UNIT 2: WATER SUPPLY AND WASTEWATER ENGINEERING

1. WATER DEMAND AND POPULATION FORECASTING

Factors Affecting Per Capita Water Demand

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

• Living Standards: Socio-economic status, house connections, plumbing fixtures.

• Industrial & Commercial Activities: Proportion of industries, commercial establishments.

• Pressure in Distribution System: Higher pressure increases consumption.

• Metering & Pricing: Metered supply reduces wastage; flat rate encourages excess use.

• Sanitation & Public Conveniences: Availability of public taps, standposts.

• Water Quality: Poor quality may reduce consumption or increase demand for alternative sources.

• System Losses: Leakage, unauthorized connections (unaccounted-for water).

[!TIP] Exam: Always list 5-6 factors with brief explanation. Link factors to design implications (e.g., high pressure requires larger pipes/pumps).

Fire Demand

• Definition: The quantity of water required to fight a fire, expressed in L/s or m³/day. It is a peak, intermittent demand.

• Importance: Critical for designing distribution mains, pumps, and storage reservoirs to ensure adequate pressure and flow during emergencies.

• Factors Influencing Fire Demand:

  • Population (but not linearly – buildings matter more).

  • Type, density, and height of buildings.

  • Fire hazard classification of the area.

  • Availability of other firefighting facilities.

  • Fire regulations and standards (e.g., NFPA).

• Estimation Formulas:

  1. Kuchling's Formula:

$$Q = 3182 \sqrt{P} \quad \text{(L/s)}$$

    where $P$ = population in thousands.

2.  **Boston's Formula (Freeman's Formula):**

$$Q = 1020 \sqrt{P} \quad \text{(for first 30 min)}$$

$$Q = 6360 \sqrt{P} \quad \text{(for next 30 min)}$$

    where $P$ = population in thousands.

3.  **National Board of Fire Underwriters (USA):**

$$Q = 4637 \sqrt{P} \left(1 - 0.01 \sqrt{P}\right) \quad \text{(L/s)}$$

    for $$\displaystyle P < 500,000 $$.

\boxed{Q = 3182 \sqrt{P} \ \text{(Kuchling's)}}

[!TIP] Exam: Fire demand is not added directly to average daily demand. It is considered as a peak hourly demand factor or for sizing critical mains/reservoirs.

Variation in Water Demand

Population Forecasting Methods

1. Arithmetic Increase Method:

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

where $$\displaystyle \bar{x} = \frac{P_2 - P_0}{t_2 - t_0} $$ (average decadal increase). Assumes constant growth rate. Suitable for **large, old cities**.

2. Incremental Increase Method:

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

where $$\displaystyle \bar{y} = \frac{(P_2-P_1) - (P_1-P_0)}{t_2 - t_0} $$ (average of incremental increases). Accounts for **accelerating/decelerating** growth. Suitable for **developing towns**.

3. Logistic Curve Method (S-Curve):

   Model:

$$P_t = \frac{P_s}{1 + e^{-r(t-t_0)}}$$

where:

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

*   $$\displaystyle P_s $$ = **Saturation (Carrying) Population** (ultimate limit)

*   $r$ = **Growth Coefficient** (intrinsic rate)

*   $$\displaystyle t_0 $$ = **Inflection Point Time** (when growth rate is max, $$\displaystyle P = P_s/2 $$)

**Determination of $$\displaystyle P_s $$ and $r$:**

From two known points $$\displaystyle (t_1, P_1) $$ and $$\displaystyle (t_2, P_2) $$:

$$\ln\left(\frac{P_s - P_1}{P_1}\right) - \ln\left(\frac{P_s - P_2}{P_2}\right) = r(t_2 - t_1)$$

Solve iteratively for $$\displaystyle P_s $$, then find $r$. $$\displaystyle t_0 $$ found from $$\displaystyle P_{t_0} = P_s/2 $$.

> [!TIP] Exam: **Logistic method is most important.** Be prepared to solve for $$\displaystyle P_s $$, $r$, and forecast $$\displaystyle P_{t+20} $$ given 3-4 population data points. Show iterative steps clearly.

Design Period & Population Projection

• Design Period: The future time horizon (e.g., 30-40 years) for which the water supply scheme is designed. Based on:

  • Useful life of components (treatment plant: 20-25 yrs, pipelines: 50+ yrs).

  • Growth rate of population/area.

  • Financial constraints and phased development.

• Projection: Forecast population for design year (end of design period) using selected method. Often, a "sanctioned population" is adopted for initial phase.

2. WATER SOURCES AND INTAKE STRUCTURES

Sources of Water: Merits & Demerits

Intake Structures

• Purpose: To safely withdraw water from source and convey to treatment plant, preventing entry of debris, floating matter, and silt.

• Types:

  • Canal Intake: From a canal. Simple, with screens and a sump well.

  • River Intake: Tower or crib structure in river. Must consider scour depth, siltation, flood levels, navigation. Often with bends to face upstream flow.

  • Reservoir Intake: Multi-level (at different depths) to draw water from best quality zone (temperature, quality).

• Factors Governing Selection:

  1. Location: Near treatment plant, away from pollution sources, stable geology.

  2. Depth: Below minimum water level, above maximum scour level.

  3. Protection: Against floods, ice, debris, vessels, sedimentation.

  4. Hydrology & Sedimentation: Flow pattern, silt load, reservoir stratification.

  5. Constructibility & Cost.

Infiltration Galleries

• Definition: Horizontal or slightly sloping tunnels/pipe networks below the water table in alluvial formations, with open joints/perforations to collect groundwater.

• Use: For subsurface water abstraction from riverbeds (underflow), lake beds, or unconfined aquifers. Provides natural filtration.

• Merits: Water is filtered naturally, low silt, stable yield.

• Demerits: High construction cost, requires high water table, susceptible to contamination if source is polluted.

3. WATER QUALITY AND STANDARDS

Water Quality Parameters

Water Quality Standards

• BIS (IS 10500:2012): Indian Standards for drinking water. Specifies permissible limits for ~40 parameters (e.g., Turbidity < 1 NTU, pH 6.5-8.5, Fluoride < 1.5 mg/L, Arsenic < 0.01 mg/L, Total Coliforms absent in 100 mL).

• WHO Guidelines: International reference, often more stringent for some chemicals.

• EPA (USA): National Primary Drinking Water Regulations (NPDWR) – enforceable standards.

[!TIP] Exam: Memorize key BIS limits: Turbidity 1 NTU, pH 6.5-8.5, Fluoride 1.0 mg/L (ideal) / 1.5 mg/L (permissible), Arsenic 0.01 mg/L, Zero tolerance for Total Coliforms.

Waterborne Diseases

Water Examination Tests

Physical Tests

• Turbidity: Cloudiness due to suspended matter.

  • Jackson Candle Turbidimeter: Historical, compares light through sample vs standard.

  • Nephelometric Turbidity Unit (NTU): Modern, measures scattered light at 90°. Standard method.

• Color: Due to dissolved organic matter (humic acids).

  • Platinum-Cobalt Scale (Hazen Units): Compare with standard Pt-Co solution.

• Odor: Threshold odor number (TON) – dilution at which odor is just detectable.

• Temperature: Affects viscosity, DO, chemical reaction rates.

Chemical Tests

• Alkalinity: Buffering capacity (HCO₃⁻, CO₃²⁻, OH⁻).

  • Phenolphthalein Alkalinity: End-point pH 8.3 (OH⁻ + ½ CO₃²⁻).

  • Methyl Orange Alkalinity: End-point pH 4.5 (OH⁻ + CO₃²⁻ + HCO₃⁻).

• Hardness: Concentration of Ca²⁺, Mg²⁺ (carbonate & non-carbonate).

  • EDTA Titration (Complexometric): Standard method. Eriochrome Black T indicator. pH 10 buffer.

• Chloride (Cl⁻): Indicates sewage contamination.

  • Argentometric (Mohr's) Method: Titration with AgNO₃, K₂CrO₄ indicator.

• Residual Chlorine: After disinfection.

  • DPD (N,N-Diethyl-p-phenylenediamine) Method: Colorimetric (pink color intensity).

• Dissolved Oxygen (DO): Critical for aquatic life & BOD test.

  • Winkler's Method (Azide Modification): Standard lab method. Mn(II) + Alkali-iodide-azide → MnO(OH)₂. Fixes DO. Titrate liberated I₂ with Na₂S₂O₃ (starch indicator).

Biological Tests

• Most Probable Number (MPN): Statistical estimate of coliform count based on presence/absence in multiple tube fermentations (lauryl tryptose broth, confirmed with BGLB). Reported as MPN/100 mL.

• Coliform Index: Total Coliform Count per 100 mL. Presence indicates possible fecal pollution.

• E. coli Confirmation: Growth on EMB (Eosin Methylene Blue) agar (metallic green sheen) or positive IMViC tests (Indole +, Methyl Red +, Voges-Proskauer -, Citrate -). Definitive indicator of fecal contamination.

4. WATER TREATMENT PROCESSES

Coagulation

• Definition: Addition of chemicals (coagulants) to destabilize colloidal particles (charge neutralization) and form flocs.

• Common Coagulants:

  1. Aluminium Sulfate (Alum): Al₂(SO₄)₃·18H₂O. Most common.

     • Reaction with water (hydrolysis):

$$\text{Al}^{3+} + 6\text{H}_2\text{O} \rightleftharpoons \text{Al(OH)}_3 \text{(gel)} + 3\text{H}_3\text{O}^+$$

    *   *Reaction with alkalinity (lime/bicarbonate):*

$$\text{Al}_2(\text{SO}_4)_3 \cdot 18\text{H}_2\text{O} + 3\text{Ca(HCO}_3)_2 \rightarrow 2\text{Al(OH)}_3 + 3\text{CaSO}_4 + 6\text{H}_2\text{O} + 18\text{CO}_2$$

2.  **Ferric Chloride (FeCl₃):** Similar hydrolysis to Fe(OH)₃. Works at lower pH.

3.  **Chlorinated Copper Arsenic (CCA):** Obsolete due to arsenic.

4.  **Lime (Ca(OH)₂):** For softening & coagulation (soda lime process).

5.  **Polymers (Polyelectrolytes):** Synthetic organic coagulants/aids (anionic, cationic, non-ionic).

• Factors Affecting Coagulation:

  • pH: Optimal for alum ~6.5-7.5 (forms Al(OH)₃). Outside range, forms soluble complexes.

  • Temperature: Higher temp → faster reaction, less coagulant needed.

  • Mixing Intensity & Duration: Rapid mixing (G ~ 500-1000 s⁻¹, t ~ 30-60 s) for dispersion, then slow mixing (flocculation).

  • Coagulant Dose: Determined by jar test.

  • Alkalinity of Water: Needed for hydrolysis reaction (consumes alkalinity). Low-alkalinity water requires lime/caustic soda addition.

• In Wastewater Treatment: Used for phosphorus removal (chemical precipitation as AlPO₄/FePO₄).

Sedimentation

• Theory: Stokes' Law

  For a spherical particle settling under gravity in a viscous fluid:

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

where:

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

*   $g$ = acceleration due to gravity (m/s²)

*   $$\displaystyle \rho_p, \rho $$ = densities of particle & fluid (kg/m³)

*   $d$ = particle diameter (m)

*   $\mu$ = dynamic viscosity (N·s/m²)

**Assumptions:** Laminar flow (Re < 0.2), spherical particle, no interaction, uniform flow.

**Temperature Effect:** Viscosity $\mu$ decreases with temperature → $$\displaystyle v_s $$ increases.

> [!TIP] Exam: **Derivation of Stokes' Law** is often asked. Balance forces: weight = buoyancy + drag (Stokes' drag $$\displaystyle F_d = 3\pi \mu d v_s $$).

• Design Parameters of Sedimentation Tank:

  1. Overflow Rate (Surface Loading Rate): $$\displaystyle q = \frac{Q}{A} $$ (m³/m²/day). Most critical parameter. Typical: plain 25-30 m³/m²/day, coagulated 40-120 m³/m²/day.

  2. Detention Time (θ): $$\displaystyle \theta = \frac{V}{Q} $$ (hours). Typical: 2-4 hrs (coagulated).

  3. Depth (H): 3-5 m. Affects sludge compaction & flow distribution.

  4. Length-to-Width Ratio (L/B): 2:1 to 5:1 (rectangular) to ensure plug flow.

• Types:

  • Plain Sedimentation: Removes coarse settleable solids. Low overflow rate.

  • Coagulation-Assisted Sedimentation (Flocculation-Sedimentation): Removes colloidal & fine particles. High overflow rate.

Design of Rectangular Sedimentation Tank

Given: $Q$ (m³/s), $q$ (m³/m²/day), $\theta$ (hrs), L/B ratio.

1. Surface Area (A): $$\displaystyle A = \frac{Q \times 86400}{q} $$ (m²)

2. Volume (V): $$\displaystyle V = Q \times \theta \times 3600 $$ (m³)

3. Depth (H): $$\displaystyle H = \frac{V}{A} $$ (m)

4. Dimensions: From $$\displaystyle A = L \times B $$ and $L/B$ ratio, solve for L & B. Check L < 100 m, B < 10-15 m.

Filtration

• Theory: Removal of remaining suspended floc & microorganisms. Mechanisms:

  1. Straining: Physical interception of particles > pore size.

  2. Sedimentation: Inertial impaction in pores.

  3. Adsorption: Van der Waals forces, electrostatic attraction.

  4. Biological: In slow sand filters (schmutzdecke layer).

• Slow Sand Filter:

  • Construction: Concrete basin, graded sand (0.3-1.0 m thick) over gravel, underdrain system. No mechanical backwash.

  • Working: Water flows top-down at 0.1-0.2 m/hr. A biological layer (schmutzdecke) forms on top, doing most filtration. Requires scraping of top 1-2 cm sand when head loss ~0.5-1 m.

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

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

  • Sketch:

    DiagramCANVAS: Slow sand filter cross-section showing sand bed, gravel layer, underdrains, inlet/outlet, and schmutzdecke layer on top.

• Rapid Sand Filter:

  • Construction: Similar basin, sand (0.5-1.0 m thick, 0.45-0.7 mm effective size), gravel support, underdrain system with wash water troughs.

  • Working: Water flows top-down at 5-15 m/hr. Filtration continues until head loss ~2-3 m or effluent quality drops. Then backwash is done.

  • Backwashing:

    • Reverse flow of clean water (or air+water) from underdrains.

    • Velocity: 0.3-0.5 m/s (to expand bed 50-60%).

    • Duration: 5-10 min.

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

$$H_e = \frac{H}{1 - n} \times (1 - n_e)$$

where $H$ = original depth, $n$ = original porosity (~0.4), $$\displaystyle n_e $$ = expanded porosity (~0.7).

    *   **Backwash Velocity ($$\displaystyle v_b $$):** Determined from **falling velocity criterion** (terminal velocity of sand particle in water = $$\displaystyle v_b $$). Use **Kynch's theory** or formula: 

$$v_b = \sqrt{\frac{g d (\rho_s - \rho)}{C \rho}}$$

(C = drag coefficient).

*   **Design:** Filtration rate 4-8 m³/m²/hr. Area based on $Q$ and rate. Number of units: minimum 2, often more for continuous operation.

*   **Sketch:** 
DiagramCANVAS: Rapid sand filter cross-section showing sand bed, gravel layers, underdrain manifold with laterals, wash water troughs at top, inlet/outlet.

• Comparison:

  | Feature | Slow Sand Filter | Rapid Sand Filter | | :--- | :--- | :--- | | Filtration Rate | 0.1-0.2 m/hr | 5-15 m/hr | | Mechanism | Biological (schmutzdecke) | Physical (straining, adsorption) | | Pretreatment | Minimal (coarse screening) | Must have coagulation & sedimentation | | Cleaning | Scraping top sand | Backwashing (mechanical) | | Area Required | Large | Small | | Operational Cost | Low (manual) | Higher (pumps, backwash) |

Disinfection

• Definition: Killing/inactivating pathogenic microorganisms (bacteria, viruses).

• Methods:

  1. Chlorination (Most Common): Forms hypochlorous acid (HOCl) – powerful disinfectant.

  2. Chloramination: Chlorine + ammonia → chloramines (longer residual, less THM formation).

  3. Ozonation: Strong oxidant, no residual, expensive.

  4. UV Radiation: Physical disruption of DNA, no chemical residual.

  5. Potassium Permanganate (KMnO₄): Oxidant, also controls taste/odor.

• Break Point Chlorination:

  • Process: Chlorine added in stages reacts with:

    1. Reducing substances (Fe²⁺, Mn²⁺, H₂S).

    2. Ammonia/Nitrogen compounds → forms chloramines (combined chlorine).

    3. Beyond break point: Free chlorine (HOCl/OCl⁻) appears. All ammonia oxidized.

  • Curve: Plot of residual chlorine vs. chlorine dose. Break point is where combined chlorine peaks and free chlorine starts rising. Superchlorination (dose beyond break point) ensures disinfection. Dechlorination (SO₂, activated carbon) may be needed to remove excess chlorine/taste.

  • Sketch:

    DiagramCANVAS: Break point chlorination curve: X-axis=Cl₂ dose, Y-axis=Residual Cl₂. Shows rising slope (reducing substances), plateau (chloramines), sharp drop (break point), then rising free Cl.

• Factors Affecting Disinfection Efficiency:

  • Type & concentration of microorganism.

  • Contact Time (Ct): Dose × time. Primary design parameter.

  • pH: HOCl (low pH) is 80x more effective than OCl⁻ (high pH).

  • Temperature: Higher temp → faster kill.

  • Turbidity: Shields microbes from disinfectant.

  • Nature of water: Presence of organic matter consumes chlorine.

Water Softening

• Objective: Remove hardness-causing ions (Ca²⁺, Mg²⁺).

• Soda Lime Process:

  • Chemicals: Soda ash (Na₂CO₃) + Lime (Ca(OH)₂).

  • Reactions:

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

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

$$\text{CaSO}_4 + \text{Na}_2\text{CO}_3 \rightarrow \text{CaCO}_3 \downarrow + \text{Na}_2\text{SO}_4$$

$$\text{MgSO}_4 + \text{Na}_2\text{CO}_3 + \text{Ca(OH)}_2 \rightarrow \text{Mg(OH)}_2 \downarrow + \text{CaCO}_3 \downarrow + \text{Na}_2\text{SO}_4$$

*   **Advantages:** Cheap chemicals, removes temporary + permanent hardness.

*   **Disadvantages:** Produces large sludge, non-selective (removes all ions), high chemical cost, not suitable for small plants.

• Ion Exchange Method:

  • Principle: Exchange of undesirable ions (Ca²⁺, Mg²⁺) with desirable ions (Na⁺) on a solid resin.

  • Resins:

    • Cation exchanger: Strong acid (H⁺ form) or weak acid. Regenerated with HCl/H₂SO₄.

    • Anion exchanger: Strong base (OH⁻ form). Regenerated with NaOH.

  • Process: Water passes through cation column (hardness removed, Na⁺ released) → anion column (anions removed, OH⁻ released) → mixed bed (for high purity). H⁺ + OH⁻ → H₂O.

  • Regeneration: When exhausted, flow concentrated brine (NaCl) or acid/alkali in opposite direction.

  • Advantages: High efficiency, produces very soft water, no sludge, automatic.

  • Disadvantages: High capital/operational cost, skilled operation, sensitive to suspended solids/turbidity (need pretreatment).

Unit Operations in Water Treatment (Sequence)

1. Screening (Coarse & fine) → 2. Mixing (Rapid) → 3. Flocculation (Slow mixing) → 4. Sedimentation → 5. Filtration → 6. Disinfection → 7. Storage & Distribution.

5. WATER DISTRIBUTION SYSTEMS

Types of Distribution Layouts (with Sketches)

Distribution Reservoirs

• Types:

  • Storage Reservoir (Raw Water): At source (dam, river). Large capacity.

  • Service Reservoir (Clear Water): Within distribution system. Balancing, emergency, pressure sustaining.

  • Elevated Reservoir (Tank on Tower): Provides gravity pressure.

  • Ground Reservoir (Underground tank): Requires pumping.

• Location Criteria:

  1. Geologically stable.

  2. Near center of demand (to minimize head loss).

  3. At highest feasible elevation (for gravity flow).

  4. Away from pollution sources.

  5. Accessible for maintenance.

• Storage Capacity Determination (Mass Curve Method for 24-hr Pumping):

  1. Plot cumulative hourly demand vs. time (24 hrs) → demand mass curve.

  2. Draw line from origin with slope = constant pumping rate ($$\displaystyle Q_p $$) such that it just touches the demand curve (tangent) and intersects it at end of cycle (24 hrs). This gives minimum required pumping rate.

  3. Storage capacity = maximum vertical difference between demand curve and pumping line.

  4. Formula: $$\displaystyle V_s = \text{Max}(D_t - Q_p \cdot t) $$ where $$\displaystyle D_t $$ = cumulative demand at time $t$.

  [!TIP] Exam: Mass curve method is must. Be able to draw the curve, find pumping rate, and calculate storage volume from given hourly demand data.

Pumps and Pumping Stations

• Types of Pumps:

  • Centrifugal Pumps: Most common. High flow, medium head. Types: radial flow, axial flow, mixed flow.

  • Reciprocating Pumps: Positive displacement. High head, low flow. Used for dosing chemicals.

• Pump Selection Factors:

  • Required discharge (Q) and head (H).

  • Variation in demand (pump characteristic curve).

  • Efficiency (best efficiency point - BEP).

  • NPSH (Net Positive Suction Head) required/available (cavitation).

  • Cost, space, maintenance.

• Pump Power Calculation (Brake Horsepower - BHP):

$$P_{in} = \frac{\rho g Q H}{\eta_{pump}}$$

$$BHP = \frac{P_{in}}{\eta_{motor}} = \frac{Q \times H}{102 \times \eta_{pump} \times \eta_{motor}} \ \text{(in kW if Q in m³/s, H in m)}$$

where $$\displaystyle \eta_{pump} $$, $$\displaystyle \eta_{motor} $$ are efficiencies (typically 0.6-0.8, 0.85-0.9).

**Total Head (H):** $$\displaystyle H = H_{static} + H_{friction} + H_{minor} + H_{velocity} $$.

• Pumping Station Design:

  • Number of units (N+1 redundancy).

  • Pump arrangement (series/parallel).

  • Suction & delivery pipe sizing.

  • Pump house layout, sump well design.

  • Pumping cycle (for variable demand).

6. WASTEWATER COLLECTION AND CHARACTERISTICS

Sewerage Systems

Sewer Appurtenances (with Sketches)

• Manholes:

  DiagramCANVAS: Circular/rectangular chamber with brick walls, benching, steps, cover. Used for inspection, cleaning, junction, alignment change.
  Function: Access for maintenance, ventilation, flow regulation.

• Lamp Holes: Small vertical pipe with glass cover, for illumination & ventilation in long sewers.

• Inspection Chambers: Similar to manholes but smaller, for domestic connections.

• Catch Basins (Gully Pots):

  DiagramCANVAS: Chamber with inlet grating, sump, outlet pipe. Traps solids & grit from street runoff before it enters storm drain.
  Function: Intercept silt/debris from surface runoff.

• Flushing Tanks: Located at dead ends. Store water & release suddenly to flush deposited solids.

• Inverted Siphons (Depressed Sewers): Sewer passing under obstruction (river, railway). Not true siphons – flow under pressure. Must be designed for self-cleansing velocity.

• Stormwater Overflows (SFO): In combined systems, devices to divert excess flow to relief sewer or water body during storms to prevent flooding.

Sewer Design & Construction

• Hydraulic Design (Manning's Formula):

  For partial flow in circular sewer (most common):

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

where:

*   $Q$ = discharge (m³/s)

*   $n$ = Manning's roughness coefficient (0.013-0.015 for concrete)

*   $A$ = flow area (m²)

*   $$\displaystyle R = A/P $$ = hydraulic radius (m), $P$ = wetted perimeter (m)

*   $S$ = slope (m/m)

**Design Criteria:**

*   **Minimum velocity (self-cleansing):** 0.6-0.9 m/s at **minimum flow** (dry weather flow).

*   **Maximum velocity (scouring):** 2.5-3.0 m/s at **maximum flow** to prevent sedimentation but avoid erosion.

*   **Maximum depth of flow:** ≤ 0.75D (for combined) or ≤ 0.9D (for separate) to allow air space.

> [!TIP] Exam: **Sewer design problem is frequent.** Given diameter, slope, n, and depth of flow (d/D), calculate Q and velocity. Use graphical method or formulas for area & wetted perimeter of circular segment.

• Design Discharge:

  • Separate System: $$\displaystyle Q_{design} = \text{Peak hourly sanitary flow} $$ (from max daily demand × peak factor).

  • Combined System: $$\displaystyle Q_{design} = \text{Sanitary flow} + \text{Stormwater flow} $$.

    • Stormwater: By Rational Method:

$$Q_{storm} = \frac{C i A}{360}$$

        where $C$ = runoff coefficient (0.4-0.9), $i$ = rainfall intensity (mm/hr) for **time of concentration ($$\displaystyle t_c $$)**, $A$ = area (hectares).

• Construction Techniques:

  1. Trenching: Open cut (most common), trench shields, deep trench methods.

  2. Pipe Laying: Bed preparation (sand/gravel), lowering pipe, jointing (rubber gasket, mortar), backfilling in layers.

  3. Testing: Water test (for leakage) or air test (for joints). Mandatory before backfilling.

• Quality Control & Safety:

  • QC: Check grade (laser level), alignment, joint integrity, material tests.

  • Safety: Shoring/trench boxes, sloping, access ladders, gas testing (H₂S, CH₄), barricades, PPE.

Wastewater Characteristics

Variation in Sewage Flow

• Average Flow: Total annual volume / 365 days.

• Dry Weather Flow (DWF): Flow during no rainfall. Base flow from domestic, industrial, infiltration. Design basis for treatment plants.

• Maximum Flow: Peak flow during wet weather (DWF + stormwater inflow + infiltration). Determines sewer size & pumping capacity.

• Estimation: Peak factor based on population, water supply, area, infiltration. For sewers: $$\displaystyle Q_{max} = (1.5 \text{ to } 2.5) \times \text{Average DWF} $$.

Population Equivalent (PE)

• Definition: The number of people whose average wastewater contribution produces the same organic load (BOD) as a given flow of industrial wastewater.

• Calculation:

$$\text{PE} = \frac{\text{Industrial BOD load (kg/day)}}{\text{Standard per capita BOD contribution (kg/day)}}$$

Standard per capita BOD = **0.06 kg/day** (60 g/day) from BIS.

*Example:* Industry discharging 300 kg BOD/day → PE = 300 / 0.06 = **5000 persons**.

7. WASTEWATER TREATMENT AND DISPOSAL

Preliminary & Primary Treatment

1. Screening: Remove large solids (rags, sticks). Coarse (50-100 mm) → Fine (6-25 mm).

2. Grit Removal: Remove sand, gravel, cinders (to prevent abrasion, deposition). Detention velocity ~0.3 m/s in grit chamber.

3. Primary Sedimentation: Remove settleable organic & inorganic solids. Overflow rate: 30-50 m³/m²/day, detention: 1.5-2.5 hrs. Removes ~50-60% SS, ~25-35% BOD.

Secondary Treatment (Activated Sludge Process - Detailed)

• Components: Aeration tank + Final clarifier + Sludge recirculation system.

• Working:

  1. Primary effluent + recycled activated sludge (RAS) enter aeration tank.

  2. Aeration (diffused or mechanical) provides DO ~2 mg/L for microbial growth (flocs).

  3. Microorganisms consume organic matter (BOD) → new cell mass + CO₂ + H₂O.

  4. Mixed liquor flows to final clarifier. Flocs settle, treated effluent discharged.

  5. Sludge recirculation: Part of settled sludge (RAS) returned to aeration tank to maintain MLSS. Excess sludge (waste activated sludge - WAS) removed.

• Key Parameters:

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

  • F/M Ratio (Food to Microorganism): $$\displaystyle \frac{\text{Influent BOD load (kg/day)}}{\text{MLSS mass (kg)}} $$. Typical: 0.2-0.4 kg BOD/kg MLSS·day.

  • Sludge Age (θc): Average time sludge remains in system.

$$\theta_c = \frac{\text{Mass of MLSS in aeration tank (kg)}}{\text{Mass of WAS wasted per day (kg/day)}}$$

. Typical: 5-15 days.

*   **SVI (Sludge Volume Index):** 

$$\text{SVI} = \frac{\text{Settled sludge volume (mL/L) after 30 min}}{ \text{MLSS (mg/L)}} \times 1000$$

. Indicates settleability. Good: 50-150 mL/g. >150 → bulking.

*   **Relative Stability:** $$\displaystyle \frac{\text{Deoxygenation rate of effluent}}{\text{Deoxygenation rate of raw sewage}} \times 100\% $$. >60% is acceptable.

• Variations: SBR (Sequencing Batch Reactor), Oxidation Ditch, Extended Aeration.

• Brief on Trickling Filter: Fixed-film reactor. Wastewater trickles over rock/plastic media. Biofilm grows on media, consumes BOD. Requires secondary clarifier. Lower MLSS, less sludge production, but prone to clogging, odor.

Natural Methods of Wastewater Disposal

1. Land Treatment:

   • Slow Rate (Irrigation): Apply wastewater to land, crops use water & nutrients. Requires pretreatment (primary/secondary).

   • Rapid Infiltration: Apply to highly permeable soil (sand), percolates to groundwater. Recharges aquifer.

   • Overland Flow: Apply to sloping land, flows as sheet flow, collected at toe. Removes BOD/N.

   • Constructed Wetlands: Mimic natural wetlands. Plants, microbes, soil remove pollutants. Low cost, aesthetic.

2. Dilution in Surface Water Bodies:

   • Self-purification: Natural process where stream re-aerates and dilutes pollutants.

   • Oxygen Sag Curve (Streeter-Phelps): Most important concept.

Oxygen Sag Curve (Streeter-Phelps)

• Explanation: Plot of Dissolved Oxygen (DO) deficit ($$\displaystyle D = D_s - D $$) vs. distance downstream from pollution point.

  • $$\displaystyle D_s $$ = Saturation DO at stream temperature.

  • $D$ = Actual DO.

  • Deficit ($$\displaystyle D_t $$): $$\displaystyle D_t = D_s - D_t $$.

• Critical Point: Location where deficit is maximum ($$\displaystyle D_{max} $$). DO is minimum here.

• Curve Shape: Initially, deoxygenation (BOD decay) consumes DO faster than reaeration → deficit rises. After critical point, reaeration dominates → deficit falls.

• Importance: Predicts minimum DO in stream, location of critical point, and required treatment level to meet water quality standards (e.g., DO > 5 mg/L).

• Sketch:

  DiagramCANVAS: Oxygen sag curve: X-axis=Distance downstream, Y-axis=DO deficit (D). Curve rises from zero at discharge point to D_max (critical point), then falls asymptotically to zero. Label: deoxygenation curve, reaeration curve, critical point, D_max.

• Equations:

  • Deoxygenation (BOD decay):

$$L_t = L_0 e^{-K_d t}$$

*   **Reaeration:** 

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

    where $$\displaystyle L_t $$ = ultimate BOD remaining at time $t$, $$\displaystyle L_0 $$ = ultimate BOD at discharge, $$\displaystyle K_d $$ = deoxygenation constant (day⁻¹), $$\displaystyle K_a $$ = reaeration constant (day⁻¹), $$\displaystyle D_0 $$ = initial deficit.

*   **Critical Deficit:** 

$$D_{max} = \frac{L_0}{1 - \frac{K_d}{K_a}} \left(1 - e^{-(K_a - K_d)t_c}\right) + D_0 e^{-K_a t_c}$$

*   **Critical Time:** 

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

• Temperature Correction:

$$K_{d,20} = K_{d,T} \theta_d^{(T-20)}$$

$$K_{a,20} = K_{a,T} \theta_a^{(T-20)}$$

Typical $$\displaystyle \theta_d = 1.135 $$, $$\displaystyle \theta_a = 1.024 $$.

[!TIP] Exam: Streeter-Phelps is a high-weightage topic. Be able to:

1. Sketch the oxygen sag curve and label.

2. Write the deficit equation.

3. Calculate $$\displaystyle D_{max} $$ and $$\displaystyle t_c $$ given $$\displaystyle L_0 $$, $$\displaystyle K_d $$, $$\displaystyle K_a $$, $$\displaystyle D_0 $$, stream velocity.

4. Apply temperature correction to $$\displaystyle K_d $$, $$\displaystyle K_a $$.

Biochemical Oxygen Demand (BOD)

• Definition: Amount of dissolved oxygen consumed by microorganisms in decomposing organic matter in a water sample over a specified time (usually 5 days) at a specified temperature (usually 20°C). Indirect measure of biodegradable organic pollution.

• Significance: Primary parameter for wastewater strength, treatment plant design, stream pollution assessment.

• 5-Day BOD Test Procedure (Standard Dilution Method):

  1. Dilute wastewater sample (to ensure DO depletion 40-70%).

  2. Measure initial DO of diluted sample ($$\displaystyle D_0 $$).

  3. Incubate in dark at 20°C for 5 days.

  4. Measure final DO ($$\displaystyle D_5 $$).

  5. BOD₅ (mg/L): $$\displaystyle BOD_5 = \frac{(D_0 - D_5) - \text{Seed correction}}{f} $$ where $f$ = dilution factor.

• BOD Calculations:

  • Ultimate BOD ($$\displaystyle L_0 $$):

$$L_0 = \frac{BOD_5}{1 - e^{-K_d \times 5}}$$

*   **Temperature Correction:**

$$BOD_{T,5} = BOD_{20,5} \left[ \frac{1 - e^{-K_{d,20} \times 5}}{1 - e^{-K_{d,T} \times 5}} \right]$$

    Since $$\displaystyle K_{d,T} = K_{d,20} \theta^{(T-20)} $$.

*   **Example (from May 2023):** Given $$\displaystyle BOD_5 $$ at 20°C = 150 mg/L, $$\displaystyle K_d = 0.23 $$/day. Find $$\displaystyle BOD_5 $$ at 15°C ($$\displaystyle \theta=1.135 $$).

    Step 1: Find $$\displaystyle L_0 $$ at 20°C: $$\displaystyle L_0 = 150 / (1 - e^{-0.23 \times 5}) = 150 / (1 - 0.313) = 218.4 $$ mg/L.

    Step 2: $$\displaystyle K_{d,15} = 0.23 \times 1.135^{-5} = 0.23 / 1.135^5 = 0.23 / 1.80 = 0.128 $$/day.

    Step 3: $$\displaystyle BOD_{5,15} = L_0 (1 - e^{-0.128 \times 5}) = 218.4 \times (1 - 0.533) = 101.8 $$ mg/L.

Advanced Wastewater Treatment (Brief)

• Nutrient Removal: Biological (nitrification-denitrification for N; enhanced biological phosphorus removal - EBPR) or chemical (alum/ferric chloride for P).

• Tertiary Filtration: Sand/anthracite filters to remove residual SS after secondary treatment.

• Disinfection: Chlorination/UV before discharge (especially for reuse or sensitive receiving waters).

• Other: Activated carbon adsorption (organics), reverse osmosis (salinity), advanced oxidation (trace organics).

Wastewater Treatment Plant Planning

1. Site Selection: Away from residential areas, stable geology, accessible, near receiving water body, land availability for expansion.

2. Process Selection: Based on wastewater characteristics, effluent standards (BOD, SS, N, P), land availability, cost, operation skill.

3. Layout: Flow diagram: Preliminary → Primary → Secondary → Tertiary → Disinfection → Sludge handling (thickening, digestion, dewatering, disposal).

4. Future Expansion: Provision for additional units, modular design.

8. DESIGN PROBLEMS AND CALCULATIONS (Key Formulas & Apps)

Population Projection (Logistic Method - Step-by-Step)

Given: $$\displaystyle P_0 $$ at $$\displaystyle t_0=0 $$, $$\displaystyle P_1 $$ at $$\displaystyle t_1 $$, $$\displaystyle P_2 $$ at $$\displaystyle t_2 $$.

1. Assume $$\displaystyle P_s $$. Calculate:

$$A_1 = \ln\left(\frac{P_s - P_1}{P_1}\right), \quad A_2 = \ln\left(\frac{P_s - P_2}{P_2}\right)$$

2. $$\displaystyle r = \frac{A_1 - A_2}{t_2 - t_1} $$.

3. Check if $r$ is consistent for both intervals. Adjust $$\displaystyle P_s $$ until $r$ is nearly same.

4. Find $$\displaystyle t_0 $$ from $$\displaystyle P_0 $$: $$\displaystyle t_0 = \frac{1}{r} \ln\left(\frac{P_s - P_0}{P_0}\right) $$.

5. Forecast $$\displaystyle P_{t3} $$: $$\displaystyle P_{t3} = \frac{P_s}{1 + e^{-r(t_3 - t_0)}} $$.

Water Demand Calculations

1. Average Daily Demand (ADD): $$\displaystyle Q_{avg} = \text{Population} \times \text{per capita supply (lpcd)} $$.

2. Maximum Daily Demand (MDD): $$\displaystyle Q_{max day} = 1.5 \text{ to } 2.5 \times Q_{avg} $$.

3. Maximum Hourly Demand (MHD): $$\displaystyle Q_{max hr} = 2 \text{ to } 3 \times \frac{Q_{avg}}{24} $$.

4. Fire Demand: Use Kuchling's/Boston's formula. Total design draft often taken as MDD + Fire Demand (but fire is intermittent).

Coagulation Dose Calculation (Alum & Lime)

• Alum Dose (mg/L): Based on jar test or alkalinity.

• Lime Requirement (if alkalinity < alum demand):

  Reaction: $$\displaystyle \text{Al}_2(\text{SO}_4)_3 + 3\text{Ca(HCO}_3)_2 \rightarrow ... $$

  1 mg/L of alum requires 0.5 mg/L of CaCO₃ alkalinity.

  If raw water alkalinity < (0.5 × alum dose), add lime:

$$\text{Ca(OH)}_2 \text{ (mg/L)} = \left[ (0.5 \times \text{Alum dose}) - \text{Alkalinity as CaCO}_3 \right] \times \frac{74}{100}$$

(MW Ca(OH)₂=74, CaCO₃=100).

Sedimentation Tank Design (Recap)

1. $$\displaystyle A = \frac{Q \times 86400}{q} $$ (q = overflow rate m³/m²/day)

2. $$\displaystyle V = Q \times \theta \times 3600 $$ (θ = detention time hrs)

3. $$\displaystyle H = V/A $$

4. $$\displaystyle L/B = 2-5 $$, $$\displaystyle L < 100 $$ m → get L, B.

Filtration Design (Rapid Sand Filter)

1. Filter Area (A_f): $$\displaystyle A_f = \frac{Q_{design}}{\text{Filtration rate}} $$ (Q in m³/day, rate ~100-200 m³/m²/day).

2. Number of Units: $$\displaystyle N = \frac{A_f}{\text{Area per unit}} $$. Usually 2-10 units.

3. Backwash:

   • Backwash velocity ($$\displaystyle v_b $$): 0.3-0.5 m/s (from manufacturer/experience).

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

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

where $n$=0.4, $$\displaystyle n_e $$=0.7.

Pump Power Calculation (Recap)

$$BHP (kW) = \frac{Q (m³/s) \times H (m)}{102 \times \eta_{pump} \times \eta_{motor}}$$

Total Head H: $$\displaystyle H = H_{static} + h_f + h_m $$. $$\displaystyle h_f = f \frac{L}{D} \frac{V^2}{2g} $$ (Darcy-Weisbach) or $$\displaystyle h_f = \frac{L}{D} \frac{V^2}{2g} \frac{1}{n^2} $$ (Manning's equivalent).

Sewer Design (Manning's for Partial Flow)

Given: $D$, $S$, $n$, $d/D$.

1. Calculate angle θ from $d/D$: $$\displaystyle \theta = 2 \cos^{-1}(1 - 2d/D) $$.

2. Area (A): $$\displaystyle A = \frac{D^2}{4} (\theta - \sin \theta) $$.

3. Wetted Perimeter (P): $$\displaystyle P = \theta D $$.

4. Hydraulic Radius (R): $$\displaystyle R = A/P $$.

5. Velocity (V): $$\displaystyle V = \frac{1}{n} R^{2/3} S^{1/2} $$.

6. Discharge (Q): $$\displaystyle Q = A \times V $$.

7. Check $V$ against 0.6-3.0 m/s.

BOD Calculations (Recap)

• Ultimate BOD: $$\displaystyle L_0 = \frac{BOD_5}{1 - 10^{-K_d \times 5}} $$ (if $$\displaystyle K_d $$ in base 10).

• Temperature Correction: $$\displaystyle K_{d,T} = K_{d,20} \theta^{(T-20)} $$; then recalc $$\displaystyle BOD_5 $$ at T using $$\displaystyle L_0 $$.

Streeter-Phelps (Critical Deficit & Location)

Given: $$\displaystyle L_0 $$, $$\displaystyle K_d $$, $$\displaystyle K_a $$, $$\displaystyle D_0 $$, stream velocity $U$ (m/s).

1. Convert $$\displaystyle K_d $$, $$\displaystyle K_a $$ to per second if $U$ in m/s: $$\displaystyle K' = K/86400 $$.

2. Calculate $$\displaystyle t_c $$ (seconds):

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

3. Critical Distance: $$\displaystyle x_c = U \times t_c $$.

4. Critical Deficit:

$$D_{max} = \frac{L_0}{1 - \frac{K_d'}{K_a'}} \left(1 - e^{-(K_a' - K_d')t_c}\right) + D_0 e^{-K_a' t_c}$$

5. BOD at critical point: $$\displaystyle L_{t_c} = L_0 e^{-K_d' t_c} $$.

Mass Curve Method for Balancing Reservoir

1. Tabulate hourly demand (cumulative).

2. Plot cumulative demand vs. time (24 hrs).

3. Draw pumping line from origin with slope = constant pumping rate, tangent to demand curve and ending at (24 hrs, total daily demand).

4. Storage capacity = max vertical distance between demand curve and pumping line.

5. Pumping rate = slope of pumping line = total daily demand / 24 hrs (if tangent at end) or higher if tangent earlier.

[!TIP] Exam: Practice numericals from past papers: Logistic forecasting (May 2022, Jun 2025), Sedimentation design (May 2023), Rapid filter design (May 2022), Pump power (May 2023), Sewer design (May 2023), BOD temp correction (May 2022), Streeter-Phelps (May 2022 - 14m question!). Always state assumptions and units clearly.