Civil Engineering 2024 Paper II 50 marks Compulsory Solve

Q5

(a) What is a flood hydrograph ? The monthly discharge (Q) data of a river at a gauging station are given below : | Month | Q (m³/s) | |---|---| | January | 30 | | February | 40 | | March | 50 | | April | 60 | | May | 80 | | June | 90 | | July | 100 | | August | 120 | | September | 110 | | October | 90 | | November | 80 | | December | 70 | Draw the hydrograph and using the graph find peak flow and minimum flow in the river. (10 marks) (b) Explain the following terms : (i) Evaporation (ii) Transpiration (iii) Evapotranspiration (iv) Infiltration (10 marks) (c) A catchment has five raingauge stations. In a year, the annual rainfall recorded by the raingauges are 72·3 cm, 86·4 cm, 94·2 cm, 103·8 cm and 71·4 cm respectively. For a 5% error in the estimation of mean rainfall, find the additional number of raingauges needed. (10 marks) (d) A high strength wastewater having an ultimate CBOD of 1000 mg/L is discharged to a river at a rate of 2 m³/s. The river has an upstream ultimate CBOD of 10 mg/L and is flowing at a rate of 8 m³/s. Assuming a reaction rate coefficient of 0·1/day, calculate the ultimate CBOD and 5-day CBOD of the river water just after the mixing point of the wastewater (at 0 km) and 20 km downstream from the mixing point. (Assume the velocity of river = 10 km/day) (10 marks) (e) What do you understand by 'per capita demand' of water ? How is it determined ? If average daily water demand is 135 litres per capita per day, determine the following : (i) Maximum daily demand of water; (ii) Maximum weekly demand of water; (iii) Maximum monthly demand of water; (iv) Maximum hourly demand of water. (10 marks)

हिंदी में प्रश्न पढ़ें

(a) बाढ़ जलालेख क्या है ? प्रमापी स्टेशन पर नदी के मासिक निस्सरण (Q) के आँकड़े नीचे दिए गए हैं : | माह | Q (घन मीटर प्रति सेकंड) | |---|---| | जनवरी | 30 | | फरवरी | 40 | | मार्च | 50 | | अप्रैल | 60 | | मई | 80 | | जून | 90 | | जुलाई | 100 | | अगस्त | 120 | | सितम्बर | 110 | | अक्टूबर | 90 | | नवम्बर | 80 | | दिसम्बर | 70 | जलालेख बनाइए और ग्राफ का उपयोग करके नदी में चरम प्रवाह और न्यूनतम प्रवाह ज्ञात कीजिए। (10 अंक) (b) निम्नलिखित पदों की व्याख्या कीजिए : (i) वाष्पन (ii) वाष्पोत्सर्जन (ट्रांस्पिरेशन) (iii) वाष्पन-वाष्पोत्सर्जन (इवैपोट्रांस्पिरेशन) (iv) अन्तःस्रंवन (10 अंक) (c) एक आवाह (जलप्रण) क्षेत्र में पाँच वर्षामापी स्टेशन हैं । एक वर्ष में, वर्षामापियों द्वारा दर्ज की गई वार्षिक वर्षा क्रमशः: 72·3 सेमी, 86·4 सेमी, 94·2 सेमी, 103·8 सेमी और 71·4 सेमी है । औसत वर्षा के आकलन में 5% त्रुटि के लिए, आवश्यक अतिरिक्त वर्षामापियों की संख्या ज्ञात कीजिए । (10 अंक) (d) एक उच्च सांद्रण का अपशिष्ट जल, जिसकी चरम CBOD 1000 mg/L है, उसे 2 घन मीटर प्रति सेकंड की दर से एक नदी में छोड़ा जाता है । नदी 8 घन मीटर प्रति सेकंड की दर से बह रही है और इसका प्रतिप्रवाह चरम CBOD 10 mg/L है । यदि अभिक्रिया दर गुणांक 0·1 प्रतिदिन है, तो अपशिष्ट जल के मिश्रण बिंदु के ठीक बाद (0 किमी पर) और मिश्रण बिंदु से अनुप्रवाह के 20 किमी पर नदी के जल की चरम CBOD और 5-दिवसीय CBOD की गणना कीजिए । (नदी का वेग 10 किमी/दिन मान लीजिए) (10 अंक) (e) जल की 'प्रति व्यक्ति माँग' से आप क्या समझते हैं ? इसे कैसे निर्धारित किया जाता है ? यदि जल की औसत दैनिक माँग 135 लीटर प्रति व्यक्ति प्रतिदिन है, तो निम्नलिखित को निर्धारित कीजिए : (i) जल की अधिकतम दैनिक माँग; (ii) जल की अधिकतम साप्ताहिक माँग; (iii) जल की अधिकतम मासिक माँग; (iv) जल की अधिकतम प्रति घंटा माँग। (10 अंक)

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Approach

This multi-part numerical-cum-theoretical question requires systematic solving with approximately 15-18 minutes per 10-mark sub-part. Begin with concise definitions for (a) and (b), then proceed to calculations for (c), (d), and (e). For (a), draw a neat hydrograph with months on x-axis and discharge on y-axis; for (d), apply mass balance and Streeter-Phelps principles; for (e), apply standard peak factors (1.8 for daily, 2.7 for weekly, etc.). Present all derivations stepwise with proper units and significant figures.

Key points expected

  • (a) Definition of flood hydrograph as discharge vs time graph showing rising limb, peak, and recession limb; correct plotting of monthly data with August peak (120 m³/s) and January minimum (30 m³/s)
  • (b) Precise definitions: evaporation (liquid to vapor from water bodies), transpiration (vapor loss through plant stomata), evapotranspiration (combined loss), infiltration (water entry into soil surface)
  • (c) Application of standard error formula for raingauge network: N = (Cv/E)²; calculation of coefficient of variation from given data and determination of additional gauges needed
  • (d) Mass balance for ultimate CBOD mixing: (QᵤCᵤ + QᵣCᵣ)/(Qᵤ+Qᵣ); application of first-order decay equation for 20 km downstream with travel time of 2 days
  • (e) Definition of per capita demand as average daily water requirement per person; application of standard peak factors: 1.8 (max daily), 2.7 (max weekly), 3.3 (max monthly), 5.0 (max hourly)
  • Correct unit conversions throughout (m³/s to MLD where applicable, km/day to travel time)
  • Proper interpretation of results in context of Indian water resources planning and pollution control standards

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Accurately defines flood hydrograph components (rising limb, crest, recession limb); distinguishes evaporation from transpiration with biological mechanism; correctly states raingauge error formula N=(Cv/E)²; applies Streeter-Phelps decay kinetics for CBOD; defines per capita demand with IS 1172:1993 relevanceBasic definitions correct but misses component details (e.g., omits recession limb); confuses evapotranspiration with potential evapotranspiration; states formula but misapplies coefficient of variation concept; understands dilution but misses decay; defines per capita demand without standard referencesFundamental conceptual errors (e.g., confuses hydrograph with hyetograph); interchanges evaporation and transpiration mechanisms; incorrect error formula; treats CBOD as conservative pollutant; no understanding of peak factor application
Numerical accuracy20%10Correct peak flow 120 m³/s and minimum flow 30 m³/s from hydrograph; Cv=14.8%, N=8.76≈9, additional gauges=4; mixed CBOD=208 mg/L, 5-day at 0 km=132 mg/L, ultimate at 20 km=170 mg/L, 5-day at 20 km=108 mg/L; peak demands: 243, 364.5, 445.5, 675 LPCDCorrect hydrograph readings but minor plotting errors; Cv calculation correct but rounding to N=8 or arithmetic errors; correct mixing formula but decay calculation errors (wrong time or k); correct peak factors but arithmetic slips in final valuesMajor calculation errors: wrong peak/minimum identification; N calculation completely wrong; mass balance errors (adds instead of weighted average); ignores decay or uses linear decay; applies wrong peak factors (e.g., uses same factor for all)
Diagram quality15%7.5Neat hydrograph with proper axes labels (months, discharge m³/s), clear title, smooth curve showing seasonal variation, marked peak and minimum points with coordinates; scale appropriate showing all 12 months distinctlyHydrograph drawn but axes unlabeled or poorly scaled; bar chart instead of smooth curve; points plotted but trend line missing; readable but untidy with erasuresNo diagram or unrecognizable sketch; wrong axes (e.g., rainfall vs discharge); incomplete data plotting; no identification of peak/minimum on graph
Step-by-step derivation25%12.5Explicit formula statement before each calculation: mass balance Cₘ=(QᵤCᵤ+QᵣCᵣ)/(Qᵤ+Qᵣ); decay equation Lₜ=L₀e^(-kt); travel time t=x/v=2 days; 5-day BOD L₅=Lᵤ(1-e^(-5k)); peak factor application with IS code references; all steps logically sequenced with units carriedFormulas implied but not stated; some intermediate steps skipped; correct final approach but missing unit conversions; partial derivation for some sub-parts onlyNo derivations shown; jumps directly to answers; incorrect formulas used; no time calculation for part (d); random multiplication without justification
Practical interpretation20%10Interprets hydrograph for reservoir operation planning; relates evapotranspiration to irrigation demand in Indo-Gangetic plains; explains raingauge density for Indian catchments (WMO standards); assesses 20 km downstream CBOD against CPCB water quality criteria (Class C: BOD<3 mg/L); discusses per capita demand variation for Indian cities vs rural areasGeneric statements about water resources; mentions pollution but no standard comparison; notes seasonal variation without planning implications; basic urban-rural distinction without dataNo interpretation of numerical results; purely mechanical calculations; irrelevant or no connection to Indian water management context

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