Derivation of Humidty and NOx Humidty Correction Factors
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1 (Ths document follows the presentatons n "Vapor Pressure Equaton for Water n the Range 0 to 00 C", by Arnold Wexler and Lews Greenspan, February 9, 97 JOURNAL OF RESEARCH of the Natonal Bureau of Standards Vol. 75A, No. 3, May-June 97 "Vapor Pressure Formulaton for Water n Range 0 to 00 C. A Revson", by Arnold Wexler, July 5, 976 JOURNAL OF RESEARCH of the Natonal Bureau of Standards Vol. 80A, Nos. 5 and 6, September-December 976 "Vapor Pressure Formulaton for Ice", by Arnold Wexler, September 23, 976 JOURNAL OF RESEARCH of the Natonal Bureau of Standards Vol. 8A, No., September 23, 976 "New Equatons for Computng Vapor Pressure and Enhancement Factor", May 98 and 5 August 98 by Arden L. Buck, 982 Journal of Appled Meterology, May 98 and 5 August 98.) Input of Ambent Condtons Baro mmhg Drybulb degc 20 Dewpont degc 0 Baro nhg Baro mmhg 25.4 Baro nhg = Baro. mb Baro nhg Baro mb = 000 Drybulb. 9 degf Drybulb degc 5 5 Drybulb degk Dewpont. 9 degf Dewpont degc 5 5 Dewpont degk Drybulb degf = 68 Drybulb degf 32 Drybulb degk = Dewpont degf = 50 Dewpont degf 32 Dewpont degk = /24/97-0:55 US-EPA-OAR-OMS-TSD
2 Compute Corrected Saturaton Vapor Pressure for Dry Bulb Temperature above and below ce pont. Ths value wll be used to compute Relatve Humdty. The followng are Wexler's most accurate formulatons: Eq. (5) (Wexler, 976) for vapor pressure over water and Eq. (5) (Wexler, 977) for vapor pressure over ce. Wexler's formulatons are gven below. These calculatons are most clearly presented n Buck's Eqs. (5a) and (5b) (Buck, 98). Absolute Temperature n K Drybulb degk = Vapor pressure over water e w. 0.0 exp ln e w = Vapor pressure over ce e. 0.0 exp ln e = The followng wll select the approprate derved vapor pressure for the temperature range. PsatDry mb f Drybulb degc 0, e, e w PsatDry mb = Wexler's formulatons relate the saturaton vapor pressure of pure water to temperature; a slght correcton must be made when one s dealng wth most ar rather than pure water vapor. Ths correcton, called the enhancement factor, s a weak functon of temperature and pressure. These calculatons are n Buck's Eq. (6) and Table 3 (Buck, 98). Baormetrc Pressure n mllbars P Baro mb P = 000 Enhancement for vapor pressure over water. f w P P 2 f w =.004 Enhancement for vapor pressure over ce. f P P 2 f =.004 The followng wll select the approprate vapor pressure enhancement for the temperature range. EnhanceDry f Drybulb degc 0, f, f w EnhanceDry =.004 Apply the correcton to fnally obtan the enhanced partal saturaton vapor pressure. PsatDryCorrected. mb PsatDry mb EnhanceDry PsatDryCorrected mb = PsatDryCorrected nhg PsatDryCorrected mb PsatDryCorrected nhg = /24/97-0:55 2 US-EPA-OAR-OMS-TSD
3 Compute Corrected Saturaton Vapor Pressure for Dew Pont Temperature above and below ce pont. Ths value wll be used n Relatve and Specfc Humdty dervatons. The followng are Wexler's most accurate formulatons: Eq. (5) (Wexler, 976) for vapor pressure over water and Eq. (5) (Wexler, 977) for vapor pressure over ce. Wexler's formulatons are gven below. These calculatons are most clearly presented n Buck's Eqs. (5a) and (5b) (Buck, 98). Absolute Temperature n K Dewpont degk = Vapor pressure over water e w. 0.0 exp ln e w = Vapor pressure over ce e. 0.0 exp ln e = The followng wll select the approprate derved vapor pressure for the temperature range. PsatDew mb f Dewpont degc 0, e, e w PsatDew mb = Wexler's formulatons relate the saturaton vapor pressure of pure water to temperature; a slght correcton must be made when one s dealng wth most ar rather than pure water vapor. Ths correcton, called the enhancement factor, s a weak functon of temperature and pressure. These calculatons are n Buck's Eq. (6) and Table 3 (Buck, 98). Baormetrc Pressure n mllbars P Baro mb Enhancement for vapor pressure over water. f w P P 2 Enhancement for vapor pressure over ce. f P P 2 The followng wll select the approprate vapor pressure enhancement for the temperature range. P = 000 f w =.004 f =.004 EnhanceDew f Dewpont degc 0, f, f w EnhanceDew =.0039 Apply the correcton to fnally obtan the enhanced partal saturaton vapor pressure. PsatDewCorrected. mb PsatDew mb EnhanceDew PsatDewCorrected mb = PsatDewCorrected nhg PsatDewCorrected mb PsatDewCorrected nhg = /24/97-0:55 3 US-EPA-OAR-OMS-TSD
4 Compute Relatve Humdty, Specfc Humdty and NOx Humdty Correctons Factors per 40 CFR 86.44, , , and PsatDewCorrected nhg RelatveHumdty. pct 00 RelatveHumdty = PsatDryCorrected pct nhg The followng equatons have the Dry Bulb Vapor Pressure factored out and are presented n Englsh Unts PsatDewCorrected nhg SpecfcHumdty grperlb SpecfcHumdty = Baro nhg PsatDewCorrected grperlb nhg NOxCorrecton gasolne SpecfcHumdty grperlb 75 NOxCorrecton gasolne = for Desel Engnes NOxCorrecton desel SpecfcHumdty grperlb 75 NOxCorrecton desel = Calcualton of Specfc Humdty - SI Unts Ra RelatveHumdty pct Grams of H2O per gram of dry ar K P a. Baro mb 00 P v. PsatDewCorrected mb 00 Specfc Humdty, Grams H2) per gram of dry ar K. P v H H = P a P v and SI Unts 6.2. RelatveHumdty. pct PsatDryCorrected mb SpecfcHumdty grperkg RelatveHumdty Baro. pct mb PsatDryCorrected mb 00 NOxCorrecton gasolne SpecfcHumdty grperkg for Desel Engnes SpecfcHumdty grperkg = NOxCorrecton gasolne = 0.93 NOxCorrecton desel SpecfcHumdty grperkg 0.7 NOxCorrecton desel = /24/97-0:55 4 US-EPA-OAR-OMS-TSD
5 The follwng dervatons support plottng of vapor pressure, humdty and NOx correcton factors e f > 273.5, ln, t 2 t e f > 273.5, e, ln t t e 0.0 exp e f f > 273.5, P P 2, 0 f f > 273.5, f, P P 2 ec. e f ec e Corrected and Uncorrected Partal Saturaton Vapor Pressure -40 to 50 C /24/97-0:55 5 US-EPA-OAR-OMS-TSD
6 SH k Baro nhg Dervaton of Humdty and NOx Humdty Correcton Factors ec ec SH k t k KhGasolne SH 75 Specfc Humdy from -0 through 20 C KhDesel SH 75. KhGasolne k KhDesel k t k Oxdes of Ntrogen Correcton Factors from -0 through 20 C /24/97-0:55 6 US-EPA-OAR-OMS-TSD
7 The followng may be compared to Buck, 98, Table to verfy agreement. (40 s added to each subscrpt to brng nto a useable range of values.) Vapor pressure pure water from -40 through 50 C e = e = e = e 0 40 = e 0 40 = e 0 40 = e = e = e = e = Enhancement 000 mb from -40 through 50 C f = f = f = f 0 40 = f 0 40 = f 0 40 = f = f = f = f = Vapor pressure of most ar at 000 mb from -40 through 50 C ec = ec = ec = ec 0 40 = ec 0 40 = ec 0 40 = ec = ec = ec = ec = /24/97-0:55 7 US-EPA-OAR-OMS-TSD
8 The follwng dervatons support plottng of vapor pressure, humdty and NOx correcton factors enoce f > 0, ln, t 2 t enoce 0.0 exp enoce fnoce f > 0, P P 2, 0 ecnoce. enoce fnoce ec ecnoce Ice Pont and No Ice Pont Partal Saturaton Vapor Pressure -40 to 50 C /24/97-0:55 8 US-EPA-OAR-OMS-TSD
9 SHnoce Baro nhg ecnoce ecnoce 600 SH 400 SHnoce KhGasolnenoce SHnoce 75 Specfc Humdy from -40 through 50 C KhDeselnoce SHnoce 75 0 KhGasolne 20 KhDesel KhGasolnenoce 40 KhDeselnoce /24/97-0:55 9 US-EPA-OAR-OMS-TSD
10 Oxdes of Ntrogen Correcton Factors from -40 through 50 C PctDeltaKhGasolne. 00 KhGasolnenoce KhGasolne KhGasolne PctDeltaKhDesel. 00 KhDeselnoce KhDesel KhDesel PctDeltaKhGasolne PctDeltaKhDesel Percent Dfference Between NOx Factors Computed wth and wthout Ice Pont Saturaton Vapor Preseure Equatons /24/97-0:55 0 US-EPA-OAR-OMS-TSD
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