Mechanical Engineering UPSC PYQ 2020

One stage comprising a pair of blade rings of a 50 percent reaction axial flow steam turbine has a mean ring diameter of 140 cm. The blade to steam speed ratio is 0.7. The speed of rotation is 3000 r.p.m. Determine the required entrance angle for the blading if the exit angle is 20°. Also, determine the work done per kg of steam flowing per second and the diagram efficiency. Calculate the percentage increase in diagram efficiency if the blades are designed for, and run at the best theoretical speed corresponding to the optimum operating condition, for the given steam speed and the exit angle.

Air enters the compressor of a gas turbine plant at ambient conditions of 100 kPa and 25 °C with negligible velocity, and exits at 1 MPa and 347 °C with a velocity of 90 m/s. The compressor is cooled at a rate of 1500 kJ/min and the power input to the compressor is 250 kW. Determine the mass flow rate of air through the compressor. For air, consider C_p = 1.005 kJ/kg-K, C_v = 0.717 kJ/kg-K and R = 0.287 kJ/kg-K.

An oil engine operating on air-standard dual cycle has cylinder bore of 250 mm and stroke length of 300 mm. The compression and expansion ratios are 10 and 6 respectively. The initial pressure and temperature of air before compression are 1.0 bar and 27 °C respectively. The heat added at constant pressure is twice the heat added at constant volume. Determine the pressure and temperature at all the salient points in the cycle, and the air-standard efficiency of the cycle. Also, calculate the clearance volume of the engine. Draw the P-V diagram of the cycle. Take, for air, \gamma = 1.4 and C_p = 1.005 kJ/kg-K.

The mass flow rate of steam flowing in a pipeline is measured with the help of a well-insulated Venturi meter. Dry saturated steam at 7.0 bar enters the Venturi. The pressure at the throat of the Venturi is measured to be 3.6 bar. The inlet and throat diameters of the Venturi are 538.5 mm and 75 mm respectively. The velocity of steam at the inlet to the Venturi is 10 m/s. Calculate the mass flow rate of steam neglecting friction. (The properties of steam are to be taken from the table as given below) : Properties of Saturated Steam [Pressure, P (bar): 3.6, 7.0 | t_{sat} (°C): 140.0, 165.0 | Specific volume (m^3/kg) v_f: 0.00108, 0.001108 | v_g: 0.511, 0.273 | Specific enthalpy (kJ/kg) h_f: 588.6, 697.2 | h_g: 2733.7, 2763.5 | Specific entropy (kJ/kg-K) s_f: 1.738, 1.992 | s_g: 6.931, 6.708]

A six-cylinder four-stroke SI engine is required to develop 190 kW of power running at 4500 r.p.m. The brake thermal efficiency is 32%. The air/fuel ratio is 12.5 : 1 and the volumetric efficiency at this speed is 68%. If the stroke/bore ratio is 0.8, determine the engine displacement required and the dimensions of bore and stroke. The calorific value of the fuel is 44200 kJ/kg and the free air conditions are 1.013 bar and 15 °C. If the mechanical efficiency is 80%, calculate the brake-specific fuel consumption and the indicated thermal efficiency. R_{air} = 0.287 kJ/kg-K.

Give a comparative statement in the form of a table of the various factors desired to be high or low which tend to reduce knock in SI and CI engines.

Explain why most of the medium-sized automobile engines are close to square shape with the cylinder bore diameter approximately equal to the stroke length.

Explain in brief as to why capillary tube is preferred to other throttling devices in household refrigerator.

The operating temperatures of a simple vapour absorption refrigeration system are-generator 100 °C; condenser and absorber 45 °C; evaporator 2 °C. The system has refrigeration capacity of 125 kW and heat input to the system is 180 kW. The solution pump work is negligible. (i) Find the COP of the system and total heat rejection rate from the system. (ii) An inventor claims that by improving the design of all the components of the above system, he could reduce the heat input to the system by 90 kW, while keeping the refrigeration capacity and operating temperature same as before. Examine the validity of the claim.

A counter-flow double-pipe heat exchanger is to heat water from 20 °C to 80 °C at a rate of 1.2 kg/s. The heating is to be accomplished by geothermal water available at 160 °C at a mass flow rate of 2 kg/s. The inner tube is thin-walled and has a diameter of 1.5 cm. If the overall heat transfer coefficient of the heat exchanger is 640 W/m^2-K, determine the length of the heat exchanger required to achieve the desired heating. Take specific heat of water and geothermal fluid as 4.18 kJ/kg-K and 4.31 kJ/kg-K respectively.

A five-bar chain is shown in the figure. Prove that it is an unconstrained chain.

Determine the moment of inertia of the shaded area with respect to the x-axis.

A steel wire is drawn from an initial diameter of $12.7\text{ mm}$ to a final diameter of $10.2\text{ mm}$ at a speed of $90\text{ m/min}$. The half-cone angle of the die is $6^{\circ}$ and the coefficient of friction at the job-die interface is $0.1$. A tensile test on the original steel specimen gives a tensile yield stress of $207\text{ N/mm}^2$. A similar specimen shows a tensile yield stress of $414\text{ N/mm}^2$ at a strain of $0.5$. Assuming a linear stress-strain relationship for the material, determine the drawing power and the maximum possible reduction with the same die. No back tension is applied.

Show, in the form of a table, how the following flow parameters change (increase/decrease/remain constant) in the rotor and stator blades of an axial flow compressor stage with 50% degree of reaction : (i) Static temperature (ii) Static pressure (iii) Stagnation temperature (iv) Stagnation pressure (v) Relative velocity (vi) Absolute velocity. Also, draw the corresponding T-s diagram.

What are the environmental and safety properties of an ideal refrigerant?

What do you understand by the term 'flash' in a forging? Explain with the help of a sketch.

Consider a 3 m diameter spherical tank that is initially filled with liquid nitrogen at 1 atm and -196 °C. The tank is exposed to ambient air at 15 °C with a combined convective and radiative heat transfer coefficient of 35 W/m^2-K. The temperature of the thin-shelled spherical tank is observed to be almost the same as the temperature of the nitrogen inside. Determine the rate of evaporation of the liquid nitrogen in the tank as a result of the heat transfer from the ambient air if the tank is (i) not insulated, (ii) insulated with 5 cm thick fiberglass wool insulation (k = 0.035 W/m-K) and (iii) insulated with 2 cm thick superinsulation which has an effective thermal conductivity of 0.00005 W/m-K. Consider the heat of vaporization of liquid nitrogen as 198 kJ/kg and its density as 810 kg/m^3 at 1 atm.

Determine the whirling speed of a shaft $25\text{ mm}$ diameter and $0.8\text{ m}$ long with a mass of $1\text{ kg}$ placed at mid span, simply supported at ends. The density of the shaft material is $50\text{ g/cm}^3$ and Young's modulus is $2\times10^6\text{ bar}$.

39.6 m^3/min of a mixture of recirculated room air and outdoor air enters a cooling coil at 31 °C dry-bulb temperature and 18.5 °C wet-bulb temperature. The apparatus dew-point temperature of the coil is 4.4 °C. The surface area of the coil is such that it would give 12.5 kW of refrigeration with the given entering air state. Determine the dry-bulb and wet-bulb temperatures of air leaving the coil, and the bypass factor. (Psychrometric Chart is given in Page No. 10)

A 2 m x 3 m flat plate is suspended in a room and subjected to air flow parallel to its surfaces along its 3 m long side. The free stream temperature and velocity of air are 20 °C and 7 m/s respectively. The total drag force acting on the plate is measured to be 0.86 N. Determine the average convective heat transfer coefficient for the plate. The properties of air at 20 °C and 1 atm are \rho = 1.204 kg/m^3, C_p = 1.007 kJ/kg-K, Pr = 0.7309.

A reversible engine works between three thermal reservoirs A, B and C. The engine absorbs an equal amount of heat from the thermal reservoirs A and B kept at temperatures T_A and T_B respectively, and rejects heat to the thermal reservoir C kept at temperature T_C. The efficiency of the engine is alpha times the efficiency of the reversible engine, which works between the two reservoirs A and C. Prove that \frac{T_A}{T_B} = (2\alpha - 1) + 2(1 - \alpha) \frac{T_A}{T_C}.

The life of a plain milling cutter of diameter $75\text{ mm}$ was found to decrease from $50\text{ minutes}$ to $30\text{ minutes}$ due to increase in speed of the cutter from $200$ to $260\text{ rpm}$ while milling a cast iron plate at given feed and depth of cut. How much would be the life of that cutter if the speed is $120\text{ rpm}$ keeping other parameters unchanged?

On the basis of 1-D isentropic flow, show that in a duct of varying area, the Mach number M at any section is related to the area A of the section by \frac{A}{A^*} = \frac{1}{M} \left[ \frac{2}{\gamma + 1} \left(1 + \frac{\gamma - 1}{2} M^2 \right) \right]^{\frac{\gamma + 1}{2(\gamma - 1)}}, where A^* is the area of the duct corresponds to M = 1.

Define the term hardenability. Which factors affect hardenability?

Two parallel shafts, about $600\text{ mm}$ apart, are to be connected by spur gears. One shaft is to run at $360\text{ rpm}$ and the other at $120\text{ rpm}$. Design the gears, if the circular pitch is to be $25\text{ mm}$.

Consider the base plate of an 800 W household electric iron with thickness of L = 0.6 cm, base area = 160 cm^2 and thermal conductivity k = 60 W/m-K. The inner surface of the base plate is subjected to uniform heat flux generated by the resistance heater inside. When steady operating conditions are reached, the outer surface temperature of the plate is measured to be 112 °C. Disregarding any heat loss through the upper part of the iron-(i) express the differential equation and boundary conditions for steady one-dimensional heat conduction through the plate; (ii) obtain a relation for the variation of temperature in the base plate by solving the differential equation; (iii) evaluate the inner surface temperature.

An axial flow fan operates at 1200 r.p.m. The blade tip diameter is 1.1 m and hub diameter is 0.8 m. The blade inlet and exit angles are 30° and 60° respectively with respect to the plane of rotation. Inlet guide vanes give the absolute flow entering the rotor at an angle of 60° with the plane of rotation. There is no change in the axial component of velocity across the rotor. Determine (i) the volume flow rate through the fan and (ii) the minimum torque and power needed to drive the fan. Take the density of air as 1.225 kg/m^3.

A frictionless piston/cylinder is loaded with a linear spring (as shown in the figure below) having a spring constant of 100 kN/m, and the piston cross-sectional area is 0.1 m^2. The cylinder having an initial volume of 20 L contains air at 200 kPa and ambient temperature 300 K. There exists a stop in the cylinder which prevents its volume from exceeding 50 L. A valve connects the cylinder to an air supply line flowing air at 800 kPa, 325 K. The valve is now opened, allowing air to flow in until the cylinder pressure and temperature reach 800 kPa and 350 K respectively. The valve is then closed and the process ends. At the final state does the piston reach the stop? Calculate the heat transfer during the process. Take C_p = 1.005 kJ/kg-K and R = 0.287 kJ/kg-K for air.

A tower guy wire is anchored by means of a bolt at A. If the magnitude of the tension in the wire is $2500\text{ N}$, determine the components of the force acting on the bolt in the x, y and z directions.

Classify the nano-materials depending on the number of dimensions in the nano range. What are the two basic approaches for processing of nano-structural materials?

(i) Establish the relation between 1st law efficiency, 2nd law efficiency and Carnot efficiency. (ii) A reversible heat engine operates between two thermal reservoirs of 1000 °C and 40 °C. The engine drives a reversible refrigerator operating between 40 °C and -10 °C. The amount of heat transfer to the engine is 4000 kJ and a net amount of work output of 1000 kJ is obtained from the combined engine-refrigerator system. Determine (1) the amount of heat transfer to the refrigerator and (2) the net amount of heat transfer to 40 °C reservoir.

Explain the process of metal transfer in gas metal arc welding process with neat sketches.

A company plans to sell an article at a local market. The articles are purchased at ₹ $5$ on the condition that all unsold articles shall be returned. The rent of the space is ₹ $2,000$. The articles will be sold at ₹ $9$. Determine the number of articles which must be sold (i) To break-even. (ii) To earn ₹ $400$ as profit. (iii) If the company sells $750$ articles, calculate margin of safety and profit.

Explain, with the help of velocity triangles, why centrifugal fans with backward-curved blading are used for forced draught fans, and centrifugal fans with forward-curved blading are used for induced draught fans in a steam power plant.

Draw the shear force and bending moment diagrams for the beam and loading shown. Also determine the maximum values of shear force and bending moment along with their respective locations.

Determine the percentage change in the machining time for a USM (Ultrasonic Machining) operation cutting WC plates when the tool material is changed from copper to stainless steel.

The sales for a critical component manufactured by a company are given below. Forecast the demand for the components for the next three years using regression method : Years | Sales ('000) 1986 | 30 1987 | 33 1988 | 37 1989 | 39 1990 | 42 1991 | 46 1992 | 48 1993 | 50 1994 | 55 1995 | 58

During pure orthogonal turning of a metal rod by a tool of the following geometry it was noted that the magnitudes of the tangential component and the axial component of the cutting force are $600\text{ N}$ and $200\text{ N}$ respectively. Inclination angle = $0^{\circ}$ Orthogonal rake = $0^{\circ}$ Principal cutting edge angle = $90^{\circ}$ Chip reduction coefficient = $1.732$ Using Merchant's circle diagram, determine the magnitudes of the shear force and the frictional force for the above condition.

The annual demand for a component is $2500\text{ boxes}$. The company procures the item from a supplier at the rate of ₹ $750\text{ per box}$. The company estimates the cost of carrying inventory to be $18\%$ per unit per annum and the cost of ordering as ₹ $1,080\text{ per order}$. The company works for $250\text{ days}$ in a year. How should the company design an inventory control system for this component? What will be the overall cost of the plan?

Air enters a compressor in steady flow at 140 kPa, 17 °C and 70 m/s and leaves it at 350 kPa, 127 °C and 110 m/s. The environment is at 7 °C. Calculate per kg of air for (i) the actual amount of work required, (ii) the minimum work required and (iii) the irreversibility of the process. For air, take C_p = 1.005 kJ/kg-K and R = 0.287 kJ/kg-K.

Show that the chain shown in the figure is not a kinematic chain.

When does reheating of steam become necessary in Rankine cycle? With the help of T-s diagram, explain the effect of reheating on the Rankine cycle output and efficiency.

A car starts from rest with an acceleration of $6\text{ m/s}^2$ which decreases linearly with time to zero in $10\text{ seconds}$ after which the car continues at a constant speed. Determine the time required for the car to travel $400\text{ m}$ from start.

A rotor is completely balanced when masses of $2\text{ kg}$ and $1.2\text{ kg}$ are added temporarily in planes A and D each at $200\text{ mm}$ radius as shown in the figure. The balanced mass in the plane A is along the x-axis whereas in the plane D, it is at $120\text{ mm}$ radius. Determine the magnitudes and the directions of the masses B and C.

Enlist the basic elements of JIT and explain Kanban card in brief.

Draw the following crystallographic planes in cubic unit cell : (i) $(101)$ (ii) $(1\overline{1}0)$ (iii) $(221)$

A component can be manufactured either on a centre lathe or on a turret lathe. The cost and time information to process a component is given below : Particulars | Centre lathe | Turret lathe ---\---|--- Set-up time | $30\text{ minutes}$ | $120\text{ minutes}$ Processing time | $10\text{ minutes}$ | $5\text{ minutes}$ Tooling-up cost (₹) | $200$ | $500$ Labour cost/hr | ₹ $2$ | ₹ $2$ Depreciation and other costs per hour | ₹ $10$ | ₹ $20$ The tooling-up cost is to be recovered within a year and there are no repeat orders. The requirements are to be met in two lots. (i) Calculate the quantity at which both alternatives result in equal cost. (BEP) (ii) Give the decision rule regarding the choice of lathes. (iii) If the quantity required is $800\text{ nos/year}$, which of the machines do you propose?

The arms of a Porter governor are $300\text{ mm}$ long. The upper arms are pivoted on the axis of rotation. The lower arms are attached to a sleeve at a distance of $40\text{ mm}$ from the axis of rotation. The mass of the load on the sleeve is $70\text{ kg}$ and the mass of each ball is $10\text{ kg}$. Determine the equilibrium speed when the radius of rotation of the balls is $200\text{ mm}$. If the friction is equivalent to a load of $20\text{ N}$ at the sleeve, what will be the range of speed for this position?

Enlist various types of plant layouts. Compare product layout and process layout.

A hole and shaft have a basic size of $25\text{ mm}$ and are to have a clearance fit with maximum clearance of $0.02\text{ mm}$ and a minimum clearance of $0.01\text{ mm}$. The hole tolerance is to be $1.5$ times the shaft tolerance. Determine limits for both hole and shaft (i) using a hole basis system. (ii) using a shaft basis system.

In a gas turbine plant, air at 1.0 bar and 27 °C is compressed to a pressure of 6.0 bar in a compressor with isentropic efficiency of 85%. The air then passes through the combustion chamber where fuel is added. The hot gases expand in the turbine with an isentropic efficiency of 90%. The maximum temperature in the cycle is 1300 °C. The calorific value of the fuel is 44 MJ/kg. If the net power output is 3.0 MW, calculate the following : (i) Cycle efficiency, (ii) Work ratio, (iii) Mass flow rate of air, (iv) Brake-specific fuel consumption (kg/kWh). Consider the working fluid to have the properties of air throughout the cycle. Assume in_{air} = in_{gases}. Neglect all other losses. For air, \gamma = 1.4 and C_p = 1.005 kJ/kg-K. Also, draw the T-s diagram of the cycle.

Obtain the following relationship between the characteristic Mach number (M^*) and actual Mach number (M) at a point in a flow field : M^{*2} = \frac{(\gamma + 1)M^2}{2 + (\gamma - 1)M^2}. A normal shock stands in a duct. The fluid is air, which can be considered as an ideal gas. Properties at upstream of the shock are T_1 = 5 °C, p_1 = 65 kPa and V_1 = 668 m/s. Determine the static temperature, static pressure and stagnation temperature downstream of the shock. For air, take C_p = 1.005 kJ/kg-K and \gamma = 1.4.

At a certain point in a piece of elastic material, there are normal tensile stresses of magnitude $120\text{ MN/m}^2$, $60\text{ MN/m}^2$ acting orthogonally to each other. In addition, there is a shearing stress of $80\text{ MN/m}^2$ acting normal to the normal stresses. Determine : (i) the magnitude and direction of the principal stresses (ii) the magnitude and direction of the maximum shearing stress (iii) the normal and shearing stress on a plane inclined at $30^{\circ}$ to the direction of $120\text{ MN/m}^2$ stress

Determine the number of teeth and the speed of the pinion where the driven gear wheel has $60\text{ teeth}$ of $10\text{ mm}$ module and rotates at $300\text{ rpm}$. The two spur gears have a velocity ratio of $\frac{1}{4}$. Also compute the pitch line velocity.

Derive an appropriate equation to show that a divergent duct acts as a supersonic nozzle.

A cylindrical shell $90\text{ cm}$ long, $20\text{ cm}$ internal diameter having thickness of metal as $8\text{ mm}$ is filled with fluid at atmospheric pressure. If an additional $20\text{ cm}^3$ of fluid is pumped into the cylinder, find (i) the pressure exerted by the fluid on the cylinder. (ii) the hoop stress induced. Given : Young's modulus = $2\times10^5\text{ N/mm}^2$ Poisson's ratio = $0.3$

A food storage chamber requires a refrigeration system of 12 TR capacity with an evaporator saturation temperature of -8 °C and condenser temperature of 30 °C. The refrigerant R-12 is sub-cooled by 5 °C before entering the throttle valve, and the vapour is superheated inside the evaporator by 6 °C before entering the compressor. If the liquid and vapour specific heats are 1.235 kJ/kg-K and 0.733 kJ/kg-K respectively, find the (i) refrigerating effect per kg, (ii) mass of refrigerant circulated per minute and (iii) COP. The relevant properties of the refrigerant R-12 are given below : [Saturation temperature (°C): -8, 30 | Enthalpy (kJ/kg) Liquid: 28.70, 64.59 | Vapour: 184.06, 199.62 | Entropy (kJ/kg-K) Liquid: 0.1148, 0.2400 | Vapour: 0.7007, 0.6853]

What are the advantages and limitations of lean manufacturing? Discuss the difficulties in adopting lean technique.