Environmental Engineering-I (CE-602) - Unit 5 Short Notes

UNIT 5: WATER SUPPLY AND WASTEWATER ENGINEERING

1.0 WATER DEMAND AND POPULATION FORECASTING

1.1 Factors Affecting Per Capita Water Demand

• Climatic Conditions: Temperature, humidity, rainfall (higher in hot/dry climates).

• Pressure in Distribution System: Low pressure reduces consumption.

• System Losses: Leakage, unauthorized connections increase apparent demand.

• Economic Status & Metering: Metered supplies reduce wastage; higher income increases use.

• Industrial/Commercial Activities: Concentration of industries, hotels, offices.

• Sanitation & Water Price: Availability of sewerage increases demand; higher price reduces consumption.

• Other: Population density, housing standards, day/night variation, water availability.

1.2 Types of Water Demand

Total Water Requirement = (Domestic + Non-Domestic + Public) × (1 + Losses%) + Fire Demand

1.3 Population Forecasting Methods

1.3.1 Arithmetic Increase Method

Assumes constant population increase per decade.

$$P_n = P_0 + n \cdot \bar{x}$$

Where, $$\displaystyle \bar{x} = \frac{(P_1 - P_0) + (P_2 - P_1) + ...}{n} $$

1.3.2 Incremental Increase Method

Similar to arithmetic but increase itself increases.

$$P_n = P_0 + n \cdot \bar{x} + \frac{n(n+1)}{2} \cdot \bar{y}$$

Where, $$\displaystyle \bar{y} = \frac{(\Delta_1 - \bar{x}) + (\Delta_2 - \bar{x}) + ...}{n-1} $$; $\Delta$ = decadal increase.

1.3.3 Geometric Progression Method

Assumes constant growth rate ($r$).

$$P_n = P_0 (1 + r)^n$$

$r$ = average of $$\displaystyle \frac{P_1}{P_0} - 1 $$, $$\displaystyle \frac{P_2}{P_1} - 1 $$, etc.

1.3.4 Logistic Curve Method

Most realistic for mature cities. S-shaped curve approaching saturation population ($$\displaystyle P_s $$).

$$\boxed{P = \frac{P_s}{1 + e^{A - Bt}}}$$

Where $P$ = population at time $t$, $$\displaystyle P_s $$ = saturation population, $A$ & $B$ = constants. Determination:

1. From graph: Plot $P$ vs. $t$, draw tangent at inflection point (where $$\displaystyle P = P_s/2 $$). $$\displaystyle P_s $$ = population where tangent meets time-axis.

2. From data (3 points): Use equations at $$\displaystyle t_1, t_2, t_3 $$ to solve for $$\displaystyle A, B, P_s $$.

[!TIP] Exam Focus: Logistic method is frequently asked. Practice deriving $A, B$ from given 3-4 census data points.

1.4 Fire Demand

1.4.1 Definition & Importance

Extra water required at high flow rates for firefighting, beyond normal consumption. Critical for designing pumping capacity and pipe sizes.

1.4.2 Influencing Factors

Population, building density/type (wooden vs RCC), street width, available pressure, proximity of fire stations.

1.4.3 Empirical Formulas

Where $P$ = population in thousands.

1.4.4 Design Fire Demand

Fire demand is added to maximum daily demand for designing pumps and peak hourly demand for distribution mains.

2.0 SOURCES OF WATER AND INTAKE STRUCTURES

2.1 Sources of Water

2.2 Intake Structures

2.2.1 Purpose & Types

To draw water from source and convey to treatment plant. Types: River, Lake, Reservoir, Canal intake (common in irrigation canals).

2.2.2 Selection Factors

Source depth, flow variation, sediment load, accessibility, protection from floods/vandalism, foundation conditions.

2.2.3 Canal Intake (with Sketch)

3.0 WATER QUALITY AND ANALYSIS

3.1 Water Quality Standards (BIS/IS 10500:2012)

3.2 Physical Examination

• Temperature: Affects biological activity, viscosity.

• Colour & Odour: Indicates organic pollution, industrial waste.

• Turbidity: Measured by Nephelometer (NTU) or Jackson Candle (JTU).

• Total Solids: Suspended (filterable) + Dissolved (after evaporation).

3.3 Chemical Examination

• pH: Acidity/Alkalinity.

• Hardness: Ca²⁺, Mg²⁺ (EDTA titration).

• Chlorides (Cl⁻): Silver nitrate titration (Mohr's method).

• Sulphates (SO₄²⁻): Turbidimetric method.

• Iron/Manganese: Colorimetric or titrimetric.

• Nitrates (NO₃⁻): Phenoldisulphonic acid or UV spectrophotometry.

• Dissolved Gases: CO₂ (affects pH/corrosion), O₂ (indicates freshness).

3.4 Biological Examination

3.4.1 Waterborne Diseases

• Bacterial: Cholera (Vibrio cholerae), Typhoid (Salmonella typhi), Dysentery (Shigella).

• Viral: Hepatitis A, Poliomyelitis.

• Protozoan: Giardiasis (Giardia lamblia), Amoebiasis (Entamoeba histolytica).

• Helminthic: Roundworm, Hookworm.

3.4.2 Indicator Organisms

Coliforms (total & fecal) indicate fecal pollution and possible pathogen presence.

• Total Coliform Index: >0/100 mL = unsatisfactory.

• Escherichia coli (E-coli): Specific fecal coliform; confirms recent fecal contamination.

3.4.3 Most Probable Number (MPN) Test

Principle: Statistical estimation of coliform density based on gas production in lactose broth tubes. Procedure (3-tube):

1. Inoculate 3 tubes of Lauryl Tryptose Broth (presumptive test) with 10 mL, 1 mL, 0.1 mL sample.

2. Incubate 35°C, 48 hrs. Note positive (gas) tubes.

3. Confirm positive tubes in Brilliant Green Lactose Bile Broth.

4. Read MPN/100 mL from standard statistical table based on number of positive tubes in each dilution.

[!TIP] Common Pitfall: MPN is an estimate, not exact count. Always report as "MPN/100 mL".

4.0 WATER TREATMENT PROCESSES - UNIT OPERATIONS

4.1 Screening, Aeration, Mixing

• Screening: Remove large debris (racks, screens).

• Aeration: Remove CO₂, O₂, volatile organics, oxidize Fe/Mn.

• Mixing: Rapid mix for coagulant dispersion (G = 500-1000 s⁻¹, T = 30-60 sec).

4.2 Coagulation and Flocculation

4.2.1 Purpose

Destabilize colloidal particles (charge neutralization) and form larger flocs (flocculation).

4.2.2 Common Coagulants

4.2.3 Factors Affecting Coagulation

• pH: Alum optimum 5.5-7.5; Ferric salts 5-8.5.

• Temperature: Lower T slows floc formation.

• Mixing Intensity: Rapid mix for dispersion, slow mix (flocculation) for aggregation (G = 20-80 s⁻¹, T = 20-30 min).

• Coagulant Dose: Determined by jar test.

• Alkalinity: Consumed by H⁺ from hydrolysis; may need lime addition.

4.3 Sedimentation

4.3.1 Theory - Stokes' Law

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

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

Where $v$ = settling velocity (m/s), $g$ = gravity, $$\displaystyle \rho_p $$, $\rho$ = particle & water density, $d$ = diameter, $\mu$ = viscosity. Assumptions: Spherical particles, still water, no wall effect, particle size > 1 µm. Limitations: Not for flocculent/zone settling.

4.3.2 Design Parameters

• Surface Overflow Rate (Hazen's velocity): $Q/A$ (m³/m²/day). Design basis. Typical: 32-40 m³/m²/day for plain, 80-120 for coagulated.

• Detention Time: 2-4 hrs (plain), 1.5-3 hrs (coagulated).

• Depth: 3-5 m (provides storage, short-circuits flow).

• L/B Ratio: 2:1 to 5:1 (horizontal flow tanks).

4.3.3 Types

• Horizontal Flow: Common, rectangular.

• Radial Flow: Circular, central inlet, peripheral weir.

• Hopper Bottom: Sludge collection by gravity.

4.3.4 Design Problem

Given $Q$, overflow rate $$\displaystyle V_o $$, detention time $$\displaystyle t_d $$:

1. Area, $$\displaystyle A = Q / V_o $$

2. Volume, $$\displaystyle V = Q \times t_d $$

3. Depth, $$\displaystyle D = V / A $$

4. Choose $L/B$ ratio (e.g., 3:1), then $$\displaystyle L = \sqrt{3A} $$, $$\displaystyle B = L/3 $$. Ensure $$\displaystyle L < 100 $$ m.

4.4 Filtration

4.4.1 Mechanisms

• Straining: Removal of particles > pore size.

• Sedimentation: Inertial impaction in pores.

• Adsorption: Van der Waals forces, electrostatic.

• Biological: Schmutzdecke layer (slow sand).

4.4.2 Slow Sand Filter

• Construction: Open basin, 0.9-1.1 m sand (effective size 0.15-0.30 mm), underdrains, gravel support.

• Working: Schmutzdecke (biological layer) forms on top after 1-3 weeks ("ripening"). Primary removal mechanism is biological.

• Cleaning: Top 1-2 cm scraped manually when head loss ~0.5 m.

• Advantages: Simple, low cost, excellent quality, no chemicals.

• Disadvantages: Large area, slow, manual cleaning, sensitive to turbidity.

4.4.3 Rapid Sand Filter

• Construction: Enclosed, multi-unit. Media: sand (ES 0.5-0.7 mm) over gravel. Underdrain system with nozzles/leaching wells.

• Working: Physical straining + adsorption. Requires coagulation pretreatment.

• Backwashing: Required when head loss 2-2.5 m or after fixed time. Expanded bed by reverse flow (5-15 min). Velocity = backwash velocity.

• Advantages: Small area, automatic, high rate.

• Disadvantages: Complex, needs pretreatment, frequent backwash.

4.4.4 Comparison

4.4.5 Backwash Calculations

Expanded Depth, $$\displaystyle h_e $$:

$$\boxed{h_e = \frac{h_o}{1 - n}}$$

Where $$\displaystyle h_o $$ = original depth, $n$ = porosity (original). Backwash Velocity, $$\displaystyle V_b $$:

$$\boxed{V_b = \frac{\phi \cdot V_f}{n_e}}$$

Where $\phi$ = shape factor (0.85 for sand), $$\displaystyle V_f $$ = filtering velocity, $$\displaystyle n_e $$ = expanded porosity (0.7-0.8).

4.4.6 Forces in Filtration

• Sedimentation: Inertial impaction.

• Van der Waals attraction.

• Electrostatic attraction.

• Bridging/Straining.

• Biological growth (slow sand).

4.5 Disinfection

4.5.1 Purpose & Methods

Kill/inactivate pathogens. Methods: Chlorination (most common), Ozonation, UV radiation, Chloramines.

4.5.2 Break Point Chlorination

Theory: Add chlorine until all reducing substances (H₂S, Fe²⁺, Mn²⁺, NH₃, organics) are oxidized and free chlorine residual appears. Chlorine Demand Curve:

1. Zone I: Cl₂ reacts with reducing agents (H₂S, Fe²⁺, etc.) – no residual.

2. Zone II: Cl₂ oxidizes NH₃ to chloramines (combined chlorine) – still no free Cl₂.

3. Break Point: All NH₃ oxidized to N₂, free Cl₂ begins to appear.

4. Zone IV: Free Cl₂ residual increases linearly with dose. Significance: Ensides all pathogens killed, minimizes THM formation, provides residual in distribution.

Dose Calculation:

$$\text{Chlorine Dose} = \text{Demand} + \text{Desired Residual}$$

Where Demand = Cl₂ consumed by impurities.

4.5.3 Factors Affecting Chlorination

• Contact Time (CT): $C \times t$ (concentration × time) is critical for kill.

• pH: HOCl (more effective) dominates at low pH (<7.5).

• Temperature: Higher T increases kill rate.

• Turbidity: Shields microorganisms.

• Nature of Organisms: Viruses/ cysts more resistant.

5.0 WATER DISTRIBUTION SYSTEMS AND RESERVOIRS

5.1 Layouts of Distribution Systems

5.2 Service and Storage Reservoirs

5.2.1 Differentiation

5.2.2 Functions of Distribution Reservoirs

1. Balance hourly demand variations.

2. Maintain constant pressure in mains.

3. Provide emergency storage (fire, breakdown).

4. Allow pump size reduction (operate at constant rate).

5.2.3 Location

• Elevated: On high ground within distribution area for gravity flow.

• Ground: At pumping station or high point; needs booster pumps.

• Central to service area, at highest feasible elevation.

5.2.4 Storage Capacity - Mass Curve Method

For 24-hr pumping:

1. Plot cumulative demand vs. time (24 hrs) from hourly demand factors.

2. Plot cumulative supply (constant line if uniform pumping).

3. Storage required = maximum vertical gap between demand and supply curves.

4. Balancing reservoir fills when supply > demand, empties when demand > supply.

Example: If max gap = 1.2 ML, storage = 1.2 ML + 25% safety.

6.0 WASTEWATER (SEWAGE) CHARACTERISTICS AND QUANTITY

6.1 Definition & Constituents

Wastewater/Sewage: Used water from community + infiltrated groundwater. Contains:

• Organic matter (proteins, carbs, fats).

• Inorganic solids (silt, grit, minerals).

• Pathogens (bacteria, viruses).

• Nutrients (N, P).

• Toxic substances (heavy metals, organics).

6.2 Characteristics

6.3 Significance of Analysis

• Determines treatment type/degree.

• Compliance with discharge standards.

• Design of sewers, treatment units.

• Health risk assessment.

• Industrial waste contribution identification.

6.4 Population Equivalent (PE)

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

$$\boxed{PE = \frac{\text{Total BOD load (kg/day)}}{0.05 \text{ kg BOD/person/day}}}$$

(Standard per capita BOD contribution = 50 g/day) Example: Industry discharging 300 kg BOD/day → PE = 300/0.05 = 6000 persons.

6.5 Variation in Sewage Flow

• Average Daily Flow (ADF): Yearly average.

• Dry Weather Flow (DWF): Flow during dry season (no stormwater). Design basis for treatment plants.

• Minimum Flow: Nighttime, ~50% of ADF.

• Maximum Flow: Peak hourly, 2-3 times ADF (due to morning/evening peaks).

• Storm Flow: In combined systems, includes runoff (very high, short duration).

Factors: Water consumption pattern, population habits, infiltration, rainfall, industrial discharge timing.

6.6 Estimation of Sewage Quantity

1. Based on Water Supply: Sewage flow = 70-80% of water supplied (accounting for losses, seepage).

$$Q_{sewage} = 0.8 \times Q_{water}$$

2. Based on Density: $$\displaystyle Q = \text{Population} \times \text{per capita sewage} \times \text{density factor} $$.

3. Infiltration/Inflow: Add 3-10% of DWF for sewers.

6.6.1 Combined System - Rational Formula

For stormwater contribution:

$$\boxed{Q = C \cdot i \cdot A}$$

Where:

• $Q$ = peak runoff (m³/s)

• $C$ = coefficient of runoff (0.4-0.9, depends on imperviousness)

• $i$ = rainfall intensity (mm/hr) for design storm duration = time of concentration

• $A$ = catchment area (ha)

7.0 SEWERAGE SYSTEM - DESIGN AND APPURTENANCES

7.1 Types of Sewer Networks

7.2 Sewer Appurtenances

7.2.1 Manholes

Purpose: Access for inspection, cleaning, junction, change direction/gradient. Types:

• Straight/Inspection: On straight runs.

• Junction: At sewer intersections.

• Drop: For vertical drop > 0.8 m (inside/outside drop).

• Flushing: At dead ends (storage + valve). Components: Cover (circular, cast iron), Chamber (brick/ concrete), Benching (sloping platform to guide flow).

7.2.2 Lamp Holes / Inspection Holes

Light, shallow openings (no ladder) for quick visual check in small sewers.

7.2.3 Others

• Inlets: Collect surface runoff (gullies).

• Traps: Prevent gas entry (water seal).

• Flushing Tanks: At dead ends for periodic scouring.

• Stormwater Overflows (SWO): In combined systems to divert excess flow.

• Inverted Siphons: Pressure conduits under obstacles (must be cleaned frequently).

7.3 Sewer Hydraulics

7.3.1 Flow in Sewers

Open channel flow, partial flow (not full). Design for self-cleansing velocity (0.6-0.9 m/s at DWF, >0.9 m/s at max flow).

7.3.2 Design Formulas

Manning's Formula (most common):

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

Where:

• $V$ = velocity (m/s)

• $n$ = Manning's roughness (0.013-0.016 for concrete, 0.015-0.017 for brick)

• $R$ = hydraulic radius = $A/P$ (m)

• $S$ = slope (m/m) Discharge: $$\displaystyle Q = A \cdot V $$

Chezy's Formula: $$\displaystyle V = C \sqrt{R S} $$, where $$\displaystyle C = \frac{1}{n} R^{1/6} $$.

7.3.3 Design Problem (Circular Sewer, Partial Flow)

Given: Diameter $D$, depth of flow $d$, slope $S$, $n$.

1. Calculate area, $$\displaystyle A = \frac{D^2}{4} \left( \theta - \sin\theta \cos\theta \right) $$, where $$\displaystyle \theta = 2 \cos^{-1}(1 - 2d/D) $$.

2. Wetted perimeter, $$\displaystyle P = \theta D $$.

3. Hydraulic radius, $$\displaystyle R = A/P $$.

4. Velocity, $$\displaystyle V = \frac{1}{n} R^{2/3} S^{1/2} $$.

5. Discharge, $$\displaystyle Q = A \cdot V $$.

7.3.4 Self-Cleansing Velocity

Minimum velocity at maximum flow (or DWF for large pipes) to prevent silt deposition.

$$V_{sc} = \frac{1}{n} R^{2/3} S^{1/2} \geq 0.9 \text{ m/s}$$

Adjust slope or diameter to achieve.

7.4 Construction and Laying

7.4.1 Process

1. Trenching: Excavate to required depth & width (with sheeting/shoring if needed).

2. Bedding: Provide uniform, stable base (sand, concrete).

3. Laying: Lower pipes, join (bell/spigot with gasket/mortar), align & grade.

4. Jointing: Cement mortar, bitumen, rubber gaskets.

7.4.2 Testing & Inspection

• Water Test: Fill sewer, check for leakage (max 0.1 L/m²/hr for concrete).

• Smoke Test: Introduce smoke, check for leaks at joints/connections.

• TV Inspection: Modern method for cracks, deformation, root intrusion.

7.4.3 Quality Control & Safety

• QC: Check alignment, grade, joint quality, bedding.

• Safety: Trench shoring, barricades, lighting, gas testing (H₂S, CH₄), PPE.

8.0 WASTEWATER TREATMENT AND DISPOSAL

8.1 Natural Methods

8.1.1 Dilution & Self-Purification

Stream receives wastewater → deoxygenation (BOD oxidation) → reoxygenation (atmospheric absorption) → recovery. Oxygen Sag Curve:

8.1.2 Land Treatment

• Slow Rate: Irrigation, high renovation.

• Rapid Infiltration: Percolation to groundwater (high rate).

• Overland Flow: Runoff over vegetated slopes.

• Subsurface Flow: Trench/ bed, no surface ponding.

8.2 Unit Processes

8.2.1 Preliminary

Screening (bar screens), grit removal (velocity control 0.3 m/s), comminution (grinders), flow equalization.

8.2.2 Primary Treatment

Primary Sedimentation Tank: Removes settleable solids (30-60% BOD, 50-70% TSS). Design Parameters:

• Surface overflow rate: 30-50 m³/m²/day.

• Detention time: 1.5-2.5 hrs.

• Depth: 3-4 m.

• Sludge removal: 2-4 hrs intervals.

8.2.3 Activated Sludge Process

Aim: Biological oxidation of dissolved/colloidal organics. Process Flow: Influent + Return Activated Sludge (RAS) → Aeration Tank (aeration by diffusers/mechanical) → Secondary Clarifier → Effluent + Waste Activated Sludge (WAS). Key Parameters:

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

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

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

• DO in Aeration Tank: >2 mg/L. Modifications: Trickling filter, Oxidation ditch, Sequencing batch reactor (SBR).

8.2.4 Sludge Digestion & Disposal

• Thickening: Gravity thickener, flotation.

• Anaerobic Digestion: Heated (35°C) closed tank, produces biogas (CH₄). Stabilizes sludge.

• Dewatering: Drying beds, centrifuges, filter presses.

• Disposal: Landfilling, incineration, land application (after stabilization).

8.3 Water Softening

8.3.1 Need

Remove hardness (Ca²⁺, Mg²⁺) to prevent scaling, soap wastage.

8.3.2 Methods

Lime-Soda Process (Chemical Precipitation):

• Reactions:

$$\text{Ca(HCO}_3)_2 + \text{Ca(OH)}_2 \rightarrow 2\text{CaCO}_3\downarrow + 2\text{H}_2\text{O}$$

$$\text{Mg(HCO}_3)_2 + 2\text{Ca(OH)}_2 \rightarrow \text{Mg(OH)}_2\downarrow + 2\text{CaCO}_3\downarrow + 2\text{H}_2\text{O}$$

$$\text{MgSO}_4 + \text{Ca(OH)}_2 \rightarrow \text{Mg(OH)}_2\downarrow + \text{CaSO}_4$$

• Advantages: Cheap, handles high hardness.

• Disadvantages: Sludge production, needs skilled operation, non-carbonate hardness not fully removed.

Ion Exchange (Zeolite Process):

• Resin (Na⁺ form): $$\displaystyle \text{Ca}^{2+} + 2\text{Na-Z} \rightarrow \text{Ca-Z}_2 + 2\text{Na}^+ $$

• Regeneration: With concentrated NaCl solution.

• Advantages: Complete softening, compact, automatic.

• Disadvantages: High cost, resin fouling by organics/iron, no removal of anions.

8.3.3 Comparison

9.0 STREAM POLLUTION ANALYSIS (OXYGEN DEMAND)

9.1 Biochemical Oxygen Demand (BOD)

9.1.1 Definition & Significance

BOD₅: Oxygen consumed (mg/L) by microorganisms in oxidizing organic matter in 5 days at 20°C in dark. Measure of biodegradable organic pollution.

9.1.2 5-Day BOD Test (Dilution Method)

1. Dilute sample (1-5%) with seeded (activated sludge) aerated water (DO ~8-9 mg/L).

2. Fill initial and final BOD bottles (300 mL).

3. Measure Initial DO (DO₀) immediately.

4. Incubate final bottle at 20°C, dark, 5 days.

5. Measure Final DO (DO₅).

6. Calculation (with seed correction):

$$\text{BOD}_5 = \frac{(DO_0 - DO_5) - (B_c \times f)}{P}$$

Where:

*   $$\displaystyle B_c $$ = DO drop in **seed control** (dilution water + seed only).

*   $$\displaystyle f = \frac{\text{Volume of seed in sample}}{\text{Volume of seed in control}} $$ (usually seed volume in sample / seed volume in control).

*   $P$ = Dilution factor (Volume of sample / Total volume of diluted mixture).

Example: If 3 mL sample + 297 mL seeded dilution water → $$\displaystyle P = 3/300 = 0.01 $$.

9.1.3 BOD Kinetics

Ultimate BOD ($$\displaystyle L_0 $$): Total oxygen required for complete oxidation.

$$\boxed{L_t = L_0 (1 - e^{-k_d t})}$$

Where $$\displaystyle L_t $$ = BOD exerted in $t$ days, $$\displaystyle k_d $$ = deoxygenation constant (day⁻¹).

9.1.4 Temperature Correction

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

Where $\theta$ = temperature coefficient (1.135 for $$\displaystyle k_d $$, 1.024 for $$\displaystyle k_a $$).

9.2 Oxygen Deficit (D) & Sag Curve

Oxygen Deficit, $D$: $$\displaystyle D = D_s - D_t $$, where $$\displaystyle D_s $$ = saturation DO at stream temperature, $$\displaystyle D_t $$ = actual DO at time $t$.

9.3 Streeter-Phelps Equation

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

Where:

• $D$ = oxygen deficit at time $t$ (mg/L)

• $$\displaystyle L_0 $$ = ultimate BOD of wastewater (mg/L)

• $$\displaystyle K_d $$ = deoxygenation constant (day⁻¹)

• $$\displaystyle K_a $$ = reaeration constant (day⁻¹)

• $$\displaystyle D_0 $$ = initial deficit at $$\displaystyle t=0 $$ (mg/L)

• $t$ = time/distance downstream (convert using stream velocity).

9.3.1 Critical Oxygen Deficit ($$\displaystyle D_c $$) & Time ($$\displaystyle t_c $$)

Occurs where $$\displaystyle dD/dt = 0 $$.

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

If $$\displaystyle D_0 $$ is negligible:

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

$$\boxed{D_c = \frac{L_0}{K_a - K_d} \left( K_d^{K_d/(K_a-K_d)} - K_a^{K_d/(K_a-K_d)} \right)}$$

9.3.2 BOD at Critical Point

$$L_{t_c} = L_0 (1 - e^{-K_d t_c})$$

9.3.3 Comprehensive Stream Pollution Problem

Given: Stream flow $$\displaystyle Q_s $$, wastewater flow $$\displaystyle Q_w $$, DO sat. $$\displaystyle D_s $$, wastewater BOD₅, temperature, velocity, $$\displaystyle k_d(20) $$, $$\displaystyle k_a(20) $$. Steps:

1. Temperature correction: $$\displaystyle k_d(T) = k_d(20) \cdot 1.135^{(T-20)} $$, $$\displaystyle k_a(T) = k_a(20) \cdot 1.024^{(T-20)} $$.

2. Ultimate BOD of wastewater, $$\displaystyle L_0 $$: $$\displaystyle L_0 = \frac{\text{BOD}_5}{1 - e^{-k_d \cdot 5}} $$.

3. Initial BOD at mixing point, $$\displaystyle L_0' $$: $$\displaystyle L_0' = L_0 \cdot \frac{Q_w}{Q_s + Q_w} $$ (assuming complete mixing).

4. Initial deficit, $$\displaystyle D_0 $$: $$\displaystyle D_0 = D_s - DO_{\text{mixed}} $$, where $$\displaystyle DO_{\text{mixed}} = \frac{Q_s \cdot DO_s + Q_w \cdot DO_w}{Q_s + Q_w} $$ (usually $$\displaystyle DO_w \approx 0 $$).

5. Time to critical point, $$\displaystyle t_c $$: Use formula (with $$\displaystyle D_0 $$).

6. Distance to critical point, $$\displaystyle x_c = t_c \times \text{stream velocity} $$.

7. Critical deficit, $$\displaystyle D_c $$: Use formula.

8. BOD at critical point, $$\displaystyle L_{t_c} $$: $$\displaystyle L_0' (1 - e^{-k_d t_c}) $$.

[!TIP] Exam Focus: Streeter-Phelps problems are highly recurrent. Always correct $$\displaystyle k_d $$, $$\displaystyle k_a $$ for temperature first. Assume $$\displaystyle D_0 $$ from mixing calculation if not given.

10.0 PUBLIC HEALTH AND ENVIRONMENTAL ASPECTS

10.1 Role of Sewerage Systems

• Public Health: Remove excreta/wastewater → break disease transmission (fecal-oral route).

• Environmental Protection: Prevent surface/groundwater pollution, protect aquatic life.

• Sustainable Development: Enable urbanization, water reuse (treated wastewater), nutrient recovery.

10.2 Waterborne Diseases (See 3.4.1)

Transmission: Ingestion of contaminated water/food. Control: Safe water supply, sanitation, hygiene.

10.3 Water Quality Standards (See 3.1)

BIS/WHO standards ensure water is safe for human consumption. Parameters set for physical acceptability, chemical safety, microbiological purity.

END OF UNIT 5 NOTES