Conventional Paper-I-2012

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1 ME-Conentional Paper-I IES-01 Conentional Paper-I-01 1.a. For an ientropic expanion o a ga wit cp a kt, c b kt and cp c R, ow tat b ab kt T e contan t. [5] 1.b. A mall lexible bag contain 0.1kg ammonia at -10ºC and bar. Te bag material i uc tat te preure inide arie linearly wit olume. Te bag i let in open pace were te incident olar radiation i 75W. Te eat energy lot to te ground and urrounding air rom bag i at te rate o 5W. Ater a wile, it i ound tat te bag i eated to 0ºC at wic time te preure o ammonia i 10bar. Etimate (i) te amount o eat energy iniltrated into te bag and (ii) te elaped time. [10] a. Propertie o ammonia: Compreed liquid ammonia at 10ºC, bar Speciic olume o aturated liquid, V m / kg Speciic internal energy o aturated liquid, 14 kj/kg b. Supereated ammonia apour at 0ºC, 10bar Speciic olume: 0.11 m / kg Speciic internal energy = 147 kj/kg 1.c. Steam enter a 15cm diameter orizontal pipe a aturated apour at 5 bar wit a elocity o 10m/ and exit at 4.5 bar and a quality o Heat i tranerred to urrounding at 00K rom te pipe urace wic i at an aerage temperature o 400K. Under te teady tate operating condition, determine: (i) (ii) (iii) (i) Te exit elocity Te rate o eat traner rom pipe urace in kw Te rate o entropy production in kw/k, or te control olume compriing o only pipe and it content and Te rate o entropy production or te enlarged control olume tat include pipe, it content and te immediate urrounding. Propertie o team at aturation condition: P bar t at ºC Sp. Volume m / kg g [10] Sp. Entalpy kj / kg g Sp. Entropy kj / kg K g India No.1 intitute or GATE Training 1 Lak+ Student trained till date 65+ Center acro India 119

2 ME-Conentional Paper-I IES d. i. A certain ga obey te equation o tate, P a RT. Sow tat te ratio o it olume expaniity, wit tat o an ideal ga, ideal and te ratio o it iotermal compreibility, K T wit tat o an ideal ga, K T,ideal are gien by RT K a T and 1 ideal RT ap KT,ideal ii. For a ubtance wit olume expaniity, 0, ow tat at eery point o ingle pae region (apour region) on a Mollier diagram, te lope o contant preure line i greater tan te lope o contant temperature line but le tan tat o contant olume line. [6+9].a. Explain wit a neat ketc, te working principle o a ybrid rocket engine. Wat are te adantage o ti engine? [10] b. Wat are te dierent type o combution camber in CI engine? Explain wit a neat ketc, an open combution camber. Wat are te merit and demerit o te open combution camber? [10] c. A our troke ingle cylinder petrol engine mounted on a motor cycle wa put to load tet. Te load meaured on dynamometer wa 0kg wit drum diameter and peed repectiely at 900mm and 000rpm. Te engine conumed 0.15kg o uel in one minute, te caloriic alue o uel being 4.5 MJ/kg. Te uel upply to te engine wa topped and wa drien by a motor wic needed 5kW o power to keep it running at te ame peed, te eiciency o te motor being 80%. Te engine cylinder bore and troke are repectiely at 150mm and 00mm. Calculate [10] (i) Brake Power (ii) Indicated Power (iii) Mecanical eiciency (i) Brake termal eiciency () Indicated termal eiciency (i) Brake mean eectie preure (ii) Indicated mean eectie preure d. Te oerall termal eiciency o a 5MW nuclear power plant or a ubmarine i 0%. Calculate te amount o natural uranium, U 5, needed to generate te power i te aerage energy releae per iion or U 5 1 i 190MeV. Take W MeV /. Aogadro Number i [10].a. Cooling water at a teady rate o 0.5kg/ low troug an inner tube aing inner diameter o 5mm and lengt 10m o a tube-in-tube condener. Te mean inlet temperature o cooling water i 10ºC. Saturated team condene in te annulu at a uniorm rate uc tat te inner urace temperature o te tube i contant trougout te lengt o te tube at 40ºC. Te aerage condening ide eat traner coeicient i W / m K. Neglect te tickne o India No.1 intitute or GATE Training 1 Lak+ Student trained till date 65+ Center acro India 10

3 ME-Conentional Paper-I IES-01 te eat excanger tube. Calculate te eectiene o te eat excanger and te exit water temperature. [15] Propertie o water are gien below: Speciic eat: 4180 J/kg K Denity: 990kg / m Dynamic icoity: Pacal ec Termal conductiity: 0.57W / m K You may ue te relation Nu Red Pr.b..c. 4.a. Te net radiation rom te urace o two plate aing equal emiiitie o 0.8 and at dierent temperature T 1 and T [T 1 >T ] i to be reduced by 90%. How many number o radiation creen aing equal emiiitie o 0.05 are to be placed between te plate to aciee te reduction in eat excange? [15] Wat i an expanion deice? Explain wit te elp o neat ketc, te working principle o a termotatic expanion ale(tev) An R-1 apour compreion plant producing 10 tonne o rerigeration operate wit condening and eaporating temperature o 5ºC and -10ºC repectiely. A uction line eat excanger i ued to ub-cool te aturated liquid leaing te condener. Saturated apour leaing te eaporator i upereated in te uction line eat excanger to te extent tat a dicarge temperature o 60ºC i obtained ater ientropic compreion. Calculate (i) Te ub-cooling acieed in te eat excanger (ii) Te rerigerant low rate in kg/ (iii) Te cylinder dimenion o te two cylinder compreor, i te peed i 900 rpm, troke-to-bore ratio i 1:1 and te olumetric eiciency i 80%. (i) Te COP o te plant and () Te power required to drie te compreor in kw. Draw te cycle on P- and T- diagram. You may ue te ollowing table: Temperature ºC Sp. Volume m / kg g Sp. Entalpy kj / kg g Sp. Entropy kj / kg K Aerage peciic eat o deuper eating apour at condener = kj/kg K Aerage peciic eat o apour between eaporator outlet and Compreion uction = kj/kg K [0] g India No.1 intitute or GATE Training 1 Lak+ Student trained till date 65+ Center acro India 11

4 ME-Conentional Paper-I IES-01 b. A rectangular in o lengt 0cm, widt 0cm and tickne mm i attaced to a urace at 00ºC. Te in i made o aluminium K 04W / mk and i expoed to air at 0ºC. Te in end i uninulated and can looe eat troug it end alo. Te conection eat traner coeicient between te in urace and air i 15W / m K. Determine: [10] (i) Te temperature o te in at 0cm rom te bae (ii) Te rate o eat traner rom te in and (iii) Fin eiciency. c. Briely decribe te ariou metod o air-conditioning duct deign. [10] 5.a. A tank wit te ertical ide meauring m x m contain water to a dept o 1.m. An oil o denity 900 kg/m wa poured in te tank upto a dept o 0.8m. Te ertical wall can wittand te trut o 58kN. Calculate te actual trut on te wall and centre o preure. I te oil leel i increaed up to 0.9m, wat will be tability o te wall? [10] 5.b. For a rate o low exceeding certain alue, te coeicient o dicarge or a enturimeter ued or meauring te dicarge o an incompreible luid i ound to be contant. Proe tat te lo o ead in te conergent portion o te enturi can be expreed a KQ under tee condition, were K i a contant (unction o cd, area o te enturimeter) and Q i low rate in m /. Wat will be te alue o K, auming te cd contant? [10] 5.c. A traigt inclined pipeline 00m long dicarge reely at a point 50m lower tan te water urace at intake. Te pipe intake project into te reeroir ke 0.8. Te irt 00m o te pipe i o 50mm diameter and te remaining 100m i o 50mm diameter k 0.1. [10] i. Find te rate o dicarge auming = ii. iii. I te junction point C o te two ize o te pipe i 40m below te intake water urace leel, ind te preure ead. Jut uptream o C and Jut downtream o C Aume udden contraction at C. i. Veriy te ead lo acro contraction C. c 5.d. Two pipe ae lengt L eac. One o tem a a diameter D and oter d. I te pipe are arranged in parallel, te ead lo i or a dicarge o Q m /. Wen te pipe are connected in erie, te ead lot i H or ame dicarge. Find te ratio o H to or D =.5d. (All dimenion are in mm) [10] India No.1 intitute or GATE Training 1 Lak+ Student trained till date 65+ Center acro India 1

5 ME-Conentional Paper-I IES a. 6.b. 6.c. 6.d. 7.a. 7.b. 7.c. Deelop (in general term) an expreion or te percent o error in Q oer a triangular weir i tere i a mall error in te meaurement o te ertex angle. Aume tere i no error in te weir coeicient. Compute te percent error in Q, i tere i a 1º error in te meaurement o total ertex angle o a triangular weir wic i aing a total ertex angle o 60º. [10] Wat i te ydraulic jump in te low in open cannel? Wat are it type and caracteritic wit repect to Froude number o low? [10] Air low iotermally in a long pipe. At one ection te preure i 600kPa ab., te temperature i 5ºC and te elocity i 0m/. At a econd ection (at ome ditance rom te irt ection) te preure i 100kPa ab. Find te energy ead lo due to riction and determine te termal energy tat mut ae been added to or taken rom te luid between te two ection. Aume te diameter o pipe to be contant. [10] Reearcer plan to tet a 1:1 model o a ballitic miile in a ig peed wind tunnel. Te prototype miile will trael at 80m/ troug air at ºC and 95.0kPa (ab). [10] i. I te air in te wind tunnel tet ection a a temperature o -0ºC at a preure o 89kPa (ab) wat mut it elocity be? And ii. Etimate te drag orce on te prototype i te drag orce on te model i 400N. Explain te eect o ane angle on manometric eiciency in a centriugal pump. Wy i ane angle in a centriugal pump not kept at alue below 0º? [10] Fluid low wit a elocity o V oer a lat plate located at y = 0. Te leading edge o te plate i located at x = 0. Te poible elocity proile in te boundary layer aing tickne x are a ollow: i. ii. iii. u y y V u y 1 y V u y 1 y V Find out wic o tee elocity proile are eaible or laminar low. Alo, identiy te mootet elocity proile rom tee tree option. [10] Decribe wit neat ketc, te contruction and working principle o Rotometer. Wat are it adantage? 7.d. A ingle acting reciprocating pump lit a liquid o peciic weigt 9.0 kn / m rom a preuried torage reeroir to an oeread container. Te ree urace in te upply reeroir i at an eleation o.5m aboe te centre o te pump. Te ambient preure oer te liquid urace in te upply reeroir i 7 kn / m (acuum). Te oter releant data relating to te pump are a ollow: India No.1 intitute or GATE Training 1 Lak+ Student trained till date 65+ Center acro India 1

6 ME-Conentional Paper-I IES-01 Lengt o te uction pipe = 6.0m Diameter o uction pipe = 10cm Atmoperic preure = 99 kn / m ab Determine te maximum peed admiible in rpm. [10] 8.a. Deine air rate, peciic power and te cycle work ratio in a ga turbine. Wat i te igniicance o tee parameter? [5] 8.b. Jutiy te election o a turbine runner wit iget peed poible. Derie an expreion or te peciic peed o a pelton weel, or peed ratio 0.46, oerall eiciency 85% and coeicient o elocity o nozzle [10] 8.c. Wat are te ortcoming o a ire tube boiler retricting it or limited ue? How are te impuritie in eed water remoed rom te boiler? [10] 8.d. Wat are te contructional eature o an axial low compreor? How air i compreed and wat i te metod o getting iger compreion ratio in uc compreor? [5] 8.e. A ga turbine utilize two-tage centriugal compreor. Te preure ratio or te irt and econd tage are.5 and.1 repectiely. Te low o air i 10kg/, ti air being drawn at 1.01 bar and 0ºC. I te temperature drop in te intercooler i 60ºC and te ientropic eiciency i 90% or eac tage, calculate: i. Te actual temperature at te end o eac tage and ii. Te total compreor power. Aume 1.4 and Cp kj/kg K or air. [10] India No.1 intitute or GATE Training 1 Lak+ Student trained till date 65+ Center acro India 14