ME-Conventional Paper-IIES-2014www.gateforum.com Indias No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 1 Conventional Paper I-2014 1.(a)Give reasons why the Carnot cycle cannot be considered as the theoretical cycle for steam powerplantseventhoughitsefficiencyisthehighestforthegivenheatsource andsink temperatures. A carnot cycle heat engine has an efficiency of 40%. If the high temperature is raised by 10%, what is the new efficiency keeping the same low temperature? (b)Whatdoyouunderstandbythelumpedcapacity?Whatarethephysicalassumptions necessary for a lumped capacity unsteady state analysis apply? Determine time required in minutes for a 50mm diameter steel sphere ( )37800 kg m , c 0.46 kJ kg K, k 35W m K = = = to cool from 600OC temperature to 100OC temperature if exposed to a cooling air at 30OC. The convection heat transfer coefficient is 10W/m-K. (c)(i)FromfundamentallawsderivethePrandtl-Mayerrelationforanormalshockin compressible fluid flow in a constant area duct for a perfect gas.(ii)Showthatthemaximumefficiencyforajetstrikingatthecentreofasingle symmetrically,curvedvane moving with avelocity u isgivenby 216cos27 2uwhereu is the curvature of the vane.(d) Definespecificspeedofahydraulicturbine.Whereisitused?Showthatthespecific speed (NS) can be expressed as: 2S 5 2 5 4N P N PNH H= =N = speed, P = power developed or shaft power and H = head under which the turbine is wokingWhat is the range of specific speed in r.p.m. for Pelton wheel? (e)Calculate the volume rate of flow of water through a pipe of100mm dia. When measuredby (a) An orifice plate of orifice size 50mm dia and (b) Venturi tube of throat size 50mm dia. The recorded. D.P. 250 pa. The density of water is 100kg/m3. Assume orifice Cd equal to 0.6 and Venturi Cd equal to 0.9. (f)A single acting reciprocating pump has a plunger 10cm diameter and a stroke of 200mm. The centre of the pump is 4m above the water level in the sump and 14m below the level ME-Conventional Paper-IIES-2014www.gateforum.com Indias No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 2 ofwaterinatanktowhichwaterisdeliveredbythepump.Thediameterandlengthof sectionpipeare40mmand6mrespectivelywhilethoseofdeliverypipeare30mmand 18m respectively. Determine the maximum speed at which the pump may be run without separation,ifseparationoccursat7.848N/cm2belowtheatmosphericpressure.Take atmospheric pressure head = 10.3m of water. (g)Use the following mathematical relation for any three properties x,y,z x yzx y z1y z x| | c c c | | | | = |||c c c\ . \ .\ . to show the following relations for the Joule-Thomson coefficient 2pjP p p hTTT RT zp C pc Tcv | | v |c | | c \ . c | | = = = ||c c\ .\ . Z is compressibility factor. (h)Write down the chemical formula of R-134a. What does a signify in the nomenclature? Explain the effect of critical temperature and critical pressure of refrigerant on the COP of the cycle. Astraight-chargedThermostaticExpansionValve(TEV)isdesignedtooperateatan evaporator temperature of 7OC with a degree of superheat of 5OC. R-134a is the refrigerant used in the refrigeration system as well as the bulb. Find: (i)The required spring pressure at the design condition, (ii)Assuming the spring pressure to remain constant, find the degree of superheat, if the same TEV operates at an evaporator temperature of -23OC. ThesaturationtemperatureandcorrespondingpressureofR-134aaregivenintheTable below: OsatT , C -23-13-12-11271213 satP , kPa116.39177.92185.24192.8314.62374.63443.01457.76 ME-Conventional Paper-IIES-2014www.gateforum.com Indias No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 3 2. (a) Acylinderhavingapistonretrainedbyalinearspring(ofspringconstant15kN/m) contains 0.5 kg of saturated vapour water at 120OC, as hown in the above figure. Heat is transferredtothewater,causingthepistontorise.Ifthepistoncross-sectionalareais 0.05m2,andthepressurevarieslinearlywithvolumeuntilafinalpressureof500kPais reached.Findthefinaltemperatureinthecylinderandtheheattransferfortheprocess. The properties of water are given in the Table below: t,OCP, kPa 3gV , m kg gu , kJ kggh , kJ kg120 198.50( )satP0.891862529.22705.9 151.83 500.00( )satP0.374772559.52746.6 801500.000.990553664.24159.2 802500.000.991473666.14161.6 803500.000.992403668.04163.9 804500.000.993333669.94166.3 805500.000.994253671.84168.6 (b)Inanoilcoolertheoilenters10mmdiametertubesof160OCandiscooledto40OC.The mean velocity of oil in the tubes is 1.5 m/s. Calculate the mean heat transfer coefficient. For turbulent flow of liquid being cooled take Nu =0.0265 Re0.8 Pr0.3 and for laminar flow Nu = 3.65. Take all properties at bulk mean temperature and the properties are listed below: tOCP kg/m3Vcenti stokesK W/m KC kJ/kg K 40878251.00.1441.96 10083920.40.1372.22 1608065.70.1312.48 1 centi stoke = 10-6m2/s ME-Conventional Paper-IIES-2014www.gateforum.com Indias No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 4 (c) Thecylinderborediameterofasingleactingreciprocatingpumpis150mmandstrokeis 300mm.Thepumprunsat50rpmandliftswaterthroughaheightif25m.Thedelivery pipe is 32 m long and 100 mm diameter. Find the theoretical discharge and power required to run the pump. If the actual discharge is4.2 lit/s find the percentage slip. Also determine the acceleration head at the beginning and middle of delivery stroke. 3.(a)InanairstandardOttocyclethemaximumandminimumtemperaturesare1400OCand 15OC.Theheatsuppliedperkgofairis800kJ.Calculatethecompressionratioandcycle efficiency. Also calculate the maximum to minimum pressure ratio in the cycle. (b)An R717 based vapour compression refrigerating machine works between 38OC and -20OC temperature.Theammonialeavesthecompressordryandsaturated.Liquidammoniais undercooledto30OCtemperatureinsidethecondenser,beforethrottling.Findthe theoreticalCOPofthemachine.Thecpofsaturatedammonialiquidis4.91kJ/kg.K.If netrefrigerationrequiredis25.0TR,findthemassflowrateofammoniainkg/h, assuming relative COP 0.75. The saturation properties of R717 are given in the following Table: LiquidVapour t,OCh,kJ/kgS,kJ/kg-Kh, kJ/kg 38380.781.61341489.36 -20108.550.65381437.68 (C)Asmallerpowerplantproducessteamat3MPa,600OCintheboiler.Itkeepthe condenserat45OCtransferof10MWoutasheattransfer.Thefirstturbinesection expandsto500kPaandthenflowisreheatedfollowedbytheexpansioninthelow pressureturbine.Findthereheattemperaturesotheturbineoutputissaturatedvapour. For this reheat find the total turbine power output and the boiler heat transfer. Properties of water are given in the Table below: O1t C p, kpa 3lv , kg m 3gv , m kg 1h , kJ kg vh , kJ kg ps kJ kg K vS , kJ kg K 459.59( )satP0.0010115.252188.420.638612583.190.63861 233.8 3000( )satP0.0012167 0.0666641008.292803.992.64556.1870 6003000-0.13245-3682.30-7.5084 ME-Conventional Paper-IIES-2014www.gateforum.com Indias No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 5 4. Ageothermalsupplyofhotwaterat500kPa,150OCisfedtoaninsulatedflash evaporator at the rate of 1.5 kg/s. A stream of saturatedliquid at 200 kPa is drained from the bottom of the chamber and a stream of saturated vapour at 200 kPa is drawn from the topandfedtoturbine.Findtherateofentropygenerationintheflashevaporator. Properties of water are given in the Table below: p, kPaOt, C 1h , kJ kgvh , kJ kg 1S , kJ kg K vS , kJ kg K 200 ( )sat120.20 t504.682706.631.53007.1271 500 ( )sat151.83 t640.082746.601.86036.8202 500150.00632.18-1.8417- (b)In a chemical plant a solution of density 1100kg/m3 and specific heat capacity 4.6 kJ/kg-K is to be heated from 65 OC to 100OC. The required flow rate of the solution is 11.8 kg/s. A tubular heat exchanger is used for this with the solution flowing about 1.2 m/s in 25 mm bore iron tubes and being heated by wet steam at 115OC. The length of the tubes is not to exceed3.5m.Takinginside,andoutsideheattransfercoefficientas5and10kW/m2K and neglecting the thermal resistance of the tube wall estimate the number of tubes and the number of tube passes required. (c)A water storage tank10m 10m 10m has a drainage opening on one of the vertical sides at thebottom whichistrapezoidal in shapewith awidth 2m at thebottom 4m at thetop and1mheight.Agateofsamedimensionhingedalongtetopedgeisusedtocloseit. What is the minimum horizontal force required to be applied at the bottom to keep the gate closed if the tank has full of water in it? Will there by any change in the force required if the tank is only half full? If yes how much? 132|ME-Conventional Paper-IIES-2014www.gateforum.com Indias No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 6 5. (a)A four cylinder 4 stroke diesel engine has a bore of 212 mm and stroke 292 mm. At full load at 720rpmthebreakmeaneffectivepressureis5.93barandspecificfuelconsumptionis 0.226kg/kWH.Theairfuelratioasdeterminedbyexhaustgasanalysisis25:1.Calculatethe breakthermalefficiencyandvolumetricefficiencyoftheengine.Atmosphericconditionsare 1.01 bar and 15OC. The calorific value of fuel may be taken as 44200 kJ/kg. (b) One kg of air at 35OC DBT and 60% RH is mixed with 2 kg of air at 20OC DBT and 13OC dew pointtemperature.Calculatethespecifichumidity,temperatureandenthalpyofthemixture. Assume specific heat of steam as 1.88kJ/kg K and the following properties may be used: Temperature OCSaturation pressure pS bar Enthalpyof saturatedsteam hgkJ/kg 130.01502525.4 200.02342538.2 260.03362549.1 270.03562550.9 350.05632565.4 (c)Airat27OCtemperatureand100kPapressureflowsoveraflatplateataspeedof2.5m/s. Calculate the boundary layer thickness at distance of 25 and 50 cm from the leading edge of the plate. Calculate the mass flow that enters the boundary layer between x = 25 cm and x= 50 cm from leading edge. The viscosity of air at 27OC is 30.8 pa m . Assume unit depth in z-direction. 6.(a)A 100 cc petrol Engine with a compression ratio of 6 compresses the air fuel mixture to 900 kPaand375OC,At theendofcompressiontheignitionisstartedandthepressurerisesalonga straightlineandattainsthehighestvalueof3.0MPaafterthepistonhastravelled4%ofthe working stroke. The air fuel ratio is 15 : 1 Take R for mixture as 0.275 kJ/kg.K, calorific value of fuel = 44 MJ/kg and cV = 0.965kJ/kg-K. find the heat loss per kg of charge during explosion. Flue gases and air has same gas constant. (b)The following data relates to an air-conditioned space: Outdoor condition38OC DBT/50% RH Room condition24OC DBT/50% RH Sensible heat load24 kW Laten heat load6 kW Bypass factor of the cooling coil0.16 ME-Conventional Paper-IIES-2014www.gateforum.com Indias No.1 institute for GATE Training 1 Lakh+ Students trained till date 65+ Centers across India 7 If the ventilation requirement is such that on mass flow rate basis 20% fresh air is introduced and 80% supply air is recirculated, determine (i) Supply air flow rate (ii) Outside air sensible heat (iii) Outside air latent heat (iv) Grand total heat (v) Effective room sensible heat factor. (c)(i)1m3ofairisheatedatconstantpressurefrom15OCto300OCandthencooledatconstant volume back to its initial temperature. If the initial pressure is 1.03 bar calculate the net heat flow and overall change in entropy. Show the process on a TS diagram. (ii)Withsimpleschematicdiagramexplainthedifferencebetweenfiretubeandwatertube boilers. Mention the merits and demerits of both. 7.(a) A sample bituminous coal gave the following ultimate analysis by mass: Carbon 81.9% Hydrogen 4.9% Oxygen 6%, Nitrogen 2.3% and Ash 4.9%. Calculate (i)the stochemetric air fuel ratio for complete combustion and(ii)the volumetric analysis of wet and dry products of combustion when the air supplied is 25% in excess of the required for complete combustion. (b)Three thin-walled, long, circular cylinders 1,2 and 3 of diameter 150mm, 250 mm and 350mm respectively are arranged concentrically. Temperature of cylinder 1 is 80K and that of cylinder 3 is 300K.Emissivityofcylinder1,2and3is0.05,0.1and0.2respectively.Assumingthatthereis vacuum inside the annular spaces, determine the steady state temperature attained by cylinder 2.(c)Find an expression for the drag force on smooth sphere of diameter. D, moving with a uniform velocity V in a fluid of density and dynamic viscosity.