(a) A storm over a catchment of area 5 km² had a duration of 14 hours. The mass curve of rainfall of the storm is as follows: |…

(a)(i)

Using the φ-index method, for each 2 h interval: P = mass-curve difference, i = P/2, and ER = (i − φ)×2 = P − 0.8 cm if i > φ; otherwise ER = 0. Here φ = 0.4 cm/h, so φ×2 = 0.8 cm. This method is valid when the φ-index is constant and the abstraction rate cannot exceed the actual rainfall intensity.

Sample calculation, 2–4 h: P = 2.8 − 0.6 = 2.2 cm; i = 2.2/2 = 1.10 cm/h > 0.4 cm/h. ER = (1.10 − 0.40)×2 = 1.40 cm.

Summary (tabular form):

• 0–2 h: P = 0.60 cm, i = 0.30 cm/h, ER = 0 cm, ER intensity = 0 cm/h
• 2–4 h: P = 2.20 cm, i = 1.10 cm/h, ER = 1.40 cm, ER intensity = 0.70 cm/h
• 4–6 h: P = 2.40 cm, i = 1.20 cm/h, ER = 1.60 cm, ER intensity = 0.80 cm/h
• 6–8 h: P = 1.50 cm, i = 0.75 cm/h, ER = 0.70 cm, ER intensity = 0.35 cm/h
• 8–10 h: P = 0.80 cm, i = 0.40 cm/h = φ, ER = 0 cm, ER intensity = 0 cm/h
• 10–12 h: P = 1.70 cm, i = 0.85 cm/h, ER = 0.90 cm, ER intensity = 0.45 cm/h
• 12–14 h: P = 0.40 cm, i = 0.20 cm/h, ER = 0 cm, ER intensity = 0 cm/h

Total effective rainfall depth = 1.40 + 1.60 + 0.70 + 0.90 = 4.60 cm.

(a)(ii)

Direct runoff volume = effective rainfall depth × catchment area. Area = 5 km² = 5 × 10⁶ m². ER depth = 4.60 cm = 0.0460 m. Volume = 0.0460 × 5 × 10⁶ = 230,000 m³ = 2.30 × 10⁵ m³.

(a)(iii)

Effective rainfall hyetograph: plot time interval on the x-axis and ER intensity on the y-axis. Bars are: 0–2 h = 0; 2–4 h = 0.70; 4–6 h = 0.80; 6–8 h = 0.35; 8–10 h = 0; 10–12 h = 0.45; 12–14 h = 0 (all in cm/h). The peak occurs in the 4–6 h interval at 0.80 cm/h.

(b)(i)

Wastewater flow = 10 MLD = 10 × 10⁶ L/d = 10⁴ m³/d. Raw SS = 250 mg/L = 250 g/m³. SS load = 250 × 10⁴ = 2.50 × 10⁶ g/d = 2500 kg/d. SS removed by PST at 62% efficiency = 0.62 × 2500 = 1550 kg/d dry solids.

At 5% sludge concentration, wet sludge mass = 1550/0.05 = 31,000 kg/d.

Specific gravity of dry solids: 1/G_s = (60/100)/0.980 + (40/100)/2.65 = 0.6122 + 0.1509 = 0.7632 G_s = 1.310.

Sludge specific gravity: 1/G_sludge = 0.05/1.310 + 0.95/1.00 = 0.9882 G_sludge = 1.012, so ρ_sludge = 1012 kg/m³. Sludge volume = 31,000/1012 = 30.6 m³/d.

Thus sludge produced ≈ 1550 kg/d dry, 31,000 kg/d wet, or 30.6 m³/d. This assumes steady flow, constant PST efficiency, and sludge concentration by weight.

(b)(ii)

Manning’s formula: V = (1/n) R^(2/3) S^(1/2). Valid for turbulent, uniform open-channel flow with constant n. D = 0.30 m, running full: A = πD²/4 = π(0.30)²/4 = 0.0707 m². R = D/4 = 0.075 m. S = 1/500 = 0.002. R^(2/3) = (0.075)^(2/3) = 0.1778. S^(1/2) = √0.002 = 0.04472. V = (1/0.015)(0.1778)(0.04472) = 0.530 m/s. Q = A V = 0.0707 × 0.530 = 0.0375 m³/s = 37.5 L/s.

Self-cleansing check: usual minimum self-cleansing velocity for sewage is about 0.6–0.9 m/s. Here V = 0.53 m/s < 0.6 m/s, so the sewer is not self-cleansing under full-flow conditions; siltation risk exists.

(c)(i)

Problems during filter operation include: rapid clogging and high head loss, short filter runs, mud-ball formation, filter-bed cracking and shrinkage causing short-circuiting, air binding, negative head, sand incrustation, gravel displacement, media loss during backwash, underdrain blockage, biological growth, and turbidity breakthrough. Controls include proper coagulation, flocculation and sedimentation before filtration, correct media grading and depth, dual-media or anthracite filters where needed, regular air-water backwashing with surface wash, controlled backwash rate, periodic cleaning or replacement of media, maintenance of underdrains, monitoring head loss and effluent turbidity, and filter-to-waste after backwashing.

(c)(ii)

Factors for intake design: location away from pollution, erosion and navigation; adequate water depth in lean season; flood safety and freeboard; low intake velocity; screens to exclude debris, fish and ice; silt control; foundation conditions; pump suction requirements; accessibility; and provision for maintenance and redundancy.

Schematic river intake: River → trash rack → intake mouth with coarse screen → bell-mouth pipe/conduit → intake well/sump → fine screen → gate valve → pump suction → pump house → treatment plant. Components: trash rack, coarse screen, intake mouth, bell-mouth entry, intake conduit, intake well/sump, fine screen, gate valve, pumps, pump house, and access arrangement.