Solutions Manual Applied Gas Dynamics 1st edition by Ethirajan Rathakrishnan

SolutionsMannualforthefourtheditionof

GasDynamics EthirajanRathakrishnan

Preface

Thismanualgivesthedetailedsolutionforalltheproblemsgivenattheend ofdiﬀerentchaptersofthe3rdeditionofGasDynamics.Mysincerethanksto mydoctoralandmastersstudentswhohelpedmeincheckingandkeyinginthe solutionsofthismanual.

MysincerethankstotheContinuingEducationCentreofIndianInstituteof TechnologyKanpurfortheﬁnancialsupporttopreparethismanual.

ERathakrishnan

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Contents 1SomePreliminaryThoughts1 2BasicEquationsofCompressibleFlow3 3WavePropagation23 4One-DimensionalFlow25 5NormalShockWaves79 6ObliqueShockandExpansionWaves119 7PotentialEquationforCompressibleFlow157 8SimilarityRules161 9TwoDimensionalCompressibleFlows165 10Prandtl-MeyerFlow169 11FlowwithFrictionandHeatTransfer173 12MOC205 13MeasurementsinCompressibleFlow207 iii

SomePreliminaryThoughts

Chapter1

1

46 One-DimensionalFlow Thus, pe = 2.2623 × 105 Pa Te = 497.8K 4.26 M =2 5 Ats =1m2 p0 =7 × 105 Pa T0 =27+273=300K (a) For M =2 5wehave, A A∗ =2.637 A∗ = 0 38m2 (b) T ∗ T0 =0 833 T ∗ =0 833 × 300=249 9K = 23.1 ◦ C (c) M = V a a = γ RT =20 04 × √T =231 5m/s V = Ma = 578.75m/s (d) ˙ m A = p0 24.743√T0 × 1 A A∗ = 7 × 105 24 743 × √300 × 1 2.637

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T1 =300K p1 =101kPa p2 =5000kPa V2 V1 Shock FigureS5.14 p2 p1 =49 5 =1+ 2γ γ +1 M 2 1 1 =1+1 167 M 2 1 1 167 Thus, M 2 1 = 49 5+0 167 1.167 =42 55 M1 =6.52 Thevelocitybecomes V1 = M1 a1 =6 52 √1 4 × 287 × 330 = 2374 16m/s Bynormalshockrelation,wehave M2 = 1+ γ 1 2 M 2 1 γ M 2 1 γ 1 2 1/2 =0.4 T2 T1 =1+ 2(γ 1) γ M 2 1 +1 (γ +1)2 M 2 1 M 2 1 1 =1+ 48 41 244 86 × 41.5=9.205 T2 =9 205 × 330=3037 65K Thespeedofsounddownstreamoftheshockis a2 = γ RT2 = √1 4 × 287 × 3038 34 =1104.9m/s

NormalShockWaves

206 MOC

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