Environmental Engineering

Syllabus

• Water and wastewater: quality standards, water demand and population forecasting, unit operations and processes (sedimentation, coagulation, filtration, disinfection), distribution, sewerage, primary, secondary and tertiary treatment, sludge treatment and disposal.
• Air pollution: pollutants and sources, meteorology and dispersion, control devices, standards.
• Municipal solid waste: characteristics, generation, collection, transport, disposal (sanitary landfill, incineration, composting).
• Noise pollution: sources, measurement and control.

Key concepts and formulas

Population forecasting. Arithmetic increase P_n = P₀ + n x̄; geometric increase P_n = P₀(1 + r)ⁿ; incremental increase P_n = P₀ + n x̄ + n(n + 1)ȳ/2.

BOD. With ultimate BOD L₀ and rate constant k (base e), the BOD exerted after t days is BOD_t = L₀(1 − e^−kt). (With a base-10 constant K, use 10^−Kt; k = 2.303K.) The rate constant changes with temperature as k_T = k₂₀ θ^T−20, with θ ≈ 1.047. For a diluted sample, BOD = (DO_i − DO_f)/P, where P is the dilution fraction.

Sedimentation.

• Stokes' law: settling velocity v_s = g(G_s − 1)d²/(18ν).
• Surface overflow rate = Q/A (plan area); a particle is fully removed if v_s ≥ Q/A. Detention time = V/Q.

Activated sludge.

• Food to microorganism ratio F/M = QS₀/(VX).
• Mean cell residence time θ_c = VX/(Q_wX_w) (sludge age).
• Sludge volume index SVI = settled volume (mL/L) × 1000 / MLSS (mg/L).

Hardness (as CaCO₃): mg/L of ion × 50/equivalent weight (Ca²⁺: 20, Mg²⁺: 12.15).

Air pollution. Gaussian plume concentration on the centreline at ground level for an effective stack height H: C = Q/(πuσ_yσ_z) · exp(−H²/(2σ_z²)). Control devices include cyclones, bag filters, electrostatic precipitators and scrubbers. Lapse rates decide stability: a superadiabatic lapse rate gives unstable air and looping plumes; an inversion gives fanning.

Noise. Sound levels add on an energy basis: L = 10 log₁₀ Σ 10^L_i/10. Two equal sources give 3 dB more than one.

Worked example

A wastewater has an ultimate BOD of 250 mg/L and k = 0.23 per day (base e). Find the 5-day BOD. Then find the settling velocity of a particle of diameter 0.05 mm and G_s = 2.65 in water at ν = 1.0 × 10⁻⁶ m²/s, and the combined level of two machines at 85 dB and 88 dB.

import math

L0, k = 250, 0.23
print(f"BOD5 = {L0 * (1 - math.exp(-k * 5)):.2f} mg/L")
g, Gs, d, nu = 9.81, 2.65, 0.05e-3, 1.0e-6
vs = g * (Gs - 1) * d * d / (18 * nu)
print(f"Stokes settling velocity = {vs * 1000:.4f} mm/s")
print(f"85 dB + 88 dB = {10 * math.log10(10 ** 8.5 + 10 ** 8.8):.2f} dB")
P0, r = 50000, 0.03
print(f"geometric growth, 20 years at 3%: {P0 * (1 + r) ** 20:.0f}")

BOD5 = 170.84 mg/L
Stokes settling velocity = 2.2481 mm/s
85 dB + 88 dB = 89.76 dB
geometric growth, 20 years at 3%: 90306

Practice questions