Civil Engineering 2022 Paper II 50 marks Derive

Q6

(a) (i) Define unit hydrograph. Explain two basic assumptions made in the derivation of a unit hydrograph. What are the applications and limitations of unit hydrograph? (10 marks) (ii) Given the ordinates of a 4 hr unit hydrograph as below, derive the ordinates of a 12 hr unit hydrograph by using the method of superposition. | Time (h) | Ordinate of 4 hr UH (m³/s) | |----------|---------------------------| | 0 | 0 | | 4 | 30 | | 8 | 120 | | 12 | 200 | | 16 | 250 | | 20 | 210 | | 24 | 130 | | 28 | 75 | | 32 | 50 | | 36 | 20 | | 40 | 10 | | 44 | 0 | (Only derive the ordinates. Do not plot the graph.) (10 marks) (b) (i) Considering the Indian conditions, is a separate system of sewerage a better choice than the combined system? Justify your answer. (10 marks) (ii) What is break point chlorination test? Why is it needed? (5 marks) (c) A city of 1 lakh population is supplied 150 lpcd of water. Assuming 80% of this emerging as wastewater, calculate the volume of a secondary reactor. The influent to the reactor has a BOD₅ of 150 mg/L. It is desired to have an effluent BOD₅ of 5 mg/L, an MLVSS of 3000 mg/L and an underflow concentration of 10,000 mg/L. Use the following constants: Y = 0·5 kg MLVSS/kg BOD₅ kₐ = 0·05 per day Take MCRT of 10 days and HRT of 4 hours. What is the volume and mass flow of sludge waste per day? (15 marks)

हिंदी में प्रश्न पढ़ें

(a) (i) एकांक जलालेख को परिभाषित कीजिए । एक एकांक जलालेख की व्युत्पत्ति में ली गई दो मूलभूत अभिधारणाओं की व्याख्या कीजिए । एकांक जलालेख के अनुप्रयोग तथा परिसीमाएं क्या हैं ? (10 अंक) (ii) एक 4 घंटे के एकांक जलालेख की कोटियाँ नीचे दी गई हैं । अध्यारोपण विधि का उपयोग करते हुए एक 12 घंटे के एकांक जलालेख की कोटियाँ व्युत्पन्न कीजिए । | समय (घंटे) | 4 घंटे एकांक जलालेख की कोटि (m³/s) | |-----------|----------------------------------| | 0 | 0 | | 4 | 30 | | 8 | 120 | | 12 | 200 | | 16 | 250 | | 20 | 210 | | 24 | 130 | | 28 | 75 | | 32 | 50 | | 36 | 20 | | 40 | 10 | | 44 | 0 | (केवल कोटि व्युत्पन्न कीजिए । ग्राफ आलेखित नहीं कीजिए ।) (10 अंक) (b) (i) भारतीय परिस्थितियों को ध्यान में रखते हुए, क्या वाहित मल की पृथक् पद्धति, संयुक्त पद्धति से बेहतर विकल्प है ? अपने उत्तर का औचित्य सिद्ध कीजिए । (10 अंक) (ii) क्रांतिक बिंदु क्लोरीनीकरण परीक्षण क्या है ? इसकी आवश्यकता क्यों है ? (5 अंक) (c) एक लाख जनसंख्या के शहर के लिए 150 lpcd जल प्रदान किया जाता है । यह मानते हुए कि इसका 80% अपशिष्ट जल के रूप में निकलता है, एक द्वितीयक रिएक्टर के आयतन की गणना कीजिए । रिएक्टर के अंतःश्वासी की BOD₅ 150 mg/L है । यह वांछनीय है कि बहिस्राव की BOD₅ 5 mg/L, MLVSS 3000 mg/L और अवप्रवाह सांद्रता 10,000 mg/L हो । निम्नलिखित नियतांकों का उपयोग कीजिए : Y = 0·5 kg MLVSS/kg BOD₅ kₐ = 0·05 प्रति दिन 10 दिन का एम.सी.आर.टी. और 4 घंटे का एच.आर.टी. लीजिए । प्रतिदिन अपशिष्ट अवपंक का आयतन और संचयी प्रवाह क्या है ? (15 अंक)

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Directive word: Derive

This question asks you to derive. The directive word signals the depth of analysis expected, the structure of your answer, and the weight of evidence you must bring.

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How this answer will be evaluated

Approach

Begin with precise definitions and assumptions for unit hydrograph theory in part (a)(i), then systematically apply superposition method for 12-hr UH derivation in (a)(ii). For (b), critically evaluate sewerage systems with Indian climatic and urban context, followed by clear explanation of breakpoint chlorination. In (c), methodically calculate wastewater volume, apply MCRT-based design equations for secondary reactor volume, and determine sludge waste parameters. Allocate approximately 35% time to part (c) due to higher marks and computational complexity, 30% to part (a) combining theory and numerical, and 35% to part (b) ensuring balanced coverage of both sub-questions.

Key points expected

  • Definition of unit hydrograph as direct runoff hydrograph from 1 cm effective rainfall occurring uniformly over the catchment for a specified duration; statement of linearity and time-invariance assumptions; applications in flood hydrograph prediction and limitations regarding non-uniform rainfall and catchment non-linearity
  • Correct application of superposition principle: three successive 4-hr UHs lagged by 4 hours, summed ordinate-wise, then divided by 3 to obtain 12-hr UH; accurate computation of all ordinates from t=0 to t=44 hours
  • Critical comparison of separate vs combined sewerage for Indian conditions: monsoon intensity, dry weather flow variations, first flush pollution, infrastructure costs, and operational maintenance considerations citing examples like Mumbai or Delhi experiences
  • Explanation of breakpoint chlorination curve showing residual chlorine vs applied chlorine, identification of breakpoint, and necessity for destroying ammonia and organic compounds to ensure disinfection
  • Calculation of wastewater flow (1.2 MLD), application of MCRT formula θc = (VX)/(QwXw + QeXe) to determine reactor volume, verification with HRT, and computation of sludge waste flow rate and mass using mass balance

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Precisely defines unit hydrograph with all three components (1 cm ER, uniform distribution, specified duration); correctly identifies linearity and time-invariance assumptions; accurately describes breakpoint chlorination chemistry and MCRT concept; demonstrates clear understanding of separate sewerage advantages for Indian monsoon conditionsBasic definition of UH present but missing key qualifiers; assumptions partially correct; breakpoint chlorination described superficially; sewerage comparison lacks Indian context specificityIncorrect or vague definitions; wrong assumptions stated; fundamental misunderstanding of chlorination breakpoint or MCRT concept; generic sewerage discussion without Indian relevance
Numerical accuracy25%12.5All UH ordinates computed correctly with proper superposition (0, 10, 50, 116.7, 183.3, 226.7, 196.7, 138.3, 85, 48.3, 23.3, 6.7, 0); wastewater flow correctly as 12,000 m³/day; reactor volume ~2000 m³; sludge waste ~240 m³/day and 2400 kg/day; all unit conversions accurateMinor arithmetic errors in UH ordinates (1-2 values wrong); correct approach but calculation mistakes in reactor volume or sludge; correct order of magnitude for final answersMajor errors in superposition method (forgetting division by 3); incorrect wastewater flow calculation; wrong formula application for MCRT; order of magnitude errors in final results
Diagram quality10%5Clear sketch of breakpoint chlorination curve with axes labeled (applied chlorine vs residual chlorine), showing combined residual, free residual, breakpoint, and chloramine destruction zone; neat tabular presentation of UH superposition stepsBasic breakpoint curve drawn but missing labels or zones; superposition table present but formatting unclear; diagrams support answer but lack precisionNo diagrams where needed; poorly labeled or incorrect breakpoint curve; missing superposition table; diagrams confuse rather than clarify
Step-by-step derivation25%12.5Systematic superposition: explicit lagging of three 4-hr UHs, clear summation at each time step, division by 3 stated; MCRT derivation shows complete mass balance with all terms defined; sludge waste calculation follows logically from solids inventory; each computational step explicitly shownSuperposition method stated but intermediate steps condensed; MCRT formula applied with some steps skipped; final answers correct but derivation not fully transparent; minor logical gaps in calculation sequenceNo derivation shown—only final answers; incorrect superposition method (e.g., simple averaging); MCRT applied without understanding; calculations disorganized or illogical
Practical interpretation20%10Relates UH limitations to real Indian catchment non-linearity; justifies separate sewerage choice with specific Indian examples (e.g., Chennai flooding, Delhi Yamuna pollution); explains why breakpoint chlorination essential for Indian water supplies with ammonia contamination; validates reactor design with practical HRT and MCRT ranges for activated sludgeGeneric practical comments without Indian specificity; basic validation of design parameters; limited connection between theory and field applicationNo practical interpretation; purely theoretical treatment; fails to justify design choices or relate to Indian engineering practice

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