UNIT 2: WASTEWATER TREATMENT PROCESSES & UNIT OPERATIONS
A. Preliminary & Primary Treatment
1. Screening & Racks
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Purpose: Remove large floating and suspended solids (rags, sticks, debris) to protect pumps and downstream equipment.
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Types:
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Coarse screens: Bar spacing 50-150 mm.
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Fine screens: Bar spacing 6-50 mm.
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Micro-screens: Bar spacing < 6 mm (used for tertiary treatment).
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Design Considerations:
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Approach velocity: 0.6-1.0 m/s (coarse), 0.6-1.5 m/s (fine) to prevent debris settling or forcing through.
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Bar spacing: Selected based on downstream process requirements.
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Screen opening area: Should be 1.5-2 times the gross area of the channel to allow for peak flows.
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Head Loss Through Bar Screens:
$$h_f = \frac{1}{2} \beta \left( \frac{b}{s} \right)^{4/3} \frac{V^2}{2g} \sin^2 \theta$$
Where:
* $$\displaystyle h_f $$ = head loss (m)
* $\beta$ = shape factor (0.7-1.0, depends on bar profile)
* $b$ = bar thickness (m)
* $s$ = clear spacing between bars (m)
* $V$ = velocity of flow through screen openings (m/s)
* $\theta$ = angle of inclination from horizontal (°)
> [!TIP] Head loss increases rapidly with reduced bar spacing ($s$). Regular cleaning is critical to avoid excessive losses.
2. Grit Removal
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Purpose: Remove sand, gravel, cinders, and other inorganic particles (specific gravity ~2.65) to prevent abrasion, deposition in pipes, and accumulation in digesters.
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Types of Grit Chambers:
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Horizontal flow: Simple, rectangular; velocity controlled by weir or orifice.
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Aerated: Creates a spiral flow; separates lighter organic solids from heavier grit.
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Vortex (mechanical/hydraulic): High efficiency, compact.
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Design of Rectangular Grit Chamber:
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Settling velocity ($$\displaystyle V_s $$): Determined by particle size and specific gravity using Stokes' law (for laminar flow, Re<1).
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Flow velocity ($V$): Set to keep grit in suspension but allow settling. Typically 0.15-0.3 m/s.
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Detention time ($t$): 60-90 seconds for horizontal flow chambers.
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Channel dimensions: Based on $$\displaystyle Q = A \times V $$, where $$\displaystyle A = B \times D $$ (width × depth). Length $$\displaystyle L = V \times t $$.
[!TIP] Grit characteristics vary; design $$\displaystyle V_s $$ range (e.g., 0.016-0.022 m/s) is often provided, not a single value.
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3. Primary Sedimentation (Primary Clarifiers)
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Purpose: Remove settleable organic and inorganic solids (primary sludge) and floating material (scum). Reduces load on secondary treatment.
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Removal Efficiencies: ~50-70% Suspended Solids (SS), ~25-40% BOD.
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Design of Rectangular Tank:
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Detention period ($t$): 1.5-2.5 hours (for plain settling).
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Overflow rate ($O.R.$): $$\displaystyle O.R. = \frac{Q}{A_l} $$ (m³/m²-day). Typical: 30-50 m³/m²-day.
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Weir loading rate: $$\displaystyle Q / L_w $$ (m³/m-day). Typical < 125 m³/m-day to prevent short-circuiting.
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Dimensions: Length:Width ratio = 3:1 to 5:1. Depth: 2-5 m.
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Types of Settling:
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Discrete: Particles settle as individual units (e.g., sand in grit chamber). Settling velocity constant.
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Flocculent: Particles agglomerate during settling, increasing $$\displaystyle V_s $$ (e.g., primary sedimentation).
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Hindered/Zone: High concentration, particles settle as a mass (interface). Occurs in secondary clarifiers.
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Compression: Particles in sludge layer compress under weight (sludge thickening).
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Septic Tank vs. Imhoff Tank:
| Feature | Septic Tank | Imhoff Tank |
|---|---|---|
| Scope | Single unit, combined sedimentation & anaerobic digestion. | Two-story unit: upper sedimentation, lower digestion. |
| Function | Raw sewage enters; settled solids digested anaerobically in same chamber. | Sewage enters upper chamber; settled sludge falls through slots to lower chamber for digestion. |
| Performance | Poor solids digestion, frequent desludging needed, odour issues. | Better solids digestion, less frequent desludging, odour controlled in lower chamber. |
| Design | Simple, single compartment. | Complex, with inclined slots between chambers. |
B. Secondary (Biological) Treatment
1. Activated Sludge Process (ASP)
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Principle: Aerobic microorganisms (activated sludge) consume organic matter. Mixture is settled; sludge is recycled.
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Components: Aeration tank, secondary clarifier, sludge recycle system.
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Flow Diagram (Configurations):
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Plug Flow: Longitudinal flow, concentration gradient.
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Complete Mix: Uniform concentration (stirred tank).
[!DIAGRAM]
DiagramCANVAS: Sketch showing flow diagram of ASP with aeration tank, clarifier, sludge recycle, and waste sludge lines. Label components. Show plug flow (long rectangular tank) and complete mix (circular/ square tank) configurations. -
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Key Parameters:
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F/M Ratio (Food to Microorganism): $$\displaystyle F/M = \frac{Q \times L_0}{V \times X} $$ (kg BOD/kg MLSS-day). Controls process stability.
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SVI (Sludge Volume Index): $$\displaystyle SVI = \frac{Settled \ Sludge \ Volume \ (mL/L)}{MLSS \ (g/L)} $$ (mL/g). Indicates sludge settleability. Ideal: 50-150.
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MLSS (Mixed Liquor Suspended Solids): Concentration of solids in aeration tank (mg/L).
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MCRT (Mean Cell Residence Time): $$\displaystyle MCRT = \frac{V \times X}{(Q_w \times X_w) + (Q_e \times X_e)} $$ (days). Equivalent to SRT.
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Oxygen Requirements:
$$O_2 \ required = (BOD_5 \ removed \times 1.47) + (Nitrifed \ NH_3-N \times 4.57) + (Endogenous \ Respiration)$$
* Actual air needed = $$\displaystyle O_2 $$ required / (Oxygen transfer efficiency × 0.21 × density of air).
2. Trickling Filters
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Principle: Wastewater distributed over a packed bed (rocks, plastic media). Microbial film (zoogleal slime) oxidizes organic matter.
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Types (by Organic Loading):
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Standard rate: 0.08-0.32 kg BOD/m³-day.
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High rate: 0.32-1.0 kg BOD/m³-day.
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Super high rate: > 1.0 kg BOD/m³-day.
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Design Calculations:
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Surface loading rate ($$\displaystyle q_s $$): $$\displaystyle q_s = \frac{Q}{A} $$ (L/m²-day or m³/m²-day).
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Organic loading ($$\displaystyle L_o $$): $$\displaystyle L_o = \frac{Q \times L_0}{V} $$ (g BOD/m³-day).
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Depth ($D$): 0.6-2.0 m (standard), up to 10 m (deep tower filters).
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Volume ($V$): $$\displaystyle V = A \times D $$.
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Diameter ($$\displaystyle D_f $$): $$\displaystyle A = \frac{\pi D_f^2}{4} $$.
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NRC Formula for Efficiency:
$$E = \frac{100}{1 + 0.0088 \sqrt[3]{L_o}}$$
Where $E$ = % BOD removal, $$\displaystyle L_o $$ = organic loading (kg/ha-day). **Use consistent units.**
> [!TIP] NRC formula is empirical; ensure units match (kg/ha-day). For $$\displaystyle L_o $$ in g/m²-day, use $$\displaystyle E = \frac{100}{1 + 0.44 \sqrt[3]{L_o}} $$ (approx).
3. Oxidation Ditches
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Principle: Modified ASP with oval-shaped channel and surface aeration rotors. Operates in extended aeration mode (high SRT).
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Working (with sketch):
DiagramCANVAS: Neat sketch of oxidation ditch. Show oval channel, multiple rotor/aerator units positioned along the channel, flow direction arrows, influent and effluent points, and return sludge line. -
Configurations:
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Carousel: Single oval channel with multiple rotors.
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Pasveer: Deep, narrow channel with single long rotor.
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Biodisc: Rotating disc contactors (less common).
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Advantages: Simplicity, robustness, good nitrification/denitrification potential, less sludge production.
4. Biological Treatment Fundamentals
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Importance of Micro-organisms:
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Bacteria: Form flocs; primary degraders (heterotrophs for BOD, autotrophs for nitrification).
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Protozoa: Consume free bacteria, improve effluent clarity.
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Metazoa (rotifers, worms): Consume floc particles, indicate healthy sludge.
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Kinetics (Monod):
$$r = \frac{k_{max} \cdot S}{K_s + S}$$
Where $r$ = substrate utilization rate, $S$ = substrate concentration, $$\displaystyle k_{max} $$ = max rate, $$\displaystyle K_s $$ = half-velocity constant.
C. Advanced & Tertiary Treatment
1. Nutrient Removal (Nitrogen & Phosphorus)
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Need for Nitrogen Removal: To prevent eutrophication (algal blooms) in receiving water bodies.
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Biological Nitrification-Denitrification:
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Nitrification (Aerobic): $$\displaystyle NH_4^+ + 2O_2 \rightarrow NO_3^- + H_2O + 2H^+ $$ (by Nitrosomonas, Nitrobacter).
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Denitrification (Anoxic): $$\displaystyle NO_3^- \rightarrow N_2 $$ (by heterotrophs using organic carbon as electron donor).
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Process: Requires separate anoxic zone (no DO, NO3 present) followed by oxic zone (DO > 2 mg/L). Carbon source needed for denitrification (may require methanol addition if influent C/N low).
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Other Methods:
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Ammonia stripping: Raise pH > 10, air stripping.
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Breakpoint chlorination: Chlorine dose > Cl:NH3 ratio 7.6:1.
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Ion exchange: Selective resin.
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2. Advanced Wastewater Treatment (AWT)
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Definition & Difference: Treatment beyond conventional secondary to meet specific reuse/discharge standards (e.g., potable reuse, sensitive ecosystems). Conventional: BOD/SS removal. AWT: Targeted removal of nutrients, dissolved solids, pathogens, emerging contaminants.
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Important AWT Processes (Tabular):
| Process | Principle | Typical Application |
|---|---|---|
| Chemical Precipitation | Add coagulants (alum, ferric chloride) to remove P, heavy metals. | Phosphorus removal. |
| Sand Filtration | Physical straining through granular media. | Polishing, SS removal. |
| Diatomaceous Earth Filter | Depth filtration with fine porous media. | Very fine SS, algae removal. |
| Ultrafiltration (UF) | Membrane separation (0.01-0.1 µm). | Remove colloids, bacteria, viruses. |
| Reverse Osmosis (RO) | Membrane separation (< 0.001 µm) under pressure. | Dissolved salts, ions, small organics. |
| Adsorption (GAC) | Surface adherence to activated carbon. | Organics, taste/odor, micropollutants. |
| Disinfection | Kill/inactivate pathogens. | Final barrier for reuse. |
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Ultrafiltration (Detailed):
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Principle: Pressure-driven membrane process. Pore size 0.01-0.1 µm removes macromolecules, colloids, bacteria, some viruses.
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Membrane: Polymeric (PSF, PES) or ceramic. Modules: hollow fiber, spiral wound, tubular.
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Applications: Tertiary treatment, pretreatment to RO, water reuse.
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Advantages: High removal efficiency, compact, no chemicals (for separation), consistent effluent quality.
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Disadvantages: Membrane fouling, high capital/operational cost, concentrate disposal.
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3. Disinfection
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Methods:
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Chlorination: Most common. Forms hypochlorous acid (HOCl). CT concept: $C \times T$ (concentration × contact time) determines kill rate.
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Chlorination-Dechlorination: Chlorine followed by sulfur dioxide or bisulfite to remove residual chlorine toxic to aquatic life.
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UV Radiation: Damages microbial DNA. No residual, no chemical by-products.
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Ozone: Strong oxidant. Very effective, but no residual, high cost.
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Chlorine Demand: Amount of chlorine consumed by reactions with organics/inorganics before free chlorine residual appears.
UNIT 2: AIR POLLUTION CONTROL & FUNDAMENTALS
A. Air Pollutants & Sources
1. Sources & Characteristics of Specific Pollutants
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Sulphur Dioxide (SO₂):
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Sources: Fossil fuel combustion (power plants, industries), smelting of sulfide ores.
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Characteristics: Colorless, pungent odor, soluble in water → forms sulfurous/sulfuric acid (acid rain).
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Hydrogen Sulphide (H₂S):
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Sources: Sewage treatment plants, petroleum refining, natural gas processing, anaerobic decomposition.
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Characteristics: Colorless, rotten egg odor (detectable at very low ppm), toxic, flammable.
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2. Major Air Pollutants (Criteria Pollutants) - Tabular
| Pollutant | Primary Sources | Key Characteristics & Health Effects |
|---|---|---|
| PM₁₀ / PM₂.₅ | Combustion, construction, agriculture. | Penetrate respiratory system. PM₂.₅ reaches alveoli → cardiopulmonary disease. |
| SO₂ | Coal/oil combustion. | Respiratory irritant, contributes to acid rain & PM formation. |
| NOₓ (NO, NO₂) | High-temperature combustion. | Respiratory problems, ozone formation, acid rain, nitrate aerosols. |
| CO | Incomplete combustion. | Binds to hemoglobin → reduces oxygen transport (asphyxiation). |
| O₃ (Ground-level) | Secondary, from NOₓ + VOCs + sunlight. | Strong oxidant → lung damage, crop damage. |
| Pb | Leaded gasoline (historical), smelters, batteries. | Neurotoxic, affects children's development. |
3. Aerosols
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Definition: System of solid or liquid particles suspended in a gas (air). Size range: 0.001 µm to 100 µm.
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Types & Characteristics:
| Type | Formation | Typical Size | Example |
|---|---|---|---|
| Dust | Mechanical disintegration. | > 1 µm | Soil, pollen. |
| Fume | Condensation of vapor. | < 0.1 µm | Metal fumes. |
| Mist | Atomization of liquid. | 0.5 - 50 µm | Spray, fog. |
| Smoke | Incomplete combustion. | 0.01 - 1 µm | Soot, fly ash. |
| Fog | Water droplet mist. | 1 - 20 µm | Natural fog. |
| Smog | Photochemical: NOₓ + VOCs + sunlight. Winter (London): SO₂ + particulates + fog. | Varies | Los Angeles (photochemical), London (sulfurous). |
B. Meteorology & Dispersion
1. Meteorological Factors Influencing Dispersion
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Wind Speed & Direction: Primary driver of horizontal transport. Higher speed → greater dilution.
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Temperature: Affects buoyancy of plume and stability.
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Atmospheric Stability: Determines vertical mixing. Classes: A (very unstable) to F (very stable). Stable → poor dispersion.
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Mixing Height: Height of the mixed layer (top of plume can rise). Higher mixing height → greater volume for dilution.
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Humidity & Precipitation: Can cause plume scavenging (rainout, washout).
2. Temperature Lapse Rate
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Environmental Lapse Rate (ELR): Actual vertical temperature profile in atmosphere. Varies with time/location.
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Adiabatic Lapse Rate (ALR): Temperature change of a parcel of air moving vertically without heat exchange.
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Dry ALR ($$\displaystyle \Gamma_d $$): ~9.8°C/km (for unsaturated air).
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Moist ALR ($$\displaystyle \Gamma_m $$): ~4-9°C/km (for saturated air; latent heat release reduces cooling).
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Stability: If ELR < ALR → atmosphere is stable (inversion possible). If ELR > ALR → unstable.
3. Gaussian Plume Model
- Equation (for continuous point source, steady state, flat terrain):
$$C(x,y,z) = \frac{Q}{2\pi \sigma_y \sigma_z U} \exp\left(-\frac{y^2}{2\sigma_y^2}\right) \left[ \exp\left(-\frac{(z-H)^2}{2\sigma_z^2}\right) + \exp\left(-\frac{(z+H)^2}{2\sigma_z^2}\right) \right]$$
Where:
* $C$ = concentration (g/m³)
* $Q$ = emission rate (g/s)
* $$\displaystyle \sigma_y, \sigma_z $$ = horizontal & vertical dispersion coefficients (m) – depend on downwind distance $x$ and stability class.
* $U$ = wind speed at effective stack height (m/s)
* $H$ = effective stack height = physical height + plume rise (m)
* $z$ = receptor height (m)
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Location of Max Pollution: On plume centerline ($$\displaystyle y=0 $$, $$\displaystyle z=0 $$ ground level), but maximum ground-level concentration occurs at some downwind distance.
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Assumptions: Steady state, constant wind, no deposition/chemical reaction, flat terrain, point source.
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Parameters: $$\displaystyle \sigma_y, \sigma_z $$ from Pasquill-Gifford curves/tables based on $x$ and stability class (A-F).
C. Air Pollution from Specific Sources & Control
1. Power Plant Emissions Estimation (Coal-Fired)
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Given: Plant capacity (MW), efficiency ($\eta$), coal properties (CV, ash%, S%), recovery factors.
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Steps:
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Coal consumption rate: $$\displaystyle \dot{m}_c = \frac{Plant \ Output \ (MW) \times 3.6 \times 10^6 \ MJ/MW-h}{\eta \times CV \ (MJ/kg)} $$ (kg/h or kg/day).
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Fly ash & Bottom ash: Total ash = $$\displaystyle \dot{m}_c \times Ash\% $$. Fly ash = Total ash × % discharged as flyash (often 60-80%). Bottom ash = Total ash - Fly ash.
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Particulate Matter (PM): Similar to ash calculation, but use PM% in coal or ESP efficiency.
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SO₂: $$\displaystyle \dot{m}_{SO_2} = 2 \times \dot{m}_c \times S\% \times \frac{32}{32} $$ (since 1 kg S → 2 kg SO₂). Or $$\displaystyle \dot{m}_{SO_2} = \dot{m}_c \times S\% \times 2 $$.
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Eco-friendly Ash Utilization:
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Cement & concrete (partial replacement for cement/clinker).
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Fly ash bricks/blocks.
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Structural fills/embankments.
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Mine reclamation (filling).
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Agriculture (soil amendment – caution for heavy metals).
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2. Control Equipment (Brief)
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Cyclones: Inertial separation of coarse particles (>10 µm).
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Electrostatic Precipitator (ESP): Charges particles, collects on plates. High efficiency for fine particles.
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Baghouses/Fabric Filters: Fabric bags filter particles. Very high efficiency.
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Scrubbers: Wet/dry spray to remove gases (SO₂) and particles.
D. Effects & Miscellaneous
1. Smog
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Photochemical Smog:
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Formation: NO₂ + sunlight → NO + O; O + O₂ → O₃; O₃ + VOCs → peroxyacetyl nitrate (PAN), aldehydes.
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Characteristics: Brownish haze, eye irritation, plant damage, rubber cracking. Occurrence: Sunny, warm, stagnant conditions (Los Angeles type).
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Industrial (London-type) Smog:
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Formation: SO₂ + particulates + fog → sulfuric acid mist.
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Characteristics: Grayish, sulfurous odor, severe respiratory distress. Occurrence: Cold, damp, coal burning (winter).
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2. Particulate Matter
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TSPM (Total Suspended Particulate Matter): All particles up to ~50-100 µm. Includes coarse and fine fractions.
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RSPM (Respirable Suspended Particulate Matter) / PM₁₀: Particles ≤ 10 µm aerodynamic diameter. Penetrate to thoracic region.
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PM₂.₅: Fine particles ≤ 2.5 µm. Penetrate to alveoli, enter bloodstream.
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Health Impact: RSPM/PM₂.₅ are more harmful than larger TSPM due to deeper lung penetration. Standards (e.g., NAAQS in India) specify limits for PM₁₀ and PM₂.₅.
UNIT 2: SHORT NOTE TOPICS (Frequently Recurring)
From Wastewater Treatment:
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Diatomaceous Earth Filter: Depth filter using fossilized diatomaceous earth (porous, fine). Used for tertiary polishing to remove very fine colloids, algae, and bacteria. Requires pre-coating and body feed. High effluent quality but high operating cost.
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Ammonia Stripping: Air stripping of ammonia from wastewater. Requires high pH (>10.5) to convert NH₄⁺ to NH₃ gas. Air is blown through packed tower. Limitations: scaling, air pollution (NH₃), sensitivity to temperature.
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Oxidation Ditch Configurations: See Section B.1.3 above. Emphasize Carousel (multiple rotors, oval), Pasveer (deep, single rotor), and operation as extended aeration ASP.
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Septic Tank vs. Imhoff Tank: See comparison table in Section A.3.
From Air Pollution:
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Photochemical Smog: See Section D.1. Focus on photochemical reactions (NOx, VOCs, sunlight), key pollutants (O₃, PAN), and LA-type conditions.
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Temperature Lapse Rate: See Section B.2. Distinguish ELR (observed) vs. ALR (theoretical, dry/moist). Link to stability.
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Gaussian Plume Model: See Section B.3. Write equation, define all terms ($$\displaystyle \sigma_y, \sigma_z, H, U $$), state assumptions, and mention use of Pasquill stability classes.
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Adsorption by Activated Carbon:
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Principle: Physical/chemical adherence of molecules to porous carbon surface.
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Isotherms: Freundlich, Langmuir (describe equilibrium).
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Use: Air (VOCs, odour control) and water (organics, taste/odor). Regeneration by steam/heat.
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Factors Affecting Dispersion: Wind speed/direction, atmospheric stability (lapse rate), mixing height, topography (valleys trap pollution), humidity/precipitation.
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Primary vs. Secondary Pollutants:
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Primary: Emitted directly from source (e.g., SO₂, CO, PM, NO).
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Secondary: Formed in atmosphere via chemical reactions (e.g., O₃, H₂SO₄ mist, PAN, sulfate/nitrate PM).
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Effect of Air Pollution on Materials:
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Corrosion: SO₂, acid deposition on metals.
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Soot/Deposition: On buildings, monuments (soiling).
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Degradation: Ozone cracks rubber, fades dyes; acid rain erodes stone (limestone, marble).
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UNIT 2: DESIGN & NUMERICAL PROBLEMS (High Weightage)
A. Wastewater Treatment Design
1. Rectangular Sedimentation Tank Design
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Given: Flow $Q$ (m³/d or L/s), detention time $t$ (hrs), overflow rate $O.R.$ (m³/m²-d), weir loading.
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Steps:
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Volume $$\displaystyle V = Q \times t $$ (use consistent time units).
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Surface area $$\displaystyle A_l = Q / O.R. $$ (ensure $Q$ in m³/d if $O.R.$ in m³/m²-d).
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From $$\displaystyle A_l = L \times B $$, choose $L:B$ ratio (3:1 to 5:1). Calculate $L$ and $B$.
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Depth $$\displaystyle D = V / A_l $$.
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Check weir loading: $$\displaystyle Q / L_w $$ (where $$\displaystyle L_w $$ = total weir length ≈ 0.8L to 0.9L). Should be < 125 m³/m-d.
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2. Grit Chamber Design (Rectangular)
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Given: $Q$, particle size $d$, specific gravity $SG$, settling velocity range $$\displaystyle V_s $$ (min, max), flow velocity $V$ (set).
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Steps:
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Channel cross-sectional area $$\displaystyle A_c = Q / V $$ (ensure $Q$ in m³/s, $V$ in m/s → $$\displaystyle A_c $$ in m²).
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Choose depth $D$ (typically 0.5-1.0 m). Then width $$\displaystyle B = A_c / D $$.
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Length $$\displaystyle L = V \times t $$, where $t$ = detention time (60-90 s). Or ensure $$\displaystyle L > 10 \times $$ channel width for good distribution.
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Check: $$\displaystyle V_s $$ (min) < $V$ < $$\displaystyle V_s $$ (max) to ensure grit settles but organics don't.
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3. Trickling Filter Design
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Given: $Q$, BOD of influent $$\displaystyle L_0 $$ (mg/L), surface loading $$\displaystyle q_s $$ (L/m²-d or m³/m²-d), organic loading $$\displaystyle L_o $$ (g BOD/m³-d or kg/ha-d), depth $D$.
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Steps:
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Surface area: $$\displaystyle A = Q / q_s $$ (consistent units).
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Volume: $$\displaystyle V = A \times D $$.
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Organic loading check: $$\displaystyle L_o = \frac{Q \times L_0}{V} $$ (ensure units match given $$\displaystyle L_o $$).
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Diameter: $$\displaystyle A = \pi D_f^2 / 4 $$ → $$\displaystyle D_f = \sqrt{4A/\pi} $$.
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Efficiency (NRC): Use formula with $$\displaystyle L_o $$ in kg/ha-day or g/m²-day (convert carefully).
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4. Alum Dosing Calculation
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Given: Dose $D$ (mg/L), flow $Q$ (MLD or L/s).
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Calculation: Mass per day = $D \times Q$.
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If $D$ in mg/L, $Q$ in MLD (million L/day): Mass (kg/day) = $D \times Q$.
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Example: $$\displaystyle D=28.6 $$ mg/L, $$\displaystyle Q=18 $$ MLD → Mass = 28.6 × 18 = 514.8 kg/day.
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B. Air Pollution Calculation
1. Power Plant Emission Estimation
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Given: Capacity $P$ (MW), efficiency $\eta$, coal CV (MJ/kg), ash% $A\%$, S% $S\%$, % fly ash of total ash, recovery % for ash.
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Steps:
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Coal consumption: $$\displaystyle \dot{m}_c = \frac{P \times 3.6 \times 10^6}{\eta \times CV} $$ (kg/h or kg/s). (Since 1 MW = 1 MJ/s, 1 MW-h = 3600 MJ).
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Total ash: $$\displaystyle \dot{m}_{ash,total} = \dot{m}_c \times A\% $$.
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Fly ash generated: $$\displaystyle \dot{m}_{FA,gen} = \dot{m}_{ash,total} \times (\% \text{ as fly ash}) $$.
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Fly ash recovered: $$\displaystyle \dot{m}_{FA,rec} = \dot{m}_{FA,gen} \times \text{recovery}\% $$.
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Bottom ash generated: $$\displaystyle \dot{m}_{BA,gen} = \dot{m}_{ash,total} - \dot{m}_{FA,gen} $$.
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Bottom ash recovered: $$\displaystyle \dot{m}_{BA,rec} = \dot{m}_{BA,gen} \times \text{recovery}\% $$.
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SO₂ emission: $$\displaystyle \dot{m}_{SO_2} = 2 \times \dot{m}_c \times S\% $$ (assuming 100% conversion of S to SO₂). If given recovery efficiency for SO₂ (e.g., FGD efficiency), subtract accordingly.
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2. Gaussian Plume Application
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Typical Question: Identify parameters, find max concentration location, or calculate concentration given all parameters and $$\displaystyle \sigma_y, \sigma_z $$ from tables.
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Key: Max ground-level concentration on centerline ($$\displaystyle y=0, z=0 $$) occurs at $$\displaystyle x_{max} \approx H / \sigma_z \times \text{some factor} $$. Usually given or asked conceptually.
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Calculation: Plug values into Gaussian equation. Ensure $U$ is at effective stack height $H$.