(a) (i) Explain Lacey's silt factor. If the value of this factor is 1.0, what does it indicate ? The longitudinal slope of a…

(a)(i) Lacey's silt factor and canal design (15 marks)

Silt factor. Lacey's silt factor is f = 1.76√d, where d is the mean particle size of the bed silt in mm. It measures how easily the bed material is scoured and carried: a larger f means coarser silt and a steeper, narrower, faster regime channel. f = 1.0 corresponds to standard (medium) silt of mean size d = (1/1.76)² ≈ 0.323 mm, the reference condition of Lacey's regime equations.

Design. The channel is in regime, so Lacey's equations apply, with S = 1/5000 = 0.0002 and f = 0.90:

S = f^(5/3)/(3340 Q^(1/6)), so Q^(1/6) = f^(5/3)/(3340 S) = 0.839/(3340 × 0.0002) = 0.839/0.668 = 1.256.

The discharge is therefore Q = 1.256⁶ = 3.92 m³/s. Then

• Velocity: V = (Q f²/140)^(1/6) = (3.92 × 0.81/140)^(1/6) = (0.02268)^(1/6) = 0.532 m/s.
• Area: A = Q/V = 3.92/0.532 = 7.37 m².
• Hydraulic radius: R = 5V²/(2f) = 5 × 0.2831/(1.8) = 0.787 m.
• Wetted perimeter: P = 4.75√Q = 4.75 × 1.980 = 9.41 m.

Bed width and depth. For side slopes ½H:1V the side length per unit depth is √(1 + 0.25) = 1.118, so

P = B + 2 × 1.118 D = B + 2.236 D and A = BD + 0.5 D².

Eliminating B = 9.41 − 2.236 D gives 1.736 D² − 9.41 D + 7.37 = 0, so D = 0.95 m (the other root, 4.5 m, is rejected because it makes B negative). Then B = 9.41 − 2.236 × 0.95 = 7.28 m. Check: A = 7.28 × 0.95 + 0.5 × 0.95² = 7.37 m², and A/P = 0.783 m, in close agreement with the Lacey R of 0.787 m.

The canal has Q = 3.92 m³/s, V = 0.53 m/s, bed width 7.3 m, depth 0.95 m, A = 7.37 m², P = 9.41 m and R = 0.79 m. Here Q is fixed by S and f through Lacey's slope equation.

(a)(ii) Effects of waterlogging (5 marks)

Waterlogging is the rise of the water table into the root zone. It drives out soil air, so roots lack oxygen, nitrification stops and crop yield falls. Capillary rise and evaporation leave salts on the surface, making the soil saline or alkaline and sometimes barren. Tillage and sowing are delayed, and the yield of crops like wheat and cotton drops sharply. Stagnant water breeds mosquitoes and spreads malaria, and it damages foundations, roads and canal linings.

(b) Emissions from a 1000 MW coal-fired plant (15 marks)

Assumptions. The percentages are on an as-received basis (8 + 7 + 78 + 2 + 2 + 1 + 2 = 100%); all carbon burns to CO₂ and all sulphur to SO₂; a year has 8760 h.

Coal consumption. Average output = 1000 × 0.70 = 700 MW, so the annual electrical energy is 700 × 8760 = 6.132 × 10⁶ MWh = 6.132 × 10⁶ × 3600 = 2.207 × 10¹⁰ MJ. The heat input is this divided by the efficiency, 2.207 × 10¹⁰/0.42 = 5.256 × 10¹⁰ MJ. Coal burnt = 5.256 × 10¹⁰/30 = 1.752 × 10⁹ kg = 1.75 × 10⁶ t/yr (about 55.6 kg/s).

Particulates, no control. Ash = 0.07 × 1.752 × 10⁹ = 1.226 × 10⁸ kg. Fly ash is 77% of this: 0.77 × 1.226 × 10⁸ = 9.44 × 10⁷ kg = 94 400 t/yr (about 9.4 × 10⁴ t/yr).

CO₂. Carbon burnt = 0.78 × 1.752 × 10⁹ = 1.367 × 10⁹ kg. C + O₂ → CO₂, so each kg of C gives 44/12 kg of CO₂: 1.367 × 10⁹ × 44/12 = 5.01 × 10⁹ kg = 5.0 Mt/yr.

SO₂. Sulphur = 0.01 × 1.752 × 10⁹ = 1.752 × 10⁷ kg. S + O₂ → SO₂, so each kg of S gives 64/32 = 2 kg of SO₂: 3.50 × 10⁷ kg = 35 000 t/yr.

Particulates with a 99% ESP. Emission = (1 − 0.99) × 94 400 = 944 t/yr, about 0.94 × 10³ t/yr. The ESP removes 93 500 t/yr of fly ash, which must be handled as a by-product (bricks, cement, road fill).

(c) SWM Rules, 2026: key additions and the paradigm shift (15 marks)

The Solid Waste Management Rules, 2026 were notified on 28 January 2026 and came into force on 1 April 2026, superseding the SWM Rules, 2016. The 2016 rules asked citizens to segregate waste into three streams, made local bodies the main actors, and left much of the burden on municipalities.

Key additions.

• Four-stream source segregation: wet, dry, sanitary and special care waste, against three streams in 2016.
• Polluter-pays compensation: environmental compensation on violators, levied by State and Union Territory pollution control boards or committees under CPCB guidelines.
• Bulk waste generators: buildings of 20,000 m² or more floor area, or 40,000 litres a day water use, or 100 kg a day of waste, about 30% of all waste, come under an extended bulk waste generator responsibility: on-site wet-waste processing or a responsibility certificate.
• Central online portal: registration, authorisation, returns and audits of the whole waste cycle are on one portal.
• Materials recovery facilities and carbon credits: MRFs are recognised as sorting and deposit points, and local bodies are encouraged to earn carbon credits.
• Landfill discipline: only non-recyclable, non-energy-recoverable and inert waste may go to landfill, with higher fees for unsegregated waste and annual audits by State boards.
• Legacy dumpsites: time-bound mapping, biomining and bioremediation with quarterly reporting.
• Waste-to-resource targets: RDF use in cement and similar industries rising from 5% to 15% over six years, and bio-methanation for wet waste.
• Special areas: provisions for hills and islands, including tourist user fees.

Paradigm shift. The 2016 framework was about collection and disposal by local bodies, with weak enforcement. The 2026 rules move to a circular economy: responsibility shifts to the generator, enforcement rests on financial liability and digital tracking, and landfill becomes the last resort, not the default.