Mechanical Engineering 2021 Paper II 50 marks Calculate

Q7

(a) (i) A single stage impulse steam turbine rotor has a diameter of 1·2 m and runs at 3000 rpm. The nozzle angle is 18°. The blade speed ratio is 0·42. The relative velocity at the outlet to the relative velocity at inlet is 0·9. The outlet angle of the blade is 3° smaller than the inlet angle. For a steam flow rate of 10 kg/s find Blade angles at inlet and outlet, Axial thrust on the bearing and Power developed. (20 marks) (ii) Describe the phenomenon of super saturated flow observed in steam nozzle using T-s diagram. How does it influence the mass flow rate through the nozzle ? (20 marks) (b) An air-conditioned space is maintained at 27°C DBT and 50% relative humidity. The ambient conditions are 40°C DBT and 27°C WBT. The space has a sensible heat gain of 14 kW. Air is supplied to the space at 7°C saturated. Determine the following : (i) Mass of moist air supplied to the space (ii) Latent heat gain of space (iii) Cooling load of air washer if 30% of the air supplied to the space is fresh, the remainder being recirculated. Assume humid specific heat = 1·022 kJ/kg K. Psychrometric chart is given. (20 marks) (c) A six-cylinder four-stroke diesel engine develops a power of 250 kW at 1500 rpm. The brake specific fuel consumption is 0·3 kg/kWh. The pressures of air in the cylinder at the beginning of injection and at the end of injection are 30 bar and 60 bar respectively. The fuel injection pressures at the beginning and end of injection are 220 bar and 550 bar respectively. Assume the coefficient of discharge for the injector to be 0·65, specific gravity of fuel to be 0·85 and the atmospheric pressure to be 1·013 bar. Also assume the effective pressure difference to be the average pressure difference over the injection period. Determine the nozzle area required per injection if the injection takes place over 15° crank angle. If the number of orifices used in the nozzle are 4, find the diameter of the orifice. (Conversion 1 bar = 10⁵ Pascal) (10 marks)

हिंदी में प्रश्न पढ़ें

(a) (i) एक एकल पद आवेग भाप टर्बाइन के चुंबक का व्यास 1·2 m है और वह 3000 rpm पर चलता है। नोजल कोण 18° है। फलक वेग अनुपात 0·42 है। निर्गम पर सापेक्ष वेग का प्रवेश पर सापेक्ष वेग से अनुपात 0·9 है। फलक का बहिर्गम कोण अंतर्गम कोण से 3° छोटा है। 10 kg/s की भाप प्रवाह दर के लिए अंतर्गम और बहिर्गम पर फलक कोणों का मान, विचरिंग पर अक्षीय प्रणोद और विकसित शक्ति का मान ज्ञात कीजिए। (20 अंक) (ii) T-s आरेख का उपयोग करते हुए भाप नोजल में अवलोकित अति-संतृप्त प्रवाह की घटना का वर्णन करें। यह नोजल में द्रव्यमान प्रवाह दर को कैसे प्रभावित करता है ? (20 अंक) (b) एक वातानुकूलित स्थान 27°C DBT और 50% (प्रतिशत) RH पर बनाए रखा जाता है। परिवेश की स्थिति 40°C DBT और 27°C WBT है। स्थान में 14 kW का संवेद उष्मा लाभ है। 7°C पर संतृप्त वायु की आपूर्ति इस स्थान में की जाती है। निम्नलिखित निर्धारित करें : (i) स्थान में आपूर्ति की गई नम हवा का द्रव्यमान (ii) स्थान में गुप्त उष्मा लाभ (iii) धावक (वॉशर) का शीतलन भार, यदि स्थान में 30 प्रतिशत ताजी हवा की आपूर्ति की जाती है, शेष हवा का पुनःप्रचालन किया जाता है। आर्द्र विशिष्ट उष्मा = 1·022 kJ/kg K मान लें। आर्द्रतामितीय लेखाचित्र संलग्न है। (20 अंक) (c) एक छः सिलेंडर चार स्ट्रोक डीजल इंजन 1500 rpm पर 250 kW की शक्ति विकसित करता है। ब्रेक विशिष्ट ईंधन की खपत 0·3 kg/kWh है। अंतःक्षेपण की शुरुआत में और अंतःक्षेपण के अंत में सिलेंडर में हवा का दाब क्रमशः: 30 बार और 60 बार है। शुरुआत में और अंतःक्षेपण के अंत में ईंधन अंतःक्षेपण का दाब क्रमशः: 220 बार और 550 बार है। अंतःक्षेपक के लिए विसर्जन गुणांक 0·65, ईंधन विशिष्ट घनत्व 0·85 और वायुमंडलीय दाब 1·013 बार मान लें। प्रभावी दाब अंतर को अंतःक्षेपण अवधि पर औसत दाब अंतर के रूप में लें। प्रति अंतःक्षेपण के लिए, अपेक्षित तुंड का क्षेत्रफल निर्धारित करें, यदि अंतःक्षेपण 15° क्रैंक कोण से अधिक पर है। यदि तुंड में प्रयुक्त ऑरिफिसों की संख्या 4 है, तो ऑरिफिस का व्यास ज्ञात करें। (संपरिवर्तन 1 बार = 10⁵ पास्कल) (10 अंक)

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Approach

Calculate numerical solutions for all six sub-parts systematically. For (a)(i), apply velocity triangle analysis for impulse turbine; for (a)(ii), explain super-saturation with T-s diagram. For (b), use psychrometric chart data to solve air-conditioning calculations with mixing of fresh and recirculated air. For (c), compute fuel injection parameters using discharge equations. Allocate ~35% time to (a) parts combined (40 marks), ~35% to (b) (20 marks), and ~30% to (c) (10 marks), ensuring all derivations are shown stepwise with proper units.

Key points expected

  • (a)(i) Blade speed u = πDN/60 = 188.5 m/s; velocity triangles constructed with α₁=18°, ρ=0.42; β₁ and β₂ calculated using relative velocity ratio 0.9 and β₂ = β₁ - 3°
  • (a)(i) Axial thrust = ṁ(V_{w1} - V_{w2}) or ṁ(V_{f1} - V_{f2}) depending on velocity components; power = ṁ(V_{w1} + V_{w2})u or ṁV_{w}u for impulse
  • (a)(ii) Super-saturated flow: steam expands below saturation line without condensation, T-s diagram shows metastable region with Wilson line; mass flow rate increases due to higher density than equilibrium conditions
  • (b) Psychrometric properties: room air ω₁, h₁ from chart; supply air at 7°C saturated gives ω₂, h₂; mass flow rate from sensible heat equation Q_s = ṁc_p(ΔT)
  • (b) Latent heat gain from moisture difference and total heat balance; cooling load of air washer using energy balance on mixing (30% fresh, 70% recirculated) and conditioning process
  • (c) Fuel flow rate from BSFC and power; average pressure difference = [(220-30)+(550-60)]/2 = 340 bar; injection time from 15° crank angle at 1500 rpm; nozzle area from ṁ_f = C_d A √(2ρΔp)

Evaluation rubric

DimensionWeightMax marksExcellentAveragePoor
Concept correctness20%14Correctly applies impulse turbine velocity triangle theory with blade speed ratio; accurately describes super-saturation metastability and Wilson line on T-s diagram; properly uses psychrometric relations for mixed air streams; correctly models fuel injection as orifice flow with time-averaged pressure difference.Uses correct basic formulas but minor errors in velocity triangle orientation or super-saturation explanation; psychrometric approach valid but mixing ratio application shaky; injection timing calculation partially correct.Confuses impulse with reaction turbine principles; misinterprets super-saturation as superheating; applies incorrect psychrometric equations (e.g., using DBT instead of enthalpy); treats injection pressure as constant rather than average.
Numerical accuracy20%14All numerical values accurate: blade angles within ±1°, axial thrust and power correct to 3 significant figures; super-saturation mass flow increase quantified; air mass flow, latent heat, cooling load all correct; nozzle area and orifice diameter precise with proper unit conversions (bar to Pa, specific gravity to kg/m³).Most final answers correct but minor arithmetic slips in velocity components or psychrometric interpolation; injection timing or nozzle area calculation partially correct; units mostly consistent.Major calculation errors in blade angles (wrong quadrant selection), power formula (missing factor of 2 for impulse), psychrometric chart reading errors, or nozzle area formula (omitting C_d or √2 factor); unit conversion errors (bar not converted to Pa).
Diagram quality20%14Clear velocity triangles for (a)(i) with all components (V₁, V_{r1}, V_{r2}, V₂, u, α₁, β₁, β₂) labelled and angles shown; T-s diagram for (a)(ii) showing saturation line, isentropic expansion, metastable region, Wilson line, and actual path; psychrometric process sketch for (b) showing mixing line and conditioning; all diagrams neat, scaled, and annotated.Velocity triangles drawn but some components unlabelled or angles approximate; T-s diagram shows basic concept but Wilson line missing or poorly marked; psychrometric chart referenced but process sketch omitted.No velocity triangles or incorrect orientation (axial/radial confusion); T-s diagram absent or confused with h-s diagram; no process representation for air-conditioning cycle.
Step-by-step derivation20%14Every sub-part shows complete derivation: (a)(i) blade speed → velocity triangles → trigonometric solutions for angles → thrust/power; (a)(ii) theoretical basis for super-saturation with degree of super-saturation formula; (b) explicit energy and mass balances for mixing; (c) injection duration from crank angle, average pressure derivation, orifice flow equation integration.Key steps shown but some shortcuts taken (e.g., direct formula for power without velocity triangle construction); mixing calculation shown but energy balance implicit; injection time calculation correct but discharge derivation abbreviated.Final answers stated without derivation; velocity components not resolved; super-saturation described qualitatively only; psychrometric values read directly without interpolation method; nozzle area formula quoted without development.
Practical interpretation20%14Interprets axial thrust significance for bearing design in high-speed turbines; explains super-saturation impact on nozzle efficiency and erosion; relates air-conditioning results to coil sizing and energy efficiency in Indian tropical climates; discusses injection orifice sizing effect on atomization and combustion quality in diesel engines like those used in Indian Railways locomotives.Mentions practical relevance but superficially (e.g., 'thrust affects bearing life' without elaboration); notes super-saturation causes wetness losses; states air-conditioning load determines equipment size; acknowledges injection pressure affects spray quality.No practical interpretation; treats all problems as abstract calculations; no connection to real engineering systems or Indian context applications.

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