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ENGG 2230 (29)
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Ch 9 Solutions.doc

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Department
Engineering
Course
ENGG 2230
Professor
Bahram Gharabaghi
Semester
Winter

Description
Chapter 9Compressible Flow91An ideal gas flows adiabatically through a duct At section 1 p140 kPa T11260C and V75 ms Farther downstream p30 kPa and T207C Calculate V 1222in ms and ss in JkgK if the gas is a air k14 and b argon k16721FigP91Solutiona For air take k140 R287 JkgK and c1005 Jkg K The adiabatic psteadyflow energy equation 923 is used to compute the downstream velocity111m222cTVconstant1005260751005207Vor AnsV335p22222s20727330MeanwhilessclnTTRlnpp1005ln287ln21p2121260273140orss105442337 JkgKAns a21b For argon take k167 R208 JkgK and c518 JkgK Repeat part ap111m222cTV51826075518207Vsolve AnsV246p22222s20727330ss518ln208ln54320bAns266JkgK2126027314092Solve Prob 91 if the gas is steam Use two approaches a an ideal gas from Table A4 and b real steam from EES or the steam tables 15Solutions ManualFluid Mechanics Seventh Edition2SolutionFor steam take k133 R461 JkgK and c1858 JkgK Thenp111m222cTV1858260751858207VsolveaAnsV450p22222s20727330ss1858ln461ln195710aAns515JkgK21260273140b For real steam we look up each enthalpy and entropy in EES or the Steam TablesJat 140 kPa and 260Creadh2993E6 1kgJat 30 kPa and 207Ch2892E6 2kg111m222ThenhV2993E6752892E6VsolvebVAns44322222sJJat 140 kPa and 260Creads7915at 30 kPa and 207Cs8427 12kgKkgKThusss84277915bAns512JkgK21These are within 15 of the ideal gas estimates a Steam is nearly ideal in this range93If 8 kg of oxygen in a closed tank at 200C and 300 kPa is heated until the pressure rises to 400 kPa calculate a the new temperature b the total heat transfer and c the change in entropySolutionFor oxygen take k140 R260 JkgK and c650 JkgK Thenv400rr TTpp200273631 K aAns358C122121300QmcT8650358200 bAnsD82E5 Jv358273JssmclnTT8650lncAns150021v21200273KP94 Consider steady adiabatic airflow in a ductAt section B the pressure is 3154 kPa and the density is 1137 kgmAt section D the pressure is 282 kPa and the temperature is 19Ca Find the entropy change if anyb Which way is the air flowingSolutionConvert T19273254 KWe need the temperature at section BDp154000PaB472TKB3Rr2871137kgmBTp472154000BBThenlnln1005ln287lnsscR BDp25428200TpDDJor623487ssAnsa133BDkgKThe entropy is higher at BTherefore the adiabatic flow is from D to B Ansb95Steam enters a nozzle at 377C 16 MPa and a steady speed of 200 ms and accelerates isentropically until it exits at saturation conditions Estimate the exit velocity and temperatureSolutionAt saturation conditions steam is not ideal Use EES or the Steam TablesAt 377C and 16 MPa readh3205E6 Jkgands7153 JkgK11At saturationfor ss7153readp185 kPa122T118Candh2527E6 Jkg22111m222ThenhV3205E62002527E6Vsolve AnsV118022222sThis exit flow is supersonic with a Mach number exceeding 20 We are assuming with this calculation that a supersonic shock wave does not formP96Use EES other software or the Gas Tables to estimate c and c their pvratio and their difference for carbon dioxide at 800K and 100 kPaCompare with estimates similar to Eqs 94
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