Sierra Series 830/840/860 Side-Trak™ and ... - Sierra Instruments

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Appendix ASeries 830/840/860 Instruction ManualWhere:H =The constant amount of heat applied to the sensor tube,m•= The mass flow rate of the gas (gm/min)Cρ = The coefficient of specific heat of the gas (Cal/gm);Cρ is given in the Table (at 0°C),∆T = The temperature difference between the downstream andupstream coils, andN =A correction factor for the molecular structure of the gasgiven by the following table:Number of Atoms in the Gas MoleculeNMonatomic 1.040Diatomic 1.000Triatomic 0.941Polyatomic 0.880The mass flow rate, m,•can also be written as:Where:m•= ! Q(3)ρ =The gas mass density at standard conditions (g/l); ρ is givenin the tables (at 0°C, 760 mm Hg).Furthermore, the temperature difference, ∆T, is proportional to theoutput voltage, E, of the mass flow meter, orwhere:a = A constant.∆T = aE (4)If we combine equations (3) and (4), insert them into equation (2),and solve for Q, we getwhere:Q = (bN/ρC p ) (5)b = H/aE = a constant if the output voltage is constant.A-4 IM-83/84/86-H
Series 830/840/860 Instruction ManualAppendix AFor our purposes, we want the ratio of the flow rate, Q 1 , for an actualgas to the flow rate of a reference gas, Q 2 , which will producethe same output voltage in a particular mass flow meter or controller.We get this by combining equations (1) and (5):Q 1 /Q 2 = K 1 /K 2 = (N 1 / ρ 1 C p1 )/(N 2 /ρ 2 C P2 ) (6)Please note that the constant b cancels out. Equation (6) is the fundamentalrelationship used in the accompanying tables. For convenience,the tables give “relative” K-factors, which are the ratios K 1 /K 2 ,instead of the K-factors themselves. In the tables, the relative K-factorisK actual /KN 2 where the reference gas is the commonly used gas, nitrogen(N 2 ). The remaining columns give Cp and ρ, enabling you to calculateK 1 /K 2 directly using Equation (6). In some instances, K 1 /K 2 from thetables may be different from that which you calculate directly. Thevalue from the tables is preferred because in many cases it was obtainedby experiment. Sierra calibrates every transducer with primarystandards using the actual gas or a molecular equivalent reference gas.The calibration certificate accompanying the transducer cites the referencegas used.Example 1:A transducer is calibrated for nitrogen (N 2 ), and the flow rate is1000 sccm for a 5.000 VDC output signal. The flow rate for carbondioxide at a 5.000 VDC output is:Q CO2 /Q N2 = K CO2 /K N2, orQ CO2 = (0.74/1.000)1000 = 740 sccmExample 2:A transducer is calibrated for hydrogen (H 2 ), and the flow rate is100 sccm for a 5.000 VDC output signal. The flow rate for nitrousoxide (N 2 O) is found as follows:Q N2O /Q H2 = K N2O/K H2, orQ N2O = (0.71/1.01) 100 = 70.3 sccmNote that the K-factors relative to nitrogen must be used in each case.Example 3:We want a transducer to be calibrated for use with dichlorosilane(SiH 2 Cl 2 ) at a 100 sccm full scale flow. We wish to use the preferredreference gas Freon-14 (CF 4 ). What flow of CF 4 must wegenerate to do the calibration?Q SiH2CL2 /Q CF4 = K SiH2CL2 /K CF4100/Q CF4 = 0.869Q CF4 = 100/0.869 = 115 sccmIM-83/84/86-H A-5
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Sierra Series 830/840/860Side-Trak
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Series 830/840/860 Instruction Manu
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Table of ContentsSeries 830/840/860
Page 11 and 12: Chapter 1 IntroductionSeries 830/84
Page 13 and 14: Series 830/840/860 Instruction Manu
Page 29 and 30: Chapter 3 OperationSeries 830/840/8
Page 38 and 39: Chapter 4 MaintenanceSeries 830/840
Page 56 and 57: Appendix ASeries 830/840/860 Instru
Page 70: Appendix B SpecificationsSeries 830
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Sierra Series 830/840/860 Side-Trak™ and ... - Sierra Instruments

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