Viscous Flow in PipesTypes of Engineering ProblemsExample Pipe Flow ProblemViscous Flow: Dimensional AnalysisLaminar and Turbulent FlowsBoundary layer growth: Transition lengthLaminar, Incompressible, Steady, Uniform FlowLaminar Flow through Circular TubesLaminar Flow through Circular Tubes: EquationsLaminar Flow through Circular Tubes: DiagramThe Hagen-Poiseuille EquationExample: Laminar Flow (Team work)Turbulent Pipe and Channel Flow: OverviewTurbulenceTurbulence: Size of the Fluctuations or EddiesTurbulence: Flow InstabilityVelocity DistributionsTurbulent Flow Velocity ProfileSlide 19Log Law for Turbulent, Established Flow, Velocity ProfilesPipe Flow: The ProblemPipe Flow Energy LossesFriction Factor : Major lossesLaminar Flow Friction FactorTurbulent Pipe Flow Head LossSmooth, Transition, Rough Turbulent FlowMoody DiagramSwamee-JainPipe roughnessSolution TechniquesMinor LossesHead Loss due to Gradual Expansion (Diffusor)Sudden ContractionSlide 34Entrance LossesHead Loss in BendsHead Loss in ValvesSlide 38Iterative Techniques for D and Q (given total head loss)Solution Technique: Head LossSolution Technique: Discharge or Pipe DiameterExample: Minor and Major LossesDirectionsExample (Continued)Slide 45Pipe Flow Summary (1)Pipe Flow Summary (2)Pipe Flow Summary (3)Columbia Basin Irrigation ProjectPipes are Everywhere!Pipes are Everywhere! Drainage PipesPipesPipes are Everywhere! Water MainsGlycerinExample: Hypodermic Tubing FlowViscous Flow in PipesViscous Flow in PipesTypes of Engineering ProblemsTypes of Engineering ProblemsHow big does the pipe have to be to carry a flow of x m3/s?What will the pressure in the water distribution system be when a fire hydrant is open?How big does the pipe have to be to carry a flow of x m3/s?What will the pressure in the water distribution system be when a fire hydrant is open?Example Pipe Flow ProblemD=20 cmL=500 mvalve100 mFind the discharge, Q.Describe the process in terms of energy!Describe the process in terms of energy!cs1cs1cs2cs2p Vgz Hp Vgz H hp t l11121222222 2       p Vgz Hp Vgz H hp t l11121222222 2       zVgz hl12222  zVgz hl12222  V g z z hl2 1 22  a fV g z z hl2 1 22  a fRemember dimensional analysis?Two important parameters!R - Laminar or Turbulent/D - Rough or SmoothFlow geometryinternal _______________________________external _______________________________Remember dimensional analysis?Two important parameters!R - Laminar or Turbulent/D - Rough or SmoothFlow geometryinternal _______________________________external _______________________________ R,DflDCp R,DflDCp22CVpp22CVppVDRVDRViscous Flow: Dimensional AnalysisViscous Flow: Dimensional AnalysisWhereandin a bounded region (pipes, rivers): find Cpin a bounded region (pipes, rivers): find Cpflow around an immersed object : find Cdflow around an immersed object : find CdTransition at R of 2000Transition at R of 2000Laminar and Turbulent FlowsLaminar and Turbulent FlowsReynolds apparatusReynolds apparatusVDRVDRdampingdampinginertiainertiaBoundary layer growth: Transition lengthBoundary layer growth: Transition lengthPipe EntranceWhat does the water near the pipeline wall experience? _________________________Why does the water in the center of the pipeline speed up? _________________________vvDrag or shearConservation of massNon-Uniform FlowvNeed equation for entrance length hereLaminar, Incompressible, Steady, Uniform FlowLaminar, Incompressible, Steady, Uniform FlowBetween Parallel PlatesThrough circular tubesHagen-Poiseuille EquationApproachBecause it is laminar flow the shear forces can be easily quantifiedVelocity profiles can be determined from a force balanceDon’t need to use dimensional analysisBetween Parallel PlatesThrough circular tubesHagen-Poiseuille EquationApproachBecause it is laminar flow the shear forces can be easily quantifiedVelocity profiles can be determined from a force balanceDon’t need to use dimensional analysisLaminar Flow through Circular TubesLaminar Flow through Circular TubesDifferent geometry, same equation development (see Streeter, et al. p 268)Apply equation of motion to cylindrical sleeve (use cylindrical coordinates)Different geometry, same equation development (see Streeter, et al. p 268)Apply equation of motion to cylindrical sleeve (use cylindrical coordinates)Laminar Flow through Circular Tubes: EquationsLaminar Flow through Circular Tubes: Equations hpdldrau422 hpdldrau422 hpdldau42max hpdldau42max hpdldaV82 hpdldaV82 hpdldaQ84 hpdldaQ84Velocity distribution is paraboloid of revolution therefore _____________ _____________Q = VA = Max velocity when r = 0average velocity (V) is 1/2 umaxVpa2a is radius of the tubea is radius of the tubeLaminar Flow through Circular Tubes: DiagramLaminar Flow through Circular Tubes: DiagramVelocityShear hpdldrau422 hpdldrau422 hpdldrdrdu2 hpdldrdrdu2 hpdldrdrdu2 hpdldrdrdu2lhrl2lhrl2ldhl40ldhl40True for Laminar or Turbulent flowShear at the wallShear at the wallLaminar flowThe Hagen-Poiseuille EquationThe Hagen-Poiseuille Equation hpdldaQ84 hpdldaQ84 hpdldDQ1284 hpdldDQ1284lhzpzp222111lhzpzp222111222111zpzphl222111zpzphl hphl hphlLhDQl1284LhDQl1284LhhpdldlLhhpdldlLhDVl322LhDVl322cv pipe flowConstant cross sectionLaminar pipe flow equationsCV equations!CV equations!h or zh or zpzVgHpzVgH hp t l111 112222 2222 2     