Handout_–Problems_Chapter_5-practice_in_class

Handout–ProblemsChapter5 1.  AnalysisofFullyDeveloped  AnalysisofFullyDevelopedlaminarFlowDownan laminarFlowDownanInclinedPlaneS InclinedPlaneSurface urface Aliquidflowsdownaninclinedplanesurfaceinasteady,fullydevelopedlaminarfilmofthicknessh.Simplify thecontinuityandNavier-Stokesequationstomodelthisflowfield.Obtainexpressionsfortheliquidvelocity profile,theshearstressdistribution,thevolumeflowrate,andtheaveragevelocity.Relatetheliquidfilm thicknesstothevolumeflowrateperunitofdepthofsurfacenormaltotheflow.Calculatethevolumeflow rateinafilmofwaterh=1mmthick,flowingonasurfaceb=1mwide,inclinedatθ=15°tothehorizontal.

Assumptions: 1. 2. 3. 4. 5.

2. LaminarViscousFlowbetweenCoaxialCylinders Aviscousliquidfillstheannulargapbetweenverticalconcentriccylinders.Theinnercylinderis stationary,andtheoutercylinderrotatesatconstantspeed.Theflowislaminar.Simplifythe continuityandNavier-Stokesequationstomodelthisflowfield.Obtainexpressionsfortheliquid velocityprofile,theshearstressdistribution,andshearstressatthesurfaceoftheinnercylinder. Assumptions: 1. 2. 3. 4. 5.

3. Twoinfinite,horizontalparallelplate Considertwoinfinite,horizontalplateinwhichanincompressible,laminar,andfullydeveloped fluidflowsbetweenthem.Findthevelocityprofile. Assumptions: 1. 2. 3.

4. PlaneCouetteFlow Awidemovingbeltpassesthroughacontainerofaviscousliquid.Thebeltmovesverticallyupward withaconstantvelocity,V0,asillustratedinthefigure.Becauseofviscousforcethebeltpicksupa filmoffluidofthicknessh.Gravitytendstomakethefluiddraindownthebelt.Assumethattheflow islaminar,steady,andfullydeveloped.UsetheNavier-Stokesequationstodetermineanexpression fortheaveragevelocityofthefluidfilmasitisdraggedupthebelt. Assumptions: 1. 2. 3. 4. 5.

5. PoiseuilleFlow-LaminarFlowinCircularTubes Steady,incompressible,laminarflowthroughastraightcirculartubeofconstantcrosssection (Hagen-Poiseuille flow). Assumptions 1. 2. 3. 4.

6. Flowthroughanannulus Steady,incompressible,laminarflow,andfullydeveloped. Assumptions 1. 2. 3. 4.