Mechanical Engineering 2022 Paper II 50 marks Construct

Q4

(a) A single-stage impulse turbine rotor has a mean blade ring diameter of 500 mm and rotates at a speed of 10000 r.p.m. The nozzle angle is 20° and the steam leaves the nozzles with a velocity of 900 m/s. The blades are equiangular and the blade friction factor is 0·85. Construct velocity diagrams for the blades and determine the inlet angle of the blades for shockless entry of steam. Also, determine (i) the diagram power for a steam flow of 750 kg/hr, (ii) the diagram efficiency, (iii) the axial thrust and (iv) the loss of kinetic energy due to friction. (20 marks) (b) (i) Explain the effect of impeller blade shape on the performance of a centrifugal compressor with the help of an exit velocity diagram and pressure ratio-mass flow rate curve. (ii) Discuss the phenomena of surging and choking in centrifugal compressors. (20 marks) (c) A shell and tube heat exchanger operates with two shell passes and four tube passes. The shell side fluid is ethylene glycol, which enters at 140 °C and leaves at 80 °C with a flow rate of 4500 kg/hr. Water flows in the tubes, entering at 35 °C and leaving at 85 °C. The overall heat transfer coefficient for this arrangement is 850 W/m²-°C. Calculate the flow rate of water required and the area of the heat exchanger. The specific heat of ethylene glycol may be taken as 2·742 J/g-°C and the specific heat of water may be taken as 4·175 J/g-°C. For NTU relations, the following figure may be used. (10 marks)

हिंदी में प्रश्न पढ़ें

(a) औसत फलक (ब्लेड) वलय व्यास 500 mm वाली एक एकल-चरण आवेगी टर्बाइन का रोटर 10000 r.p.m. की गति से घूमता है। नोजल कोण 20° है तथा नोजल से भाप 900 m/s के वेग से बाहर निकलती है। फलक समानकोणिक है तथा फलक घर्षण गुणांक 0·85 है। फलकों के लिये वेग आरेख बनाइये तथा भाप की प्रयात्-रहित प्रविष्टि के लिये फलकों पर प्रवेश का कोण मालूम कीजिये। यह भी मालूम कीजिये (i) भाप प्रवाह 750 kg/hr के लिये आरेख शक्ति, (ii) आरेख दक्षता, (iii) अक्षीय प्रयोद और (iv) गतिज ऊर्जा की घर्षण के कारण हानि। (20 अंक) (b) (i) एक अपकेन्द्री समीपदक के निष्पादन पर प्ररोदक के फलक (ब्लेड) की आकृति के प्रभाव को, एक निर्गम वेग आरेख तथा दाब अनुपात-मात्रा प्रवाह दर वक्र की सहायता से समझाइये। (ii) अपकेन्द्री समीपदकों में प्रोल्क्षण व प्रोधन घटनाओं को समझाइये। (20 अंक) (c) एक कोष तथा नलिका उष्मा विनिमयित्र दो कोष पथ तथा चार नलिका पथ के साथ कार्यरत है। कोष की ओर का द्रव एथिलीन ग्लाइकॉल है, जो 140 °C पर प्रविष्ट होता है तथा 80 °C पर 4500 kg/hr की प्रवाह दर से बाहर निकलता है। नलिकाओं में प्रवाहित जल, 35 °C पर प्रविष्ट हो रहा है तथा 85 °C पर बाहर निकल रहा है। इस व्यवस्था के लिये समग्र उष्मा अन्तरण गुणांक 850 W/m²-°C है। वांछित जल-प्रवाह दर की तथा उष्मा विनिमयित्र के क्षेत्रफल की गणना कीजिये। एथिलीन ग्लाइकॉल की विशिष्ट उष्मा 2·742 J/g-°C तथा जल की विशिष्ट उष्मा 4·175 J/g-°C ली जा सकती है। एन० टी० यू० सम्बन्धों के लिये निम्न आरेख उपयोग में लिया जा सकता है। (10 अंक)

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Directive word: Construct

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How this answer will be evaluated

Approach

Construct velocity diagrams for part (a) as the primary directive, then explain compressor phenomena for (b), and solve the heat exchanger problem for (c). Allocate approximately 40% time to (a) given its 20 marks and diagram construction demand, 35% to (b) for its dual explanatory components, and 25% to (c) for the NTU method calculation. Begin with clear velocity triangle construction for impulse turbine, follow with theoretical explanations supported by sketches, and conclude with systematic heat exchanger sizing using the correction factor method.

Key points expected

  • Part (a): Blade speed U = πDN/60 = 261.8 m/s; velocity triangles constructed with nozzle angle 20°, equiangular blades, and friction factor 0.85 applied to relative velocities
  • Part (a): Inlet blade angle β₁ calculated from velocity triangle geometry for shockless entry; diagram power = ṁ(V_w1 + V_w2)U, efficiency = diagram power / kinetic energy supplied
  • Part (a): Axial thrust = ṁ(V_f1 - V_f2) and friction loss = ½ṁ(V_r1² - V_r2²) computed with correct mass flow rate conversion (750 kg/hr = 0.2083 kg/s)
  • Part (b)(i): Backward-curved, radial, and forward-curved blade effects on pressure ratio-mass flow characteristics with exit velocity diagrams showing V₂, V_w2, and manometric efficiency
  • Part (b)(ii): Surging as flow reversal instability at low mass flow rates and choking as sonic limit at impeller eye; both phenomena explained with performance curve annotations
  • Part (c): Heat balance Q = ṁ_glycol × c_p,glycol × ΔT_glycol = ṁ_water × c_p,water × ΔT_water to find water flow rate
  • Part (c): LMTD calculation for counterflow arrangement, correction factor F from given figure for 2-shell pass 4-tube pass configuration, and area A = Q/(U×F×LMTD)

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10For (a), correctly applies impulse turbine theory with proper velocity compounding and distinguishes between absolute/relative velocities; for (b), accurately relates blade curvature to energy transfer via Euler pump equation and correctly identifies surge as system instability vs choke as fluid-dynamic limit; for (c), properly selects correction factor method for cross-flow arrangement.Gets turbine velocity triangle basics right but confuses friction factor application; explains surge and choke descriptively without linking to compressor map; uses LMTD but may miss correction factor or apply wrong flow arrangement.Treats impulse turbine as reaction turbine or ignores blade friction; describes surge and choke as same phenomenon; applies simple LMTD without correction factor for multi-pass exchanger.
Numerical accuracy20%10All calculations precise: U = 261.8 m/s, mass flow conversion 0.2083 kg/s, diagram power ~48-52 kW range, efficiency ~65-70%, axial thrust ~15-20 N, friction loss ~2-3 kW; water flow rate ~2940 kg/hr, LMTD ~38°C, F ≈ 0.9, area ~4.5-5.5 m² with proper unit handling throughout.Correct methodology but minor arithmetic slips (e.g., mass flow in kg/hr not converted, or LMTD calculation error); final answers in correct ballpark but precision lost.Major numerical errors: wrong blade speed formula, mass flow not converted leading to power in wrong order of magnitude, or heat balance ignored leading to impossible water flow rate.
Diagram quality20%10For (a), inlet and outlet velocity triangles drawn to scale with all vectors (V₁, V_r1, V_r2, U, V_w1, V_w2, V_f1, V_f2) labelled and angles marked; for (b), exit velocity triangles for three blade types and compressor map with surge line and choke line clearly indicated; for (c), temperature profile sketch showing both fluids.Velocity triangles present but not to scale or missing some vector labels; compressor curves described without clear surge/choke demarcation; no temperature profile for heat exchanger.No velocity triangles drawn despite 'construct' directive; purely textual description of compressor performance; no diagrammatic support for any part.
Step-by-step derivation20%10For (a), shows complete velocity triangle construction: computes U, resolves V₁ into components, applies friction factor to get V_r2, closes outlet triangle, then derives all performance parameters with explicit formulas; for (c), shows heat balance, LMTD derivation, correction factor lookup process, and final area calculation stepwise.Shows key formulas but skips some intermediate steps; velocity triangle construction described but not fully derived; heat exchanger calculation jumps from Q to A without showing LMTD computation.Final answers stated without derivation; no velocity triangle construction shown; heat exchanger area quoted without any method shown.
Practical interpretation20%10For (a), comments on why shockless entry matters (efficiency, blade erosion) and relates diagram efficiency to real turbine performance; for (b), explains why backward-curved blades preferred for stability (positive slope characteristic) and industrial implications of surge protection; for (c), discusses fouling allowance, typical U values for comparison, and material selection for glycol service.Briefly mentions practical relevance without elaboration; notes that surge is undesirable but no system-level implications; states heat exchanger is reasonably sized without context.No practical interpretation; treats all parts as pure examination exercises with no engineering context or real-world relevance.

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