有机无机化学化工热力学教学课件管道计算

1CHAPTER5

IncompressibleFlowinPipesandChannels

1CHAPTER5

IncompressibleFlow2content5.1SHEARSTRESSANDSKINFRICTIONINPIPES5.2LAMINARFLOWINPIPESANDCHANNELS5.3TURBULENTFLOWINPIPESANDCHANNELS5.4FRICTIONFROMCHANGESINVELOCITYORDIRECTION5.5DESIGNOFPIPESYSTEM***

2content5.1SHEARSTRESSAND35.1SHEARSTRESSANDSKINFRICTIONINPIPES1.Shear-stressdistribution

2.Relationbetweenskinfrictionandwallshear

3.Thefrictionfactor

4.Relationsbetweenskinfrictionparameters

5.Flowinnoncircularchannels35.1SHEARSTRESSANDSKINFR41.Shear-stressdistributionConsiderthesteadyflowoffluidofconstantdensityinfullydevelopedflowthroughahorizontalpipe.41.Shear-stressdistribution5Applymomentumequation(4.42)betweentwofacesofthedisk.(4.42)(5.1)rearranging5Applymomentumequation(4.426SubtractingEq.(5.1)fromEq.(5.2)gives

(5.2)(5.3)also(5.1)6SubtractingEq.(5.1)fromEq7Astraightlinewithsloprwwt7Astraightlinewithsloprww82.RelationbetweenskinfrictionandwallshearWritingBernoulliequationoveradefinitelengthLofthecompletestream.

L82.Relationbetweenskinfric9Eq.(5.2)(5.2)become(5.5)9Eq.(5.2)(5.2)become(5.5)10(5.5)f10(5.5)f113.Thefrictionfactor

------Fanningfrictionfactory

(5.6)------BlasiusorDarcyfrictionfactor113.Thefrictionfactor124.RelationsbetweenskinfrictionparametersTherelationofcommonquantitiesusedtomeasureskinfrictioninpipes.

Pressuredropcausedbyfrictionloss阻力降,Pa(5.7)124.Relationsbetweenskinfr135.Flowinnoncircularchannelsequivalentdiameter

hydraulicradius

135.Flowinnoncircularchann14Flowbetweenparallelplates,whenthedistancebetweenthembismuchsmallerthanthewidthoftheplates

Aannulusbetweentwoconcentricpipes

(5.15)Asquareductwithawidthofsideb

14Flowbetweenparallelplates155.2LAMINARFLOWINPIPESANDCHANNELS1.Laminarflowofnewtonianfluids

2.Hagen-Poiseuilleequation

☆3.Laminarflowofnon-newtonianliquids4.Laminarflowinanannulus

155.2LAMINARFLOWINPIPESA161.LaminarflowofnewtonianfluidsNewtonianfluidisflowinginacircularchannelinlaminarflow.161.Laminarflowofnewtonian17Velocitydistribution

Newton'slaw

(5.13)EliminatingτbyTherefore(5.14)17VelocitydistributionNewton18IntegrationofEq.(5.14)withtheboundaryconditionu=0,r=rwgives

(5.15)Whenr=0(5.16)18IntegrationofEq.(5.14)wi19Theratioofthelocalvelocitytothemaximumvelocity

(5.17)Inlaminarflowthevelocitydistributionwithrespecttotheradiusisaparabola.

19Theratioofthelocalveloc202021Averagevelocity

(5.18)21Averagevelocity(5.18)22(5.19)Theaveragevelocityispreciselyone-halfthemaximumvelocity.22(5.19)Theaveragevelocityi23Kineticenergycorrectionfactor

Momentumcorrectionfactor

23Kineticenergycorrectionfa242.Hagen-Poiseuilleequationtoeliminate(5.7)UsingInEq.5.7242.Hagen-Poiseuilleequation25(5.20)------Hagen-Poiseuilleequation

Comparewith(5.22)ThereforeInlaminarflow,frictionfactorisonlyinfluencedbyRe.25(5.20)------Hagen-Poiseuill26☆3.Laminarflowofnon-newtonianliquids26☆3.Laminarflowofnon-new274.Laminarflowinanannulus

Velocitydistributionforthelaminarflowofanewtonianfluidthroughanannularspace

where=radiusofouterwallofannulus=ratio=radiusofinnerwallofannulus(5.28)274.Laminarflowinanannul28ForannularflowtheReynoldsnumberis(5.29)(5.30)28ForannularflowtheReynold2929305.3TURBULENTFLOWINPIPESANDCHANNELS1.Velocitydistributionforturbulentflow

2.Universalvelocitydistributionequations

3.Limitationsofuniversalvelocitydistributionlaws

4.Flowquantitiesforturbulentflowinsmoothroundpipes305.3TURBULENTFLOWINPIPES315.Relationsbetweenmaximumvelocityandaveragevelocity

6.Effectofroughness

7.Thefrictionfactorchart

☆8.Reynoldsnumbersandfrictionfactorfornon-newtonianfluids

9.Dragreductioninturbulentflow10.Nonisothermalflow

11.Turbulentflowinnoncircularchannels

315.Relationsbetweenmaximum321.VelocitydistributionforturbulentflowFlowinturbulentthroughaclosedchannel

321.Velocitydistributionfor33Viscousstresses粘性应力Viscousstress+TurbulentstressTurbulentstressorReynoldstress湍流应力or雷诺应力viscoussublayer:bufferlayer:turbulentcore:33ViscousstressesViscousstr34viscoussublayer:bufferlayer:turbulentcore:Velocitygradientlargemiddlesmall34viscoussublayer:Velocitygr353536Itiscustomarytoexpressthevelocitydistributioninturbulentflowintermsofdimensionlessparameters

(5.31)Frictionvelocity摩擦速度，m/sFrictiondistance,摩擦距离，m.36Itiscustomarytoexpresst37(5.32)velocityquotient,dimensionless无量纲速度(5.33)dimensionlessdistance,无量纲距离

y=distancefromwalloftube(5.34)37(5.32)velocityquotient,dim382.Universalvelocitydistributionequations通用速度分布方程382.Universalvelocitydistri39viscoussublayer

(5.35)(5.36)fortheviscoussublayer:39viscoussublayer(5.35)(5.3640bufferlayer

:anempiricalequation(5.37)forthebufferzone:40bufferlayer:anempirical41turbulentcore:(5.38)fortheturbulentcore:41turbulentcore:(5.38)fort4242433.Limitationsofuniversalvelocitydistributionlaws

433.Limitationsofuniversal444.Flowquantitiesforturbulentflowinsmoothroundpipes444.Flowquantitiesforturbu45Averagevelocity

(5.46)(5.47)45Averagevelocity(5.46)(5.4746TheReynoldsnumber-frictionfactorlawforsmoothtubes

vonKarmanequation

(5.50)46TheReynoldsnumber-friction47Thekineticenergyandmomentumcorrectionfactors

(5.51)(5.52)47Thekineticenergyandmomen48ForaReynoldsnumberof104,thefrictionfactorforasmoothtubeis0.0079,αis1.084,andβis1.031.

Forexample:ForRe=106thevaluesaref=0.0029,α=1.032,andβ=1.011.

Forturbulentflowtheerrorisusuallyverysmallifαandβareassumedtobeunity48ForaReynoldsnumberof104495.RelationsbetweenmaximumvelocityandaveragevelocityExperimentallymeasuredvaluesofasafunctionoftheReynoldsnumberareshowninFig.5.8,495.Relationsbetweenmaximum5050516.Effectofroughness516.Effectofroughness52kandiscalledtheroughnessparameter粗糙度

.k/Disdefinedasrelativeroughness相对粗糙度.52kandiscalledtheroughnes53Smoothpipe光滑管Roughpipe粗糙管hydraulicallysmoothpipe:hydraulicallyroughpipe:DrawncopperandbrasspipeOld,foul,andcorrodedpipe53Smoothpipe光滑管hydraulically54Fig.5.10givetheroughnessparameterofseveralmaterialofnewpipe.(p112)54Fig.5.10givetheroughness55TheeffectofroughnessonthefrictionfactorRoughnesshasnoappreciableeffectonthefrictionfactorforlaminarflowunlesskistoolarge.55Theeffectofroughnessont56Fromdimensionalanalysis.

f

isafunctionofbothReandtherelativeroughnessk/D

56Fromdimensionalanalysis.f577.ThefrictionfactorchartFromdimensionalanalysisf

isafunctionofbothReandtherelativeroughnessk/D

Frictionfactorchartisalog-logplotoffversusRe.

577.Thefrictionfactorchart585859二、管内湍流的摩擦系数59二、管内湍流的摩擦系数6060616162LaminarflowBufferTurbulenceCompleteturbulence（完全湍流区,阻力平方区）62Laminarflow63Laminarflow63Laminarflow64Turbulentflow:forhydraulicallysmoothpipeCoburnequationBlasiusequationThisappliesoverRefromabout50,000to1x106.ApplicableoverRefrom3,000to3x106

64Turbulentflow:forhydrauli65Completeturbulentflow:Turbulentflow:forroughpipe65Completeturbulentflow:Turb66☆8.Reynoldsnumbersandfrictionfactorfornon-newtonianfluidsforpseudoplasticfluidsandlaminarflow

(5.56)66☆8.Reynoldsnumbersandfr67CHAPTER5

IncompressibleFlowinPipesandChannels

1CHAPTER5

IncompressibleFlow68content5.1SHEARSTRESSANDSKINFRICTIONINPIPES5.2LAMINARFLOWINPIPESANDCHANNELS5.3TURBULENTFLOWINPIPESANDCHANNELS5.4FRICTIONFROMCHANGESINVELOCITYORDIRECTION5.5DESIGNOFPIPESYSTEM***

2content5.1SHEARSTRESSAND695.1SHEARSTRESSANDSKINFRICTIONINPIPES1.Shear-stressdistribution

2.Relationbetweenskinfrictionandwallshear

3.Thefrictionfactor

4.Relationsbetweenskinfrictionparameters

5.Flowinnoncircularchannels35.1SHEARSTRESSANDSKINFR701.Shear-stressdistributionConsiderthesteadyflowoffluidofconstantdensityinfullydevelopedflowthroughahorizontalpipe.41.Shear-stressdistribution71Applymomentumequation(4.42)betweentwofacesofthedisk.(4.42)(5.1)rearranging5Applymomentumequation(4.4272SubtractingEq.(5.1)fromEq.(5.2)gives

(5.2)(5.3)also(5.1)6SubtractingEq.(5.1)fromEq73Astraightlinewithsloprwwt7Astraightlinewithsloprww742.RelationbetweenskinfrictionandwallshearWritingBernoulliequationoveradefinitelengthLofthecompletestream.

L82.Relationbetweenskinfric75Eq.(5.2)(5.2)become(5.5)9Eq.(5.2)(5.2)become(5.5)76(5.5)f10(5.5)f773.Thefrictionfactor

------Fanningfrictionfactory

(5.6)------BlasiusorDarcyfrictionfactor113.Thefrictionfactor784.RelationsbetweenskinfrictionparametersTherelationofcommonquantitiesusedtomeasureskinfrictioninpipes.

Pressuredropcausedbyfrictionloss阻力降,Pa(5.7)124.Relationsbetweenskinfr795.Flowinnoncircularchannelsequivalentdiameter

hydraulicradius

135.Flowinnoncircularchann80Flowbetweenparallelplates,whenthedistancebetweenthembismuchsmallerthanthewidthoftheplates

Aannulusbetweentwoconcentricpipes

(5.15)Asquareductwithawidthofsideb

14Flowbetweenparallelplates815.2LAMINARFLOWINPIPESANDCHANNELS1.Laminarflowofnewtonianfluids

2.Hagen-Poiseuilleequation

☆3.Laminarflowofnon-newtonianliquids4.Laminarflowinanannulus

155.2LAMINARFLOWINPIPESA821.LaminarflowofnewtonianfluidsNewtonianfluidisflowinginacircularchannelinlaminarflow.161.Laminarflowofnewtonian83Velocitydistribution

Newton'slaw

(5.13)EliminatingτbyTherefore(5.14)17VelocitydistributionNewton84IntegrationofEq.(5.14)withtheboundaryconditionu=0,r=rwgives

(5.15)Whenr=0(5.16)18IntegrationofEq.(5.14)wi85Theratioofthelocalvelocitytothemaximumvelocity

(5.17)Inlaminarflowthevelocitydistributionwithrespecttotheradiusisaparabola.

19Theratioofthelocalveloc862087Averagevelocity

(5.18)21Averagevelocity(5.18)88(5.19)Theaveragevelocityispreciselyone-halfthemaximumvelocity.22(5.19)Theaveragevelocityi89Kineticenergycorrectionfactor

Momentumcorrectionfactor

23Kineticenergycorrectionfa902.Hagen-Poiseuilleequationtoeliminate(5.7)UsingInEq.5.7242.Hagen-Poiseuilleequation91(5.20)------Hagen-Poiseuilleequation

Comparewith(5.22)ThereforeInlaminarflow,frictionfactorisonlyinfluencedbyRe.25(5.20)------Hagen-Poiseuill92☆3.Laminarflowofnon-newtonianliquids26☆3.Laminarflowofnon-new934.Laminarflowinanannulus

Velocitydistributionforthelaminarflowofanewtonianfluidthroughanannularspace

where=radiusofouterwallofannulus=ratio=radiusofinnerwallofannulus(5.28)274.Laminarflowinanannul94ForannularflowtheReynoldsnumberis(5.29)(5.30)28ForannularflowtheReynold9529965.3TURBULENTFLOWINPIPESANDCHANNELS1.Velocitydistributionforturbulentflow

2.Universalvelocitydistributionequations

3.Limitationsofuniversalvelocitydistributionlaws

4.Flowquantitiesforturbulentflowinsmoothroundpipes305.3TURBULENTFLOWINPIPES975.Relationsbetweenmaximumvelocityandaveragevelocity

6.Effectofroughness

7.Thefrictionfactorchart

☆8.Reynoldsnumbersandfrictionfactorfornon-newtonianfluids

9.Dragreductioninturbulentflow10.Nonisothermalflow

11.Turbulentflowinnoncircularchannels

315.Relationsbetweenmaximum981.VelocitydistributionforturbulentflowFlowinturbulentthroughaclosedchannel

321.Velocitydistributionfor99Viscousstresses粘性应力Viscousstress+TurbulentstressTurbulentstressorReynoldstress湍流应力or雷诺应力viscoussublayer:bufferlayer:turbulentcore:33ViscousstressesViscousstr100viscoussublayer:bufferlayer:turbulentcore:Velocitygradientlargemiddlesmall34viscoussublayer:Velocitygr10135102Itiscustomarytoexpressthevelocitydistributioninturbulentflowintermsofdimensionlessparameters

(5.31)Frictionvelocity摩擦速度，m/sFrictiondistance,摩擦距离，m.36Itiscustomarytoexpresst103(5.32)velocityquotient,dimensionless无量纲速度(5.33)dimensionlessdistance,无量纲距离

y=distancefromwalloftube(5.34)37(5.32)velocityquotient,dim1042.Universalvelocitydistributionequations通用速度分布方程382.Universalvelocitydistri105viscoussublayer

(5.35)(5.36)fortheviscoussublayer:39viscoussublayer(5.35)(5.36106bufferlayer

:anempiricalequation(5.37)forthebufferzone:40bufferlayer:anempirical107turbulentcore:(5.38)fortheturbulentcore:41turbulentcore:(5.38)fort108421093.Limitationsofuniversalvelocitydistributionlaws

433.Limitationsofuniversal1104.Flowquantitiesforturbulentflowinsmoothroundpipes444.Flowquantitiesforturbu111Averagevelocity

(5.46)(5.47)45Averagevelocity(5.46)(5.47112TheReynoldsnumber-frictionfactorlawforsmoothtubes

vonKarmanequation

(5.50)46TheReynoldsnumber-friction113Thekineticenergyandmomentumcorrectionfactors

(5.51)(5.52)47Thekineticenergyandmomen114ForaReynoldsnumberof104,thefrictionfactorforasmoothtubeis0.0079,αis1.084,andβis1.031.

Forexample:ForRe=106thevaluesaref=0.0029,α=1.032,andβ=1.011.

Forturbulentflowtheerrorisusuallyverysmallifαandβareassumedtobeunity48ForaReynoldsnumberof1041155.RelationsbetweenmaximumvelocityandaveragevelocityExperimentallymeasuredvaluesofasafunctionoftheReynoldsnumberareshowninFig.5.8,495.Relationsbe