Civil Engineering 2025 Paper I 50 marks Compulsory Solve

Q5

(a) A rigid body having dimensions of 0·6 m wide, 0·9 m high and 1·2 m long weighs 10 kN when submerged in water. What will be its weight and density in air ? (Assume specific weight of water as 9790 N/m³.) 10 marks (b) With neat sketches explain Hydrodynamically smooth surface, Hydrodynamically rough surface and Boundary layer separation. What are the effects of separation in a fluid flow problem ? 10 marks (c) A Kaplan turbine develops 20,000 kW power at a head of 40 m. The diameter of the boss is 0·4 times the diameter of the runner. Calculate : (i) Diameter of the runner (ii) Rotational speed of the turbine (iii) Specific speed of the turbine (Assume a speed ratio of 2·5, flow ratio of 0·80 and an overall efficiency of 80%.) 10 marks (d) In a laboratory, the liquid limit test by Casagrande's apparatus is performed and following results are obtained : | Test No. | 1 | 2 | 3 | 4 | |---|---|---|---|---| | Moisture Content (%) | 68 | 58 | 50 | 45 | | No. of blows | 4 | 9 | 28 | 46 | The plastic limit of the soil is 27%. Draw the flow curve and find flow index. Also classify the soil. 10 marks (e) The unconfined compressive strength of a saturated clay is 90 kN/m². Determine the net ultimate bearing capacity of a square footing of side 0·75 m, resting on the surface of the saturated clay. What will be the safe bearing capacity if factor of safety is 2·5 ? 10 marks

हिंदी में प्रश्न पढ़ें

(a) 0·6 m चौड़ी, 0·9 m ऊँची और 1·2 m लम्बी विमाओं वाले एक दृढ़ पिण्ड को पानी में डुबोए जाने पर भार 10 kN है। वायु में इसका भार और घनत्व क्या होगा ? (जल का विशिष्ट भार 9790 N/m³ मान लीजिए।) 10 अंक (b) स्वच्छ रेखाचित्रों के साथ द्रवगतिक मसृण सतह, द्रवगतिक रूक्ष सतह और सीमान्त परत पृथक्करण की व्याख्या कीजिए। तरल प्रवाह समस्या में पृथक्करण के क्या प्रभाव हैं ? 10 अंक (c) एक कैपलन टरबाइन 40 m की दाबोच्चता पर 20,000 kW ऊर्जा उत्पन्न करता है। बॉस का व्यास, रनर के व्यास का 0·4 गुना है। गणना कीजिए : (i) रनर का व्यास (ii) टरबाइन की घूर्णन गति (iii) टरबाइन की विशिष्ट गति (गति अनुपात 2·5, प्रवाह अनुपात 0·80 और समग्र दक्षता 80% मान लीजिए।) 10 अंक (d) प्रयोगशाला में, कासाग्रांडे के उपकरण द्वारा द्रव सीमा परीक्षण किया गया और निम्नलिखित परिणाम प्राप्त हुए : | परीक्षण क्रमांक | 1 | 2 | 3 | 4 | |---|---|---|---|---| | जलांश (%) | 68 | 58 | 50 | 45 | | वारों की संख्या | 4 | 9 | 28 | 46 | मृदा की सुग्राह्यता सीमा 27% है। प्रवाह वक्र बनाइए और प्रवाह सूचकांक ज्ञात कीजिए। मृदा को वर्गीकृत भी कीजिए। 10 अंक (e) एक संतृप्त मृत्तिका का अपरिबद्ध संपीडन सामर्थ्य 90 kN/m² है। संतृप्त मृत्तिका की सतह पर आधारित 0·75 m की भुजा वाले वर्गाकार पाद की निवल चरम धारक क्षमता का निर्धारण कीजिए। यदि सुरक्षा गुणक 2·5 है, तो सुरक्षित धारक क्षमता क्या होगी ? 10 अंक

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Approach

This is a multi-part numerical and descriptive problem requiring equal time allocation (~20% per sub-part) since all carry 10 marks each. Begin with concise statements of governing principles for each part, then execute calculations systematically. For part (b), prioritize neat sketches with clear labeling. For parts (a), (c), (d), (e), show all steps with proper units and significant figures. Conclude each part with a boxed final answer and brief physical interpretation where applicable.

Key points expected

  • Part (a): Apply Archimedes' principle correctly—calculate buoyant force from displaced water volume, then determine weight in air and bulk density; avoid confusing mass density with specific weight
  • Part (b): Distinguish hydrodynamically smooth vs rough surfaces using roughness Reynolds number criterion; explain boundary layer separation mechanism with pressure gradient reversal; illustrate with velocity profiles and streamlines
  • Part (c): Use Kaplan turbine fundamental equations—speed ratio, flow ratio, and power equation; correctly relate boss diameter to runner diameter; calculate specific speed using consistent N-metric units
  • Part (d): Plot flow curve on semi-log or log-log paper as per IS:2720; determine flow index from slope; classify soil using IS classification system based on LL, PL, and plasticity index
  • Part (e): Apply Terzaghi's bearing capacity theory for cohesive soils (φ=0); use Skempton's correction for surface footing; apply factor of safety to net ultimate bearing capacity, not gross

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly identifies and applies: Archimedes' principle for (a), Reynolds roughness criterion and adverse pressure gradient for (b), Kaplan turbine dimensionless parameters for (c), Casagrande's apparatus methodology and Atterberg limits for (d), and φ=0 bearing capacity theory with Skempton's shape factor for (e)Minor conceptual errors such as using mass density instead of specific weight, confusing absolute with kinematic roughness, or applying gross instead of net bearing capacityFundamental misconceptions like treating submerged weight as buoyant force, equating hydrodynamic roughness with geometric roughness, or using bearing capacity equations for cohesionless soils
Numerical accuracy20%10All five parts yield correct numerical answers with proper significant figures: (a) weight ≈16.3 kN, density ≈2510 kg/m³; (c) runner diameter ≈4.7 m, N≈107 rpm, Ns≈550; (d) flow index ≈0.12-0.15; (e) qu(net)≈67.5 kN/m², safe≈27 kN/m²Correct method but arithmetic errors in 1-2 parts, or unit conversion mistakes (kN vs N, rpm vs rad/s)Multiple calculation errors, order-of-magnitude mistakes, or answers without any numerical working
Diagram quality20%10Part (b) contains three distinct, neatly drawn sketches: velocity profiles showing viscous sublayer for smooth/rough surfaces with roughness Reynolds number zones, and separation point with wake formation; part (d) shows properly labeled flow curve with moisture content vs log(blows)Sketches present but poorly proportioned, missing labels, or conflating smooth and rough surface characteristics; flow curve plotted but axes unlabeledNo diagrams for (b) or (d), or diagrams that contradict physical principles (e.g., separation shown with favorable pressure gradient)
Step-by-step derivation20%10Each part shows logical progression: stated formula → substitution with units → intermediate calculation → final answer; for (c) explicitly derives runner diameter from power equation before finding N and Ns; for (d) shows slope calculation methodSome steps skipped or combined, making verification difficult; missing statement of assumptions (e.g., neglecting atmospheric pressure in (a))Only final answers with no derivation, or incorrect formula application without explanation of variable meanings
Practical interpretation20%10Interprets results contextually: (a) identifies material as likely concrete/masonry; (b) relates separation to drag increase and energy loss in hydraulic structures; (c) confirms turbine suitability for low-head high-flow conditions (e.g., Himalayan foothills); (d) identifies high compressibility clay requiring preloading; (e) discusses settlement implications for shallow foundationsGeneric statements without specific connection to calculated values or Indian engineering contextNo interpretation provided, or physically absurd conclusions (e.g., negative density, turbine speed exceeding synchronous limits)

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