WPC 83@nrmX$ o3i#CbD25h청w""LE2yE:=d:;=t{679*E$V[+4C 8>当(lH~׭X~T̳ۛ DpDtB$ܐ t'@ 2kSJ ΅ 3X6}ܢ16#J?-0 n[|- QtNA6{j %LhϹ^W z_{Rz3dҞ뫽.|<]RM+VY LG}n$1-"]c'1ph|q>$M]i!-W ( #u .ShZ}6)EC񾂍Iҗ|R깣ԙLOup@O=pAA[FUB %Z`UH& n 0O E o 3q 0O  n 04 B 9U:UHRUPUHhw.47|`$&'    0 .  ^ ______________________________________________________________________________; EMISSION MEASUREMENT TECHNICAL INFORMATION CENTER ; GUIDELINE DOCUMENT ; ______________________________________________________________________________; Derivation of H @ ; INTRODUCTION ; The term H @ given in Equation 1 below is determined during the calibration of the orifice meter in the Environmental Protection Agency (EPA) M< +9Z 0Courier (W1) Regular  P'   XeX&&XXXXeX? ' xdE!?   EMCTID001  EMCTECHNICALINFOMATIONDOCUMENT L   PAGE  1    ? ' xdE!? ('2P$  U!    )  P)   XeX&&XXXXeX? ' xdE!?  Preparedby LoriT.Lay and RogerT.Shigehara   L   EMCTID001   EMAD,OAQPS,EPA  <      D     Rev. L March20,1989  ? ' xdEv!?('2P$  U!   3|d 7|`$&&d|@&@( U$   d /  P)   XeX&&XXXXeX? ' xdE!?  Preparedby LoriT.Lay and RogerT.Shigehara   L   EMTICTID001   EMB,TSD,OAQPS,EPA <      D      L Rev.  March20,1989  ? ' xdEv!?7|`$< +9Z 0Courier (W1) Regular  P'   XeX&&XXXXeX? ' xdE!?   EMTICTID001  EMTICTECHNICALINFOMATIONDOCUMENT   ! PAGE  1    ? ' xdE!? 7|`$< +9Z 0Courier (W1) Regular{E {$  U!   ,XXeX&&XXXXe     ? ' $xdE$!?  @..' EMISSIONMEASUREMENTTECHNICALINFORMATIONCENTEReEmsMISSIONMEASUREMENTCENTER  # @z z % TECHNICALINFORMATIONDOCUMENT   ? ' $xdE$!?  @4   DERIVATIONOFH@      INTRODUCTION   n ThetermH@giveninEquation1belowisdeterminedduringthecalibration  &  oftheorificemeterintheEnvironmentalProtectionAgency(EPA)Method5samplingtrain.Thepurposeofthisdocumentistoexplainthederivationofthisterm.  ̀2   ЀE0.0319HET(tw+460)7   ЀH@=E"""""""""""""*""""""""""""E*Eq.1 N  ЀPb(to+460))Vw󀀀/ f    DERIVATION   Theflowratethroughanorificemeterisdefinedbythefollowingequation:̀""""""̀TmH  ЀQm=Km󀀀"""""E󀀀Eq.2 ~ ЀPmMm F where:    =. Qm=volumetricflowratethroughtheorificemeter,cfm.Q .~  Ѐ̀Km=orificemetercalibrationconstant,[(in.Hg)(lbmole)]/ " Ѐ[($R)(in.H20)]. #   Tm=absoluteorificemetertemperature,$R. !f%   HE=orificemeterpressuredifferential,in.H20. "'   Pm=absoluteorificemeterpressure,in.Hg. 6$)   Mm=molecularweightofgasflowingthroughtheorificemeter, %!+ Ѐlb/lbmole.  InsteadofusingtheorificemetercoefficientKm,thetermH@wasderived (n#. toreflectthegeneralsamplingconditionsofsamplingtrainsandorificemeterdesignswithacalibrationconstantthatcouldberelatedtothedesiredflowrate.Forexample,aH@of1.84meansthattheorifice v*%1 pressuredifferentialHwouldbeabout1.84whensamplegasisflowing >+&2 throughtheorificemeter.ThereferenceconditionsforHwerechosento ,V'3 be0.75dcfmofairat68$Fand29.92in.Hg.UsingEquation2,H@is ,(4 thendefinedas: ^.)6 ЀQ@2P@M@  ЀH@="""""""""EEq.3 N ЀKm2T@    wherethesubscript"@"representsthereferenceconditionsof0.75dcfmofairat68$Fand29.92in.Hg. n  Substitutingthevaluesforthereferenceconditions(exceptM@)into  x Equation3,thefollowingisobtained:̀(0.752)(29.92)M@󀀀M@ V  ЀH@=""""""""""""""""""=0.0319"""EEq.4   Ѐ528Km2󀀀Km2 `  Now,therelationshipbetweenQmandthevolumetricflowratethroughthe v  wettestmeter(Qw)isasfollows(thesubscript"w"referstotheflow >  rateconditionsatthewettestmeter):̀PmQm󀀀PwQw  Ѐ"""""="""""EE󀀀Eq.5 ^ ЀTm󀀀Tw & SubstitutingEquation2intoEquation5andsolvingforKm2: 0 Ѐ""""""̀PmKm󀀀TmHPwQw F Ѐ""""""""""="""""̀Tm󀀀PmMm󀀀Tw P ̀MmTmPw2Qw2 b ЀKm2=""""""""""""Eq.6 * ЀHTw2Pm x IntheMethod5calibrationsetup,thepressureattheorificemeterandthewettestmeterareatbarometricpressure.Thus,Pw=Pm=Pb,Equation  J" 6simplifiesto:̀MmTmPbQw2 (#% ЀKm2="""""""""""Eq.7 #j& ЀHTw2 $2' SubstitutingEquation7intoEquation4:̀0.0319M@HTw2 (", ЀH@="""""""""""""""EE󀀀Eq.8 h)"- ЀMmTmPbQw2 0*#. Sinceairisbeingusedtocalibratetheorifice,M@=Mm.Inaddition, +:%0 Qw=Vw/,whichisthevolumemeasuredbythewettestmeterdividedby ,&1 time,andTmisthesametemperaturemeasuredattheoutletofthedrygas P-&2 meter,i.e.,Tm=To.Furthermore,Tw=tw+460,andTo=to+460.Making .'3 thesesubstitutionsinEquation8yields: .Z(4 Ї2  ЀEE󀀀0.0319HT(tw+460)7 N ЀH@=E"""""""""""""*""""""""""""E*Eq.1  ЀPb(to+460))Vw󀀀/ X   Ӏwhere:  H@=Hthatgives0.75dcfmofairat68$Fand29.92in.Hg,in.  x H20.  @ ̀0.0319E=constant,(0.752)(29.92)/(68+460). V  ̀HE=orificemeterpressuredifferential,in.H20. `  ̀tw=wettestmetertemperature,$F. v  ̀E=time,min.     Pb=barometricpressure,in.Hg.    to=outlettemperatureofdrygasmeter,$F. &   Vw=volumemeasuredbythewettestmeter,cf. 0   BIBLIOGRAPHY  F 1.0  CodeofFederalRegulations.Title40,Part60.U.S.Government x PrintingOffice,Washington,D.C.July1,1987. %% 2.0  Shigehara,R.T.AdjustmentsintheEPANomographforDifferentPitot V TubeCoefficientsandDryMolecularWeights.In:StackSamplingTechnicalInformationACollectionofMonographsandPapers,Vol.III.U.S.EnvironmentalProtectionAgency.PublicationNo.EPA450278042c.October1978.pp.4849. %% 3.0  Smith,W.S.,R.M.Martin,D.E.Durst,R.G.Hyland,T.J.Logan,and "# C.B.Hager.StackGasSamplingImprovedandSimplifiedwithNewEquipment.Presentedatthe60thAnnualMeetingoftheAirPollutionControlAssociation,June1116,1967,Cleveland,Ohio.APCAPaperN.67119.