Mechanical Engineering 2022 Paper II 50 marks Calculate

Q6

(a) A four-cylinder diesel engine with swept volume of 0·98 litre is tested on a performance bed. The engine running at a speed of 2500 r.p.m. against a brake with arm of 0·3 m produces brake load of 190 N with fuel consumption of 6·8 litres/hr. The calorific value of fuel is 45000 kJ/kg and specific gravity of fuel is 0·82. A Morse test is carried out on the engine by cutting off the fuel supply of individual cylinder in the order 1, 2, 3, 4 with corresponding brake loads 131 N, 135 N, 133 N and 137 N, respectively. Calculate the b.p., b.m.e.p., brake thermal efficiency, b.s.f.c., i.p., mechanical efficiency and i.m.e.p. of the engine at test speed. (20 marks) (b) A power plant operates on a regenerative steam cycle with one closed feedwater heater. Steam enters the first turbine stage at 125 bar, 500 °C and expands to 10 bar, where some of the steam is extracted and diverted to the closed feedwater heater. Condensate exiting the feedwater heater as saturated liquid at 10 bar passes through a trap into the condenser. The feedwater exits the heater at 120 bar with a temperature of 170 °C. The condenser pressure is 0·06 bar. Assuming isentropic turbine and pump work, determine the thermal efficiency of the cycle. At 125 bar, 500 °C for steam, h = 3343·6 kJ/kg and s = 6·4651 kJ/kg-K. [Use steam tables provided at the end of this Paper] (20 marks) (c) Explain NH₃-water vapor absorption refrigeration system with a neat diagram. What are the desired properties of refrigerant-absorber combination? (10 marks)

हिंदी में प्रश्न पढ़ें

(a) एक चार-सिलिन्डर डीजल इंजन, जिसका प्रस्पीत आयतन 0·98 लीटर है, का निष्पादन फर्श पर परीक्षण किया गया। 2500 r.p.m. की चाल से चलने वाला इंजन 0·3 m भुजा के ब्रेक के प्रतिकूल 6·8 लीटर/घंटा की ईंधन खपत दर पर 190 N का ब्रेक भार उत्पादित करता है। ईंधन का कैलोरी मान 45000 kJ/kg तथा विशिष्ट गुरुत्व 0·82 है। 1, 2, 3, 4 के क्रम में पृथक-पृथक सिलिन्डर की ईंधन आपूर्ति रोककर तदनुसार ब्रेक भार 131 N, 135 N, 133 N तथा 137 N के क्रम में इंजन पर एक मोर्स परीक्षण किया गया। इंजन की इस परीक्षण चाल पर गणना कीजिये—ब्रेक शक्ति, ब्रेक माध्य प्रभावी दाब, ब्रेक तापीय दक्षता, ब्रेक विशिष्ट ईंधन खपत, सूचित शक्ति, यांत्रिक दक्षता तथा सूचित माध्य प्रभावी दाब। (20 अंक) (b) एक शक्ति संयंत्र, एक बंद भरण-जल तापक के साथ एक पुनर्जीवी भाप चक्र पर कार्य करता है। भाप प्रथम टरबाइन के चरण पर 125 बार, 500 °C पर प्रविष्ट होती है तथा 10 बार तक प्रसारित होती है, जहाँ कि कुछ भाप निकाल ली जाती है तथा बंद भरण-जल तापक को भेज दी जाती है। भरण-जल तापक में स्थित संयुक्त संतृप्त द्रव के रूप में 10 बार पर एक ट्रेप में होता हुआ संयंत्र में पहुँचता है। तापक से भरण-जल 120 बार तथा 170 °C तापमान के साथ बाहर निकलता है। संयंत्र दाब 0·06 बार है। टरबाइन तथा पम्प कार्य को समपद्रूपी मानते हुए चक्र की तापीय दक्षता निर्धारित कीजिये। 125 बार, 500 °C पर भाप की एन्थैल्पी h = 3343·6 kJ/kg तथा एन्ट्रॉपी s = 6·4651 kJ/kg-K है। [इस पत्र के अंत में दी हुई भाप सारणियों का प्रयोग कीजिये] (20 अंक) (c) एक स्वच्छ चित्र की सहायता से NH₃-जलवाष्प अवशोषण प्रशीतन तंत्र को समझाइये। प्रशीतक-अवशोषक संयोजन के वांछित गुण कौन-से हैं? (10 अंक)

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Directive word: Calculate

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How this answer will be evaluated

Approach

Calculate all performance parameters for the diesel engine in part (a) using Morse test principles, then solve the regenerative steam cycle in part (b) by applying energy balance and steam table interpolation. For part (c), explain the NH₃-water absorption system with a neat schematic. Allocate approximately 40% time to (a) due to multiple calculations, 40% to (b) for steam table work, and 20% to (c) for the descriptive portion with diagram.

Key points expected

  • Part (a): BP = 2πNT/60 = 2π×2500×(190×0.3)/60000 = 14.92 kW; BSFC = ṁf/BP in kg/kWh
  • Part (a): IP from Morse test = Σ(indicated power of each cylinder) using BP - BPcutoff for each cylinder
  • Part (a): Mechanical efficiency = BP/IP; IMEP = IP×60/(L×A×N/2×n) or using swept volume
  • Part (b): Apply energy balance on closed feedwater heater: y×h2 + (1-y)×h6 = h7 + (1-y)×h3 for extraction fraction
  • Part (b): Determine h at turbine exit using s1 = s2 = s3; pump work h6 - h5 = v5×(P6-P5); thermal efficiency = Wnet/Qin
  • Part (c): NH₃-water system: generator, condenser, evaporator, absorber with heat exchanger; NH₃ as refrigerant, water as absorber
  • Part (c): Desired properties: high solubility of refrigerant in absorber, large boiling point difference, low specific heat of solution, non-toxic, non-corrosive, chemically stable

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly applies Morse test principle (IP of cut cylinder = BPnormal - BPcut) for part (a); understands closed feedwater heater with trap in part (b); distinguishes refrigerant (NH₃) from absorber (water) in part (c).Applies Morse test but confuses BP and IP relationships; understands regenerative cycle but mixes open/closed heater concepts; describes absorption system but blurs refrigerant-absorber roles.Treats Morse test as cutting spark instead of fuel; confuses feedwater heater with reheat; cannot distinguish absorption from compression refrigeration.
Numerical accuracy20%10All calculations precise: BP=14.92 kW, IP from correct averaging of cylinder contributions, extraction fraction y≈0.25-0.30 in (b), thermal efficiency ≈42-45%; consistent units (kW, kJ/kg, bar).Correct final BP and IMEP but minor arithmetic slip in IP calculation; correct approach in (b) but steam table interpolation error; order-of-magnitude correct in (a) but wrong by 10-15%.Major errors: forgets 4-cylinder factor in IMEP, uses total swept volume per cylinder incorrectly; wrong turbine exit state in (b); no numerical attempt in (a) or (b).
Diagram quality20%10Clear T-s diagram for regenerative cycle in (b) showing states 1-7 with extraction point; neat schematic of NH₃-water system in (c) with all components (generator, rectifier, condenser, evaporator, absorber, pump, heat exchanger) labelled with flow directions.T-s diagram present but states not labelled or extraction point unclear; absorption system diagram missing rectifier or has confused flow directions.No diagrams; or sketches without labels, wrong cycle direction, or components missing (e.g., no trap shown, no pump in absorption system).
Step-by-step derivation20%10Shows all formulas before substitution: BP=2πNT, fuel mass flow from volume flow and SG, IPindicated = Σ(IPcylinders) from Morse data, energy balance on FWH with derivation of y, pump work integration; clear logical flow with numbered steps.Uses correct formulas but skips some intermediate steps; jumps from given data to final answers; energy balance stated but not derived.No working shown—only final answers; or incorrect formulas used throughout; no energy balance setup for feedwater heater.
Practical interpretation20%10Comments on why Morse test overestimates IP (pumping losses ignored); notes optimal extraction pressure selection in regenerative cycles; explains why NH₃-water suits industrial applications (waste heat utilization) vs LiBr-water for air conditioning; mentions Indian context (solar absorption cooling).Brief mention of Morse test limitations or regeneration purpose; states absorption uses heat not work but no application context.No interpretation; treats all parts as pure calculation; no comment on practical significance of any result.

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