VacTran 3 Manual (779748), страница 36
Текст из файла (страница 36)
The cone will function as the exit loss. This only applies if the upstream pipe has the same diameter asthe small diameter of the cone.If a cone is a pipe contraction (reducer) that is upstream from a pipe in series, don't add an entrance loss for thedownstream pipe. The cone will function as the entrance loss. This only applies if the downstream pipe has thesame diameter as the small diameter of the cone.© 2011 Professional Engineering ComputationsCalculation Formulas351Pipe expansion- viscous flowFor a pipe expansion, the total K factor is the sum of a body and an exit K factor.
The body K factor is calculatedbased on the smaller diameter and the length of the cone. The exit K factor varies from zero for a straight pipe to1.0 for a 180 degree expansion angle. The figure below shows a nearly 180 degree expansion cone. As itapproaches 180 degrees, the cone behaves like a pipe exit with a diameter equal to the small diameter of the cone.In viscous flow, a pipe exit has a K factor of 1.A Nearly 180 degree cone approaches thebehavior of a pipe exit.A nearly zero degree cone approaches the behavior of a pipe.The variation of K factor with cone angle is shown in the graph below:K values for a pipe expansionK factor for a Pipe Expansionfor a cone angle of 0 to 45 degrees:1.000.900.80for a cone angle of 45-180 degrees:0.70K0.600.500.40From Crane's Flow of Fluids, TechnicalPaper 410, equations 3-17 and 3-17.10.300.20Equivalent length for exit:0.100.0004590135180LKAngle (degrees)diameter© 2011 Professional Engineering ComputationsDfbased on smaller352VacTran 3Pipe reducer- viscous flowFor a pipe reducer, the total K factor is the sum of a body and an entrance K factor.
The entrance K factor variesfrom zero for a straight pipe to 0.5 for a 180 degree contraction angle. The figure below shows a nearly 180 degreecontraction cone. As it approaches 180 degrees, the pipe transition between the large and small pipe behaves likea pipe entrance. In viscous flow, a sharp-edged pipe entrance has a K factor of 0.5.A nearly 180 degree cone approaches thebehavior of a pipe entrance.A nearly zero degree cone approaches the behavior of a pipe.The variation of K factor with cone angle is shown in the graph below:K values for a pipe reducerK factor for a Pipe Reducerfor a cone angle of 0 to 45 degrees:1.000.900.80for a cone angle of 45-180 degrees:0.70K0.600.500.400.30From Crane's Flow of Fluids, TechnicalPaper 410, equations 3-18 and 3-18.10.200.100.00Equivalent length for entrance:04590Angle (degrees)135180LKDfbased on smallerdiameter© 2011 Professional Engineering ComputationsCalculation Formulas353Pipe expander or reducer- molecular flowIn molecular flow, pipe expanders and reducers have the same body conductance formula shown below.
Thisformula is for long pipes. As the cone angle approaches 180 degrees, the cone behaves like a pipe entrance if it iscontracting or a pipe exit if it is expanding. In either case, the diameter used for calculations approaches the smalldiameter of the cone as the cone angle approaches 180 degrees. As the cone angle approaches 0 degrees, thediameter approaches the that shown in the formula below.Berman Equation 6.10aSolve for equivalent diameter straight pipe:Straight pipe formulaCm = molecular weightL = cmT = KelvinC = liters/secondd1 = smaller diameterd2 = larger diameter3.81D3LTmEquate C and solve for D2D32d1 d22d1 d2for molecular flowThe following illustrations fixes d1 with a value of 1 and varies the value of d2.
The ratio of d1 and d2 is plottedagainst the Equivalent Diameter, based on the formula above.E q u iv alen t d iameter for lon g c on esin molec u lar flow7.000R atio of equivalent diam eter tos m all diam eter6.0005.0004.0003.0002.0001.0000.000020406080R a tio of inle t a nd outle t dia m e te rs© 2011 Professional Engineering Computations100120354VacTran 3Molecular flow diameter for cones between "long" and "short"As previously mentioned, the short cone with an angle of 180 degrees behaves as a pipe entrance or exit using thesmall end diameter of the cone.
A long cone has an equivalent diameter that is a function of both diameters asexplained in the previous section. What diameter do we use for cones that are between long and short extremes?A transition function is required to obtain reasonable intermediate values for equivalent diameter between the twoextreme cases.Such a transition formula has not been found in the literature by PEC. Therefore, a custom function is used tocombine the two extreme cases into a single continuous curve that is an approximation for intermediate values inbetween.The example below plots the combination function for a long tube equivalent diameter of 5 and a small diameter of 1.The actual diameters used in VacTran will be dependent on the geometry of your cone.
For this example, at anangle of zero degrees, the equivalent diameter is 5, and at 180 degrees the diameter is 1. A phase-shifted sinfunction is applied to each value and the two are added to create a smooth curve for all angles. Note that hisapproximation has not been verified by experimental data, and is provided as a best fit until a published method isfound.T rans ition func tionF or long and s hort c ones(E x ample diameters s hown as 5 and 1)5.0000Diam eter4.00003.0000Zero angle diameter180 degree c one diameter2.0000S um1.00000.000004590135180Ang le (de g re e s)see also:Annulus calculationsBend calculationsConical pipe calculationsElbow and miter calculationsEllipse calculationsRectangle calculationsTriangle calculations© 2011 Professional Engineering ComputationsCalculation Formulas18.3.5.13 Conical pipe examplesSelect from the following examples:Long reducing conical pipeLong expanding conical pipeShort reducing coneShort expanding cone© 2011 Professional Engineering Computations355356VacTran 318.3.5.13.1 Long reducing conical pipeThis example shows that a nearly zero degree cone approaches the behavior of a pipe.To demonstrate this, open the file Long reducing conical pipe.VTSYS in your VacTran examples folder.
Theexample system model has two conductance elements, as shown below:Under the Graphs menu, select "Compare conductance in station". Observe that the cone and the pipe havenearly identical conductance curves in viscous flow, demonstrating that a long reducing cone is equivalent to a longpipe in this flow regime.
Also note the difference between the pipe and the cone in molecular flow. This is due tothe larger diameter calculated for the cone in molecular flow. The pipe has a diameter of 1 cm, while the cone hasan effective diameter of 1.39 cm in molecular flow. See cone molecular flow calculations.© 2011 Professional Engineering ComputationsCalculation Formulas© 2011 Professional Engineering Computations357358VacTran 318.3.5.13.2 Long expanding conical pipeThis example shows that a nearly zero degree cone approaches the behavior of a pipe.To demonstrate this, open the file Long expanding conical pipe.VTSYS in your VacTran examples folder. Theexample system model has two conductance elements, as shown below:Under the Graphs menu, select "Compare conductance in station". Observe that the cone and the pipe have nearlyidentical conductance curves in viscous flow, demonstrating that a long expanding cone is equivalent to a long pipewith a pipe exit in this flow regime.
Also note the difference between the pipe and the cone in molecular flow. Thisis due to the larger diameter calculated for the cone in molecular flow. The pipe has a diameter of 1 cm, while thecone has an effective diameter of 1.39 cm in molecular flow. See cone molecular flow calculations.© 2011 Professional Engineering ComputationsCalculation Formulas© 2011 Professional Engineering Computations359360VacTran 318.3.5.13.3 Short reducing coneThis example shows that a nearly 180 degree cone approaches the behavior of a pipe entrance.To demonstrate this, open the file Short reducing cone.VTSYS in your VacTran examples folder.
The examplesystem model has two conductance elements, as shown below:Under the Graphs menu, select "Compare conductance in station". Observe that the cone and the pipe have nearlyidentical conductance curves, demonstrating that a short reducing cone is equivalent to a pipe entrance.© 2011 Professional Engineering ComputationsCalculation Formulas© 2011 Professional Engineering Computations361362VacTran 318.3.5.13.4 Short expanding coneThis example shows that a nearly 180 degree cone approaches the behavior of a pipe exit.To demonstrate this, open the file Short expanding cone.VTSYS in your VacTran examples folder.
The examplesystem model has two conductance elements, as shown below:Under the Graphs menu, select "Compare conductance in station". Observe that the cone and the pipe have nearlyidentical conductance curves, demonstrating that a short expanding cone is equivalent to a pipe exit.© 2011 Professional Engineering ComputationsCalculation Formulas© 2011 Professional Engineering Computations36336418.4VacTran 3Gas load throughput calculationsGas load throughput is defined as the mass flow of gas entering a vacuum system, usually in pressure-volume/timeunits (such as torr-liters/second).
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