Fundamentals of Vacuum Technology (1248463), страница 66
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cooled)Turbomolecular pumpGas filter, generalTable XVI: Symbols used in vacuum technology (extract from DIN 28401)157HomeTables, Formulas, DiagramsFiltering apparatus, generalRight-angle stop cockBaffle, generalGate valveCooled baffleButterfly valveCold trap, generalNonreturn valveCold trap with coolant reservoirSafety shut-off valveSorption trapThrottlingModes of operationManual operationVacuum chambersVariable leak valveVacuum chamberElectromagnetic operationVacuum bell jarHydraulic or pneumatic operationElectric motor driveShut-off devicesWeight-operatedShut-off device, generalShut-off valve, straight-through valveConnections and pipingRight-angle valveFlange connection, generalStop cockBolted flange connectionThree-way stop cockSmall flange connectionTable XVI: Symbols used in vacuum technology (extract from DIN 28401) (continuation)158HomeTables, Formulas, DiagramsClamped flange connectionMeasurement andgaugesThreaded tube connectionBall-and-socket jointGeneral symbol for vacuum **)Spigot-and-socket jointVacuum measurement, vacuum gauge head **)Taper ground joint connectionVacuum gauge, operating and display unit for vacuumgauge head **)Intersection of two lines with connectionVacuum gauge, recording **)Intersection of two lines without connectionVacuum gauge with analog measured-value display **)Branch-off pointVacuum gauge with digital measured-value display **)Combination of ductsMeasurement of throughputFlexible connection (e.g.
bellows, flexible tubing)Linear-motion leadthrough, flange-mountedLinear-motion leadthrough, without flangeLeadthrough for transmission of rotary and linear motionRotary transmission leadthroughElectric current leadthroughTable XVI: Symbols used in vacuum technology (extract from DIN 28401) (continuation)159HomeTables, Formulas, DiagramsBoiling point H2OBody temperature 37¡CRoom temperatureFreezing point H2ONaCl/H2O 50:50Freezing point HgCO2 (dry ice)Boiling point LN2Absolute zero pointKelvin Celsius37310031037293202730255Ð1834Ð39195Ð7877Ð1960Ð273RŽaumur Fahrenheit Rankine8021267230995591668527032492Ð140460Ð31Ð39422Ð63Ð109352Ð157Ð321170Ð219Ð4600KKelvin¡CCelsiusKKelvin1K Ð 273¡CCelsius¡C + 2731¡CRŽaumur5á ¡R + 2734¡FFahrenheit¡RRankineConversion in¡RRŽaumur4(K Ð 273)59(K Ð 273) + 325¡RRankine9K = 1,8 K54á ¡C59á ¡C + 3259(¡C + 273)55á ¡R419á ¡R + 3245 (¡F Ð 32) + 27395 (¡F Ð 32)94 (¡F Ð 32)91¡F + 4605 (¡R)95 (¡R Ð 273)9¡R Ð 460145¡FFahrenheit[ 59 (¡R Ð 273) ]59[ 54 (¡R + 273) ]V2ÐpZAZMean free path λ [cm]Ð p2Table XVII: Temperature comparison and conversion table (rounded off to whole degrees)λ~ 1pPressure p [mbar]Pressure p [mbar]λnZAZVFig.
9.1:Variation of mean free path λ (cm) with pressure for various gasesFig. 9.2:: mean free path in cm (λ ~ 1/p): particle number density in cmÐ3 (n ~ p): area-related impingement rate in cmÐ3 á sÐ1 (ZA ~ p2): volume-related collision rate in cmÐ3 á sÐ1 (ZV ~ p2)Diagram of kinetics of gases for air at 20 ¡C160HomeTables, Formulas, Diagrams106105conductance [l á cmÐ1]Temperature (K)Pressure [mbar]10410310210186Altitude [km]4Fig.
9.3:2Decrease in air pressure (1) and change in temperature (2) as a function of altitude100101246 8102103104Pipe length l [cm]Altitude (km)Pipe length l [cm]Molecules/atoms [cmÐ3]Fig. 9.6:Fig. 9.4:Conductance values for piping of commonly used nominal width with circular crosssection for laminar flow (p = 1 mbar) according to equation 53a. (Thick lines refer topreferred DN) Flow medium: air (d, l in cm!)conductance [l á sÐ1]Fig. 9.5:Change in gas composition of the atmosphere as a function of altitudeConductance values for piping of commonly used nominal width with circular cross-sectionfor molecular flow according to equation 53b.
(Thick lines refer to preferred DN) Flowmedium: air (d, l in cm!)161HomeTables, Formulas, DiagramspSTART Ð pend, PR=pEND Ð pend, PpSTART < 1013 mbarColumn ➀: Vessel volume V in litersColumn ➁: Maximum effective pumping speed Seff,max at thevessel in (left) liters per second or (right) cubicmeters per hour.Column ➂: Pump-down time tp in (top right) seconds or(center left) minutes or (bottom right) hours.Column ➃: Right:Pressure pEND in millibar at the END of the pumpdown time if the atmospheric pressurepSTART ( pn = 1013 prevailed at the START of thepump-down time. The desired pressure pEND is tobe reduced by the ultimate pressure of the pumppult,p and the differential value is to be used in thecolumns. If there is inflow qpV,in, the valuepend Ð pult,p Ð qpV,in / Seff,max is to be used in thecolumns.Left:Pressure reduction ratio R = (pSTART Ð pult,p ÐqpV,in / Seff,max)/(pend Ð pult,p Ð qpV,in / Seff,max), ifthe pressure pSTART prevails at the beginning ofthe pumping operation and the pressure is to belowered to pEND by pumping down.The pressure dependence of the pumping speedis taken into account in the nomogram and isexpressed in column ➄ by pult,p.
If the pumppressure pult,p is small in relation to the pressurepend which is desired at the end of the pumpdown operation, this corresponds to a constantpumping speed S or Seff during the entirepumping process.Fig. 9.7:pEND – pend, pmbarpSTART = 1013 mbarExample 1 with regard to nomogram 9.7:Example 2 with regard to nomogram 9.7:A vessel with the volume V = 2000 l is to be pumped downfrom a pressure of pSTART = 1000 mbar (atmosphericpressure) to a pressure of pEND = 10-2 mbar by means of arotary plunger pump with an effective pumping speed at thevessel of Seff,max = 60 m3/h = 16.7 l á s-1.
The pump-down timecan be obtained from the nomogram in two steps:A clean and dry vacuum system (qpV,in = 0) with V = 2000 l (asin example 1) is to be pumped down to a pressure ofpEND = 10-2 mbar. Since this pressure is smaller than theultimate pressure of the rotary piston pump (Seff,max = 60 m3/h= 16.7 l ( s-1 = 3 á 10-2 mbar), a Roots pump must be used inconnection with a rotary piston pump. The former has astarting pressure of p1 = 20 mbar, a pumping speed ofSeff,max = 200 m3/h Ð 55 l á s-1 as well as pult,p Ð 4 á 10-3 mbar.From pstart = 1000 mbar to p = 20 mbar one works with therotary piston pump and then connects the Roots pump fromp1 = 20 mbar to pEND = 10-2 mbar, where the rotary pistonpump acts as a backing pump. For the first pumping step oneobtains the time constant τ = 120 s = 2 min from thenomogram as in example 1 (straight line through V = 2000 l,Seff = 16.7 l á s-1).
If this point in column ➂ is connected withthe point p1 - pult,p = 20 mbar Ð 3 á 10-2 mbar = 20 mbar (pult,pis ignored here, i.e. the rotary piston pump has a constantpumping speed over the entire range from 1000 mbar to 20mbar) in column 5, one obtains tp,1 = 7.7 min. The Rootspump must reduce the pressure from p1 = 20 mbar topEND = 10-2 mbar, i.e. the pressure reduction ratioR = (20 mbar Ð 4 á 10-3 mbar) / (10-2 mbar-4 á 10-3) =20/6 á 10-3 mbar = 3300.1) Determination of τ: A straight line is drawn throughV = 2000 l (column ➀) and Seff = 60 m3/h-1 = 16.7 l á s-1(column ➁) and the value t = 120 s = 2 min is read off at theintersection of these straight lines with column ➂ (note thatthe uncertainty of this procedure is around ∆τ = ± 10 s sothat the relative uncertainty is about 10 %).2) Determination of tp: The ultimate pressure of the rotarypump is pult,p = 3 á 10-2 mbar, the apparatus is clean andleakage negligible (set qpV,in = 0); this is pSTART Ð pult,p =10-1 mbar Ð 3 á 10-2 mbar = 7 á 10-2 mbar.
Now a straight lineis drawn through the point found under 1) τ = 120 s (column➂) and the point pEND Ð pult,p = 7 á 10-2 mbar (column ➄) andthe intersection of these straight lines with column ➃tp = 1100 s = 18.5 min is read off. (Again the relativeuncertainty of the procedure is around 10 % so that therelative uncertainty of tp is about 15 %.) Taking into accountan additional safety factor of 20 %, one can assume a pumpdown time oftp = 18.5 min á (1 + 15 % + 20 %) = 18.5 min á 1.35 = 25 min.The time constant is obtained (straight line V = 2000 l incolumn ➀, Seff = 55 l á sÐ1 in column ➁) at = 37 s (in column➂).
If this point in column ➂ is connected to R = 3300 incolumn ➄, then one obtains in column ➃ tp, 2 = 290 s =4.8 min. If one takes into account tu = 1 minfor the changeovertime, this results in a pump-down time of tp = tp1 + tu + tp2 =7.7 min + 1 min + 4.8 min = 13.5 min.Nomogram for determination of pump-down time tp of a vessel in the rough vacuum pressure range162HomeTables, Formulas, DiagramsExample: What diameter d must a 1.5-m-long pipe have sothat it has a conductance of about C = 1000 l / sec in theregion of molecular flow? The points l = 1.5 m andC = 1000 l/sec are joined by a straight line which is extendedto intersect the scale for the diameter d.
The value d = 24 cmis obtained. The input conductance of the tube, which dependson the ratio d / l and must not be neglected in the case ofshort tubes, is taken into account by means of a correctionfactor α. For d / l < 0.1, α can be set equal to 1.
In ourFig. 9.8:Tube diameterConductance for molecular flowTube lengthCorrection factor for short tubesCexample d/l = 0.16 and α = 0.83 (intersection point of thestraight line with the a scale). Hence, the effectiveconductance of the pipeline is reduced toC á α = 1000 á 0.83 = 830 l/sec. If d is increased to 25 cm,one obtains a conductance of 1200 á 0.82 = 985 l / sec(dashed straight line).Nomogram for determination of the conductance of tubes with a circular cross-section for air at 20 ¡C in the region of molecular flow (according to J. DELAFOSSE and G. MONGODIN: Lescalculs de la Technique du Vide, special issue ÒLe VideÓ, 1961).163HomeTables, Formulas, DiagramsCTube internal diameter [cm]Uncorrected conductance for mol. flow [m3 á hÐ1]conductance [ l á sÐ1]Clausing factorLaminar flowMol.
flowKnudsen flowCorrection factor for higher pressuresPressure [mbar]Pressure [mbar]Tube length [meters]Air 20 ¡CProcedure: For a given length (l) and internal diameter (d),the conductance Cm, which is independent of pressure, mustbe determined in the molecular flow region. To find theconductance C* in the laminar flow or Knudsen flow regionwith a given mean pressure of p in the tube, the conductancevalue previously calculated for Cm has to be multiplied by thecorrection factor a determined in the nomogram: C* = Cm á α.Fig. 9.9:Example: A tube with a length of 1 m and an internal diameterof 5 cm has an (uncorrected) conductance C of around 17 l/sin the molecular flow region, as determined using theappropriate connecting lines between the ÒlÓ scale and the ÒdÓscale.
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