Cost: Major operational cost; use variable speed drives for efficiency.

7.0 Sewerage Systems and Sewer Appurtenances

7.1 Sewer Appurtenances

7.2 Variation in Sewage Flow

1. Average Flow ($$\displaystyle Q_{avg} $$): $$\displaystyle Q_{avg} = 0.8 \times \text{water supply} \times \text{population} $$ (lit/day).

2. Dry Weather Flow (DWF): Flow during dry season; base flow = $$\displaystyle Q_{avg} + $$ industrial + infiltration.

3. Maximum Flow (Peak Flow): $$\displaystyle Q_{peak} = K \times Q_{avg} $$

   • $K$ = peak factor (1.5–3.0 depending on population).

   • Formula: $$\displaystyle K = 1 + \frac{18}{\sqrt{P}} $$ (for $P$ in 1000s) – old empirical.

   • Modern: Use ratio method or hydrograph from data.

[!TIP]

Design sewers for peak flow, but pumps and treatment units for DWF + storm flow (if combined).

7.3 Sewer Design

7.3.1 Hydraulic Design (Manning's Formula)

$$ V = \frac{1}{n} R^{2/3} S^{1/2} $$

$$ Q = A \cdot V $$

• $V$ = Velocity (m/s)

• $Q$ = Discharge (m³/s)

• $n$ = Manning's roughness coefficient (0.013–0.016 for sewers)

• $R$ = Hydraulic radius = $A/P$ (m)

• $S$ = Slope (m/m)

Self-cleansing velocity: $$\displaystyle V_{sc} = 0.9 \text{ to } 1.5 $$ m/s (to prevent siltation).

7.3.2 Design of Circular Sewers

• Flow at partial depth: Use Kutter's diagram or Boussinesq's equation.

• Simplified: For $$\displaystyle d/D < 0.5 $$, $$\displaystyle Q \propto (d/D)^{10/3} $$.

• Design steps:

  1. Estimate $$\displaystyle Q_{design} $$ (peak flow).

  2. Assume $$\displaystyle d/D = 0.5–0.75 $$ (for self-cleansing).

  3. Assume $S$ (min. 1:500 for small sewers).

  4. Calculate $D$ from Manning's formula iteratively.

  5. Check $$\displaystyle V > 0.6 $$ m/s (min) and $$\displaystyle < 2.5 $$ m/s (max to avoid erosion).

7.3.3 Sewer Design Calculations

• Example: Given $Q$, $S$, $n$, find $D$ and $d$ (flow depth).

• Use nomographs or trial-and-error with $$\displaystyle A = \frac{\pi D^2}{4} \cdot \frac{d}{D} $$ and $$\displaystyle P = \pi D \cdot \frac{d}{D} $$.

7.4 Sewer Construction Techniques

1. Trenching: Open cut (most common), trench shields for safety.

2. Laying: Bed preparation (sand/lean concrete), lower pipes carefully, jointing (rubber gasket, cement mortar).

3. Testing: Water test (pressure) or air test for leakage.

4. Backfilling: In layers, compacted.

5. Safety: Shoring, sloping, barricades, gas testing in old sewers.

7.5 Types of Sewer Networks

• Separate preferred for new developments (treatment feasible).

• Combined causes CSOs (combined sewer overflows) during storms → pollution.

8.0 Wastewater Characteristics

8.1 Physical, Chemical, Biological Parameters

8.2 Organic Matter Decomposition

1. Aerobic Stage: Aerobic bacteria oxidize organics → CO₂, H₂O, NH₃, nitrates. BOD consumed.

2. Anaerobic Stage: After DO depleted → facultative → anaerobic bacteria → CH₄, CO₂, H₂S, organic acids, NH₃. Foul odours.

3. Nitrification: $$\displaystyle NH_3 \rightarrow NO_2^- \rightarrow NO_3^- $$ (aerobic, slow).

4. Denitrification: $$\displaystyle NO_3^- \rightarrow N_2 $$ (anoxic).

8.3 Population Equivalent (PE)

• Definition: Number of persons producing same pollution load (usually BOD) as given wastewater flow.

• Formula: $$\displaystyle PE = \frac{\text{Total BOD load (kg/day)}}{0.05 \text{ kg BOD/person/day}} $$ (standard).

• Example: Industrial wastewater BOD = 300 kg/day → $$\displaystyle PE = 300 / 0.05 = 6000 $$ persons.

8.4 BOD and DO Measurements

8.4.1 5-Day BOD Test (BOD₅)

• Procedure:

  1. Dilute wastewater (to have residual DO > 1 mg/L after 5 days).

  2. Measure initial DO ($$\displaystyle DO_i $$).

  3. Incubate at 20°C for 5 days (dark).

  4. Measure final DO ($$\displaystyle DO_f $$).

• Calculation:

$$ BOD_5 = (DO_i - DO_f) \times \text{Dilution Factor} $$

• Limitation: Does not include nitrification (use seed control to suppress).

8.4.2 Temperature Correction of BOD (θ factor)

• BOD rate increases with temperature.

• Correction to 20°C:

$$ BOD_{20} = BOD_T \times \theta^{(20-T)} $$

• $\theta$ = temperature coefficient (1.135 for BOD, 1.024 for reaeration).

• $T$ = test temperature (°C).

• Example: $$\displaystyle BOD_{25} = 100 $$ mg/L → $$\displaystyle BOD_{20} = 100 \times 1.135^{(20-25)} = 100 \times 1.135^{-5} = 100 / 1.135^5 \approx 100 / 1.87 = 53.5 $$ mg/L.

8.4.3 Dissolved Oxygen (DO) Sag

• Oxygen Sag Curve: DO profile downstream of wastewater discharge.

• Causes: BOD exertion consumes DO; reaeration from atmosphere replenishes.

• Critical Point: Minimum DO location.

• Importance: Determines minimum DO for aquatic life; sets waste load allocation.

9.0 Wastewater Treatment Methods

9.1 Activated Sludge Process (ASP)

• Process: Aeration tank + secondary clarifier + sludge recirculation.

• Key Parameters:

  • F/M ratio (Food to Microorganism): 0.2–0.4 kg BOD/kg MLSS·day.

  • MLSS (Mixed Liquor Suspended Solids): 2000–4000 mg/L.

  • SRT (Solids Retention Time): 5–15 days.

  • HRT (Hydraulic Retention Time): 4–8 hours.

• Variations:

  • Conventional: Plug flow aeration.

  • Tapered Aeration: Air quantity varies along tank.

  • Step Aeration: Return sludge and waste introduced at multiple points.

  • Complete Mix: Uniform concentration; shock load resistant.

  • SBR (Sequencing Batch Reactor): Time-based (fill, react, settle, decant, idle).

9.2 Natural Treatment Methods

9.2.1 Land Treatment

9.2.2 Disposal by Dilution

• Concept: Wastewater discharged into water body with sufficient assimilative capacity.

• Requirement: Minimum DO after mixing ≥ 5 mg/L (for fish).

• Design: Use Streeter-Phelps to predict DO sag.

• Not sustainable; only for secondary effluent in large streams.

9.3 Considerations in Planning WWTP

• Site Selection: Near water body (outfall), away from residential areas, geology, accessibility, expansion space.

• Process Selection: Based on influent characteristics, effluent standards, land availability, cost, operator skill.

• Future Expansion: Modular design; land for future units.

• Sludge Management: Thickening, digestion, dewatering, disposal.

9.4 Chemical Treatment in Wastewater

• Coagulation/Flocculation: For tertiary treatment – remove suspended solids, phosphorus.

  • Alum, Ferric Chloride, Lime.

• Phosphorus Removal: Chemical precipitation (Al/Fe salts) or biological (EBPR).

• Disinfection: Chlorination, UV, Ozone (as in water treatment).

10.0 Stream Pollution and Self-Purification

10.1 Oxygen Sag Curve

• Explanation:

  1. Upstream: DO = saturation (DO_sat).

  2. Mixing Point: Wastewater (low DO) mixes → initial DO (DO_i) calculated by mass balance.

  3. Downstream: BOD exertion consumes DO (deoxygenation); reaeration adds DO.

  4. Critical Point: Where DO is minimum (D_crit). Location where $$\displaystyle t_c = \frac{1}{K_a - K_d} \ln \left[ \frac{K_a}{K_d} \left(1 - \frac{D_c}{D_a} \right) + \frac{D_c}{D_a} \right] $$.

  5. Recovery: Reaeration dominates → DO returns to DO_sat.

10.2 Deoxygenation and Re-aeration Constants

• Deoxygenation constant ($$\displaystyle K_d $$): Rate of BOD exertion. Typical 0.05–0.3 day⁻¹ at 20°C.

• Re-aeration constant ($$\displaystyle K_a $$): Rate of oxygen transfer from air. Depends on depth, velocity, turbulence. Typical 0.3–1.0 day⁻¹ at 20°C.

• Temperature Correction:

$$ K_{T} = K_{20} \cdot \theta^{(T-20)} $$

• $$\displaystyle \theta_{d} $$ = 1.135 (for deoxygenation)

• $$\displaystyle \theta_{a} $$ = 1.024 (for reaeration)

10.3 Critical Oxygen Deficit (Streeter-Phelps Equation)

• Oxygen Deficit ($D$): $$\displaystyle D = DO_{sat} - DO $$

• Equation:

$$ D_t = \frac{K_d L_0}{K_a - K_d} \left( e^{-K_d t} - e^{-K_a t} \right) + D_0 e^{-K_a t} $$

• $$\displaystyle L_0 $$ = Ultimate BOD at mixing point (mg/L)

• $$\displaystyle D_0 $$ = Initial deficit at mixing point (mg/L)

• $t$ = Time/distance downstream

• Critical Deficit ($$\displaystyle D_{crit} $$):

$$ D_{crit} = D_0 \left( \frac{K_a}{K_d} \right)^{-\frac{K_d}{K_a - K_d}} \quad \text{or} \quad D_{crit} = \frac{L_0}{1 + \frac{K_a}{K_d} \cdot \frac{K_d}{K_a}} \text{ (simplified)} $$

Actually: $$\displaystyle D_{crit} = \frac{L_0}{1 + \frac{K_d}{K_a}} $$? No.

Correct: $$\displaystyle D_{crit} = D_0 \left( \frac{K_a}{K_d} \right)^{-\frac{K_d}{K_a - K_d}} $$ is standard.

• Critical Time ($$\displaystyle t_c $$):

$$ t_c = \frac{1}{K_a - K_d} \ln \left( \frac{K_a}{K_d} \right) + \frac{1}{K_a - K_d} \ln \left(1 + \frac{D_0 K_a}{L_0 K_d} \right) $$

If $$\displaystyle D_0 = 0 $$ (typical), $$\displaystyle t_c = \frac{1}{K_a - K_d} \ln \left( \frac{K_a}{K_d} \right) $$.

• Critical DO: $$\displaystyle DO_{crit} = DO_{sat} - D_{crit} $$.

[!TIP]

If $$\displaystyle K_a > K_d $$, sag curve shows minimum DO. If $$\displaystyle K_a \leq K_d $$, DO decreases continuously → severe pollution.

11.0 Stormwater and Combined Sewers

11.1 Rational Method for Stormwater Sewer Design

• Formula: $$\displaystyle Q = C \cdot i \cdot A $$

  • $Q$ = Peak discharge (m³/s or cumec)

  • $C$ = Runoff coefficient (dimensionless)

  • $i$ = Rainfall intensity (mm/hr or m/s) for time of concentration ($$\displaystyle t_c $$)

  • $A$ = Catchment area (ha or km²)

• Steps:

  1. Determine $A$, $C$ (from land use table).

  2. Calculate $$\displaystyle t_c $$ (Kirpich formula: $$\displaystyle t_c = 0.0195 L^{0.77} S^{-0.385} $$ for overland flow; $L$ in m, $S$ slope).

  3. From IDF curve, get $i$ for $$\displaystyle t_c $$ and design storm (e.g., 5-year, 30-min).

  4. Compute $Q$.

• Design: Size sewer for $Q$ with Manning's formula.

11.2 Design of Combined Sewers

• Design Flow = Sanitary Flow + Storm Flow.

  • Sanitary flow: $$\displaystyle Q_{san} = \text{peak sewage flow} $$ (from 7.2).

  • Storm flow: $$\displaystyle Q_{storm} = C \cdot i \cdot A $$ (rational method).

• Combined Flow: $$\displaystyle Q_{combined} = Q_{san} + Q_{storm} $$.

• Consideration: During dry weather, only $$\displaystyle Q_{san} $$ flows; during storm, combined.

• Overflow Provision: Sewer overflow (SO) or CSO structures to bypass excess flow to water body during storms (to prevent surcharge).

11.3 Runoff Calculations

• Runoff Coefficient ($C$):

  | Surface | C | |-------------|-------| | Roofs, paved areas | 0.9–1.0 | | Residential areas | 0.4–0.6 | | Parks, open spaces | 0.1–0.3 | | Agricultural | 0.2–0.5 |

• Time of Concentration ($$\displaystyle t_c $$): Time for water from farthest point to reach outlet.

  • Kirpich: $$\displaystyle t_c = 0.0195 \frac{L^{0.77}}{S^{0.385}} $$ (minutes; $L$ in m, $S$ = slope m/m).

  • Kerby-Hathaway: $$\displaystyle t_c = \frac{L^{0.47}}{S^{0.385}} $$ (for overland flow).

• Rainfall Intensity ($i$): From IDF (Intensity-Duration-Frequency) curves for the region.

  • Formula: $$\displaystyle i = \frac{A}{(t + B)^n} $$ (empirical).

[!TIP]

For separate storm sewers, design for 5–10 year storm; for combined, often 1–2 year (due to cost), with overflows for higher storms.

END OF UNIT 3 NOTES
Always cross-check with latest BIS/IS codes (e.g., IS 456 for concrete, IS 1742 for water supply, IS 5572 for sewer design).