(a) Two settling tanks – one rectangular, with length to width ratio of 3 : 1 and side water depth of 3·5 m; and the other circular, with side water depth of 4·0 m – are to be designed to treat 20,000 m³/d of water required for a city's water supply.

Question

(a) Two settling tanks – one rectangular, with length to width ratio of 3 : 1 and side water depth of 3·5 m; and the other circular, with side water depth of 4·0 m – are to be designed to treat 20,000 m³/d of water required for a city's water supply. The surface overflow rate for satisfactory removal of solids is 20 m/d. Determine the dimensions of the settling zone of the two tanks. Check for retention time, horizontal velocity and weir overflow rate which should respectively be 3–5 hours, less than 10 m/h and 6 to 10 m³/h per m. Also determine the overall dimensions of the basins keeping length of inlet zone and outlet zone equal to the side water depth of the basin. (20 marks)

(b) Although it would be expected that the value of the ultimate carbonaceous BOD would be as high as the COD, this is seldom the case. What are the reasons for the observed differences? (15 marks)

(c) Determine the storage capacity of a reservoir for the given cropping pattern, canal losses are 15% and reservoir losses are 10%. (15 marks)

UPSC Answer Check · Accepted Answer

Begin with a clear statement of given data and design criteria for both tanks in part (a). Allocate approximately 40% of effort to part (a) as it carries 20 marks, with detailed step-by-step calculations for rectangular and circular tank dimensions, followed by verification checks for retention time, horizontal velocity and weir overflow rate. For part (b) (15 marks), explain the theoretical basis for BOD/COD relationship, then enumerate practical reasons for divergence including biodegradability limitations, toxic substances, and microbial kinetics. For part (c) (15 marks), present the cropping pattern data clearly, apply sequential monthly water balance calculations accounting for crop water requirements, effective rainfall, canal losses (15%) and reservoir losses (10%) to determine storage capacity. Conclude with a summary table comparing both tank designs and key insights on BOD/COD differences.
- Part (a): Correct application of surface overflow rate formula (Q/As = 20 m/d) to determine plan areas; calculation of rectangular tank dimensions (L:B = 3:1, SWD = 3.5m) yielding L ≈ 55 m, B ≈ 18.3 m; circular tank diameter ≈ 35.7 m with SWD = 4.0 m
- Part (a): Verification of retention time (3-5 hours), horizontal velocity (<10 m/h), and weir overflow rate (6-10 m³/h/m) with clear pass/fail assessment; overall dimensions including inlet/outlet zones each equal to SWD
- Part (b): Explanation that COD measures total oxidizable matter while BOD measures only biodegradable fraction; reasons for BOD < COD including: presence of refractory organic compounds, toxic/inhibitory substances, insufficient acclimatization period, nitrification interference, and soluble non-biodegradable organics
- Part (b): Reference to typical BOD/COD ratios (0.4-0.8 for municipal wastewater, lower for industrial wastewater) and significance for treatment plant design
- Part (c): Monthly water balance computation: Crop water requirement (CWR) = CWR peak × kc × area; net irrigation requirement = CWR - effective rainfall; gross irrigation = net/(1-canal losses); reservoir yield accounting for 10% losses; storage capacity as maximum cumulative deficit
- Part (c): Application to typical Indian cropping pattern (e.g., kharif paddy + rabi wheat) with proper unit conversions (ha-m or Mm³) and final reservoir capacity determination

Dimension	Weight	Max marks	Excellent	Average	Poor
Concept correctness	20%	10	Correctly identifies and applies fundamental principles: surface overflow rate and tank geometry relationships for (a); microbial degradation kinetics and analytical chemistry distinctions for (b); irrigation water requirement calculations and reservoir operation studies for (c). Uses appropriate IS codes (IS 1172, IS 2470) and CPHEEO guidelines where relevant.	Identifies most principles correctly but with minor conceptual errors (e.g., confusing detention time with retention time, or mixing up canal and reservoir loss application sequence). Shows basic understanding of BOD/COD relationship but misses key inhibitory factors.	Major conceptual errors such as using wrong formulas (velocity instead of overflow rate), fundamental misunderstanding of BOD as 'oxygen demand' versus 'oxygen consumed', or applying losses incorrectly (adding instead of dividing by efficiency factor).
Numerical accuracy	25%	12.5	All calculations accurate to appropriate significant figures; correct unit conversions throughout; verification checks in (a) yield values within specified ranges with clear commentary; part (c) shows correct monthly accumulation with proper handling of carry-over storage. Final answers explicitly stated with units.	Minor arithmetic errors (±5-10%) or unit conversion mistakes that don't fundamentally alter design; correct methodology but occasional calculator errors; partial verification checks in (a) or incomplete monthly table in (c).	Major calculation errors (>20% deviation), wrong order of magnitude, missing units, or completely omitted numerical sections. No verification of design criteria in (a) or incorrect application of loss percentages in (c).
Diagram quality	15%	7.5	Clear, labeled schematic diagrams for both rectangular and circular settling tanks in (a) showing: inlet zone, settling zone, outlet zone, sludge zone, weir arrangements, and flow patterns. Neat freehand or ruled drawings with dimensions indicated. For (c), optional reservoir operation diagram showing inflow-outflow mass curve.	Basic diagrams present but lacking detail (e.g., missing inlet/outlet zone demarcation, no flow arrows, or unlabeled dimensions). Diagrams support answer but don't enhance understanding significantly.	No diagrams despite clear need for visual representation; or extremely poor sketches that confuse rather than clarify; diagrams copied without relevance to calculated dimensions.
Step-by-step derivation	25%	12.5	Logical, sequential presentation with explicit formula statements before substitution; clear distinction between given data, assumptions, and derived values; systematic verification of each design check in (a); structured monthly water balance table in (c) with all intermediate steps visible. Cross-referencing between sub-parts where relevant.	Most steps shown but with some shortcuts or 'jumped' calculations; verification checks present but not systematically derived; water balance table present but with some aggregated values obscuring methodology.	Disorganized presentation with no clear flow; missing intermediate steps making verification impossible; final answers appear without supporting derivation; no tabular format for complex calculations in (c).
Practical interpretation	15%	7.5	Critical comparison of rectangular vs circular tank merits (sludge removal efficiency, construction cost, land use) in (a); discussion of implications of BOD/COD ratio for treatment plant design and effluent standards in (b); sensitivity analysis of loss percentages and discussion of live storage vs dead storage in (c). References to Indian conditions (e.g., high temperature effects on settling, monsoon cropping patterns).	Brief mention of practical implications without elaboration; standard textbook comparisons without critical insight; generic statements about 'safety factors' without specific application.	No practical interpretation provided; purely mathematical exercise without engineering judgment; fails to recognize that calculated dimensions may need standardization or that BOD/COD ratio has operational significance.

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