Engineering Services Examination - UPSC MECHANICAL ENGINEERING. Topic-wise Conventional Papers I & II (Last 30 Years Questions)

Transcription

1 Engineering Services Examination - UPSC MECHANICAL ENGINEERING Toic-wise Conventional Paers I & II (Last 0 Years Questions)

2 Dedicated to Mechanical Engineers and Engineering Services asirants. 04 by Engineers Institute of India ALL RIGHTS RESERVED. No art of this work covered by the coyright herein may be reroduced, transmitted, stored or used in any form or by any means grahic, electronic, or mechanical & chemical, including but not limited to hotocoying, recording, scanning, digitizing, taing, Web distribution, information networks, or information storage and retrieval systems. Engineers Institute of India 8-B/7, Jia Sarai, Near IIT Hauz Khas New Delhi-006 Tel: For ublication information, visit ISBN Price: Rs. 0

3 A word to the students Engineering services examination offers one of the most romising and restigious careers for service to the nation. Over the ast few years, it has become more cometitive as a number of asirants are increasingly becoming interested in government jobs due to decline in other career otions and reutation and future security. In my oinion, ESE rigorously tests candidates overall understanding of concets, ability to aly their knowledge and ersonality level by screening them through various stages. A candidate is suosed to smartly deal with the syllabus not just mugging u concets. Thorough understanding with critical analysis of toics and ability to exress clearly are some of the re-requisites to crack this exam. The syllabus and questioning attern has remained retty much the same over the years. Conventional aer ractice is very imortant to score good marks, as it checks your writing skills, dee understanding of a subject. Mechanical engineers refer ESE over other otions due to attractive career otions and diverse deartments. Railways, Central engineering services and other deartments are highly sought after. General category cut-off in ESE 0 was 5/00 and a total 69 candidates were finally recommendedd in ESE 0. For more details visit our website Established in 006 by a team of IES and GATE toers, we at Engineers Institute of India-E..I.I. have consistently rovided rigorous classes and roer guidance to engineering students over the nation in successfully accomlishing their dreams. We believe in roviding exam-oriented teaching methodology with udated study material and test series so that our students stay ahead in the cometition. The faculty at EII are a team of exerienced rofessionals who have guided thousands to asirants over the years. They are readily available before and after classes to assist students and we maintain a healthy student-faculty ratio. Many current and revious year toers associate with us for contributing towards our goal of roviding quality education and share their success with the future asirants. Our results seak for themselves. Past students of EII are currently working in various deartments and PSU s and ursuing higher secializations. We also give scholarshis to meritorious students. A detailed solution of the ast years conventional questions, reared by toers, will be available very soon. R.K. Rajesh Director Engineers Institute of India eii.rkrajesh@gmail.com eiidelhi

4 CONTENTS IES-Conventional Paer-I (ME) THERMODYNAMICS HEAT & MASS TRANSFER REFRIGERATION AND AIR CONDITIONING FLUID MECHANICS & HYDRAULIC MACHINE I.C. ENGINE POWER PLANT ENGINEERING IES-Conventional Paer-II (ME) THEORY OF MACHINES MACHINE DESIGN STRENGTH OF MATERIALS MATERIAL SCIENCE MANUFACTURING TECHNOLOGY OPERATION RESEARCH ELEMENTS OF COMPUTATION... 0-

5 MECHANICAL ENGINEERING ENGINEERING SERVICES EXAMINATION CONVENTIONAL PAPER-I (Last 0 Years Questions) 8-B/7, Jia Sarai, Near IIT, Hauz Khas, New Delhi-006. Ph ENGINEERS INSTITUTE OF INDIA. All Rights Reserved

6

7 ME-Convectional Paer-I. THERMODYNANIC []. THERMODYNAMICS Last 0 Years Questions Paer 985. (a) A cylinder closed at both ends is thermally insulated from the surroundings. It contains a movable, thermally insulated, frictionless and leak roof iston. Initially the ressure, volume and temerature on each side of the iston are 0, V0 and T 0. The number of moles of gas on each side is n. Heat is now slowly sulied to the gas on the left side of the iston by an electric heating coil. As a result the gas on the left-hand side exands and dislaces the iston, comressing the gas on the right-hand side until its ressure 7 C reaches 0. If the ratio of secific heats is.5 of n, C v, M and T 0 (i) the 8 Cv work done on the gas on the right-hand side, (ii) the final temerature of the gas on the right-hand side, (iii) the final temerature of the gas on the left hand side and (iv) the heat sulied to the gas on the left-hand side. All assumtions made must be clearly stated. (b) Two reversible heat engines E and E are ket in series between a hot reservoir at a temerature T of 600 K and a cold reservoir at a temerature T of 00 K. Engine E receives 500 kj of heat from the reservoir at T. The thermal efficiency of both the engines is the same. Determine (i) the temerature at which heat is rejected by engine Eand received by engine E, (ii) work done by engine E, (iii) work done by engine E, (iv) heat rejected by engine E to the cold reservoir and (v) the efficiency of the engines. Paer 986. (a) During some integral number of comlete cycles a reversible heat engine absorbs 800 kj from a heat reservoir at 000 K and erforms 800 kj mechanical work. The engine exchanges heat with two other heat reservoirs one of which is 5400 K and the other at 600 K. Determine the heat exchanged (whether absorbed or rejected) with these two reservoirs, the change in entroy of each of the three reservoirs and the change in the entroy of the universe. Draw a NEAT sketch of the system. (b) An engine in outer sace oerates on the Carnot cycle. The only way in which heat is rejected by the engine to the surroundings is by radiation which is roerty not to the roduct of the fourth ower of the absolute temerature of the radiating surface and its area. For a given ower outut of the engine, hot reservoir temerature T and radiator T temerature T determine the ratio T for which the area of the radiating surface as a minimum. 8B/7 Jiasarai Near IIT Hauzkhas Newdelhi-006 h

8 ME-Convectional Paer-I. THERMODYNANIC [] (c) A system maintained at constant volume is initially at temerature T. If a heat reservoir at temerature T 0 which is less than T is available, determine the maximum work obtainable as the system is cooled to T 0 in terms of T 0, T and C v. Paer 987. Two identical bodies of constant heat caacity are at the same initial temerature T. A refrigerator oerates between these two bodies until one body is cooled to the temerature T. If the bodies remain at constant ressure and undergo no change of hase, obtain an exression for the minimum amount of work required to achieve this. Paer A mass m of water at T is isobarically and adiabatically mixed with an equal mass of water T. Show that (T + T ) S total = m C ln T T Paer (a) A reversible heat engine oerates between 600 C and 40 C and drives a reversible refrigerator oerating between 40 C and 8 C. Still there is a net outut of work equal to 70 kj, while the heat received by the engine is 00 kj. Determine the cooling effect. (b) A comressor takes in 500 kg/min of air at 0.98 bar and 8 C and delivers it at 5.5 bar and 68 C. The diameters of inlet and delivery ies are resectively 450 mm and 00 mm. The ower inut is 000 kw. Determine the rate and direction heat flow. ( C =.005 kj/kg C). 6. A reversible cycle using an ideal gas as the working substance consists of a isentroic comression from an initial temerature to 555ºK, a constant volume rocess from 555º to 85º K, a reversible adiabatic exansion to 555º K, a constant ressure exansion from 555º K to 85º K followed by a constant volume rocess to the initial temerature. Draw the cycle on -v and the T.S. diagrams and determine the initial temerature. ( γ =.40). Also comute the work done. 7. (a) A rigid tank of Paer m volume contains air at bar and. C. The tank is equied with a relief valve that oens at a ressure of 8.68 bar and remains oen until the ressure dros to 8.74 bar. If a fire causes the valve to oerate once as described, determine the air temerature just before the valve oens and the mass of air lost due to the fire. Assume that the temerature of the air remains constant during discharge and air in the tank behaves as an ideal gas. V 8B/7 Jiasarai Near IIT Hauzkhas Newdelhi-006 h

9 ME-Convectional Paer-I. THERMODYNANIC [] (b) The scales are so chosen that a reversible cycle lots clockwise as a circle on the T-S lane. The minimum and maximum values of the temerature are 05 and 67 K and the entroy. and.85 kj/k, resectively. Find the cycle work and efficiency. Paer (a) Discuss flow energy. Comressed air is used to exel the liquid roellant from the roellant tank as shown below. The initial ressure of the air is 00 bar. The roellant has a density of. gm/cc and the roellant tank is filled to caacity and contains 900 kg of roellant. The roellant leaves at a constant ressure of 00 N/ cm (0 bar). Considering the air as the system, determine the work done by the air in forcing the roellant from the roellant tank. Determine the volume of comressed air tank necessary to um all the fuel in the rocket. Would the use of helium instead of air alter the erformance? Is the inlet air temerature is of any consequence? Throttle value Proellant tank Comressed air tank (00 bar) To rocket engine (0 bar) (b) The steam, initially at a ressure of 5 bar and temerature of 50 C, exand reversibly and oly-troically to.5 bar. Find the final temerature, work done, and change of entroy, if the index of exansion is.5. (Assume bar = assumtions made.) kgf/ cm. State the 9. (a) A reversible engine receives heat from a mixture of water vaour and liquid water at atm and rejects 775 kj/hr of heat at 00º K below temerature of a mixture of ice and liquid water at atm. It delivers 0.86 kw ower. Find the number of degrees searating absolute zero and ice oint on Kelvin scale. (b) A working fluid goes through a Carnot cycle of oerations, the uer absolute temerature of the fluid being θ and the lower absolute temerature being θ. The amount of heat taken in and rejected by the working fluid are Q and Q resectively. On account of losses of heat due to conduction etc., the heat source temerature T is higher than θ and the heat sink temerature T is lower than θ. If T = ( θ + KQ ); T = ( θ KQ ) where K is the same constant for both the equations, show that the efficiency of the lant is given by T η = T KQ 8B/7 Jiasarai Near IIT Hauzkhas Newdelhi-006 h

10 ME-Convectional Paer-I. THERMODYNANIC [4] 0. (a) Starting from first law equation dq = du + dv show that change in entroy of an ideal gas system is given b. T V s = Cv ln + R ln T V (b) A system oerating in a reversible cycle receives 5 kj of heat at 5 C ( ). This is followed by an adiabatic exansion ( ) to 5 C at which temerature 5 kj of heat is received ( 4). Then a further adiabatic exansion (4 5) to C occurs after which 5 kj of heat is rejected at constant temerature (5 6) followed by an adiabatic comression (6 7). Find the change in entroy during the last rocess (7 ) which occurs after adiabatic comressions (6 7) to 5 C. Paer 99. (a) kg of air at.50 bar ressure and 87º C temerature at condition is comressed olytroically to condition at ressure 7.50 bar, index of comression being.. It is then cooled at constant ressure to condition and then finally heated at constant temerature to its original condition. Find the net work done and heat transferred. (b) 500 kj of heat is removed from a constant temerature heat reservoir maintained at 85 K. The heat is received by a system at constant temerature of 70 K. The temerature of the surroundings, the lowest available temerature is 80 K. Illustrate the roblem by T S diagram and calculate the net loss of available energy as a result of this irreversible heat transfer. Paer 99. (a) 0.5 kg of air (ideal gas) executes a Carnot ower cycle having a thermal efficiency of 50 ercent. The heat transfer to the air during the isothermal exansion is 40 kj. At the beginning of the isothermal exansion the ressure is 7 bar and the volume is 0. m. Determine the maximum and minimum temeratures for the cycle, in K, the volume at the end of isothermal exansion, in m, and the work and heat transfer for each of the four rocesses, in kj. For air C v = 0.7 and C =.008 kj/kg.k. (b) Steam flows through an adiabatic steady flow turbine. The enthaly at entrance is 44 kj/kg and at exit 585 kj/kg. The values of flow availability of steam at entrance and exit are 787 kj/kg and 40 kj/kg, resectively. If the dead state temerature T o is 00 K, determine, er kg of steam, the actual work, the maximum ossible work for the given change of state of steam, and the change in entroy of steam. Neglect changes in kinetic and otential energy.. (a) A comressed air bottle of 0.05 m volume contains air at.5 atm ressure. This air is used to drive a turbo-generator sulying ower to a device which consumes 5 W. Calculate the time for which the device can be oerated if the actual outut of the turbogenerator is 60 ercent of the maximum theoretical outut. The ambient ressure is C atm. For air, =.4. CV 8B/7 Jiasarai Near IIT Hauzkhas Newdelhi-006 h

11 ME-Convectional Paer-I. THERMODYNANIC [5] (b) An insulated vessel is divided into two comartments connected by a valve. Initially, one comartment contains steam at 0 bar, 500º C, and the other is evacuated. The valve is oened and the steam is allowed to fill the entire volume, achieving a final ressure of bar. Determine the final temerature, in º C, the ercentage of the vessel volume initially occuied by steam and the amount of entroy roduced, in kj/kg.k. Paer (a) A Piston-cylinder device contains kg of wet steam at.4 bars. The initial volume is.5m. The steam is heated until its temerature reaches 400º C. The iston is free to move u or down unless it reaches the stos at the to. When the iston is u against the stos the cylinder volume is to or from steam. (b) An evacuated bottle of 4.65 m. Determine the amounts of work and heat transfer 0.5 m volume is slowly filled from atmosheric air at.05 bars until the ressure inside the bottle also becomes.05 bars. Due to heat transfer, the temerature of air inside the bottle after filling is equal to the atmosheric air temerature. Determine the amount of heat transfer. 5. Two blocks of metal, each of mess M and secific heat C, initially at absolute temeratures T and T resectively, are brought to the same final temerature by means of a reversible rocess. Derive an exression for the amount of work obtained during the rocess in terms of M, C, T and T. 6. In an air-standard Brayton cycle the minimum and maximum temeratures are 00 K and 00 K, resectively. The ressure ratio is that which maximizes the net work develoed by the cycle er unit mass of air flow. Calculate the comressor and turbine work, each in kj/kg air, and the thermal efficiency of the cycle. Paer (a) A tank containing 40 kg of water, initially at 40º C, has one inlet and one exit with equal mass flow rates. Water enters the tank at 40º C at the rate of 00 kg/hr. Energy is removed from the water at the rate of 8 kw by means of a cooling coil immersed in the water. The water is well mixed by a mechanical stirrer that the water temerature in the tank is uniform. The ower inut to the water from the stirrer is 0. kw. Derive an exression for the variation of water temerature in the tank with time. The secific heat of water is 4. kj/kg.k. Neglect kinetic and otential energy effects. (b) A closed system executes a reversible cycle consisting of six rocesses. During rocesses - and -4 the system receives 000 kj and 800 kj of heat, resectively, at constant temeratures of 500 K and 400 K, resectively. Processes - and 4-5 are adiabatic exansions in which the system temerature is reduced from 500 K to 400 K and from 400 K to 00 K, resectively. During rocess 5-6 the system rejects heat at a constant temerature of 00 K. Process 6- is an adiabatic comression rocess. Determine the work done by the system during the cycle and the thermal efficiency of the cycle. 8B/7 Jiasarai Near IIT Hauzkhas Newdelhi-006 h

12 ME-Convectional Paer-I. THERMODYNANIC [6] 8. A rigid vessel is divided into two arts A and B by means of a frictionless, erfectly conducting iston. Initially, art A contains and art B contains 0.4 m of air (ideal gas) at 0 bars ressure 0.4 m of wet steam at 0 bars. Heat is now added to both arts until all the water in art B is evaorated. At this condition the ressure in art B is 5 bars. Determine the initial quality of steam in art B and the total amount of heat added to both arts. Paer (a) 0.4 m of steam at 0 bar and 50º C is exanded reversibly and oly-troically to bar. Find the final temerature, work done, heat transferred and change of entroy, if the index of exansion is.5. (b) The secific heats of gas are of the form C = a + k T and CV = b + k T, where a, b and k are constants and T is in K. Derive the formula T b a v b e kt = constant, for adiabatic exansion of the gas. (c) A closed system contains 0.5 kg of air. It exands from bar, 60º C to bar, 40º C. During exansion it receives kj of heat from a reservoir at 00º C. Assuming atmosheric conditions to be at 0.95 bar and 0º C, calculate (i) the maximum, work, (ii) work done on atmoshere, and (iii) change in availability. Paer (a) An ideal gas is heated from temerature T to T by keeing its volume constant. The gas is exanded back to its initial temerature according to the law n v = constant. If the entroy changes in the two rocesses are equal, find the value of n in terms of the adiabatic index γ. (b) A cylinder contains one kg of water and steam at a ressure of.8 bar and 0.4 dry. Heat is sulied at constant volume until the ressure reaches to 0 bar. The steam is then exanded according to the law v = constant, until the ressure is bar. Calculate (i) Heat transfer during constant volume heating. (ii) Heat transfer during v = constant exansion. (iii) Temerature of steam after the exansion. (c) An adiabatic cylinder of volume of volume 6 m and 0 m is divided into two comartments A and B, each 4 m resectively, by a thin sliding artition. Initially the comartment A is filled with air at 6 bar and 600 K, whilst there is a vacuum in the comartment B. Suddenly the artition is removed, the fluid in comartment A exands and fills both the comartments. Calculate the loss in available energy. Assume atmoshere is at bar and 00 K. 8B/7 Jiasarai Near IIT Hauzkhas Newdelhi-006 h

13 ME-Convectional Paer-I. THERMODYNANIC [7] Paer 998. (a) Using the Maxwell relation derive the following Tds equation δv T ds = C d T T d δt (b) A comressed air bottle of volume 0.5 m contains air at 40 bar and 7º C. It is used to drive a turbine which exhausts to atmoshere at bar. If the ressure in the bottle is allowed to fall to bars, determine the amount of work that could be delivered by the turbine. (c) A rigid tank contains air at.5 bar and 60º C. The ressure of air is raised at.5 bar by transfer of heat from a constant temerature reservoir at 400º C. The temerature of surroundings is 7º C. Determine er kg of air, the loss of available energy due to heat transfer.. (a) Show that the cyclic integral of (b) Paer 999 d Q for a reversible cycle is equal to zero. T 00 K 00 K 00 K Q Q =5MJ Q E w = 840 kj A reversible engine as shown in the above figure during a cycle of oeration draws 5 MJ from the 400 K reservoir and does 840 kj of work. Find the amount and direction of heat interaction with other reservoirs. (c) Exhaust gases leave an internal combustion engine at 800º C and atmoshere, after having done 050 kj of work er kg of gas in the engine ( C of gas =. kj/kg K). The temerature of the surroundings is 0º C. (i) How much available energy er kg of gas is lost by throwing away the exhaust gases? (ii) What is the ratio of the lost available exhaust gas energy to the engine work?. What are the differences between heat um and refrigeration cycle? What is the relation between (C.O.P.) Heat um and (C.O.P.) Refrigerator? What are the differences between Kelvin Planck and Clausius Statements of nd Law? 8B/7 Jiasarai Near IIT Hauzkhas Newdelhi-006 h

14 ME-Convectional Paer-I. THERMODYNANIC [8] Paer (a) A reversible engine receives equal quantity of heat from two reservoirs A and B maintained at temeratures T and T resectively. The engine rejects heat to a reservoir C at temerature T. In case the thermal efficiency of the above engine is K times, the efficiency of reversible engine receiving heat only from reservoir A and rejecting heat to reservoir C and also if the heat sulied by the reservoir C and also if the heat sulied by the reservoir A is the same as it sulied in the combined case show that: (T T ) T T K = (T T ) + T T (b) A heat source at 67º C transfer heat at the rate of 000 kj/min. to a system maintained at 87º C. A heat sink is available at 7º C. Assuming these temeratures to remain constant, find: (i) change in entroy of source (ii) Entroy roduction accomanying heat transfer (iii) The original available energy (iv) The available energy after heat transfer Paer (a) Using Maxwell s relations, show that for a ure substance T ds = C d T T vβ d β KC C v d = Cv d T + T dv = + dv K β β v where β is coefficient of cubical exansion, K is coefficient of comressibility and C and C v are secific heats at constant ressure and at constant volume resectively. (b) State the Calusius inequality in words. An inventor claims that he has develoed a heat engine which absorbs 00 kj and 800 kj from reservoirs at 800 K and 600 Kelvin resectively and rejects 600 kj and 00 kj as heat to reservoirs at 400 K and 00 K resectively. It delivers 00 kj work. Determine whether the heat engine is theoretically ossible. (c) A mass m of fluid at temerature T is mixed with an equal mass of the same fluid at temerature T. Prove that the resultant change entroy of the universe is (T + T ) mc l T T 8B/7 Jiasarai Near IIT Hauzkhas Newdelhi-006 h

15 ME-Convectional Paer-I. THERMODYNANIC [9] Paer (a) An insulated tank of m volume contains air at 0. MPa and 00 K. The tank is connected to a high ressure line in which air at MPa and 600 K flows. The tank is quickly filled with air by oening the valve between the tank and high ressure line. If the final ressure of air in the tank is MPa, determine the mass of air which enters the tank and the entroy change associated with filling rocess. Take Universal Gas Constant R = 8.4 kj/kg-mol-k. (0) (b) By using Maxwell s relations of thermodynamics, show that Joule-Thomson coefficient, µ of gas can be exressed as, (0) T T v µ = = C T T h (c) A heat driven refrigeration system absorbs heat from low temerature TE and rejects it to temerature T C. This is run by heat sulied from a high temerature source at temerature T H, TH > TC > T E. Using first and second laws of thermodynamics derive the exression for maximum COP of refrigeration system in terms of temerature. (0) Paer (a) Exlain the terms (i) coefficient of cubical exansion, β and (ii) coefficient of comressibility K. Hence, show that β P =. K T v (b) Using Maxwell s and other equations, show that (5) u v C Cv = P + v T T P Hence show that v = β (0) K C Cv T. (c) A reversible engine A absorbs energy from a reservoir at temerature T and rejects energy to a reservoir at temerature T. A second engine B absorbs the same amount of energy as rejected by engine A, from the same reservoir at temerature T and rejects energy to a reservoir at temerature T. What will be the relation between T, T and T if (i) the efficiencies of both the engines A and B are the same and (ii) the work delivered by both the engines is the same? (5) (d) An ideal gas is heated at constant volume until its temerature is times the original temerature, then it is exanded isothermally till it reaches its original ressure. The gas is then cooled at constant ressure till it is restored to the original state. Determine the net work done er kg of gas if the initial temerature is 50 K. (0) 8B/7 Jiasarai Near IIT Hauzkhas Newdelhi-006 h

16 ME-Convectional Paer-I. THERMODYNANIC [0] Paer (a) Derive the following Claeyron Clausius-Claeyron equations: d hfg d hfg = and = d T. d T T(V V ) RT g f Exlain the hysical significance of these equations. (0) (b) A heat um oerates between two identical bodies. In the beginning, both the bodies are at the same temerature T but oeration of heat um cools down one of the body to temerature T. Show that for the oeration of heat um the minimum work inut needed by the heat um for unit mass is given T Wmin = c + T T T where c is the secific heat of bodies. Discuss whether the system satisfies first and second law of thermodynamics or not. (0) (c) A large vessel contains steam at a ressure of 0 bar and a temerature of 50º C. This large vessel is connected to a steam turbine through a valve followed by a small initially evacuated tank with a volume of 0.8m.During emergency ower requirement, the valve is oened and the tank fills with steam until the ressure is 0 bar. The temerature of the tank is then 400º C. Assume that the filling rocess takes lace adiabatically and the changes in otential and kinetic energies are negligible. By drawing the control volume, calculate the amount of work develoed by the turbine in kj. (0) Paer (a) Derive the exression for ( h) T for a substance that obeys the equation of state given by: RT a = υ υ (b) 4 kg of water at 40º C are mixed with 6 kg of water at 00º C in a steady flow rocess. Calculate: (i) the temerature of resulting mixture, (ii) the change in entroy, and (iii) the unavailable energy with resect to the energy receiving water at 40º C. (0) (c) An inventor claims to have develoed a device which requires no energy transfer by work or heat transfer, yet able to roduce hot and cold stream of air from a single stream of air at an intermediate temerature of º C and a ressure of 5. bar, searate streams of air exit at a temerature of bar. Sixty ercent of mass entering the device exists at the lower temerature. Evaluate the inventor s claim, assuming ideal gas as working fluid and neglecting changes in kinetic and otential energy. (0) (0) 8B/7 Jiasarai Near IIT Hauzkhas Newdelhi-006 h