Civil Engineering 2022 Paper II 50 marks Compulsory Solve

Q5

(a) A catchment has six rain gauge stations. In a year, the annual rainfall recorded by the rain gauges are as follows: | Station | A | B | C | D | E | F | |---------|---|---|---|---|---|---| | Rainfall (cm) | 90 | 100 | 200 | 130 | 120 | 150 | Determine: (i) The standard error in the estimation of mean rainfall in the existing set of rain gauges. (ii) Optimum number of rain gauges in the catchment for 22% error and 5% error. (10 marks) (b) In a confined aquifer whose thickness is 40 m, a well is fully penetrated. Under steady state condition, it is pumped with a constant discharge of 0·04 m³/s. The drawdowns observed at two wells located at 20 m and 200 m from the well are 3·5 m and 0·5 m respectively. Determine the transmissibility and permeability of the aquifer. (10 marks) (c) With the help of a neat sketch, explain the effect of frequency of irrigation on average moisture content, field capacity and permanent wilting point. During a particular stage of crop growth, consumptive use of water is 3 mm/day. Determine frequency of irrigation and depth of water to be applied if the amount of water available in the soil is 50% and root zone depth is 100 mm. Assume irrigation efficiency to be 80%. (10 marks) (d) Determine the UBOD and BOD₅ (in mg/L) of a mixture of 100 mg/L glutamic acid (C₅H₁₀N₂O₃) and 100 mg/L glucose (C₆H₁₂O₆). Assume the value of the BOD₅ first order reaction rate constant as 0·23/d (base 'e'). (10 marks) (e) A multiple tube fermentation test of a river water sample gives the following results: | Serial dilution | 1·0 | 0·1 | 0·01 | 0·001 | 0·0001 | |-----------------|-----|-----|------|-------|--------| | Number of positives | 5 | 5 | 3 | 2 | 0 | The standard values for MPN or coliforms per 100 mL of sample are given below: Number of positive tubes | 10 mL | 1 mL | 0·1 mL | MPN | |-------|------|--------|-----| | 5 | 5 | 3 | 920 | | 5 | 3 | 2 | 140 | | 3 | 2 | 0 | 14 | What is the MPN for the river water sample? (10 marks)

हिंदी में प्रश्न पढ़ें

(a) एक आवाह (जल-ग्रहण) क्षेत्र में छः वर्षामापी स्टेशन हैं । एक वर्ष में, वर्षामापियों द्वारा अंकित वार्षिक वृष्टिपात निम्नानुसार है : | स्टेशन | A | B | C | D | E | F | |--------|---|---|---|---|---|---| | वृष्टिपात (सेमी) | 90 | 100 | 200 | 130 | 120 | 150 | निर्धारित कीजिए : (i) वर्षामापियों के वर्तमान समूह के लिए औसत वृष्टिपात के आकलन में मानक त्रुटि । (ii) 22% त्रुटि तथा 5% त्रुटि के लिए आवाह (जल-ग्रहण) क्षेत्र में वर्षामापियों की इष्टतम संख्या । (10 अंक) (b) एक 40 m मोटाई के परिबद्ध जलवाही स्तर को एक कूप पूर्णतया बेधता है । स्थायी दशा अवस्था में, इसमें से 0·04 m³/s का नियत निस्सरण पंप किया जाता है । इस कूप से 20 m तथा 200 m दूरी पर स्थित दो कूपों में क्रमशः 3·5 m तथा 0·5 m का अपकर्ष प्रेक्षित किया जाता है । जलवाही स्तर की पारगमन क्षमता तथा पारगम्यता ज्ञात कीजिए । (10 अंक) (c) एक स्वच्छ रेखाचित्र की सहायता से औसत जलांश, क्षेत्र क्षमता और स्थायी म्लानी बिंदु (विल्टिंग पॉइंट) पर सिंचाई की आवृत्ति के प्रभाव की व्याख्या कीजिए । फसल वृद्धि की एक विशेष अवस्था के दौरान, पानी का उपभुक्त उपयोग 3 मिमी/दिन है । सिंचाई आवृत्ति तथा प्रयोग की जाने वाली पानी की गहराई ज्ञात कीजिए यदि मृदा में पानी की उपलब्ध मात्रा 50% है तथा मूल क्षेत्र गहराई 100 mm है । सिंचाई दक्षता को 80% मान लीजिए । (10 अंक) (d) एक 100 mg/L ग्लूटेमिक एसिड (C₅H₁₀N₂O₃) तथा 100 mg/L ग्लूकोस (C₆H₁₂O₆) के मिश्रण की UBOD तथा BOD₅ (mg/L में) ज्ञात कीजिए । BOD₅ प्रथम कोटि अभिक्रिया दर नियतांक के मान को 0·23/d (आधार 'e') मान लीजिए । (10 अंक) (e) एक नदी के जल के नमूने पर बहु-नली किंवन परीक्षण से निम्नलिखित परिणाम प्राप्त हुए : | क्रमिक तनुकरण | 1·0 | 0·1 | 0·01 | 0·001 | 0·0001 | |---|---|---|---|---|---| | धनात्मकों की संख्या | 5 | 5 | 3 | 2 | 0 | नमूने के लिए एम.पी.एन. अथवा कोलीफॉर्म प्रति 100 mL के मानक मान नीचे दिए गए हैं : | धनात्मक नलियों की संख्या | | | | |---|---|---|---| | 10 mL | 1 mL | 0·1 mL | एम.पी.एन | | 5 | 5 | 3 | 920 | | 5 | 3 | 2 | 140 | | 3 | 2 | 0 | 14 | नदी के जल के नमूने का एम.पी.एन. क्या है ? (10 अंक)

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Approach

Solve all five numerical sub-parts systematically, allocating approximately 15-18 minutes per part. For (a), apply statistical formulas for standard error and optimum rain gauges; for (b), use Thiem's equation for confined aquifers; for (c), sketch the moisture content diagram before calculations; for (d), compute theoretical oxygen demand using stoichiometric equations; for (e), apply MPN table interpolation. Present each solution with clear formula-statement, substitution, and final answer with units.

Key points expected

  • (a)(i) Calculate mean rainfall (131.67 cm), standard deviation (~37.4 cm), and standard error of mean (σ/√n = 15.27 cm) for existing 6 stations
  • (a)(ii) Apply optimum stations formula N = (Cv/E)² to find 9 stations for 22% error and 176 stations for 5% error
  • (b) Apply Thiem's equation for confined aquifer: T = [Q·ln(r₂/r₁)]/[2π(s₁-s₂)] to get T ≈ 0.0041 m²/s and K = T/b ≈ 1.03×10⁻⁴ m/s
  • (c) Sketch showing moisture content vs time with FC, PWP, and available water range; calculate irrigation frequency = (100×0.5×0.5)/3 ≈ 8.33 days and depth = 62.5 mm at 80% efficiency
  • (d) Calculate ThOD for glutamic acid (C₅H₁₀N₂O₃ → 5CO₂ + 5H₂O + 2NH₃, ThOD = 1.031 mg/mg) and glucose (C₆H₁₂O₆ → 6CO₂ + 6H₂O, ThOD = 1.067 mg/mg); mixture UBOD = 209.8 mg/L; BOD₅ = UBOD(1-e⁻ᵏᵗ) = 209.8(1-e⁻⁰·²³ˣ⁵) ≈ 136.5 mg/L
  • (e) Apply MPN table interpolation for dilutions 1.0, 0.1, 0.01 (equivalent to 10, 1, 0.1 mL with positives 5,5,3); interpolate between 920 (5-5-3) and 140 (5-3-2) to estimate MPN ≈ 920 for river water

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly identifies and applies: coefficient of variation method for rain gauge optimization; Thiem's steady-state equation for confined aquifers; soil moisture concepts (FC, PWP, available water); ThOD/BOD₅ stoichiometric relationships; and MPN statistical estimation with proper dilution interpretationUses correct formulas but with minor conceptual errors (e.g., confusing confined vs unconfined aquifer equations, or misinterpreting dilution factors in MPN)Applies wrong formulas (e.g., Dupuit equation for unconfined aquifer in part b, or simple arithmetic mean without standard error in part a) or fundamental misunderstanding of BOD kinetics
Numerical accuracy20%10All calculations precise to 2-3 significant figures with correct unit conversions; standard error = 15.3 cm, optimum stations rounded appropriately, T = 0.0041 m²/s, K = 1.03×10⁻⁴ m/s, BOD₅ = 136-137 mg/L, MPN correctly interpolatedCorrect method but arithmetic errors (e.g., ln(10) calculation error, or efficiency factor applied incorrectly in part c) leading to answers within 10% of correct valueMajor calculation errors (wrong logarithm values, unit conversion errors m/cm, or order of magnitude mistakes in permeability) or missing units throughout
Diagram quality15%7.5Clear, labeled sketch for part (c) showing: x-axis as time/frequency, y-axis as moisture content, horizontal lines for FC and PWP, curve showing moisture depletion between irrigations, and shaded area for readily available water; diagram aids explanation of irrigation frequency effectsSketch present but missing key labels (FC, PWP not marked) or unclear axes; diagram supports answer but doesn't enhance understanding significantlyNo diagram for part (c), or completely incorrect sketch showing wrong relationships (e.g., FC below PWP, or linear instead of curved depletion)
Step-by-step derivation25%12.5Each sub-part shows: stated formula, substitution of values with units, intermediate steps visible, and boxed final answer; for (d) shows complete ThOD derivation with balanced equations; logical flow allows marks to be awarded even if final answer incorrectSome steps skipped or formulas implied rather than stated; calculations correct but working condensed making error tracing difficult; missing intermediate valuesOnly final answers with no working; or disorganized presentation mixing parts; impossible to follow logic or award partial credit
Practical interpretation20%10Interprets results practically: comments on cost-effectiveness of 176 rain gauges vs 5% accuracy; discusses aquifer productivity significance; relates irrigation frequency to crop stress avoidance; explains BOD₅/UBOD ratio implications for wastewater treatment design; notes MPN significance for Ganga water quality standardsBrief mention of practical significance without elaboration; generic statements about 'important for design' without specific contextPurely mathematical treatment with no interpretation of what results mean for engineering practice or water resource management

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