Mechanical Engineering 2024 Paper II 50 marks Solve

Q7

(a) In a cooling tower used in a thermal power plant, 26,000 kg/s of air enters at DBT = 20°C and relative humidity at 20%. It leaves the cooling tower at 35°C DBT and 80% relative humidity. I. Find the following : (i) Total heat added to the air (ii) Evaporation loss of water (iii) WBT of the air at inlet and exit (iv) Change in the volume flow rate of the air in the cooling tower II. Explain the process on the Psychrometric chart. Use Psychrometric chart attached at the end. (20 marks) (b) A steam power plant operates with a boiler output of 20 kg/s steam at 2 MPa and 600°C. The condenser operates at 50°C, dumping energy into a river that has an average temperature of 20°C. There is an open feed heater with extraction from the turbine at 600 kPa, at its exit is saturated liquid. Find the mass flow rate of the extracted flow (liquid). If the river water should not be heated more than 5°C, how much water should be pumped from the river to the heat exchanger (condenser)? The steam properties at 2 MPa, 600°C are : h = 3690·14 kJ/kg s = 7·7023 kJ/kg K At 600 kPa and for s = 7·7023 kJ/kg K, take h = 3270·25 kJ/kg. Use the Steam Tables given at the end to get other properties. (20 marks) (c) IC engine cooling is a complex issue. Discuss in brief various factors affecting the heat transfer from IC engines. (10 marks)

हिंदी में प्रश्न पढ़ें

(a) एक ऊष्मीय शक्ति संयंत्र में प्रयोग होने वाली एक शीतन मीनार में 26,000 kg/s की दर से वायु DBT = 20°C एवं आपेक्षिक आर्द्रता 20% पर प्रवेश करती है। वह शीतन मीनार को 35°C DBT व 80% आपेक्षिक आर्द्रता पर छोड़ती है। I. निम्नलिखित को ज्ञात कीजिए : (i) वायु में योग की गई कुल ऊष्मा (ii) जल की वाष्पन हानि (iii) प्रवेश व निकास पर वायु का WBT (iv) शीतन मीनार में वायु के आयतन प्रवाह दर में परिवर्तन II. साइक्रोमीट्रिक चार्ट पर प्रक्रम को समझाइए। अंत में संलग्न साइक्रोमीट्रिक चार्ट का प्रयोग कीजिए। (20 अंक) (b) एक भाप शक्ति संयंत्र बॉयलर से 20 kg/s भाप उत्पादन 2 MPa व 600°C पर करने के साथ, काम करता है। संघनित्र 50°C पर काम करता है, जबकि वह ऊर्जा का क्षेपण, 20°C औसत तापमान वाली नदी में करता है। एक खुला प्रभरण तापक है जो टरबाइन से निष्कर्षण 600 kPa पर निर्गम पर संतृप्त द्रव के रूप में करता है। निष्कर्षित प्रवाह (द्रव) की द्रव्यमान प्रवाह दर ज्ञात कीजिए। यदि नदी के जल को 5°C से ऊपर गर्म नहीं करना चाहिए, तो कितना जल नदी से उष्मा विनियमित्र (संघनित्र) में पंप करना चाहिए? 2 MPa, 600°C पर भाप के गुण हैं : h = 3690·14 kJ/kg s = 7·7023 kJ/kg K 600 kPa पर तथा s = 7·7023 kJ/kg K, h = 3270·25 kJ/kg लीजिए। अन्य गुणों के लिए अंत में संलग्न भाप सारणियों का उपयोग कीजिए। (20 अंक) (c) IC इंजन का शीतन एक जटिल समस्या है। IC इंजनों से उष्मा अंतरण को प्रभावित करने वाले विभिन्न कारकों की संक्षेप में विवेचना कीजिए। (10 अंक)

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Approach

Solve the multi-part thermodynamics problem by allocating approximately 40% time to part (a) cooling tower psychrometrics, 40% to part (b) regenerative Rankine cycle with feedwater heater, and 20% to part (c) IC engine cooling factors. Begin with clear state-point identification, apply mass and energy balances systematically, and conclude with practical implications for Indian thermal power plants.

Key points expected

  • Part (a): Calculate specific humidity at inlet (ω₁ ≈ 0.0029 kg/kg) and exit (ω₂ ≈ 0.0286 kg/kg) using psychrometric relations or chart
  • Part (a): Determine enthalpies h₁ ≈ 25.5 kJ/kg and h₂ ≈ 110 kJ/kg; total heat added = ṁₐ(h₂-h₁) ≈ 2.2×10⁶ kW
  • Part (a): Evaporation loss = ṁₐ(ω₂-ω₁) ≈ 668 kg/s; WBT₁ ≈ 12°C, WBT₂ ≈ 31.5°C; volume flow change using specific volumes
  • Part (a) II: Sketch psychrometric chart showing heating and humidification process (sensible heating + adiabatic saturation)
  • Part (b): Apply mass balance at FWH: ṁₑₓₜ = ṁₛₜₑₐₘ × (h₂-h₃)/(hₑₓₜ-h₃) with h₃ = h_f at 600 kPa; find ṁₑₓₜ ≈ 4.2 kg/s
  • Part (b): Condenser heat rejection Q̇_c = (ṁₛₜₑₐₘ-ṁₑₓₜ)(h₄-h₅); river water flow ṁ_river = Q̇_c/(c_p×ΔT_max) with ΔT = 5°C
  • Part (c): Discuss factors—combustion temperature, engine speed, load, cooling system type, material conductivity, ambient conditions, lubrication

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%10Correctly applies psychrometric relations for part (a), regenerative Rankine cycle analysis with open feedwater heater for part (b), and comprehensively identifies IC engine heat transfer mechanisms for part (c); distinguishes between sensible and latent heat in cooling tower.Uses correct basic formulas but confuses open vs closed feedwater heater or misses some psychrometric property definitions; lists IC engine factors without explaining heat transfer mechanisms.Misapplies steady-flow energy equation, confuses relative humidity with specific humidity, or treats cooling tower as simple heat exchanger without mass transfer; fails to identify any IC engine cooling factors.
Numerical accuracy20%10All calculations precise: specific humidity values within 5% of chart readings, heat transfer rates correctly computed with proper unit handling (kW, kg/s), mass extraction fraction accurate, river water flow correctly determined using Q̇ = ṁc_pΔT constraint.Final answers approximately correct but intermediate values (enthalpies, specific volumes) show minor deviations; correct approach but arithmetic slips in mass flow calculations.Order-of-magnitude errors in heat transfer rates, confuses mass flow of air with water in cooling tower, or violates energy balance by >10%; ignores given steam table data.
Diagram quality20%10Clear psychrometric chart sketch for part (a) showing state points 1 and 2, constant WBT lines, and process direction; T-s diagram for part (b) with all state points (1-2-3-4-5-6) and extraction line labelled; schematic of IC engine cooling system for part (c).Psychrometric chart drawn but missing constant WBT lines or incorrect process path; T-s diagram shows cycle but extraction point unclear or missing labels; no diagram for part (c).No psychrometric chart provided despite explicit requirement; T-s diagram confused with P-v or h-s; diagrams unlabelled or misleading.
Step-by-step derivation20%10Systematic derivation: mass balance on dry air, energy balance with enthalpy terms for (a); complete FWH analysis with y = (h₂-h₃)/(hₑₓₜ-h₃) derivation for (b); structured discussion with equations for heat transfer coefficients in (c).Shows main equations but skips intermediate steps like specific humidity calculation from p_v = φp_sat; jumps to final formula for extraction fraction without derivation.No derivation shown—only final answers stated; or incorrect formula application without explanation of assumptions.
Practical interpretation20%10Relates cooling tower performance to NTPC plant efficiency and water conservation; discusses make-up water requirements and drift losses; connects regenerative cycle efficiency improvement to Indian coal plants; addresses environmental impact of condenser heat rejection on river ecosystems; cites relevance for BS-VI engine thermal management.Brief mention of water scarcity or efficiency improvement but no quantitative link; generic statements about pollution without specific context.No practical interpretation; treats problem as purely academic exercise with no connection to power plant operation or environmental constraints.

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