EPA-AA-CPSB-83-01
Technical Report
Humidity Calculations
Used For
Mobile Source Emission Testing
Eric Zellin
February, 1983
NOTICE
Technical Reports do not necessarily represent final EPA decisions
or positions. They are intended to present technical analysis of
issues using data which are currently available. The purpose in the
release of such reports is to facilitate the exchange of technical
information and to inform the public of technical developments which
may form the basis for a final EPA decision, position, or regulatory
action.
This document has been approved under the EPA peer review process and is available
for internal and external distribution.
U. S. Environmental Protection Agency
Office of Air, Noise, and Radiation
Office of Mobile Sources
Certification Division
Certification Policy and Support Branch
2565 Plymouth Road
Ann Arbor, Michigan 48105
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Humidity Calculations Used for Mobile Source Emission Testing
measurement of specific humidity in units of grains of water per
pound of dry air, grams of water per gram of dry air, or grams of
water per kilogram of dry air.
The measurement of percent relative humidity is required for
analysis of carbon monoxide (CO) whenever water vapor is extracted
from exhaust gas to prevent interference in CO analyzers. The
carbon monoxide analyzers used at the EPA laboratory in Ann Arbor
are essentially free of interference from water vapor, and for this
reason, CO measurements at MVEL are no longer corrected for relative
humidity; however, the correction is applied at other testing
facilities that use equipment susceptible to interference.
Emission measurements for 1979-1983 model-year engines must be
converted from a dry to a wet basis. The calculation used to
perform the conversion includes a term for the water-vapor volume
concentration, on a dry basis, of the engine intake air. The water-
vapor volume concentration equals the specific humidity of the
engine intake air multiplied by a constant.
Many methods exist for measuring humidity and are classified as
primary and secondary. Secondary methods must be calibrated by
means of a primary method and are not ordinarily used for emission
testing because most secondary methods lack sufficient accuracy.
Primary methods are used that provide good accuracy, are relatively
easy and economical to use, and are capable of providing a repeated
(or continuous) humidity measurement. Two instruments that satisfy
these requirements, and are used for most emission testing, are the
dew-point hygrometer and the wet-bulb psychrometer.
Dew-point hygrometers and wet-bulb psychrometers both have
acceptable accuracy, when properly calibrated and optimized, and are
capable of continuously measuring humidity. In the past, the wet-
bulb psychrometer was the most common instrument in use because it
was easier and cheaper to use than the hygrometer. The dew-point
hygrometer has always had the advantage of superior accuracy.
Within the last ten years, improvements in the design of the dew-
point hygrometer have produced an instrument that is easier to use
for emission testing than the wet-bulb psychrometer and has superior
reliability, as well as better accuracy. The dew-point hygrometer
is still more expensive than the wet-bulb psychrometer; however,
steady cost reduction, plus the operational superiority of the
hygrometer, are rapidly making it the preferred instrument -for
humidity measurement.
February, 1983
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Humidity Calculations Used for Mobile Source Emission Testing
Humidity Calculations Used for Mobile Source Emission Testing
Abstract
This reference document provides a summary of the calculations used
to determine relative and specific humidity of moisture in air for
mobile source (motor vehicle and engine) emission and fuel economy
testing at the U.S. Environmental Protection Agency Motor Vehicle
Emissions Laboratory in Ann Arbor, Michigan. The reference includes
calculations required to determine the saturation vapor pressure of
water, psychrometric equations used to calculate the partial
pressure of water vapor for wet-bulb psychrometers, and equations
for the enhancement factor of water and ice. Described are the
methods used from 1971 to 1983.
Purpose. This reference provides a description of the procedures
used to calculate humidity at the EPA Motor Vehicle Emissions
Laboratory (MVEL). Several procedures have been used at MVEL for
different applications. For heavy duty engine certification between
1979 and 1983, the humidity calculation procedure was defined in the
Federal Register; for light duty motor vehicles, the procedure was
determined ' by the testing laboratory from technical and operational
considerations, as well as the state of the art of humidity
measurement. Manufacturers, EPA contractors, and EPA employees
often need to know what procedure is, has been, or, in some
instances, should be used to calculate humidity. This reference
provides a single document that describes the procedures used
historically at MVEL, plus information about procedures that have
not been used, but which may be useful in the future.
Overview. Humidity measurement is required for three different
calculations used in the analysis of mobile source emission and fuel
economy: (1) to correct the measurement of oxides of nitrogen for
the effect of moisture in engine intake air, (2) to correct the
measurement of carbon monoxide (CO) when water is extracted from
exhaust gases., and (3) to convert heavy duty engine emissions from a
dry to a wet basis.
The humidity of water in air has an effect on the measurement of
oxides of nitrogen. As a result of a study made for EPA by Scott
Research Laboratories Inc. in 19701 * , EPA test procedures correct
the measurement of oxides of nitrogen for the specific humidity of
water in air. Several different correction equations have been used
historically to correct oxides of nitrogen for humidity. These can
be found in various editions of the Federal Register and are not
described here; however, all of these equations required the
February, 19~83
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Humidity Calculations Used for Mobile Source Emission Testinq
Humidity measurements. Three measurements are required to measure
relative and specific humidity: barometric pressure, ambient (dry-
bulb) temperature, and either wet-bulb temperature, dew-point
temperature, or for temperatures below freezing, ice-point
temperature. From these measurements, several intermediate
calculations are performed. First, it is necessary to calculate the
saturation vapor pressure of water at each temperature; several
different equations have been used for this at MVEL. Second, it is
necessary to calculate the partial pressure of water vapor. For a
dew-point hygrometer this is a trivial calculation; however for the
wet-bulb psychrometer a special equation, the psychrometric
equation, is required. Relative and -specific humidity are then
directly calculated from these values. Each of these calculations
is described in detail below.
Experimental variables. All of these methods are similar and
require the measurement of barometric pressure, ambient temperature,
and either dew-point (ice-point) temperature measured with a dew-
point hygrometer or wet-bulb temperature measured with a wet-bulb
psychrometer. In this article, the following symbols are used to
represent values of each measured variable for different units of
temperature and pressure.
Tamb(K) = ambient temperature
Tamb(C) = ambient temperature
Tamb(F) = ambient temperature
degrees Kelvin.
degrees Celsius.
degrees Fahrenheit.
Twet(K) =. wet-bulb temperature
Twet(C) = wet-bulb temperature
Twet(F) = wet-bulb temperature
degrees Kelvin.
degrees Celsius.
degrees Fahrenheit.
Tdew(K) = dew-point temperature
Tdew(C) = dew-point temperature
Tdew(F> = dew-point temperature
degrees Kelvin.
degrees Celsius.
degrees Fahrenheit
Tice(K) = ice-point temperature — degrees Kelvin.
Pbaro = barometric pressure — same pressure units as
saturation vapor pressure.
Many of the equations presented in this article are pressure unit
independent; that is, the equation is valid for any pressure unit as
long as all pressures are expressed in the same units, and as long
as the pressure of a perfect vacuum is defined to equal zero.
February, 1983
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Humidity Calculations Used for Mobile Source Emission Testing
Saturation vapor pressure. Ambient temperature and either dew-
point, ice-point, or wet-bulb temperature are measured
experimentally and the saturation vapor pressure of water (or ice)
is calculated at each temperature. The following variables are used
to represent saturation vapor pressure at different temperatures and
pressures:
Pamb(Pa) = the saturation vapor pressure at the ambient
temperature — Pascals.
Pamb(InHg) = the saturation vapor pressure at the ambient
temperature — inches of mercury.
Pwet(Pa) = the saturation vapor pressure at the wet-bulb
temperature — Pascals.
Pwet(InHg) = the saturation vapor pressure at the wet-bulb
temperature — inches of mercury.
Pdew(Pa) = the saturation vapor pressure at the dew-point
temperature — Pascals.
Pdew(lnHg) = the saturation vapor pressure at the dew-point
temperature — inches of mercury.
Pice(Pa) = the saturation vapor pressure at the ice-point
temperature — Pascals.
Historically, MVEL has used four different equations to calculate
saturation vapor pressure. The actual difference between equations
is not large and the effect of differences is much less.significant
than other sources of error in vehicle emission testing.
The oldest equation used at MVEL is formula 2 of Smith, Keyes, and
Gerry3, equation (1) below, which has been used for light duty
vehicle testing to the present date (1983). Equation (1) determines
saturation vapor pressure Psat (inches of mercury) at temperature
T(K) (degrees Kelvin ITS-26). Pamb(InHg), Pdew(InHg), or Pwet(InHg)
can be determined by substituting Tamb(K), Tdew(K), or Twet(K) for
T(K) in equation (1):
February, 1983
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Humidity Calculations Used for Mobile Source Emission Testinq
Psat(InHg)
(1)
where
-[X / T(K)] [A+BX+CX ] / [1 + D X]
29.92 PC 10
Tc = 647.27
PC = 218.167
A = 3.2437814
B = 5.86826E-3
C = 1.1702379E-8
D = 2.1878462E-3
T(K) = .5555 [ T(F) -
X = Tc - T(K)
T(F) = temperature degrees
32 ] + 273.16
Formula 2 of Smith, Reyes, and Gerry
range of 10 to 150 degrees Celsius.
Fahrenheit,
is valid for a temperature
In 1947 the Goff-Gratch formulation for the saturation vapor
pressure of water over water and ice, which is not presented here,
was adopted for international use in Resolution 164 of the Twelfth
Conference of Directors of the International Meteorological
Organization4. The Goff-Gratch formulation, which is still used in
meteorology, was used at the U.S. National Bureau of Standards
until 1971, when the NBS developed a new equation. The 1971 NBS
equation, equation 23 of Wexler and Greenspan, is the second
equation used at MVEL5. This equation, (2) below, has been used for
heavy duty engine testing from 1979 to 1983. Equation (2)
determines saturation vapor pressure Psat (Pascals) at temperature
T(K) (degrees Kelvin IPTS-68). Pamb(Pa), Pdew(Pa), or Pwet(Pa) can
be determined by substituting Tamb(K), Tdew(K), or Twet(K) for T(K)
in equation (2):
(2)
where
Psat(Pa)
B
F(0) '
P(D '•
F(2) ••
F(3) :
F(4) '
B In T(K)
• exp
-1.21507990E+01
-8.49922000E+03
-7.42318650E+03
+9.61635147E+01
+2.49176460E-02
-1.31601190E-05
9
I
i=0
F(5)
F(6)
F(7)
F(8)
F(9)
i-2
T(K)
-1 . 14604540E-08
+2.17012890E-11
-3.61025800E-15
+3.85045190E-18
-1.43170000E-21
Equation (2) is valid for a temperature range of 0 to 100 degrees C.
February, 1983
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Humidity Calculations Used for Mobile Source Emission Testing
In 1976 Wexler published a revision to the original saturation vapor
pressure equation'. Equation 15 from the revision, equation (3)
below, can be used to calculate saturation vapor pressure Psat
(Pascals) at temperature T(K) (degrees Kelvin IPTS-68). Pamb(Pa),
Pdew(Pa), or Pwet(Pa) can be determined by substituting Tamb(K),
Tdew(K), or Twet(K) for t(K) in equation (3):
(3) Psat(Pa)
where F(0) =
F(7) In T(K)
exp
6
+ I
i=0
i-2
F(2) =
F(3) =
-0.2991272900E+04 F(4)
-0.6017012800E+04 F(5)
+0.1887643854E+02 F(6)
-0.2835472100E-01 F(7)
T(K)
+0.1783830100E-04
-0.8415041700E-09
+0.4441254300E-12
+0.2858487000E+01
Equation
Celsius.
(3) is valid for a temperature range of 0 to 100 degrees
In 1977 Wexler published a third equation
determine the saturation vapor pressure of
equation
(Pascals)
that
ice
this reference
pressure Psat
can be used to
Equation 54 from
(4) below, determines saturation vapor
at temperature T(K) (degrees Kelvin IPTS-
68). Pwet(Pa) or Pice(Pa) is determined by substituting Twet(K) or
Tice(K) for T(K) in equation (4):
(4) Psat(Pa)
where F(0) =
F(2) =
F(5) In T(R)
exp
4
Z
j-o
J-1
-0.58653696E+04 F(3)
+0.22241033E+02 F(4)
+0.13749042E-01 F(5)
T(K)
-0.34031775E-04
+0.26967687E-07
+0.69186510E+00
Equation (4) is valid for temperatures less than or equal to the
triple point of water, 0.1 degrees Celsius.
Equations (1)-(4) determine saturation vapor pressure of pure water
or ice (without air). The saturation vapor pressure of water in air
differs from the vapor pressure of pure water or ice by small
amounts: about 1/2 percent at atmospheric temperature and pressure.
A correction, the enhancement factor, can be applied to correct
saturation vapor pressure for the effect of air—although Mr Saburo
Hasegawa of the U.S. National Bureau of Standards has stated that
the magnitude of this correction is usually much smaller than
sources of error in humidity measurement.8
other
Hyland developed equations that can be used to determine the
enhancement factor'. Because these equations are difficult to use
for computation, Buck developed simpler equations based on Hyland1s
February, 1983
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Humidity Calculations Used for Mobile Source Emission Testing
data10. These equations are described below for water, equation
(5), and ice, equation (6). Equations (5) and (6) determine the
enhancement factor of water, Fw5, or ice, Fi5, from temperature
T(K), degrees Kelvin, and barometric pressure Pbaro(Pa), Pascals.
Because Buck's original equations are based on Celsius temperature
and millibar pressure units, coefficients B, C, and E have been
modified for use with Kelvin temperature and Pascal pressure units.
The equation for the enhancement factor of liquid water is given by:
(5) Fw5 = 1 + A
2
+ Pbaro(Pa) [B + C [ T(K) - 273.15 + D + E Pbaro(Pa) ] 3
where A = 4.1E-04
B = 3.48E-08
C = 7.4E-12
D = 30.6
E = -3.8E-04
Equation (5) is valid for a temperature range of -20 to 50 degrees
Celsius.
The equation for the enhancement factor of ice is given by:
(6) Fi5 = 1 + A
2
+ Pbaro(Pa) [B + C [ T(K) - 273.15 + D + E Pbaro(Pa) ] ]
where A = 4.8E-04
B = 3.47E-08
C = 5.9E-12
D = 23.8
E = -3.1E-04
Equation (6) is valid for a temperature range of -60 to 0 degrees
Celsius.
To apply the enhancement factor, one simply multiplies the
uncorrected saturation vapor pressure by the enhancement factor to
determine the corrected value as illustrated in equation (7) below
for water and equation (8) for ice:
Pamb(corrected) = Fw5 Pamb(uncorrected), 50 C ^ T £ -20 C
(7) Pdew(corrected) = Fw5 Pdew(uncorrected)
Pwet(corrected) = Fw5 Pwet(uncorrected)
(8) Pice(corrected) = Fi5 Pice(uncorrected), 0 C £ T £ -60 C
Equations (7) and (8) are valid for any consistent set of pressure
units.
MVEL has not applied an enhancement factor correction to any
February, 1983
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Humidity Calculations Used for Mobile Source Emission Testing
humidity measurement before 1983.
Partial pressure of water vapor. Saturation vapor pressure values
are used to determine the partial pressure of water vapor Pv. If
dew-point or ice-point temperatures are measured, the partial
pressure of water vapor is defined td.equal the saturation vapor
pressure, corrected for enhancement factor, at the dew-point or ice-
point temperature—equations (9) and (10) below:
(9) Pv = Pdew or
(10) Pv = Pice
If a wet-bulb psychrometer is used to measure humidity, several
psychrometric equations are available for calculating the partial
pressure of water vapor Pv. Equation (11) is based on a
thermodynamic model of wet-bulb behavior:
[Pbaro - Pwet] [Tamb(F) - Twet(F)]
(1.1) Pv = Pwet - :
2831 - 1.43 Twet(F)
Pressure can have any consistent set of units in equation (11).
Equation (11) is included here because it is in fairly common use
and has been used by several automobile manufacturers for emission
testing. In addition, equations similar to (11) have been used to
prepare several published psychrometric charts. The author does not
feel qualified to make a statement about the merits of equation
(11); however, it is important to point out that there is poor
correlation between results calculated using equation (11) and
results calculated from the equations used at MVEL.
Although a thermodynamic model of wet-bulb behavior has been used to
prepare many psychrometric charts, it has been stated that classical
thermodynamics does not provide a completely satisfactory
description of a wet-bulb system11 12 13 14. Several empirical
equations have been developed which may be preferable to equation
(11) because they are based on experimental results. Equations (12)
and (13) are equivalent forms of Ferrels equation4 14 1S 14 that can
be used to determine the partial pressure of water vapor. Equation
(12) determines Pv from ambient and wet-bulb temperature (degrees
Fahrenheit) and has been used at MVEL to determine humidity for
light duty vehicle testing to 1983. Equation (13) determines Pv
from temperature measured in degrees Kelvin and has been used at
MVEL to determine humidity for heavy duty engine testing.
February, 1983
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Humidity Calculations Used for Mobile Source Emission Testing
(12) Pv = Pwet - [Tamb(F) - Twet(F)]
.000367 Pbaro [Twet(F) + 1539] / 1571
(13) Pv = Pwet - [Tamb(K) - Twet(K)]
.000660 Pbaro [1 + .00115 [Twet(K) - 273.15]]
Equation (14), developed at the Japan Meteorology Agency, is similar
in form to Ferrels equation, and appears to be superior for Assmann
psychrometers of the type used by the Japan Meteorology Agency17.
(14) Pv = Pwet - [Tamb(K) - Twet(K)]
.000700 Pbaro [1 - .00560 [Twet(K) - 273.15]]
Any consistent set of .pressure units may be used in equations (12)-
(14).
Relative and specific humidity. Equation (15) is used to determine
percent relative humidity R,
(15) R = 100 Pv / Pamb
for any consistent set of pressure units.
The specific humidity H (grains of water per pound of dry air) is
used to correct oxides of nitrogen emission measurements for the
effect of humidity. Equation (16) is used for light duty vehicle
testing:
(16) H = 4347.8 Pv / [Pbaro - Pv]
for any consistent set of pressure units. In the Federal Register,
equation (16) is sometimes combined with equation (15)andwritten
as:
(17) H = 43.478 R Pamb / [Pbaro - R Pamb / 100] .
It can be seen that equations (16) and (17) are equivalent.
Equation (16) is preferable because it is simpler and more
fundamental than (17).
Equation (18) is an alternative representation of equation (16) that
calculates specific humidity in units of grams of water per kilogram
of dry air:
(18) H = .0006211 Pv / [Pbaro - Pv]
A slightly different version of equation (16) has been used
internally at MVEL to investigate humidity calculation procedures.
The constant 4347.8 can be expressed more accurately as
February, 1983
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Humidity Calculations Used for Mobile Source Emission Testing 10
18.01534 (kg/mole water)
(19) (7000 grains/lb) = 4353.484
28.967 (kg/mole air)
Equation (20) has been published in internal documentation at MVEL
investigating humidity calculation procedures, but it has not been
used for official certification or fuel economy testing.
(20) H = 4353.484 Pv / [Pbaro - Pv]
for any consistent set of pressure units.
A third constant has been used for heavy duty engine testing for
model years 1979-1983. The constant in the specific humidity
equation can be expressed as
18.01534 (kg/mole water)
(21) = .62198 * .62200
28.9645 (kg/mole air)
This value has been used to calculate specific humidity in units of
grams of water per gram of dry air—equation (22) below:
(22) H = .622 Pv / [Pbaro - Pv]
The same heavy duty test procedure calculates specific humidity in
units of grains of water per pound of dry air by converting the
constant in equations (21) and (22):
(23) H = [453.59 gm/lb / .0648 gm/gr] .622 Pv / [Pbaro - Pv]
= 4353.904 Pv / [Pbaro - Pv]
A third value, the water vapor volume concentration Y, is calculated
from equation (22) to determine Pv / [Pbaro - Pv]—equation (24)
(24) Y = [28.9645 / 18.01534] .622 Pv / [Pbaro - Pv]
= 1.000032 Pv / [Pbaro - Pv]
For model years 1984 and later, the equation used to calculate
specific humidity for heavy duty engine testing is the same as light
duty, namely, equations (16)-(18).
If a user wishes to use the most accurate specific humidity equation
available, equations (25) and (26) can be used:
18.01534 (kg/mole water)
(25) : (7000 grains/lb) = 4353.86
28.9645 (kg/mole air)
(26) H = 4353.86 Pv / [Pbaro - Pv]
February, 1983
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Humidity Calculations Used for Mobile Source Emission Testing n
Humidity measurement below freezing. Although MVEL does not
presently test manufacturer emission and fuel economy vehicles at
temperatures below freezing, equations in this article can be used
at low temperatures.
At temperatures below 0°C, relative humidity should be determined
with respect to water, that is, Pamb should be determined with
respect to the saturation vapor pressure of liquid water at the
ambient temperature4 14. If temperature is below freezing and
saturation vapor pressure equation (1), (2), or (3) (for water) is
used, it is necessary to extrapolate below 0°C.
To determine Pv, one can use a dew-point hygrometer or a wet-bulb
psychrometer. For dew-point hygrometers, it is necessary to
determine whether the hygrometer measures ice-point temperature, in
which case equations (4) and (6) can be used, or whether the
hygrometer measures the dew-point temperature of supercooled water.
Equations (1)-(3) can be extrapolated for supercooled water, and
used with equation (5).
If a photoelectric detector is used to maintain a mirror at the dew
point or frost point for temperatures below 0°C, the saturation
vapor pressure equation for ice should probably be used. For
photoelectric control, Wexler states "There can be little question
of whether the liquid or solid phase is involved, for supercooled
liquid will not long last under such conditions without changing to
ice"
If a wet-bulb psychrometer is used, Ferrels equation is valid below
0°C and can be used.14 If the wet bulb wick is covered with ice, the
Pwet term in equation (12) or (13) should be calculated with respect
to ice.14 As mentioned above, however, the Pamb term would still be
calculated with respect to water. If a bare bulb is covered with
ice, special corrections may be required that are not described
here4.
Caution is required for any attempt to measure humidity at low
temperatures with a wet-bulb psychrometer. Wexler states "At
temperatures below freezing, the psychrometer continues to function,
but the magnitude of the depression is greatly reduced and proper
precautions must be taken to obtain reliable data."1* For
temperatures below freezing, dew-point hygrometers appear to have
greater than ordinary advantages versus the wet-bulb psychrometer.
Summary. This article describes several procedures for calculating
humidity that have been of interest to MVEL, either because they
have been used for vehicle emission testing, or because they may be
useful in the future. Equations (4), (6), and (14) have not been
used at MVEL in the past and there are presently (1983) no plans to
use them for certification or fuel economy testing. Nevertheless,
these equations are included here because they appear to be the best
equations currently available for testing under important
conditions: cold temperature or with Assmann psychrometers.
February, 1983
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Humidity Calculations Used for Mobile Source Emission Testing
Information about these equations may be important in the future.
Readers should not assume that humidity calculation procedures in
use elsewhere are unacceptable for emission or fuel economy testing
simply because they are not described here. Many high quality
equations are described in the literature, especially for the
calculation of saturation vapor pressure. Most saturation vapor
pressure equations agree very closely with the ones presented here.
On the other hand, readers should carefully evaluate any
psychrometric equation used to calculate the partial pressure of
water vapor from ambient and wet-bulb temperature. Wide variation
exists between results produced by different psychrometric equations
and a choice of incompatible psychrometric equations can easily
cause correlation problems.
Appendix A contains a summary of the humidity equations used by MVEL
for vehicle emission and fuel economy testing at different times in
history.
February, 1983
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Humidity Calculations Used for Mobile Source Emission Testing 13
References
1. Effect of laboratory ambient conditions on exhaust emissions.
Final report to Nat'l Air Pollution Control Admin., Project CPA 22-
69-156, Scott Research Labs., Inc., April 24, 1970.
2. Manos, M. J., Bozek, J. W., and Huls, T. A., Effect of
laboratory ambient conditions on exhaust emissions, SAE
Transactions, paper 720124, (1972)
3. Keenan, J. H. and Keyes, F. G., Thermodynamic Properties o_f_
Steam, John Wiley and Sons, New York p.14,(1936).
4. List, Robert J. editor, 6th ed., Smithsonian Meteorological
Tables. Smithsonian Institute Press.
5. Wexler, A. and Greenspan, L., Vapor pressure equation for water
in the range 0 to 100° C, J. Res. Nat. Bur. Stand. (U.S.), 75A,
Phys. and Chem., No. 3, 213-230 (1971).
6. Wexler, A., Vapor pressure formulation for water in the range 0
to 100° C—A Revision. J. Res. Nat. Bur. Stand. (U.S.), 80A,
Phys. and Chem., No. 5 and 6, 775-785 (1976).
7. Wexler, A., Vapor pressure formulation for ice. J. Res. Nat.
Bur. Stand. (U.S.), 81A, Phys. and Chem., No. 1, 775-785 (1977).
8. Hasegawa, S., Telephone conversation with Zellin, E., February,
1983.
9. Hyland, R. W., A correlation for the second interaction virial
coefficients and enhancement factors for moist air. J. Res. Nat.
Bur. Stand. (U.S.), 79A, Phys. and Chem., No. 4, 551-560 (1975).
10. Buck, A. L., New equations for computing vapor pressure and
enhancement factor. J. Appl. Metero., 20, 1527-1532 (1981).
11. Sherwood, T. K. and Comings, E. W., An experimental study of
the wet-bulb hygrometer, Trans. Am Insti. Chem. Eng. 28, 88
(1932).
12. Arnold, J. H., The theory of the psychrometer. Physics 4, 255
(1933).
13. Carrier, W. H. and Mackey, C. 0., A review of existing
psychrometric data in relation to practical engineering problems.
ASME Trans. 59, 32, and 528 (1937).
14. Bindon, H. H., A critical review of tables and charts used in
psychrometry. Humidity and Moisture; Measurement and Control in
Science and Industry, vol 1, pp 3, Wexler, Arnold editor.
February, 1983
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Humidity Calculations Used for Mobile Source Emission Testing 14.
15. Wexler, A. and Brombacher, W. G., Methods of Measuring
Humidity and Testing Hygrometers, NBS Circular 512 (1951).
16. Ferrel, Annual Report, Chief, U.S. Signal Officer, Appendix
24, 233-259 (1886).
17. Yoshitake, M. and Shimizu, I., Experimental results of the
psychrometer constant. Humidity and Moisture; Measurement and
Control _in_ Science and Industry, vol 1, pp 70, Wexler, Arnold
editor.
February, 1983
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Appendix A -- Summary of Humidity Calculations Used at MVEL
April. 1983
.
Saturat ion
Vapor Pressure
Enhancement
Factor
Psychrometr ic
Equation
Specif ic
Humidity
Relative
Humidity
Water Vapor
Volume
Concentrat ion
Light
Vehicle
Tri
to
1983'
(1)
None
(12)
(17)
(15)
None
Duty
i And
jck
1983+'
(3)
(5)
(13)'
(16)
(15)
None
Heav>
to
1978'
(1)
None
(12)
(17)
(15)
None
/ Duty Enc
1979-
1983'
(2)
None
(13)
(22)
(23)
(15)
(24)
jine
1984+'
(3)
(5)
(13)1
(16)
(15)
None
Humii
to
1983'
<'>
None
(13)
(20)
(15)
None
dlty Evali
1983+'
(water)
(3)
(5)
(13)
(16)
(26)
(15)
None
jat ion
1983+'
(ice)
(4)
(6)
(13)
(16)
(26)
(15)
None
Numbers in parenthesis refer to equations in the body of the Technical Report.
1. Revised light duty humidity calculation procedures were implemented April 4, 1983.
2. Model year.
3. PsychrometrIc equation not required for dew-point hygrometers.
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