Civil Engineering 2024 Paper II 50 marks Calculate

Q7

(a) A sewer having a 60 cm diameter (D) is required to flow at 0·4 depth (i.e., a proportional depth d/D = 0·4) on a grade ensuring a degree of self-cleansing equivalent to that obtained at full depth at a velocity of 80 cm/s. Determine the required grade, associated velocities and discharges at full depth and 0·4 depth. The value of Manning's rugosity coefficient (N) = 0·015 may be taken same at all depths of flow. (20 marks) (b) Explain the following: (i) Aquitard (ii) Specific retention (iii) Storage coefficient (iv) Coefficient of permeability (v) Darcy's Law (15 marks) (c) (i) For the gravity dam shown in the following figure, determine I. Factor of safety against sliding II. Factor of safety against overturning. Take the following data: μ = 0·70, γc = 24 kN/m³, γw = 10 kN/m³, q = 1400 kN/m² (ii) Explain duty and delta. What is the discharge capacity required of the outlet to irrigate 2200 ha of sugarcane having a Kor depth of 17 cm and a Kor period of 30 days? (15 marks)

हिंदी में प्रश्न पढ़ें

(a) 60 सेमी व्यास (D) वाले सीवर को 0·4 गहराई (यानी आनुपातिक गहराई d/D = 0·4) पर एक प्रवणता पर इस तरह से प्रवाहित होना है कि 80 सेमी प्रति सेकंड के वेग पर पूर्ण गहराई पर प्राप्त के तुल्य स्वतः-अपमार्जन की कोटि को सुनिश्चित किया जा सके। पूर्ण गहराई और 0·4 गहराई पर आवश्यक प्रवणता, संबंधित वेगों और निस्सरणों को निर्धारित कीजिए। मैनिंग रूक्षता गुणांक (N) = 0·015 का मान प्रवाह की सभी गहराइयों पर समान लिया जा सकता है। (20 अंक) (b) निम्नलिखित की व्याख्या कीजिए: (i) क्षावी जलरोधी स्तर (जलरोधक) (ii) विशिष्ट धारण (iii) संग्रह गुणांक (iv) पारगम्यता गुणांक (v) डार्सी का नियम (15 अंक) (c) (i) निम्नलिखित चित्र में दर्शाए गए भाराक्षित बांध के लिए, ज्ञात कीजिए: I. सर्पण के विरुद्ध सुरक्षा गुणांक II. अपवर्तन के विरुद्ध सुरक्षा गुणांक। निम्नलिखित आँकड़ों का उपयोग कीजिए: μ = 0·70, γc = 24 किलो न्यूटन प्रति घन मीटर, γw = 10 किलो न्यूटन प्रति घन मीटर, q = 1400 किलो न्यूटन प्रति वर्ग मीटर (ii) कर्ति (ड्यूटी) और डेल्टा की व्याख्या कीजिए। 17 सेमी कोर गहराई और 30 दिनों की कोर अवधि वाले 2200 हेक्टेयर गन्ने की सिंचाई के लिए निगम (आउटलेट) की आवश्यक निस्सरण क्षमता क्या है? (15 अंक)

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Directive word: Calculate

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How this answer will be evaluated

Approach

This is a multi-part calculation-heavy question requiring precise numerical work across sewer hydraulics, groundwater theory, and dam/irrigation engineering. Allocate approximately 40% time to part (a) given its 20 marks and complex Manning's equation iterations for partial flow; 30% to part (b) for concise definitions with units and inter-relationships; and 30% to part (c) for stability calculations and duty-delta-discharge computation. Begin each part with stated assumptions, show all formulae with units, and conclude with practical significance.

Key points expected

  • Part (a): Apply Manning's equation for full depth to find required slope, then use proportional flow relationships (v/V = (d/D)^0.6, q/Q = 0.97 for d/D=0.4) to determine velocities and discharges at both depths, ensuring self-cleansing velocity equivalence
  • Part (b): Define aquitard as semi-confining layer; specific retention as volume retained against gravity; storage coefficient as S = γ_w × n × (1/β_w + 1/nβ_s); coefficient of permeability with units m/s; and Darcy's Law v = ki with validity conditions
  • Part (c)(i): Calculate factor of safety against sliding as μΣW/ΣH and against overturning as ΣM_R/ΣM_O for the gravity dam using given data, showing free body diagram with hydrostatic pressure distribution
  • Part (c)(ii): Define duty as area irrigated per cumec (ha/cumec) and delta as total depth of water; compute outlet discharge Q = (8.64 × B × D)/Δ where B=2200 ha, D=17 cm, Δ=30 days
  • Demonstrate unit consistency throughout (cm/s to m/s, kN/m³ conversions) and verify self-cleansing criteria against CPHEEO/MoUD standards for Indian sewer design

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly identifies that self-cleansing equivalence requires equal shear stress or velocity ratio approach; accurately defines all five groundwater terms with proper geological context; correctly applies stability equations for gravity dam and understands duty-delta relationship for Indian irrigation practiceBasic definitions correct but misses nuances (e.g., confuses specific retention with specific yield; applies wrong proportional flow formula; uses approximate rather than exact stability equations)Fundamental conceptual errors such as using full flow velocity for partial depth directly, defining aquitard as aquifer, or applying sliding formula without considering uplift pressure distribution
Numerical accuracy25%12.5Precise calculations with correct unit conversions: slope S ≈ 1 in 285-300 for part (a); v_0.4 ≈ 0.55-0.60 m/s; q_0.4 ≈ 0.085 m³/s; FOS_sliding ≈ 1.2-1.5 and FOS_overturning ≈ 2.0-2.5 for dam; discharge ≈ 10.5-11 cumec for sugarcane irrigationCorrect method but arithmetic errors or unit inconsistencies (e.g., cm/s not converted to m/s in Manning's; wrong hydraulic radius for partial flow; approximate duty values without standard formulas)Major calculation errors, order of magnitude mistakes, or omission of critical components like uplift pressure in dam analysis or wrong Kor depth application
Diagram quality15%7.5Clear free body diagram for gravity dam showing: hydrostatic pressure triangle, uplift pressure distribution (linear or parabolic), weight components, and dimension labels; neat sewer cross-section showing 0.4 depth with wetted perimeter and hydraulic radius markedDiagrams present but missing key elements like uplift pressure or incorrect pressure distribution; sewer diagram lacks geometric relationships for partial flowNo diagrams, or seriously flawed diagrams that misrepresent force directions, pressure distributions, or geometric properties
Step-by-step derivation25%12.5Explicit derivation showing: Manning's equation setup → full depth velocity → required slope → proportional flow equations (Camp's or similar) → partial depth calculations; complete dam stability derivation with moment arms; duty formula derivation from water balanceKey steps shown but skips intermediate derivations or assumes proportional relationships without stating; partial credit for correct final answers with incomplete workingNo derivations, only final answers stated, or incorrect formula application without explanation of variables and their sources
Practical interpretation15%7.5Interprets results: comments on adequacy of FOS values against IS 6512 standards for dam; discusses sewer self-cleansing adequacy for Indian conditions; relates duty-delta to regional water availability; suggests practical implications for design modifications if values are marginalBrief mention of standards or practical relevance without specific reference to Indian codes (IS, CPHEEO, CWC) or context-specific interpretationNo practical interpretation, or irrelevant discussion not connected to calculated values; fails to assess whether designs are acceptable for actual implementation

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