VacTran 3 Manual (779748), страница 34
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“Clean commercial steel pipe” having the relative roughness (0.00015)typically encountered in vacuum systems has a friction factor that varies from 0.03 for small diameters (about 0.5inches or 1.27 cm) to 0.01 for large diameters (about 24 inches or 61 cm).In laminar viscous flow conditions, where Reynold’s number is generally less than 2000, friction factor varies as 64/Re.
Laminar flow friction factor is always greater than turbulent flow friction factor for a given relative roughnesspipe.In transition viscous flow conditions, between laminar and turbulent regimes, the friction factor variesasymptotically between the laminar and turbulent values.Fluid flow handbooks often provide factors (for elbows, miters, and pipe bends) in terms of fT, the turbulent flowfriction factor. For example, a standard 90 degree elbow has a K factor of 30 fT. Note that when we substitute thisvalue into the equation for equivalent length, friction factor cancels and we have L = 30D. In other words, a 90degree elbow has an equivalent length of 30 diameters of pipe, independent of the turbulent or laminar friction factoreffects.
Therefore, the previous discussion on friction factor calculation does not affect the results of the equivalentlength calculation for this case.K factors for pipe exits and entrances are not given in terms of fT, so the friction factor is not eliminated from theequivalent length equation. For example, a pipe exit has a K factor of 1.0, resulting in L = D/f. For this version ofVacTran, the turbulent viscous flow friction factor is used for all exit and entrance calculations, which can result inconservatively high equivalent length values if your system operates encounters laminar flow at these transitions.However, this is unlikely under many conditions because the randomizing nature of entrances and exits will tend topreclude laminar flow except at very low pressures.As with molecular flow equivalent length,Total equivalent length =entrance equivalent length+ body equivalent length+ exit equivalent lengthThe calculations for these three components of viscous equivalent length are provided in the following sections:Viscous entrance equivalent lengthViscous body equivalent lengthViscous exit equivalent lengthMolecular flow equivalent lengthSummary- geometric equivalency© 2011 Professional Engineering ComputationsCalculation Formulas32718.3.4.2 Viscous entrance equivalent lengthAs described in the molecular flow section, a conductance entrance is defined as a transition from a larger diameterconductance (or vessel) to the subject conductance.An entrance can be inward projecting relative to the upstream volume, or it can be flush (no projection) to theupstream volume.Projecting entrances are assumed to be cut square to the pipe cross section, while flush entrances can have anedge radius that tends to smooth the flow transition and reduce losses.Projecting entrance example:The pipe entry dialog, shown on the right, has an Entrance Detail tab showing the flush and projecting options.The projecting entrance has a K factor of 0.78.To determine the equivalent length of pipe for this entrance having a K factor of 0.78, we again use the formula :LKDfIf the pipe is 2 inches in diameter, the handbook friction factor for turbulent flow is 0.019, and the resulting equivalentlength is(of 2 inch diameter pipe)© 2011 Professional Engineering Computations328VacTran 3Flush entrance example:The pipe entry dialog Entrance Detail tab shown below has “no projection” selected.
This entrance has an edgeradius of 0.3 inches, which minimizes the entrance loss. The K factor for this geometry is 0.04, which issignificantly lower than the projecting geometry K factor of 0.78. The resulting equivalent length for this entrance isDfLKL0.0420.0194 inches(of 2 inch diameter pipe)© 2011 Professional Engineering ComputationsCalculation Formulas32918.3.4.3 Viscous body equivalent lengthEach body geometry has a geometric equivalent length that is calculated using the K factor formula. These Kfactors are determined experimentally and published in handbooks.The equivalent length for a pipe is simply the pipe length.An orifice has 0 length.Elbows and miters have K factors (and equivalent lengths) that vary with angle.Bends have K factors that vary with both the angle and the ratio of bend radius over pipe diameter.18.3.4.4 Viscous exit equivalent lengthA conductance exit is defined as a transition to a larger diameter conductance (or vessel) from the subjectconductance.
All exits have a K factor of 1.0, regardless of whether they are projecting or flush. For the previousexample of a 2-inch diameter pipe, the exit loss equivalent length would be(of 2 inch diameter pipe)18.3.4.5 Molecular flow equivalent lengthMolecular Flow Summary of equivalent length calculationsThe following table summarizes the applicable approaches to calculating molecular flow equivalent length forVacTran conductance elements.Entrance lossBody lossOrificeNot applicableNot applicable (0)=1SlitNot applicableNot applicable (0)=1Included in bodyText book formulaSame as orificePipe Corrected L’ formulaSame as pipe lengthSame as orificeAnnulus Corrected L’ formulaSame as pipe lengthSame as orificeEllipse Corrected L’ formulaSame as pipe lengthSame as orificeTriangle Corrected L’ formulaSame as pipe lengthSame as orificeRectangle Corrected L’ formulaSame as pipe lengthSame as orificeText book formulaSame as orificeCones*BendIncluded in body© 2011 Professional Engineering ComputationsExit loss330VacTran 3ElbowIncluded in bodyText book formulaSame as orificeMiterIncluded in bodyText book formulaSame as orificeRaw dataconductanceNot applicableNot applicableNot applicableConstantconductanceNot applicableNot applicableNot applicable*Note - Cones have a set of transition equations that degenerate to a pipe entrance or exit depending on aspectratio.
See the section on cone formulas for more details.© 2011 Professional Engineering ComputationsCalculation Formulas33118.3.4.6 Summary- geometric equivalencyThe following table summarizes the applicable approaches to calculating viscous flow equivalent length for VacTranconductance elements.Entrance lossBody lossExit lossK value calculationSame as pipe lengthK value calculationRectangle Calculate equivalentSame as pipe lengthCalculate equivalentdiameter pipe, thenuse pipe K valuecalculationPipeTriangleEllipsediameter pipe, thenuse pipe K valuecalculationAnnulusOrificeK value calculationNot applicable (0)K value calculationSlitK value calculationNot applicable (0)K value calculationBendNot applicableK value calculationK value calculationElbowNot applicableK value calculationK value calculationMiterNot applicableK value calculationK value calculationRaw dataconductanceNot applicableNot applicableNot applicableConstantconductanceNot applicableNot applicableNot applicable© 2011 Professional Engineering Computations332VacTran 3Geometric equivalency in molecular FlowLengthElement typeCircular pipeEntranceBodyGiven Lbody, DLentrance = L’ formulaLbodyGiven Lbody4D3Le n tr an ce4D3LExitGivenDiameter=1RearrangingLexit= 4D/3Given D4D3LAnnular pipeSame as pipeSame as pipeSame as pipeDerived fromequivalencyformulaElliptical pipeSame as pipeSame as pipeSame as pipeDerivedTriangular pipeSame as pipeSame as pipeSame as pipeDerivedRectangular pipeSame as pipeSame as pipeSame as pipeDerivedBendLentrance = 0Lbody From RothequationSame as pipeGiven D4D3LElbowLentrance = 0Same as bendSame as pipeGiven DMiterLentrance = 0Same as bendSame as pipeGiven DConeSame as pipeSame as pipe, usederived diameterSame as pipeDerived fromequivalencyformula© 2011 Professional Engineering ComputationsCalculation FormulasGeometric equivalency in viscous flowLengthElement typeEntranceBodyExitGiven Kentrancefrom Crane r/D dataLentrance=KentranceD/fGiven LbodyGiven Kexit=1Kbody = fLbody /DLexit =KexitD/fAnnular pipeSame as pipeSame as pipeElliptical pipeSame as pipeTriangular pipeRectangularpipeCircular pipeDiamete Friction factor (f)rGivenLookup from Crane data andGiven DiameterSame as pipeDerivedfromequivalency formulaLookup based on derivedDiameterSame as pipeSame as pipeDerivedLookup based on derivedDiameterSame as pipeSame as pipeSame as pipeDerivedLookup based on derivedDiameterSame as pipeSame as pipeSame as pipeDerivedLookup based on derivedDiameterBendGiven Kentrance=0Given Lentrance=0Kbody fromCraneLbody=D *KbodyGiven Kexit=1Lexit =KexitD/fGivenDiameterLookup from Crane data andGiven DiameterElbowGiven Kentrance=0Given Lentrance=0Kbody fromCraneGiven Kexit=1GivenDiameterLookup from Crane data andGiven DiameterMiterGiven Kentrance=0Given Lentrance=0Kbody fromCraneGiven Kexit=1GivenDiameterLookup from Crane data andGiven DiameterConeEntrance Kapplicable to reduceronly, Crane formulaSame as pipeExit K applicableto expander only,Crane formulaGivensmallDiameterLookup from Crane data andsmall Diameter© 2011 Professional Engineering Computations333334VacTran 318.3.5 Geometry-specific conductance casesThe following sections provide additional details on how VacTran calculates volume and equivalent length for viscousand molecular flow.See also:Elbow and miter calculationsBend calculationsRectangle calculationsRectangular pipe efficiencyAnnulus calculationsAnnular pipe efficiencyTriangle calculationsTriangular pipe efficiencyEllipse calculationsElliptical pipe efficiencyConical pipe calculationsComparison of long pipe equations© 2011 Professional Engineering ComputationsCalculation Formulas33518.3.5.1 Elbow and miter calculationsFor molecular flowEquivalent LengthL = 2D + 1.33( /180)D (eqn 3.130, Reference 2)where= bend angle in degreesD = elbow inside diameterFor viscous flowEntrance K factor = 0 (already a randomizer)Viscous entrance equivalent length = 0Body K Factor is interpolated from handbook values (elbow or miter)Body Equivalent Length = Diameter * Body K FactorExit K factor = 1 {Crane exit loss factor}Exit Friction Factor (f) is interpolated from handbook values (elbow or miter)Viscous exit equivalent length = Exit K factor * Diameter / Exit Friction FactorNet K Factor = Entrance K + Body K Factor + Exit KVolume calculationAn equivalent volume of two diameters of pipe approximates the standard elbow or miter used in VacTran.
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