Mechanical Engineering UPSC PYQ 2023

A 50 kg block of iron at 500 K is placed into open atmosphere which is at a temperature of 285 K. The iron block eventually reaches thermal equilibrium with the atmosphere. Assuming an average specific heat of 0·45 kJ/kg-K for iron, determine the (i) entropy change for the iron block and the atmosphere, and (ii) irreversibility. Show that for normal shock in a perfect gas, M′x M′y = 1. In the axial flow compressor, for 50% reaction, the blading design is sometimes called symmetrical blading. Explain, with proper equations and justification, why it is called so. An industrial furnace (blackbody) is emitting radiation at 2700 °C. Calculate the following : (i) Spectral emissive power at λ = 1-2 µm (ii) Wavelength at which the emissive power is maximum (iii) Maximum spectral emissive power (iv) Total emissive power Use Planck’s distribution law equation given below : Eλb = C1 / [λ5 (exp(C2 / λT) – 1)] where C1 = 3·742 × 108 W · µm4 / m2, C2 = 1·438 × 104 µm-K Take σ = 5·67 × 10-8 W / m2 · K4. Write down three basic assumptions for LMTD method in case of heat exchanger analysis. Write down in which case LMTD method and in which case NTU method will be applicable in basic heat exchanger analysis.2b:["$","section","2023",{ Write down three basic assumptions for LMTD method in case of heat exchanger analysis. [5M] Write down in which case LMTD method and in which case NTU method will be applicable in basic heat exchanger analysis. [5M] <!--qid:MAINS_2023_Mechanical_Engineering-II_Q1-->

A 15 m high cylinder with a cross-sectional area of 0·6 m2 contains 3 m3 of liquid water at 25 °C on the top of a thin insulated piston of mass 20 kg. Below the piston, argon gas is at 15 °C with a volume of 3 m3, as shown in the figure. Heat is supplied to argon such that the piston rises and pushes the water out over the top edge. Find the (i) work done (kJ) to remove the whole water from the top of the piston and (ii) heat transferred (kJ) to argon during the process. (iii) Plot the process on a P-v diagram for argon. Assume atmospheric pressure (P0) as 101 kPa, Cv and R for argon as 0·312 kJ/kg-K and 0·2081 kJ/kg-K respectively. The specific volume of water at 25 °C is 0·001003 m3/kg. Neglect piston thickness. Air at 100 kPa and 290 K enters a gas turbine cycle with two stages of compression and two stages of expansion. This system uses ideal regenerator, reheater and intercooler. The pressure ratio across each stage is 4. 300 kJ/kg of heat is added in combustion chamber and reheater each. The regenerator increases the air temperature by 20 °C. Draw a T-s plot and determine the (i) total heat rejected (kJ/kg), (ii) net work output (kJ/kg) and (iii) thermal efficiency of the system. Assume isentropic operation for all compressors and turbines. Take Cp of air = 1·005 kJ/kg-K and γ = 1·4. A convergent-divergent nozzle has a throat area of 250 mm2 and an exit area of 500 mm2. Air enters the nozzle with a stagnation temperature of 350 K and stagnation pressure of 1 MPa. Determine the maximum flow rate of air through the nozzle and the static pressure, static temperature, Mach number and velocity at the exit from the nozzle. Given γ = 1·4, R = 0·287 kJ/kg-K. Use Gas Table to solve the problem.3e:["$","div", <!--qid:MAINS_2023_Mechanical_Engineering-II_Q2-->

Heat is generated in a stainless steel plate (thermal conductivity = 22 W/m-K) of thickness 1 cm, at a uniform rate of 600 MW/m3. The left side of the plate is maintained at 200 °C and the right side is maintained at 100 °C. What will be the (i) temperature distribution across the plate, (ii) location and value of maximum temperature and (iii) heat flux from both sides of the plate and its direction? Assume one-dimensional, steady-state heat conduction. A combination of a heat engine driving a heat pump (see the figure) takes waste energy at 50 °C as a source, Q̇w1, to the heat engine rejecting heat at 30 °C. The remainder, Q̇w2, goes into the heat pump that delivers Q̇H at 150 °C. If the total waste energy is 5 MW, find the rate of energy delivered at the higher temperature. Assume heat engine and heat pump as reversible. <!--qid:MAINS_2023_Mechanical_Engineering-II_Q3-->

A medium carbon steel cylindrical rod is being machined under orthogonal cutting condition with an HSS cutting tool having rake angle as 12°. While machining, following data were recorded: Vertical component of cutting force = 1600 N Horizontal component of cutting force = 1250 N Chip thickness ratio = 0·25 Calculate the following for the above-mentioned machining condition: (i) Normal force on the rake face (ii) Friction force along the rake face (iii) Resultant cutting force (iv) Coefficient of friction at chip–tool interface (v) Normal force on the shear plane (vi) Shear force along the shear plane <!--qid:MAINS_2023_Mechanical_Engineering-I_Q1-->

A manufacturing company wants to arrange work-centres A, B, C and D so as to minimize inter-departmental parts handling costs. The flow of parts and existing work-centres layout are shown below: A B C D A – 400 500 50 B 300 – 200 0 C 0 0 – 700 D 0 0 0 – (Parts moved between work-centres) Existing layout with distances: A B C D (30 m between successive centres) Suggest a modified layout. <!--qid:MAINS_2023_Mechanical_Engineering-I_Q2-->