Civil Engineering 2025 Paper II 50 marks Solve

Q8

(a) The figure shows an overflow spillway which is 40 m high. At the design energy head of 2·5 m over the spillway, determine— (i) the sequent depths; (ii) the energy loss; (iii) the percentage of initial energy lost for the hydraulic jump formed on a horizontal apron at the toe of the spillway. 20 marks (b) 20 MLD of water with 80 mg/L of suspended solids is treated with alum [Al₂(SO₄)₃ · 14·3H₂O] dose of 60 mg/L. Find the quantity of sludge produced assuming that sufficient natural alkalinity is available. Take specific gravity of sludge as 1·04 and removal efficiency as 60%. 15 marks (c) Explaining the procedure for developing a wind rose, discuss the applications of wind rose using a typical sketch. 15 marks

हिंदी में प्रश्न पढ़ें

(a) चित्र में एक अधिप्रवाही उत्प्लाव दर्शाया गया है, जो 40 m ऊँचा है। उत्प्लाव के ऊपर 2·5 m की अभिकल्पन ऊर्जा दाबोच्चता एवं क्षैतिज अंचल (एप्रन) पर उत्प्लाव के पदार पर बने जलोच्छल के लिए निम्नलिखित को निर्धारित कीजिए : (i) अनुक्रम गहराइयाँ (ii) ऊर्जा ह्रास (iii) ह्रास हुई प्रारंभिक ऊर्जा का प्रतिशत 20 अंक (b) 20 MLD जल, जिसमें 80 mg/L निलम्बित ठोस पदार्थ है, को फिटकरी [Al₂(SO₄)₃ · 14·3H₂O] की 60 mg/L की खुराक के साथ उपचारित किया जाता है। यह मानते हुए कि पर्याप्त प्राकृतिक क्षारीयता उपलब्ध है, उत्पन्न अवपेक की मात्रा को ज्ञात कीजिए। अवपेक के विशिष्ट घनत्व को 1·04 और पृथक्कीकरण दक्षता को 60% लीजिए। 15 अंक (c) एक विंड रोज को विकसित करने की प्रक्रिया को समझाते हुए एक विशिष्ट रेखाचित्र का उपयोग करके विंड रोज के अनुप्रयोगों की चर्चा कीजिए। 15 अंक

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Approach

This question requires solving three distinct problems: (a) hydraulic jump calculations for spillway energy dissipation (40% time, 20 marks), (b) sludge production calculation in water treatment (30% time, 15 marks), and (c) explaining wind rose construction with diagram (30% time, 15 marks). Begin with clear problem identification for each part, show all formulae with standard notation (Froude number, sequent depth equation, sludge mass balance), execute calculations systematically, and conclude with physical interpretation of results.

Key points expected

  • For (a): Apply specific energy equation to find velocity at spillway toe; calculate Froude number and use Belanger's momentum equation for sequent depths y₁ and y₂; determine energy loss ΔE = (y₂-y₁)³/(4y₁y₂) and percentage loss
  • For (a): Correct identification that total head = 40 + 2.5 = 42.5 m, velocity V₁ = √(2g×42.5), and critical assessment of whether apron is truly horizontal or needs correction
  • For (b): Calculate suspended solids removed (80 × 0.6 = 48 mg/L), alum reaction stoichiometry with alkalinity, sludge mass using specific gravity 1.04, and convert to daily volume in m³/day
  • For (c): Explain wind rose construction procedure: collect wind speed/direction data, create 16-point compass sectors, calculate frequency percentages, draw radial plot with concentric circles representing frequency
  • For (c): Sketch standard wind rose showing calm percentage, prevailing wind direction, and applications: air pollution dispersion modeling (e.g., NTPC thermal plant siting), airport runway orientation, urban planning for Delhi/Mumbai airshed management
  • Cross-cutting: Unit consistency throughout (MLD to m³/s, mg/L to kg/m³), proper significant figures, and physical reasonableness checks on all numerical answers

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly applies hydraulic jump theory (Froude number, sequent depth ratio) for (a); understands alum coagulation chemistry and sludge mass balance for (b); comprehends meteorological data processing for (c); cites relevant IS codes (IS 5182 for wind, IS 6934 for spillways)Identifies basic concepts but misapplies formulae (e.g., uses energy equation instead of momentum for sequent depths); partial understanding of alum hydrolysis; knows wind rose is circular plot but unclear on construction stepsFundamental conceptual errors: treats hydraulic jump as energy gain, confuses alum with chlorine disinfection, or describes wind rose as actual rose flower; no awareness of governing principles
Numerical accuracy20%10Precise calculations: (a) y₁ ≈ 0.57 m, y₂ ≈ 3.8 m, energy loss ~12.5 m, ~29% loss; (b) sludge volume ~115-120 m³/day with proper stoichiometry; all values checked for dimensional consistency and physical reasonablenessCorrect method but arithmetic errors (wrong powers of 10, unit conversion mistakes); approximate sequent depths without exact solution; sludge calculation misses water of hydration or alkalinity contributionGross calculation errors: negative energy loss, sludge volume exceeding raw water volume, or wind frequencies summing to >100%; no verification of results
Diagram quality20%10For (a): Clear spillway profile with energy grade line, hydraulic jump profile showing y₁, y₂, and roller; for (c): professional wind rose with 16 sectors, percentage circles, calm circle center, arrow for north, and title block; labeled with Indian station data (e.g., Delhi IGI Airport)Basic sketches present but missing key elements: no EGL/HGL for spillway, or wind rose without calm percentage; rough freehand without scale or proper proportionsNo diagrams despite explicit sketch requirement; irrelevant diagrams (e.g., draws bar screen for wind rose); illegible or completely unlabeled sketches
Step-by-step derivation20%10Systematic derivation: (a) states assumptions, applies Bernoulli, calculates Fr₁, derives y₂/y₁ = 0.5[√(1+8Fr₁²)-1], computes ΔE; (b) shows mass balance: SS removed + Al(OH)₃ precipitate + entrained water; (c) tabular data processing example with 8-direction frequency tableJumps between steps without justification; skips derivation of standard formulae; presents final equations without showing substitution; wind rose procedure listed as bullet points without logical flowNo working shown—only final answers; or incoherent jumble of unrelated equations; no logical progression from given data to solution
Practical interpretation20%10Interprets (a) results for stilling basin design (need for USBR Type I/II basin if jump unstable); (b) discusses sludge handling options (dewatering, disposal at Aravali mines); (c) applies wind rose to CPCB air quality monitoring network design and industrial siting upwind of residential areasGeneric statements without specific application: 'energy loss is good' or 'wind rose helps environment'; mentions real-world relevance but no concrete Indian examplesNo interpretation of numerical results; fails to explain what 29% energy loss means for spillway safety, or why wind rose matters beyond 'it shows wind direction'

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