UPSC Mechanical Engineering 2021 — Paper II

(a) Discuss briefly the functional differences between a fan, a blower and a compressor. (10 marks) (b) Prove that shock cannot occur in subsonic flow. (10 marks) (c) Consider a large plane wall of thickness L = 0·4 m, thermal conductivity k = 2·3 W/m°C and surface area A = 20 m². The left side of the wall is maintained at a constant temperature of T₁ = 80°C while the right side loses heat by convection to the surrounding air at Tₐ = 15°C with a heat transfer coefficient of h = 24 W/m²°C. Assuming constant thermal conductivity and no heat generation in the wall, (i) obtain a relation for the variation of temperature in the wall. (ii) evaluate the rate of heat transfer through the wall. (10 marks) (d) The following equation has been proposed for the heat transfer coefficient in natural convection from long vertical cylinders to air at atmospheric pressure: h̄_c = (536.5(Tₛ - T_∞)⁰.33)/T where T = the film temperature = ((Tₛ + T_∞))/2 and T is in the range 0 to 200°C. The corresponding equation in dimensionless form is (h̄_c L)/K = C(Gr Pr)^m. Compare the two equations to determine the values of C and m such that the second equation will give the same results as the first. Use properties of dry air at 100°C and one atmosphere: K = 0·0307 W/(mk), g = 9·8 m/sec², μ = 21·673×10⁻⁶ NS/m², Cₚ = 1022 J/(kg K). The absolute pressure of one atmosphere = 101,000 N/m². The gas constant R (for air) = 287 J/kg K. Symbols have their usual meaning. (10 marks) (e) Combustion in a diesel engine is assumed to begin at inner dead centre and to be at constant pressure. The air-fuel ratio is 27 : 1, the calorific value of the fuel is 43000 kJ/kg, and the specific heat (at constant volume) of the products of combustion is given by: Cᵥ = (0·71 + 20 × 10⁻⁵ T) kJ/(kg K). R for products = 0·287 kJ/(kg K). If the compression ratio is 15 : 1, and the temperature at the end of compression is 870 K, determine the percentage of stroke at which combustion is completed. (10 marks)

(a)(i) 3 kg of air is compressed in a reversible steady flow polytropic process from 100 kPa, 40°C to 1000 kPa. During this process the law of compression followed is PV^1.25 = C. Determine the shaft work, heat transferred and the change in entropy. Assume for air C_v = 0.717 kJ/kg K and R = 0.287 kJ/kg K. (ii) Distinguish between pdv work and -vdp work. (20 marks) (b) Calculate the displacement thickness and momentum thickness of a laminar boundary layer, in terms of the nominal boundary layer thickness δ, for the following velocity distribution: u/U_0 = sin(π/2 y/δ) (20 marks) (c) An ideal gas turbine engine operates with air as the working fluid at a pressure ratio 18 : 1 and a maximum temperature of 700°C. The air enters the compressor at 100 kPa and 20°C. Determine the thermal efficiency, the heat addition and the temperature of exhaust air. For air take C_p = 1.0035 kJ/kg K and γ = 1.4. (10 marks)

(a)(i) Show that the effective conductance, (A_1F̄₁₂) for two black, parallel plates of equal area connected by re-radiating walls at constant temperature is A_1F̄₁₋₂ = A₁((1+F₁₋₂)/2). (ii) Determine the steady-state temperatures of two radiation shields placed in the evacuated space between two infinite planes at temperatures of 555 K and 278 K. The emissivity of all surfaces is 0.8. [σ = Stefan-Boltzmann constant = 5.670 × 10⁻⁸ W/m²K⁴] (20 marks) (b) Assume that the velocity distribution in the turbulent core for tube flow may be represented by u/(u_c) = (1-r/(rₒ))¹/7 where u_c is the velocity at the centre of the tube and rₒ is the tube radius. Using the Blasius relation for friction factor, derive an equation for the thickness of the laminar sublayer. For this problem the average flow velocity may be calculated using the turbulent velocity distribution. Assume linear profile in sublayer. (20 marks) (c) Explain how the process of reheating in a gas turbine affects its operational performance. (10 marks)

(a) Two walls A and B are maintained at temperatures T_A and T_B, respectively. One end of a metal rod of length l is embedded in the wall A, while the other end is fixed to wall B, the rod loses heat by convection to the environment at T_∞. Derive an expression to determine (i) the temperature distribution in the rod (ii) the total heat lost by the rod (iii) the heat transferred from the wall A (20 marks) (b) Air enters a constant-area duct at p_1 = 90 kPa, V_1 = 520 m/s and T_1 = 558°C. It is then cooled with negligible friction until it exists at p_2 = 160 kPa. Estimate : (i) V_2 (ii) T_2 and (iii) the total enthalpy of cooling in kJ/kg. Use attached chart. (20 marks) (c) Why is it more difficult to turbocharge spark ignition engines than compression ignition engines ? Under what circumstances might supercharger be more appropriate ? (10 marks)

(a) What do you understand by the term EGR? Explain how EGR reduces NOₓ emission in CI engines. (10 marks) (b) The flue gas composition measured by Orsat apparatus for a boiler burning a fuel of unknown hydrocarbon CₓHᵧ is given as follows: CO₂: 8·0%, CO: 0·9%, O₂: 8·8% and N₂: 82·3%. Determine (i) the composition of the fuel (ii) the air fuel ratio on mole and mass basis (iii) the percentage of excess air used. (10 marks) (c) Describe the following terms with reference to stream nozzle: (i) Efficiency (ηₙ) (ii) Velocity coefficient (Cᵥ). (10 marks) (d) Explain the concept of balance point between the compressor and the capillary tube in refrigeration systems. (10 marks) (e) Briefly explain the 'Equal Friction Method' of air-conditioning duct design procedure. (10 marks)

(a) (i) How does the mixture combustion in the combustion chamber of a C.I. engine differ from that of an S.I. engine? (ii) What is meant by combustion induced swirl? Show with sketches two important designs of C.I. combustion chamber using this method of swirl. (20 marks) (b) In a single-heater regenerative cycle the steam enters the turbine at 30 bar, 400°C and the exhaust pressure is 0·1 bar. The feed water heater is a direct-contact type which operates at 0·3 MPa. Find the efficiency of the cycle neglecting pump work. (At 30 bar, 400°C: h = 3230·9 kJ/kg and s = 6·9212 kJ/kg K. Also use steam tables given towards the end of booklet for steam/water properties). (20 marks) (c) A moist air sample has dry bulb temperature of 30°C and specific humidity of 11·5 gm of water vapour per kg dry air. If the saturation vapour pressure of water at 30°C is 4·24 kPa and the total pressure is 90 kPa then what is the relative humidity of the air sample? (10 marks)

(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)

(a) An ammonia vapour compression refrigeration system works between temperature limits of −6·7°C and 26·7°C. The vapour is dry at the end of compression and there is no under cooling of the liquid which is further throttled to the lower temperature. Find the COP of the machine. Use the above properties of ammonia. (20 marks) (b) In a cogeneration plant, steam enters the HP stage of a two-stage turbine at 1 MPa, 200°C and leaves it at 0·3 MPa. At this point some of the steam is bled off and passed through a heat exchanger which it leaves as saturated liquid at 0·3 MPa. The remaining steam expands in the LP stage of the turbine to 40 kPa. The turbine is required to produce a total power of 1 MW and the heat exchanger is required to provide a heating rate of 500 kW. Assuming all processes to be ideal, calculate the required mass flow rate of steam into the HP stage of the turbine. (At 1 MPa, 200°C : h = 2827·9 kJ/kg and s = 6·6939 kJ/kg K) Also use Steam Tables given at the end of the booklet. (20 marks) (c) Compare the throttling processes happening at the following two locations in the steam power plant and using T-s diagrams contrast the observed phenomena : (i) throttling of steam at inlet to turbine for governing. (ii) throttling of condensate in closed feed heater trap exit. (10 marks)