Civil Engineering 2025 Paper II 50 marks Compulsory Solve

Q5

(a) A box culvert has an expected life of 10 years. (i) If the acceptable risk of at least one event exceeding the culvert capacity during the design life is 5 percent, what design period should be used? (ii) What is the chance that the box culvert designed for an event of this return period will not have its capacity exceeded for 50 years? 10 (b) A well fully penetrates a 50 m thick confined aquifer. After a long period of pumping at a constant rate of 0·10 m³/s, the drawdowns at distances of 50 m and 150 m from the well are observed to be 3 m and 1·2 m respectively. With the help of a sketch, determine the hydraulic conductivity and the transmissivity. 10 (c) Enumerate any five adverse effects of reservoir sedimentation. How can it be reduced? 10 (d) The BOD of wastewater sample incubated @ 30 °C for 1 day was 120 mg/L. Find 5-day BOD @ 20 °C and estimate the percent of unoxidized BOD @ 20 °C after 20 days. Take rate constant as 0·1/day @ 20 °C. 10 (e) Explaining the process of composting municipal solid wastes, discuss the important design considerations of aerobic composting. 10

हिंदी में प्रश्न पढ़ें

(a) एक बॉक्स पुलिया का अपेक्षित कार्यकाल 10 वर्ष है। (i) यदि अभिकल्पना अवधि के दौरान कम-से-कम एक घटना के पुलिया की क्षमता से अधिक होने का स्वीकार्य जोखिम 5 प्रतिशत है, तो कितनी अभिकल्पना अवधि का उपयोग किया जाना चाहिए? (ii) इसकी क्या संभावना है कि इस पुनरागमन अवधि की एक घटना के लिए अभिकल्पित बॉक्स पुलिया की क्षमता 50 वर्ष तक पार नहीं होगी? 10 (b) एक कुआँ 50 m मोटे एक परिरुद्ध जलभृत का पूर्ण रूप से अंतर्वेशन करता है। 0·10 m³/s की नियत दर से लम्बे समय तक पम्पिंग के बाद कुएँ से 50 m और 150 m की दूरी पर अपकर्ष (ड्रॉडाउन) क्रमशः 3 m और 1·2 m प्रेक्षित किए गए हैं। एक रेखाचित्र की सहायता से द्रवीय चालकता (कंडिक्टिविटी) और संचरणीयता (ट्रांसमिसिविटी) निर्धारित कीजिए। 10 (c) जलाशय के तलछटीकरण (सेडिमेंटेशन) के किन्हीं पाँच प्रतिकूल प्रभावों का उल्लेख कीजिए। इसे कैसे कम किया जा सकता है? 10 (d) 30 °C पर 1 दिन के लिए उष्मायन किए गए अपशिष्ट जल के नमूने का बी० ओ० डी० 120 mg/L था। 20 °C पर 5 दिनों का बी० ओ० डी० ज्ञात कीजिए और 20 दिनों के बाद 20 °C पर अन-ऑक्सीकृत बी० ओ० डी० के प्रतिशत का आकलन कीजिए। 20 °C पर दर नियतांक को 0·1 प्रतिदिन लीजिए। 10 (e) नगरीय ठोस अपशिष्ट की कम्पोस्टिंग की प्रक्रिया की व्याख्या करते हुए वायुजीवी (एरोबिक) कम्पोस्टिंग के महत्वपूर्ण अभिकल्पना विचारों पर चर्चा कीजिए। 10

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Approach

This is a multi-part numerical and descriptive problem requiring systematic solving of five distinct sub-parts. Allocate approximately 20% time to each part: (a) risk analysis using probability concepts, (b) Thiem's equation application with sketch, (c) enumeration with mitigation measures, (d) BOD kinetics with temperature correction, and (e) composting process explanation with design considerations. Begin with clear identification of given data, apply appropriate formulae with proper units, and conclude with practical significance for Indian water resources and waste management contexts.

Key points expected

  • (a)(i) Apply risk formula R = 1 - (1 - 1/T)^n to find design return period T ≈ 195 years for 5% risk over 10 years
  • (a)(ii) Calculate probability of non-exceedance as (1 - 1/195)^50 ≈ 77% for 50-year period
  • (b) Apply Thiem's steady-state equation with sketch showing confined aquifer, well, and observation wells; compute K ≈ 4.17×10⁻⁴ m/s and T ≈ 2.08×10⁻² m²/s
  • (c) List five effects: reduced storage capacity, upstream flooding, delta formation, turbine abrasion, and ecological impacts; suggest watershed management, check dams, and sediment flushing
  • (d) Apply temperature correction k₃₀ = k₂₀ × θ^(T-20) with θ=1.047, then L₀ = BOD₁/(1-e^(-kt)), compute 5-day BOD₂₀ ≈ 162 mg/L and unoxidized % after 20 days ≈ 13.5%
  • (e) Explain composting phases (mesophilic, thermophilic, maturation) with C/N ratio control, moisture 50-60%, aeration, and turning frequency for aerobic design

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly identifies and applies: risk probability for hydrologic design, Thiem's equation assumptions for confined aquifer, reservoir sedimentation mechanisms, first-order BOD kinetics with temperature effects, and aerobic composting microbiology; no conceptual errors across any sub-partGenerally correct concepts with minor errors—e.g., confuses return period with annual exceedance probability, or applies unconfined aquifer equation to confined problem, or misses temperature correction necessityFundamental misconceptions—e.g., treats risk as simple division, uses wrong aquifer type equation, ignores BOD rate constant temperature dependency, or describes anaerobic instead of aerobic process
Numerical accuracy20%10All calculations precise: (a) T=195 years, 77.3% probability; (b) K=4.17×10⁻⁴ m/s, T=2.08×10⁻² m²/s; (d) k₃₀=0.158/day, L₀=207 mg/L, BOD₅=162 mg/L, 13.5% unoxidized; proper significant figures and unit conversionsCorrect method but arithmetic errors—e.g., wrong exponent handling in risk formula, or calculation errors in Thiem's equation, or incorrect temperature coefficient application yielding BOD errors of 10-20%Major calculation errors—wrong formulae, order-of-magnitude mistakes, missing units, or incomplete numerical work for any sub-part; demonstrates inability to handle engineering computations
Diagram quality15%7.5Clear labeled sketch for (b) showing: confined aquifer with impermeable layers, fully penetrating well, two observation wells at r₁=50m and r₂=150m, drawdowns s₁=3m and s₂=1.2m, flow direction arrows, and aquifer thickness b=50m; neat freehand acceptableSketch present but incomplete—missing labels for distances/drawdowns, or unclear aquifer boundaries, or shows unconfined instead of confined conditions; diagram supports answer but requires examiner interpretationNo diagram for (b), or completely wrong sketch showing wrong aquifer type, or illegible drawing without essential elements; fails to demonstrate visual understanding of well hydraulics
Step-by-step derivation25%12.5Systematic derivations: (a) shows R=1-(1-1/T)^n rearrangement; (b) derives Thiem's equation Q=2πKb(s₁-s₂)/ln(r₂/r₁) before substitution; (d) shows k temperature correction, then L₀ determination, then BOD₅ calculation; all steps logically sequenced with formulae stated firstSome steps shown but gaps exist—jumps from formula to answer without intermediate values, or skips Thiem's equation statement, or omits temperature correction derivation; final answers correct but process unclearNo derivations shown—only final answers, or completely wrong equation usage without explanation; demonstrates rote memorization without understanding of mathematical modeling in engineering
Practical interpretation20%10Connects to Indian context: (a) discusses how 195-year design affects cost-benefit for NHAI culverts; (b) interprets K value for typical alluvial aquifer suitability; (c) cites Bhakra or Hirakud sedimentation; (d) relates BOD standards to CPCB discharge norms; (e) references Okhla or Hyderabad composting plants with design parametersGeneric practical mentions without specific Indian examples—e.g., 'sedimentation is bad for dams' or 'composting helps environment' without institutional or regulatory contextPurely theoretical with no practical interpretation, or irrelevant examples; fails to demonstrate awareness of how these calculations inform actual civil engineering decisions in Indian water resources and environmental management

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