(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 750.062 Drybulb degc 20 Dewpont degc 0 Baro nhg Baro mmhg 25.4 Baro nhg = 29.53 Baro. mb Baro nhg Baro mb = 000 Drybulb. 9 degf Drybulb degc 5 5 Drybulb degk 273.5. 9 Dewpont. 9 degf Dewpont degc 5 5 Dewpont degk 273.5. 9 32 Drybulb degf = 68 Drybulb degf 32 Drybulb degk = 293.5 32 Dewpont degf = 50 Dewpont degf 32 Dewpont degk = 283.5 /24/97-0:55 US-EPA-OAR-OMS-TSD
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 = 293.5 Vapor pressure over water e w. 0.0 exp 2.858487. ln 299.2729 607.028 2 8.87643854 0.02835472..783830. 0 5. 2 8.45047. 0 0. 3 e w = 23.3854 4.442543. 0 3. 4 Vapor pressure over ce e. 0.0 exp 0.698650. ln 5865.3696 22.2403300.3749042. 0 2. 3.403775. 0 5. 2 2.6967687. 0 8. 3 e = 28.345 The followng wll select the approprate derved vapor pressure for the temperature range. PsatDry mb f Drybulb degc 0, e, e w PsatDry mb = 23.3854 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 0.0004 P. 3.48. 0 6 7.4. 0 0. 273.5 30.6 0.038. P 2 f w =.004 Enhancement for vapor pressure over ce. f 0.00048 P. 3.47. 0 6 5.9. 0 0. 273.5 23.8 0.03. 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 = 23.4792 PsatDryCorrected nhg PsatDryCorrected mb PsatDryCorrected nhg = 0.693 /24/97-0:55 2 US-EPA-OAR-OMS-TSD
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 = 283.5 Vapor pressure over water e w. 0.0 exp 2.858487. ln 299.2729 607.028 2 8.87643854 0.02835472..783830. 0 5. 2 8.45047. 0 0. 3 e w = 2.2794 4.442543. 0 3. 4 Vapor pressure over ce e. 0.0 exp 0.698650. ln 5865.3696 22.2403300.3749042. 0 2. 3.403775. 0 5. 2 2.6967687. 0 8. 3 e = 3.5203 The followng wll select the approprate derved vapor pressure for the temperature range. PsatDew mb f Dewpont degc 0, e, e w PsatDew mb = 2.2794 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 0.0004 P. 3.48. 0 6 7.4. 0 0. 273.5 30.6 0.038. P 2 Enhancement for vapor pressure over ce. f 0.00048 P. 3.47. 0 6 5.9. 0 0. 273.5 23.8 0.03. 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 = 2.3272 PsatDewCorrected nhg PsatDewCorrected mb PsatDewCorrected nhg = 0.364 /24/97-0:55 3 US-EPA-OAR-OMS-TSD
Compute Relatve Humdty, Specfc Humdty and NOx Humdty Correctons Factors per 40 CFR 86.44, 86.344, 86.544, and 86.342 PsatDewCorrected nhg RelatveHumdty. pct 00 RelatveHumdty = PsatDryCorrected pct 52.503 nhg The followng equatons have the Dry Bulb Vapor Pressure factored out and are presented n Englsh Unts.. 4347.8. PsatDewCorrected nhg SpecfcHumdty grperlb SpecfcHumdty = Baro nhg PsatDewCorrected grperlb 54.265 nhg NOxCorrecton gasolne. 0.0047 SpecfcHumdty grperlb 75 NOxCorrecton gasolne = 0.92 86.342 for Desel Engnes NOxCorrecton desel. 0.0026 SpecfcHumdty grperlb 75 NOxCorrecton desel = 0.9488 86.344 Calcualton of Specfc Humdty - SI Unts Ra RelatveHumdty pct Grams of H2O per gram of dry ar K 0.6220 P a. Baro mb 00 P v. PsatDewCorrected mb 00 Specfc Humdty, Grams H2) per gram of dry ar K. P v H H = 0.00776 P a P v 86.44 and 86.342 SI Unts 6.2. RelatveHumdty. pct PsatDryCorrected mb SpecfcHumdty grperkg RelatveHumdty Baro. pct mb PsatDryCorrected mb 00 NOxCorrecton gasolne. 0.0329 SpecfcHumdty grperkg 0.7 86.342 for Desel Engnes SpecfcHumdty grperkg = 7.752 NOxCorrecton gasolne = 0.93 NOxCorrecton desel. 0.082 SpecfcHumdty grperkg 0.7 NOxCorrecton desel = 0.9489 /24/97-0:55 4 US-EPA-OAR-OMS-TSD
The follwng dervatons support plottng of vapor pressure, humdty and NOx correcton factors. 0.. 90 40 273.5 e f > 273.5, 2.858487. ln, 0 299.2729 607.028 8.87643854 0.02835472. t 2 t e f > 273.5, e,.783830. 0 5. 2 8.45047. 0 0. 3 4.442543. 0 3. 4 0.698650. ln 5865.3696 22.2403300.3749042. 0 2. t 3.403775. 0 5. 2 t.. 2.6967687 0 8 3 e 0.0 exp e f f > 273.5, 0.0004 P. 3.48. 0 6 7.4. 0 0. 273.5 30.6 0.038. P 2, 0 f f > 273.5, f, 0.00048 P. 3.47. 0 6 5.9. 0 0. 273.5 23.8 0.03. P 2 ec. e f 273.5 20 00 80 ec e 60 40 20 40 30 20 0 0 0 20 30 40 50 Corrected and Uncorrected Partal Saturaton Vapor Pressure -40 to 50 C /24/97-0:55 5 US-EPA-OAR-OMS-TSD
4347.8. SH k 30.. 60 Baro nhg Dervaton of Humdty and NOx Humdty Correcton Factors ec ec 00 80 SH k 60 40 20 0 5 0 5 0 5 20 t k KhGasolne. 0.0047 SH 75 Specfc Humdy from -0 through 20 C KhDesel. 0.0026 SH 75. KhGasolne k KhDesel k 0.9 0.8 0 5 0 5 0 5 20 t k Oxdes of Ntrogen Correcton Factors from -0 through 20 C /24/97-0:55 6 US-EPA-OAR-OMS-TSD
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 40 40 = 0.28486 e 30 40 = 0.380239 e 20 40 =.03276 e 0 40 = 2.599229 e 0 40 = 6.536 e 0 40 = 2.279396 e 20 40 = 23.385445 e 30 40 = 42.45202 e 40 40 = 73.8273 e 50 40 = 23.44779 Enhancement factor @ 000 mb from -40 through 50 C f 40 40 =.005264 f 30 40 =.004766 f 20 40 =.004387 f 0 40 =.00425 f 0 40 =.00398 f 0 40 =.003895 f 20 40 =.004007 f 30 40 =.004268 f 40 40 =.004676 f 50 40 =.005233 Vapor pressure of most ar at 000 mb from -40 through 50 C ec 40 40 = 0.2963 ec 30 40 = 0.38205 ec 20 40 =.03729 ec 0 40 = 2.60995 ec 0 40 = 6.35863 ec 0 40 = 2.327225 ec 20 40 = 23.4796 ec 30 40 = 42.633204 ec 40 40 = 74.5792 ec 50 40 = 24.093784 /24/97-0:55 7 US-EPA-OAR-OMS-TSD
The follwng dervatons support plottng of vapor pressure, humdty and NOx correcton factors. 0.. 90 40 273.5 enoce f > 0, 2.858487. ln, 0 299.2729 607.028 8.87643854 0.02835472. t 2 t.783830. 0 5. 2 8.45047. 0 0. 3 4.442543. 0 3. 4 enoce 0.0 exp enoce fnoce f > 0, 0.0004 P. 3.48. 0 6 7.4. 0 0. 273.5 30.6 0.038. P 2, 0 ecnoce. enoce fnoce 273.5 20 00 80 ec ecnoce 60 40 20 40 30 20 0 0 0 20 30 40 50 Ice Pont and No Ice Pont Partal Saturaton Vapor Pressure -40 to 50 C /24/97-0:55 8 US-EPA-OAR-OMS-TSD
4347.8. SHnoce Baro nhg ecnoce ecnoce 600 SH 400 SHnoce 200 40 30 20 0 0 0 20 30 40 50 KhGasolnenoce. 0.0047 SHnoce 75 Specfc Humdy from -40 through 50 C KhDeselnoce. 0.0026 SHnoce 75 0 KhGasolne 20 KhDesel KhGasolnenoce 40 KhDeselnoce 60 80 40 30 20 0 0 0 20 30 40 50 /24/97-0:55 9 US-EPA-OAR-OMS-TSD
Oxdes of Ntrogen Correcton Factors from -40 through 50 C PctDeltaKhGasolne. 00 KhGasolnenoce KhGasolne KhGasolne PctDeltaKhDesel. 00 KhDeselnoce KhDesel KhDesel 0.4 0.35 0.3 0.25 PctDeltaKhGasolne PctDeltaKhDesel 0.2 0.5 0. 0.05 0 40 30 20 0 0 0 20 30 40 50 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