ENVIRONMENTAL PROTECTION AGENCY
OFFICE OF ENFORCEMENT
EPA-330/1-78-003
AIR FLOW MEASUREMENTS
Paul Urone, Ph.D.
IPA Fellow
NATIONAL ENFORCEMENT INVESTIGATIONS CENTER
DENVER, COLORADO
JUNE 1978
-------
Environmental Protection Agency
Office of Enforcement
EPA-330/1-78-003
AIR FLOW MEASUREMENTS
By
Paul Urone, Ph.D.
IPA Fellow
June 1978
National Enforcement Investigations Center
Denver, Colorado
-------
CONTENTS
I INTRODUCTION 1
II SUMMARY 3
III BASIC PRINCIPLES 6
THE ATMOSPHERE 6
STRUCTURE 6
COMPOSITION OF AIR 8
THE GAS LAWS 11
THE MOLE 13
WEIGHT-VOLUME RELATIONSHIPS 15
CONCENTRATIONS 15
DERIVATION OF MASS-RATIO RELATIONSHIPS 17
PHYSICAL VOLUMES AND GASEOUS VOLUMES 18
WATER VAPOR: 21
IV AIR FLOWRATE AND VOLUME MEASUREMENTS 24
PRIMARY STANDARDS 26
Spirometers 26
Frictionless Pistons 28
Aspirator Bottles 32
Pitot Tubes 34
"S-Type" Pitot tube 38
INTERMEDIATE STANDARDS 40
Wet Test Meters 40
Dry Test Meters 46
Rotary Displacement Meters 48
SECONDARY STANDARDS 51
Rotameters 51
Orifice Meters 57
Capillary Orifice Meters 61
Critical Orifices 63
Heat Transfer Anemometers 70
-------
TABLES
1. Composition of Clean Dry Air 9
2. Comparison of Trace Gas Concentrations 10
3. Typical Mass-Ratio Relationships 19
4. Water Vapor Pressure as a Function of Temperature . 23
5. Gas Viscosity Data 64
6. Variation of Viscosity of Air with Temperature ... 65
7. Flowrate as a Function of Needle Gauge and Length . 71
8. Summary of Flowmeter Characteristics 4
FIGURES
1. Structure of Atmosphere 7
2. Cross-sectional View of a Spirometer 27
3. Mercury-seal Piston Flowmeter 29
4. Soap-bubble Flowmeter 30
5. Aspirator Bottle for Measuring Low Gas Flowrates . . 33
6. The Standard Pitot Tube 35
7. "S" Type Pitot Tube and Manometer Assembly 39
8. Particulate Sampling Train . 41
9. Relative Positions of Sampling Probe
and Pitot Tube 42
10. Front and Cross-sectional View
of a Wet Test Meter 44
11. Calibrating a Wet Test Meter with a Spirometer ... 45
12. How a Dry Test Meter Works 47
13. Principle of Gas Flow Through a Roots Meter .... 49
14. Cross-sectional View of a Variable Area Rotameter. . 52
15. Various Types of Rotameter Floats 53
16. Calibration of a Rotameter with a Wet Test Meter . . 55
17. Venturi Meter 58
18. Thin Plate Orifice Meter 59
19. Typical Capillary Orifice Meter and
Calibration Curve 62
20. Calibration of a Critical Orifice with
a Wet Test Meter 66
21. Variation of Volumetric Flowrate Through
a No. 27 Gauge Hypodermic Needle 68
22. Cross-section of a Temperature-compensated
Gas Flow Anemometer 73
-------
SYMBOLS
A Cross-sectional area
a Ambient. Actual.
C Discharge coefficient. Specific Heat. Degrees Celcius.
Correction factor.
c Velocity of light. Corrected. Calibration condition.
D Diameter
E Energy. Compressibility Factor.
f Measurement made in field. Rotameter float.
G Gravity
g Gas
H Heat loss.
AH Rotameter float height. Manometer liquid height.
h Gas or liquid height.
K Degrees Kelvine. Collection of critical flow constants.
k Thermal conductivity.
L Length
£ Liquid
m Pipe to orifice diameter ratio (D /D ). Meter.
N Avogadro's number.
n Number of moles.
MW Molecular weight.
o Orifice. Observed.
P Pressure
P. Barometric pressure
P Ambient or actual pressure. Upstream pressure.
a
PPM Parts per million (generally by volume in air data).
Q Volumetric flowrate.
R Gas constant. Degrees Rankine
r Radius.
RH Relative humidity.
STP Standard temperature and pressure (0°C, 760 mm).
-------
SYMBOLS (Continued)
Std Standard conditions other than STP. (25°C, 760-mm; 70°F,
29.92 in Hg, etc.)
T Temperature (°K; °R).
t Temperature (°C; °F). Time.
V Volume.
Vbo Exterior spirometer volume.
V . Metal Volume.
mt
V Displaced liquid volume.
v Velocity.
w Weight. Water.
a Orifice coefficient of discharge.
•y Ratio specific heat at constant pressure to specific heat
at constant volume (C /C ).
6 Number of degrees above gas temperature.
A Wavelength.
u Viscosity. Micro.
u Frequency of radiant energy.
p Density.
<|> Ratio of upstream to downstream pressures (P,/P2).
-------
I. INTRODUCTION
Air flow measurement constitutes an essential step in the pro-
cess of moving controlled streams of air for quantitative evaluation
of their physical or chemical properties. In this report, the em-
phasis has been placed on those types of air flow measurements com-
monly encountered in the field of air pollution control.
Such measurements involve a wide range of devices employing prin-
ciples of volumetric displacement, velocity impaction, viscosity,
pressure, thermal conductivity, etc. The choice of a particular device
or technique depends on a number of engineering as well as economic
factors. In addition to the prime requirement that a device or tech-
nique must be able to make the desired measurement, other important
considerations include accuracy, precision or repeatability, depend-
ability in both field and laboratory operations, length of time and
history of successful use, installation, calibration and maintenance
costs.
Some devices can measure the volume or flowrate of a gas with a
high degree of accuracy and dependability. They are consequently
classified as primary standards. The primary standards can be used
to calibrate the velocity or volumetric flowrate responses of inter-
mediate and secondary standards. Any or all of these can subsequently
be used directly or indirectly to measure the air streams being processed
in the field or laboratory.
To use air flow measurement devices intelligently, their mechanical
and theoretical operational principles should be understood at least
on a qualitative basis. Changes in the gas composition, relative
humidity, velocity and pressure have different effects on different
-------
devices. For these purposes, this report discusses in a condensed
manner the basic operational and theoretical principles of the more
commonly used air pollution air flow measurement instruments.
The instruments are described briefly with respect to their mechan-
ical use and operation. Simplified drawings of each representative
type are shown. In each case the basic theoretical factors are illus-
trated through the presentation of a generalized mathematical equation
which quantitatively indicates the role of such factors as pressure,
temperature, viscosity, density, and specific heat. Additionally, in
each case condensed mathematical equations are given for calculating
volumetric flowrates when the temperature and pressure of the ambient
or actual air significantly (>4%) differ from the temperature and air
pressure at the time of calibration.
In air pollution measurements, it is generally correct to assume
that the composition of ambient air does not significantly change
except for its water vapor content, which varies from 0 to 5% of the
air volume. Whenever water vapor content might seriously affect the
measurement, then the mathematical equations will indicate the correc-
tive calculations that need to be made.
Special efforts have been made to use consistent symbols through-
out the report. The subscripts used to indicate, for example, whether
a volumetric flowrate (Q) is that measured under calibration conditions
(Q ) or at ambient, or actual, conditions (Q ) are important. The
C a
same holds true for many of the other specified properties or qualities
of the air being measured. The Summary Table contains the essential
information on the various flow measurement devices which should help
give an overall perspective.
-------
II. SUMMARY
This report contains in a condensed form the basic mechanical
and theoretical principles of air flow measurement devices commonly
used in air pollution control monitors. The first part is devoted to
a review of the composition and properties of the atmosphere. Air,
to a large extent, behaves as an ideal gas. Simple temperature, pres-
sure and volume relationships hold for most ambient air conditions.
Volume ratios such as parts per million (ppm) or parts per billion
(ppb) are shown to be easy to calculate. The mole-volume concept is
described in such a manner as to make weight-volume conversions from
parts per million to micrograms per cubic meter (ug/ma), and vice
versa, easy to perform. The role of water vapor in the air is also
explained in absolute and relative humidity terms.
The latter part of this report describes in sequence the physical
and mechanical features, as well as the theoretical and applied air
flow relationships, of primary, intermediate, and secondary standards.
The primary standards which are described and discussed include spi-
rometers, frictionless pistons, aspirator bottles, and pitot tubes.
The intermediate standards include wet and dry test meters, and the
"Roots" type volume displacement meters. The secondary standards
include v^loci.ty type meters such as rotameters, orifice meters, hot
wire anemometers and pressure transducers. The Summary Table which
follows includes pertinent relationships of the various meters and
appears in this section for convenience.
-------
Table VIII. Summary of Flowmeter Characteristics
Meter Type
Primary Standards
Spirometers
Frictionless
Pistons:
Mercury Seal
Frictionless
Pistons Soap
Bubble Flow Meter
Aspirator
Bottles
Standard
Pi tot Tubes
"S" - Type
Pilot Tubes*
* These are secondary
Intermediate Standards
Wet Test
Meters
Dry Test
Meters
Rotary Displacement
KI_ ^ *».*•• / Drtrt f <- Ma f «**e 1
Measurement
Principle
Volume
Displacement
Volume
Displacement
Volume
Displacement
Volume
Displacement
Velocity
5'i.pact of
Air
Velocity
Impact of
Air
standards
Volume
Displacement
Volume
Displacement
Vo 1 ume
rii c nl aromont*
Temperature - Pressure
Theory Corrections
Vg ' Vm Qm = V*
- U V + V ~ P T
' vbo vmt * ve Q d . Q fm 'std
std m
Q =Q liZt
V = V Q = V /t
g m mm
Q . and Q as above
V=V-V • 0=V/t
vg vm vw wm ¥g'
Pb ' Pw (1 ' RH) Q.td and Q as above
m Pb
\ - Vbt - Vw Qm = V
PL - P (1-RH) Q 4.^ and Q, as above
n D W Stu a
bt Pb
Velocity = \/2Gh Q = (Velocity) x (Cross-
Sectional Area)
= KPCp ^iprV Q.td = Qa Pa Tstd
v q g sto a Q j
rstd a
(Theory same as above) Q = (Velocity) x (Cross-
Sectional Area)
|aPstd QrfJ as in Standard Pitot Tube
Cp - Cp v| ,p sta
s-type std V S-type
ii _ u _y _u Q = V /t
g rn iP w 99
p.-AP -P (1-RH) Qcf^ and Q, as above
„ D m w s LU «
b
Q0 = Vg/t
P, -AP 0 . j and Q, as above
.. D m siu a
m Pb
Q m AP a Q
J m
as above
-------
Table VIII. Summary of Flowmeter Characteristics (Continued)
Meter Type
Secondary Standards
Rotameters
Orifice Meters
Capillary Meters
Critical Orifice
Hot Wire
Anemometer
Pressure Trans-
ducer (Magnehelic
Guaae)
Measurement
Principle
Variable Area
Velocity Meters
Pressure drop
across constric-
tion in gas line
Pressure drop
across capillary
Maximum obtain-
able flowrate
through a small
orifice
Loss of heat
from hot wire
related to
mass flow of
air
Velocity Impact
Air
Theory
Wt. Float - Buoyancy = Drag Force
2
v r I \ - fpq m
VfG (Pf-Pg) - 2
|2VfG(pf-Pq)
Qc = Vm
= Function of flH
Pressure Drop is a Function
of Gas Velocity, Density,
Specific Heat, and Viscosity
|2P(] flH
(Plot AH vs known Q )
Q = H6H 1 + AH r4
8uL
(Plot AH vs known QC)
o = °AOPI&™ ±- (Y+1)/(
"w-max RT y+1
KoAoPl
\rr
H = ke + (27tkCvpdv)*8
Response is not linear with
flowrate, but may be elec-
tronically adjusted to be
Same as standard pi tot tube above
Temperature - Pressure
Corrections
Theory
a c' a c
Experimental
CD = 8 x 10"4 Liter/mm Hg
Q . . as in Standard Pitot Tube
Q' = q<\fR
Q t. as in Standard Pi tot Tube
<••<•!&
Q . as in Standard Pi tot Tube
Y-1F
J
Theory Pg ff^"
a-max c-max c y a
Experimental
Ci for needle guage no.
18 = 1.1 ml/mm Hg
20 = 0.47 ml/mm Hg
22 = 0.38 ml/mm Hg
24 = 0.35 ml/mm Hg
27 = 0.12 ml/mm Hq
Meter may be calibrated to give
volumetric flowrate at standard
temperature and pressure (OsttJ-
Qa = Qstd %td la
"a std
*-vR
-------
III. BASIC PRINCIPLES
THE ATMOSPHERE
The atmosphere is a gaseous mixture composed largely of nitrogen
and oxygen which envelopes the earth in a thin layer. It is held by
gravity, but moves easily in complex patterns depending upon the earth's
rotational forces, topography, and the sun's energy. The atmosphere
thins rapidly with increasing elevation. More than half of the air
lies below 3.5 miles and less than 1% exists above 18 miles.
STRUCTURE
At least three classification systems are used to describe the
atmosphere [Figure 1]. These are based on a) molecular composition,
b) thermally related regions, and c) chemical and physical properties.
The molecular composition classification divides the atmosphere
into two regions: the homosphere and the heterosphere. The homosphere
extends to some 55 miles and is distinguished by the uniformity of
its composition. On a dry basis, the air in the homosphere is often
treated as a single gas with a molecular weight of 28.96. Above the
homosphere, the heterosphere includes successive layers which contain
increasing relative amounts of nitrogen, atomic oxygen, helium and
hydrogen, respectively.
The thermal regions include the more popular classifications of
troposphere, stratosphere, mesosphere, and thermosphere. The pauses,
as shown on Figure 1, refer to the transition zones between the regions.
-------
140
Altitude
Miles km
nor1'80
100+160
SO
80
70-
60-
60+80-
40
30
20
10-
100
Atmospheric
pressure:
(fraction of
sea-level value)
J _
100.000
Air temperature
-60'C O'C -HOO'C
I . . ^ . . . . I
Temperature
lones:
•60
•40
20
THERMOSPHERE
Mesopause
MESOSPHERE
—4— —— 4 Stratopause
STRATOSPHERE
Tropopause
TROPOSPHERE
;:F layer 125 mi
Molecular nitrogen
layer (N,)
•/(Kennelly-Heaviside layer);.';.'
CHEMOSPHERE
1000^
'-^.-i'-.'.V.!.v-J*.iI.:-{:?f *;:-!-.>.•*.'.*!*.-'!»•.•V-.i-w.:-5'.j.A : T»»^; «? iiift.
Figure 1.
Structure of the Atmosphere
-------
8
The troposphere envelopes the biosphere of the earth and contains all
weather phenomena. The stratosphere includes a stable "stratified"
temperature region above the troposphere and forms an oxidative sink
for air contaminants as well as a filter for high energy sun rays.
The chemical-physical view of the atmosphere classifies the
lower part of the atmosphere as a chemosphere, or a region where
chemical reactions occur. The upper part is considered a highly
ionized region or ionosphere. Radio and television waves are re-
flected from this region.
COMPOSITION OF AIR
The composition of clean, dry air is uniform throughout the
homosphere except for slight variations in the trace gases [Table 1].
On a dry-volume basis, air is nearly 78% nitrogen, 21% oxygen, and 1%
argon. All the other components including carbon dioxide do not amount
to over 0.04%. Their concentrations are generally expressed as parts
per million rather than as percentages.
Water vapor is often a major component of air and its presence
should always be taken into consideration. Because its concentration
varies widely, from 0.02% to as much as 6%, it is rarely cited as an
important component. The same is true for particulate matter which
can vary in concentration from 15 ug/m3 in remote regions of the ocean
to 2,700 ug/m3 and more in polluted areas.
Polluted atmospheres contain a wide variety of gases and particu-
late matter. Table 2 compares the concentrations of the more common
pollutant gases in clean air with their concentrations in typically
polluted atmospheres. The actual concentrations can vary quite widely
depending on nearness to emission sources, wind direction, velocity,
-------
Table 1
COMPOSITION OF CLEAN DRY AIR (V/V)
Gas % ppm
Nitrogen (Np)
Oxygen (02)
Argon (Ar)
Carbon Dioxide (C02)
Neon (Ne)
Helium (He)
Methane (CH4)
Krypton (Kr)
Nitrous Oxide (N20)
Hydrogen (H2)
Xenon (Xe)
Ozone (03)
78.09
20.94
0.93
0.03 320
18
5.2
1.5
1
0.5
0.5
0.08
0.01-0.04
-------
10
Table 2
COMPARISON OF TRACE GAS CONCENTRATIONS
Gas
Carbon Dioxide (C02)
Carbon Monoxide (CO)
Methane (CH4)
Nitrous Oxide (N20)
Nitrogen Oxides
(N02) (NOX)
Ozone (OJ
Sulfur Dioxide (S02)
Ammonia (NHL)
Clean Air
ppm
320
0.1
1.5
0.25
0.001
0.02
0.0002
0.01
Polluted Air
ppm
400
40-70
2.5
(?)a
0.2
0.5
0.2
0.02
Ratio
Polluted to Clean
1.3
400-700
1.3
200
25
1,000
2
a Not well known.
-------
11
and turbulence. Participate matter in polluted atmospheres can vary
widely in composition, size distribution patterns, and concentration.
THE GAS LAWS
At ambient temperatures and pressures, most gaseous substances
in the atmosphere may be considered to obey the perfect gas laws.
This is because the partial pressures of all but the heaviest
molecular weight (MW) substances are well below their saturation
vapor pressure.
At a given temperature and pressure, all gaseous molecules occupy
essentially the same volume regardless of their atomic or molecular
weight. This is because their molecular size is much smaller than
their mean free path. Hence, a gram mole of most gases (i.e., 2 grams
of H2; 32 grams of 02 ; 44 grams of C02 ; 131 grams of Xe, etc.) occupies
22.4 liters of space at 0°C (273°K) and 760 mm pressure and contains
6.02 x 1023 molecules.
This leads to the following relationships for a given gas mixture:
Volume % = pressure % = molecule (mole) % ? weight %
For a given parcel of gas, Charles' and Boyle's Laws state that
the pressure times the volume divided by the absolute temperature is
a constant. Hence, for a gas under different conditions of tempera-
ture and pressure, 1 and 2:
constant
n]
-------
12
A "universal" gas constant (R) has been developed from the above
relationship for a mole of a gas under standard temperature and pres-
sure conditions.
- = constant = R
STP
The constant, R, may have several numerical values depending on
the units used for P, V, and T (i.e., mm Hg or lb/in2 for P, liters,
milliliters, or cubic feet for V and °Kelvin or °Rankine for T).
For any amount of gas which may be more or less than one mole:
STP
[3]
where R1 is a constant for the given amount of gas and n is equal to
the number of moles of the given gas:
_ Weight of Gas _
_
Molecular Weight of Gas
[4]
Equation 3 combined with equation I becomes what is commonly called
the ideal gas law expression.
PV = nRT
For use in air flow measurement, the density (p) of any gas can
be obtained from equations 4 and 5.
_
p "
_ Weight of Gas
"
Volume
• MW
RT
-------
13
For a given gas under different temperature and pressure conditions
[7]
Pi T2
1 2 T
Pi - Po T~~ D~~
In gaseous mixtures (such as air) the total pressure is equal to
the sum of the pressures of each of its components.
P = P + P + P
•total HN2 H02 K
The gases of clean, dry air form an ideal mixture whose composi
tion varies but little throughout the troposphere. Because of this
composition, a "molecular" weight of air is calculated from the mo-
lecular weights of the individual gases times their respective per-
centages.
MWair = [28(% N2> + 32(% °2^ + 40(% Ar> + 44(% ^ + etCt] ;
= 28.96
* 29.0
THE MOLE
The mole is a most useful concept in chemistry and physics.
The gram mole refers to that amount of an element or compound whose
mass (or weight) is equal to the formula weight. Because atomic
weights and, consequently, the molecular (or formula) weights are
-------
-14
based on relative mass on a per-atom basis, the aggregate result is
that a gram mole of any element or compound contains the same number
of atoms or molecules. This number turns out to be 6.022 x 1023 and
is called Avogadro's number.
As stated above, gaseous molecules at a given temperature and
pressure occupy essentially the same amount of space irrespective of
mass. Thus, 6.022 x TO23 molecules, or one gram mole, of any gas
occupies 22.4 liters of volume at 0°C (273° Kelvin) and 760 mm Hg
pressure. Avogadro's number is a huge number. A simple calculation
shows that one cubic centimeter of air contains 2.4 x 1019 molecules
at 25°C and one atmosphere. What is still more interesting is that
if a pollutant, such as hydrogen sulfide, were in air at a concentra-
tion of one-tenth part per billion, it could not be detected by
smell, but one cubic centimeter of the polluted air would contain 2.4
billion (2.4 x 109) hydrogen sulfide molecules. This latter number
is quite large, but making analytical contact with the specific mo-
lecules in the presence of billions of times as much other molecules
is, at present, a very difficult task.
The mole is not limited to the gram as a unit of mass. The pound
mole and, in some cases, the ton mole is used extensively in the
English system. A pound mole is simply the same relative mass based
on molecular or formula weights but measured in pounds rather than
grams. Since 1 pound equals 453.6 grams, then a pound mole occupies
453.6 times as much volume (10,161 liters or 359 ft3 at STP) and has
453.6 times as many molecules (2.732 x 1026). In the English system,
70°F or 530°R is taken as the standard temperature, and the pound
mole occupies 387 ft3 at this temperature and one atmosphere pres-
sure. For example, a gram mole of oxygen (MW = 32) weighs 32 grams,
has 6.022 x 1023 molecules and occupies 22.4 liters at 273°K and 760
mm pressure; a pound mole of oxygen (MW = 32), on the other hand,
-------
15
weighs 32 pounds, has 2.732 x 1026 molecules, and occupies 387 ft3 at
530°R (70°F) and 760 mm pressure.
WEIGHT-VOLUME RELATIONSHIPS
The mole is very convenient for making weight to volume or vol-
ume to weight conversions. The weight of any substance or the volume
of any gas can readily be converted to moles. The number of moles of
that substance can then be converted to volume by multiplying by the
molar volume (22.4 liters/gram mole or 359 ftVlb mole at STP). The
conversion of moles to weight is readily achieved by multiplying by
the molecular weight.
1
Vol -^ VolSTp x Mo1Vo1 x Mol Weight = Weight
Moles
l x"" ^A.
We1ght * Mol Wt Mo1 Volume = VolSTP
where:
Vol = volume of given gas, any temperature and pressure
VolSTp = volume at standard temperature and pressure
Mol Vol = mole volume (22.4 liter or 359 ft3 at STP)
Weight = weight of given substance (grams or Ibs)
Mol Wt = molecular (or formula) weight of substance
CONCENTRATIONS
Concentrations in air are frequently expressed as weight (mass)
per unit volume such as micrograms per cubic meter (pg/m3). They are
-------
16
also frequently referred to as volume (or weight) ratios such as
parts per million (ppm), or parts per billion (ppb). The principles
are straightforward, but some confusion does exist as to the exact
meaning and relationship of the terms in common use.
In air, ratios are generally understood to be on a volume-to-volume
basis unless specifically stated otherwise. Just as percentage is
calculated by:
Part
Percent = x 100 (usually volume T volume in air)
then:
ppm = x 106 = percent x 104
ppb = SfioTe x 1C)9 = ppm x 1C)3
Weight % = Vol % (M°^gWt) Gases in Ai
100
yg/m3 = ppm x 40.9 x MW (at 25°C, 1 atm)
3 Pa
ug/m = ppm x 16.04 x ^- x MW (at any T , P )
'a a a
where:
P = ambient pressure, mm Hg
T. = ambient temperature °K
a
MW = molecular weight
-------
17
DERIVATION OF MASS-RATIO RELATIONSHIP
In deriving the mass-ratio relationship it is convenient to use
the assumption that one liter of a given pollutant (x) exists per one
million (106) liters of air for each part per million of x (ppmx).
1 llterx
Vol = ppm ' —, x
106literai>
To convert this volume to weight, the volume is adjusted to standard
temperature and pressure (STP: 273°K, 760 mm Hg).
*
STP 10b liter . 'x HSTP
Oil
The volume of x is then changed to moles of x.
1 literx TSTP Px ] molex MOI
Moles x = ppm ' —= *- . =-STP Fx < 00 , * [12]
x 106 liters,, Tx PSTP 22A lltersx
a 1 r
The moles of x are subsequently converted to weight by multiplying by
the molecular weight of x (MW ) which gives the weight in grams.
J\
This is converted to micrograms by multiplying by the factor
10s ug/gram and to cubic meters of air by the factor 1,000 liters
air/m3. The entire equation becomes:
3 ] literx TSTP Pv ] molev
Wt /mj = ppm —7 « J*TP H-X * x .
x X106literai> Tx PSTP 22.4 liter/
mx grams t IQ^g 103liter .
mole * gram * 3 air
A m -
air
-------
18
= ppm . 16.04 • MW =*• ^
X
For T equal to 298°K (25°C) and P equal to 760 mm Hg,
X A-
Wt/m3 = ppmv • 40.9 - MWv ^ [15]
A A A 0
mair
where: TSTp = 273°K
PSTR = 760 mm Hg
T = ambient temperature, °K
/\
P = ambient pressure, mm Hg
Table 3 gives some typical applications.
PHYSICAL VOLUMES AND GASEOUS VOLUMES
In atmospheric measurements there is, at times, some confusion
regarding the true concept of the volume under consideration. In
some cases, the word volume is intended to represent a measured por-
tion of space with due consideration to the air or the atmospheric
pollutant occupying that volume. Such a volume may be called a
physical volume. A physical volume is described by a three dimen-
tional configuration or its equivalent. Its units are cubic inches,
cubic feet, cubic meters, gallons, liters, etc. The size of such
units is fixed and does not change with temperature, .pressure, time,
or place. Containers of such specified volumes will always measure
and deliver air (or other gases) whose volume is equal to the volume
of the container at the temperature and pressure of the measurement.
-------
19
Table 3
TYPICAL MASS-RATIO RELATIONSHIPS
Compound
CO
NO
N02
so2
C8H18
DDT
MW
28
30
46
64
114
354
1 ppb
1.15
1.23
1.88
2.62
4.66
14.48
uq/m3 (25
0.1 ppm
115
123
188
262
466
1,448
°C, 1 Atm.j
1 ppm
1,150
1,230
1,880
2,620
4,660
14,480
1
10 ppm
x 103
11.5
12.3
18.8
26.2
46.6
144.8
-------
20
A gaseous volume, on the other hand, is considered to be that
volume occupied by a specified amount of air (or gas) at a given tem-
perature and pressure. The temperature and pressure may be the ac-
tual temperature and pressure of the air, or a standard type of temper-
ature and pressure which may have been selected for uniformity of
comparison. If so, then the volume cited would not necessarily be
that of the actual air parcel but the calculated equivalent volume
for the temperature and pressure selected. Such volume adjustments,
when properly used, are highly desirable for uniformity of comparison
and regulation.
However, overuse of standard temperature and pressure adjust-
ments leads to loss of understanding of the spatial relationships of
pollutants. Light scattering particles, for example, when collected
from a cubic meter of air at high altitudes would be interpreted to
be more crowded and scattering more light when the volume of the
sampled air is converted to a standard temperature and pressure. For
example, an atmosphere containing 50 micrograms per cubic meter at
30°C and 630 mm pressure (Denver in summer), could be interpreted to
contain 61 micrograms per cubic meter at a standardized temperature
and pressure of 25°C and 760 mm. Such an interpretation is simply
not true both in terms of light scatter or amount of particulate mat-
ter to which a person is exposed.
Additional confusion arises when a volumetric or flowrate device
is calibrated in a laboratory, has a calibration curve drawn to stan-
dard temperature and pressure, and is used in the field where the
temperature and pressure may differ significantly from those of both
the laboratory and standard curve.
The correction of measurements made by volumetric devices (wet
and dry test meters, soap bubble flowmeters, etc.) follows simple
-------
21
ideal gas law calculations. But the correction of velocity flowrate
measurement devices (pitot tubes, rotameters, orifice meters, etc.)
is not straightforward and must be made with proper precautions. If
at all feasible, flowrate measurement devices should be calibrated in
the field reasonably close to where they are being used. This is not
always possible in spot sampling, balloon and aircraft measurements,
for example. In any event, due caution must be exercised in order
that the reported data reflect either a measurement of an event or
substance occurring with a given unit of space (physical volume) or
occurring within a given unit of air (gaseous volume). The former
reflects properties of a given place or environment, while the latter
reflects the relative quantity per standard unit of volume. Improper
use of either concept can lead to erroneous conclusions.
WATER VAPOR
The amount of water vapor in air is highly variable. It depends
on the nearness of water bodies, soil moisture, vegetative cover, wind
direction, ambient temperature, etc. It may be present from a low of
0.1% (200 ppm) in arid regions or at low temperatures, to as high
as 6% (60,000 ppm) in warm, humid climates.
The water vapor content of the air is generally measured as per-
cent relative humidity and is calculated as the percent of the satura-
tion vapor pressure of water that is present at the given temperature.
v nu _ Water Vapor Pressure ,nn Mcn
A Saturated Water Vapor Pressure LlbJ
The relative humidity does not indicate the actual amount of
water vapor that is present. At 50% relative humidity, for example,
-------
22
the actual amount of water in the air would be approximately 3%
(30,000 ppm) at 100°F and only 0.06% (600 ppm) at 0°F. Table 4 gives
the saturation vapor pressure of water over the general tropospheric
range of temperatures.
More commonly the relative humidity is obtained from wet bulb-
dry bulb temperature measurements (or other similarly related physi-
cal measurements) where the difference between the measurements is a
function of the relative humidity rather than the absolute humidity
of the air.
Relative humidity, however, is an important parameter in that it
gives a measure of the tendency of water to adsorb on, or evaporate
from, condensation nucleii, solid surfaces, liquid droplets, etc. As
temperatures drop, the relative humidity increases for a given amount
of moisture in the air. When 100% relative humidity is attained,
water vapor condenses spontaneously and the "dew point" is said to be
attained.
The water molecule is highly polar and readily adsorbs on most
materials to form mono- or multiple molecular layers of adsorbed
water, even at low relative humidities. At higher relative humi-
dities >60% relatively thick layers of water are adsorbed and at-
mospheric aerosols are observed to increase significantly in size.
Many pollutant gases dissolve in the adsorbed water and react
chemically with each other, absorbed oxygen, or with the substrate
material. This is particularly true of sulfur dioxide which readily
dissolves in water to react catalytically with absorbed oxygen and
water to form sulfuric acid. The acid thus formed is corrosive to
metals, various industrial and commercial materials, and plays an
important role in the increase of the acidity in rainwater.
-------
23
Table 4
WATER VAPOR PRESSURE AS A FUNCTION OF TEMPERATURE
°c
-40
-30
-20
-17.8
-10
0
5
10
15
20
25
30
35
40
45
50
55
60
°F
-40
-22
- 4
0
14
32
41
50
59
68
77
86
95
104
113
122
131
140
Vapor Pressure
mm Hg
0.97a
0.29a
0.78a
0.96a
1.95a
4.58
6.54
9.21
12.8
17.5
23.8
31.8
42.2
55.3
71.9
92.5
118
149
a Vapor pressure given is that of ice at the given
temperature.
-------
IV. AIR FLOWRATE AND VOLUME MEASUREMENTS
Flowrate and volume measurements when used for the collection
and estimation of the concentrations of atmospheric pollutants often
contribute a major portion of the uncertainty in the reliability of
the measurement. Involved are not only the accuracy and magnitude of
the response of the measuring device to airflow variations, but also
the effects of changes in temperature, atmospheric pressure, relative
humidity, flow patterns and pressure drop changes due to the accumu-
lation of collected or deposited matter on filters, regulating
valves, floats, and other moving parts. To minimize such errors, an
understanding of the operating principles and the effects of the op-
erational and environmental variables is important.
Instruments used for calibrating and measuring air flowrates may
be described according to several possible categories. In this case,
they have been grouped as: primary standards; intermediate stan-
dards; and secondary standards. Except for the pi tot tube, the pri-
mary standards are volume displacement meters wherein the metering
volume can be measured directly and accurately. Such meters include
spirometers, frictionless pistons, and aspirator bottles. The in-
ternal volumes of volume displacement meters are constant and do not
change with temperature or pressure (altitude) except for very minor
changes caused by temperature expansion coefficients of the meter
materials. Often, the gaseous volumes measured by the meters are
converted to some desired ambient or standard temperatures and pres-
sure by ideal gas law calculations or by adjusted calibration curves.
However, the true volume of the air being measured is a direct func-
tion of the volume of the metering chamber.
-------
25
The pilot tube is a velocity measuring instrument. The theory
of operation is well known, and it has long been established as a
dependable standard for measuring gas flow velocities.
The intermediate standards include the wet and dry test meters
and the rotary displacement meters. These are all volume displace-
ment meters whose internal volumes cannot be measured accurately.
When calibrated with primary standards or known volumes they make
excellent laboratory and field volumetric flowrate devices. Tem-
perature and pressure conversions are straightforward involving the
usual ideal gas law corrections.
Secondary standards include devices that depend upon the ve-
locity of the air to produce some physical change or force which can
theoretically or empirically be related to a volumetric flowrate.
Such devices include rotameters, orifice meters, hot wire anemom-
eters, pressure transducers, and vane anemometers. Their response is
often conveniently observed by visual, mechanical, or electronic
means. However, the response is generally not a simple function of
the flowrate of the gas alone. In addition to temperature and pres-
sure, other factors which may be important are gas density, molecular
weight, viscosity, specific coefficients of heat and flow turbulence
(Reynolds numbers).
In the following sections, emphasis will be placed on those de-
vices which are commonly used for air flow measurements. The prin-
cipal factors and relationships which control and affect the measure-
ments will be discussed and illustrated mathematically. Wherever
possible, simplified formulas for temperature and pressure correc-
tions will be given.
-------
26
PRIMARY STANDARDS
Spirometers
The spirometer is perhaps the most widely accepted primary standard
for airflow and volume calibrations [Figure 2]. A moveable bell whose
internal volume can be accurately measured is used to collect air
moving through or from a gas measuring device. The bell rises above
a liquid reservoir seal [Figure 2] as the air enters. The rise of
the bell gives the volume of the entering gas, and the time of flow
is used to calculate the flowrate. The bell is carefully counter
weighted with a cycloidal counterpoise that compensates for the de-
creasing buoyancy of the liquid seal as the bell rises. In some in-
stances, the spirometer is used to deliver known volumes of air or
other gases.
Most spirometers are calibrated at the factory against standards
certified by the U.S. Bureau of Standards. They can also be rechecked
by accurate internal measurement or against Bureau of Standards certi-
fied volumes if found necessary after damage or readjustment. For
proper use, the spirometer must be carefully aligned to provide free
vertical movement. All leaks must be eliminated; the liquid level
must be correct; and the temperature of the liquid reservoir must not
differ from the ambient air by more than 0.3°C. Proper adjustment of
the cycloidal counterpoise should cause no drift of the bell when all
valves are open. When calibrating a spirometer by physical measure-
ment, the volume of the gas (V ) is equal to the increase in the in-
ternal volume of the bell (V^O, plus the drop in displacement of the
liquid level as the bell rises (V ).
V = V. . + V
9 bi ve
-------
27
Cycloid counterpoise
Counterbalance
wheel
Isolating liquid
Gos
Shut-off
lever
Counterweight-
Figure 2.
Cross-Sectional View of a Spirometer
-------
28
The internal volume of the bell (V..) is equal to the external volume
of the bell (V. ) less the volume of the metal (V .). Hence,
V = v. - V ^ + V []8]
g bo mt e
For a more complicated spirometeric apparatus, careful evaluation of
all factors, including the volumes of the inlet and outlet lines,
will reduce experimental errors to a minimum.
Frictionless Pistons
Frictionless pistons furnish a convenient method of calibrating
gas flowrates and volumes. The mercury-sealed piston [Figure 3] is a
simple, directly observable device for measuring small volumes or low
gas flowrates. The volume of the piston can readily be calibrated by
directly weighing water added to or withdrawn from portions or the
entire contents of the piston, much as one would calibrate a burette
in quantitative analysis.
For flowrates up to several liters per minute, soap-bubble flow-
meters are widely popular standards for air flow measurements. Soap-
bubble flowmeters come in a variety of designs and sizes [Figure 4].
The basic principle involved is the insertion of a thin aqueous film
in the path of a stream of air as it moves through a burette or gra-
duated cylinder. The volume of either can be calibrated as was de-
scribed for the mercury-sealed frictionless piston. The time of pas-
sage between marks is used to calculate the flowrate.
The film is inserted into the air stream by allowing the air to
momentarily pass though a soap or surface active solution. A bubble
-------
29
TIMING MARKS
IT
3AS
3T
MERCURY O-RING
Figure 3.
Mercury-seal Piston Flowmeter
-------
30
TIMING MARKS
AIR
RUBBER BULB
Figure 4.
Soap-bubble Flowmeter
-------
31
is formed which travels through the burette at the same velocity as
the air stream. It usually takes a number of bubbles before the in-
side of the burette is wet enough to maintain the film throughout the
length of the burette. The flowmeter may be used at either the out-
let or inlet ends of the metering device to be calibrated. If used
at the inlet end, precautions must be taken to prevent overflow of
the film or spray from bursting bubbles being carried with the air
into the measuring device.
As the air (or gas) passes through the soap-bubble meter, it
picks up water vapor to the saturation vapor pressure of water for
that temperature. This increases the volume of the gas being mea-
sured from 0 to 4%, depending upon the temperature and the amount of
moisture (relative humidity) in the original air stream. In general,
this effect is ignored. It can be important, however, for dry gases
at ambient and higher temperatures. Corrections for the volume in-
crease may be calculated as follows:*
Q = Corrected flowrate
0 = Observed flowrate
o
P. = Barometric pressure
P = Saturated water vapor pressure at temperature of test
[Table 4].
RH = Relative humidity (0 to 1.00)
For dry gases, where RH = 0, equation 19 becomes:
«c • "o
It is to be noted that when the air or gas which passes through
the soap-bubble flowmeter is used in any manner without drying,
the water vapor correction must not be applied.
-------
32
At low flowrates or when a large diameter cylinder is being used,
there is a possibility that air will diffuse through the soap bubble
film giving low results. This effect can be essentially eliminated
by reading the movement of the second of a double or triple set of
films moving with the air stream.
Aspirator Bottles
Aspirator bottles sometimes form a convenient means of flowrate
measurement in the 0 to 500 ml/min range. Air flow generally is from
the device to be calibrated to the aspirator bottle [Figure 5]. The
air flows into the bottle at a rate that is equal to the rate that
water flows out of the bottle into a graduated cylinder. Alter-
nately, the bottle itself may be calibrated. The air flowrate is
then equated to the water flowrate.
Serious errors can be introduced by either positive or negative
gas pressure changes caused by the manner that the water is allowed
to flow out of the bottle. Positive pressures can be developed, for
example, by air moving into the bottle faster than the water is flow-
ing out. Negative pressures can be caused by a siphoning action if
water flowing out of the bottle passes through a vertical tube. It
should also be recognized that the flowrate of water out of the as-
pirator bottle can change when controlled by a stopcock, screw clamp,
or similar flow restrictor. The pressure head of the water inside
the bottle against the restrictor will decrease as the water level
inside the bottle drops. This can amount to as much as 20 or more
inches of water depending upon the size of the aspirator bottle.
If the relative humidity of the air (or gas) being measured is
less than 1.00, the volume of the air in the aspirator bottle will
-------
on
manometer
Water
\
Groduoted cylinder*
Filling funnel
33
TKrec-woy stopcock
Aspirator bottle
Figure 5.
Aspirator Bottle for Measuring Low Gas Flow Rates
-------
34
expand depending upon the degree of equilibration and the saturation
vapor pressure of the water at the temperature of the water as ex-
plained above for the soap-bubble flowmeter (Equation 19). Again,
this many not amount to more than 4% error and may be ignored if
other variables are not being controlled to this degree of accuracy.
Indeed, of the primary calibration standards, although popular in
use, this may be one of the more difficult techniques to control for
high accuracy.
Pi tot Tubes
Pitot tubes have been used as primary standards for measuring
gas velocities for many years under wide ranges of velocities, gas
types, and mixtures. Their theory is well developed and understood.
Their application is widespread—in research, industry, and commerce.
In its most common form, the pitot tube consists of two concentric
tubes which are used to measure the differential pressure between the
impact and static pressures of a moving gas stream, respectively
[Figure 6].
The basic theoretical relationship for a pitot tube finds that
the velocity of a moving fluid is a function of the impact velocity of
the fluid. The relationship has been verified for a large number of
both compressible and noncompressible fluids. When applied to air:
Qa=
Q = Flowrate of air
a
G = Force of garvity
h = Height of column of air supported by the impact pressure
-------
15/16 in.
5m
m.-
2-1/2m.-
0.04-«n.
Kolet, equolly
spaced
Static pressure
Section A-A
7
'Inner tubing (1/8 in. o.d., copper)
-Outer tubing (5/16 in. o.d., copper)
•Total pretiure
35
A— -
i
t
A^J
••^
1/4 in.
~\
— 1
/Sin.
.
— ^— —
5/l6ln1
Figure 6.
The Standard Pi tot Tube
-------
36
The differential pressure of the moving air is generally mea-
sured by a manometer whose two arms are connected to the velocity
impact and pressure tubes, respectively. For flowrates encountered
in air pollution source measurements where an "S-type" pi tot tube is
used (see below), the manometer is usually of the inclined plane type
filled with a nonvolatile colored fluid of known density. Hence the
impact of the moving air which according to equation 21, above, would
support a column of air (of density p ) to a height of h , instead
o 3
supports in the manometer a liquid of density, p., to a height of h..
Since the height times the density of one liquid equals that of another:
v. • v* [22]
pa
Substituting for ti from equation 22 into equation 21:
a
l?nh 0
A [23]
pa
The density of clean, dry air (p ) in equation 23 is calculated
3
from its mole weight and volume as 28.96 grams for 22.4 liters (or
1.29 grams per liter) at 273°K and 760 mm Hg pressure as obtained
from the perfect gas laws:
273 P P
Pa = 1.29 Y— 7g| grams/liter = 0.463 ya
a a
P = Pressure of air, mm Hg
a
T = Temperature of air, °K
a
-------
37
If, as often happens when working with air pollution emission
sources, composition of the stack gases being emitted may differ con-
siderably from air, then the density of that gas (p ) may be calcu-
y
lated from the molecular weight of that gas relative to air.
MW
Jg = pa MW
273 P
^— 7gg- grams/liter
[25]
Substituting equation 25 into equation 23, one obtains a general equa-
tion for the velocity of any gas.
[26]
273
760
MW = Molecular weight of gas being measured (see equation 9)
MW = Molecular weight of dry air, 28.96.
3
For a known pressure reading device, such as an inclined manometer
whose scale is adjusted to read in inches of water, many of the terms
of equation 26 become known and the equation can be simplified to:
"g = KPCP
- KPCP
[27]
where AP is the height of the manometer liquid in inches of water
and K is a collection of the known terms of equation 26. When
P !<
English units are used K is equal to 85.48 ft/sec (Ib/lb-mole °R) .
The pitot tube correction factor, C , is generally assumed to be 0.99
or 1.00 for the standard pitot tube and approximately 0.85 for the
Stauscheibe ("S-type") pitot tube used in stack gas measurements (see
below).
-------
38
"S-Type" PI tot Tube
In stack gas measurements, the standard pi tot tube plugs up rather
easily. In its place, the federal reference method for measuring
stack gas velocities uses the Stauscheibe or "S-type" pitot tube
[Figure 7]. Essentially, the S-type pitot tube consists of two ap-
proximately k" (6 mm) i.d. metal tubes attached to each other and
bent in such a manner as to present a tapered opening directly into a
flowing gas stream. This tube measures the velocity impact of the
gas stream. The other tube, bent and tapered in the same manner but
facing 180° from the first, measures the static pressure of the gas
stream. The difference between the velocity impact and the static
pressure as measured by an inclined plane liquid manometer [Figure 7]
is used to calculate the gas velocity just as in the case of the stan-
dard pitot tube (equation 27). However, the pitot tube correction
factor (C ) will differ significantly from that of the standard pitot
tube. The turbulance in the air stream as it passes the edges of the
two tubes in essence reduces the static pressure measured by the down-
stream tube. This results in a high manometer reading (AP0). A
ji*
smaller correction factor C , adjusts for the high reading. As in-
dicated above, the C value for the S-type tubes generally is in the
vicinity of 0.85. However, it should be determined for each tube and
checked periodically. In particular, it should be rechecked whenever
the tapered edges of the pitot tube have been bent or damaged in any
manner.
The equation for calculating C is:
C = -L [28]
V = Velocity of gas stream
p = Density of gas
-------
39
PIPE COUPLING
TUBING ADAPTER
J—C
t
J..-.I,
TYPE S PITOT TUBE'
MANOMETER
Figure 7.
S" Type Pi tot Tube and Manometer Assembly
-------
40
In practice, the correction factor for the S-type pitot tube CC /^_t N
is obtained by comparing its response to that of the standard pitot tube
(C , . .v for the same position in the same gas stream. From equation 28
it follows:
r - C rstd C29]
Cp(S-type) ' Cp(std) J-
The above equation is the equation specified in the Federal Register for
calibrating the S-type pitot tube used in the Federal reference method
for stack sampling [Figure 8].
When measuring stack gas velocities it is not always possible to
expose the velocity impact (upstream) tube perpendicularly to the di-
rection of flow. Stack and cyclone gases near points of entry, turns,
etc., will tend to swirl, pitch, and yaw. Measuring this "non-
tangential" flow correctly can be difficult. Care should be taken to
have the velocity impact tube opening as close to perpendicular to
the direction of flow as possible. A recent study showed that the
configuration shown in Figure 9 gave reproducible C values over +20°
variations from perpendicular flow.
INTERMEDIATE STANDARDS
Wet Test Meters
Wet test meters are used extensively in laboratories where gas
flow or gas volumes are measured. They are inconvenient to use out-
side the laboratory and as a rule are not used in the field. They
can be used directly as part of an air flow apparatus, or they can be
used to calibrate secondary standards and flowrate devices.
-------
41
PROBE
REVERSE-TYPE
PITOT TUBE
1MPINGER TRAIN OPTIONAL MAY BE REPLACED
BY AN EQUIVALENT CONDENSER
HEATED AREA F,ILTER HOLDER / THERMOMETER CHECK
,VALVE
..VACUUM
LINE
sff STACK
U-WALL
IMPINGERS ICE
BY-PASS VALVE
W
PITOl MANOMETER
ORIFICE
THERMOMETERS
VACUUM
GAUGE
MAIN VALVE
DRY TEST METER
AIR-TIGHT
PUM?
Figure 8.
Participate Sampling Train
-------
42
I
5 cm
Figure 9.
Relative Positions of Sampling Probe and Pitot Tube
-------
43
The wet test meters consist of cylindrical tanks of varying sizes
approximately two-thirds full of water [Figure 10]. The tank con-
tains a rotary drum that is divided into four sections. Each section
contains an inlet and an outlet. The gas being measured enters at
the center of the tank passing into one of the rotating sections.
The buoyant force of the gas rotates the drum until the gas inlet is
closed and the outlet is exposed. Gas starts to enter the following
section while the gas in the first section is displaced outward as
the section rotates into the water. The drum is furnished with a
pointer and associated gears and dials to indicate the volume of gas
that has passed through the meter. To keep the drum running smoothly,
a minimum flowrate of one to two liters per minute must be maintained.
Maximum flowrates are limited to less than 100 liters/min. due to
excessive pressure differentials that may develop.
The meter is supplied with a water level gauge, a filling fun-
nel, and a drain plug. The water level is critical and must be care-
fully adjusted to obtain the correct values. A thermometer and a
water manometer give the temperature and pressure differential be-
tween the gas being measured and ambient pressures. The meter can be
calibrated with a spirometer [Figure 11], a Bureau of Standards
bottle of known volume, or an aspirator bottle of known volume. The
volume indicated by the wet test meter should agree within 0.5 to
0.25% of the known volume.
For more precise measurements, the volume of gas indicated by
the meter should be corrected for the increased amount of water vapor
picked up by the gas as it passes through the meter as well as the
pressure differential developed.
C30]
See footnote page 31.
-------
44
Colibration point
for water level'
monome-*r
Rotating partitioned drum
Go* outlet
Direction of
rotation
Got inlet
•Leveling screws
Figure 10.
Front and Cross-sectional View of a Wet Test Meter
-------
45
Goi-temp«folure thermometer
onfrol votvt
To vocuvnr
Wei tetl m.ler
Figure 11.
Calibrating a Wet Test Meter with a Spirometer
-------
46
v .¥ ISM!.
V9Std VgT
V = Volume of gas at room temperature and pressure (f , P )
g a a
V = Volume observed from meter
o
P. = Barometric pressure during measurement
T = Temperature of ambient air, °K
cl
H = Height of test meter manometer, inches H00
m c.
P = Saturation water vapor pressure, mm Hg at T
W O
RH = Relative humidity at T (0 to 1.00)
o
V std = Volume of gas at standard temperature and pressure
1.87 = Conversion factor: inches H20 to mm Hg pressure
Dry Test Meters
Dry test meters are very popular, both for use in the laboratory
and in the field. Millions of them are used in industry, commerce, and
residential homes for measuring natural and other gas volumes. They
are versatile, come in many sizes, and can operate over wide ranges of
temperature (-30 to 140°F), pressure (350 psig maximum) and flowrates
(5 to 50,000 liters/min). They may be made from various types of ma-
terials including iron, aluminum, brass, copper, and plastics. Their
basic structure consists of two bellows like chambers inside two larger
compartments giving a total of four chambers [Figure 12]. The chambers
fill and empty sequentially. Gas flow direction is controlled by two
"D-slide" (because of their shape) valves. As the gas enters one of the
bellows-like chambers, it expands pushing gas out of the outer chamber
[Figure 12]. Through proper linkage and timing the gas flow is shifted
to the second bellows chamber when the first is filled, repeating the
process. The third sequential step has the gas entering into the first
outer chamber, pushing gas out of the inner flexible chamber. The
-------
Chamber 1 is emptying, Chamber 1 is now empty, Chamber 1 is filling,
2 is filling, 3 is empty, 2 is full, 3 is filling, 2 is emptying, 3 has
and 4 has just filled. and 4 is emptying. filled, and 4 has
emptied.
Chamber 1 is now completely
filled, 2 is empty, 3 is
emptying, and 4 is filling.
From Crabtree
Figure 12.
How a Dry Test Meter Works
-------
48
expanding and contracting motion of the bellows operate the slides and
the calibrated dials. The diaphragms are generally made of long-lasting
flexible synthetic materials. A differential pressure in the order of
0.5 inch H20 results from operational and friction losses. Unless
excessively corrosive gases are used, dry test meters last up to thirty
years with proper maintenance.
Dry test meters can be calibrated in the same manner as wet test
meters. The usual accuracies are of the order +1%. If larger varia-
tions are found, they may be corrected by adjusting tangential weights
which affect the volume-dial linkage.
Rotary Displacement Meters
A popular positive displacement meter is the two-lobe or "Figure
8" meter. A commercial unit in common use is known as a Roots meter.
This type of meter consists of two contra-rotating lobes within a close-
fitting housing [Figure 13]. The rotating lobes act as impellers which
measure and dispense the gas with only a slight pressure drop of approxi-
mately 0.5 to 2.5 inches of water. The lobe contours are mathematically
developed and accurately manufactured to form a continuous seal with
each other without actual contact during rotation. The tips of the
lobes form a like seal with the semicircular portions of the meter
housing. As each lobe reaches a vertical position [Figure 13; Posi-
tion 2], it traps a known volume of gas and displaces it to the outlet.
In one complete revolution four similar gas parcels will be measured
and passed to the outlet. The total volume of the four parcels is
called the displacement volume per revolution of the meter. This
displacement volume is permanent and non-adjustable. It is established
by the machined contours of the non-wearing rotating parts and the non-
wearing fixed parts. The displacement volume of the meter may be
determined either by using a known volume of gas at a given temperature
-------
49
INLET
POSITION I
POSITION 2
OUTLET
POSITION 3
K-I24-I7
Figure 13.
Principle of Gas Flow Through a Roots Meter
-------
50
and pressure, or by mathematical calculation from the known manufacturer's
dimensions.
The meter is suitable for most non-corrosive, clean gases at either
constant or widely varying flowrates. Various sizes of meters are avail-
able for flowrates varying from 0.5 to 3,000 liters per minute with
accuracies of +1%. Maximum flowrates and pressures are specified by
the manufacturer for a specific flowmeter and should not be exceeded.
The meters can operate over a temperature range of -40° to 140°F depend-
ing on the manufacturers specifications. The meter is not suitable for
liquids, corrosive gases, or gases that contain liquid or solid parti-
culate matter that would tend to jam the moving parts.
Total volume of the gas passing through the meter is indicated
by appropriate gearing and dials. Flowrates are obtained by dividing
the indicated volume by the elapsed time. Some models have a timing
mechanism which will give the flowrate directly. Gas volume correc-
tions are made just as they are for the dry test meter. The observed
meter volume (V ) may be corrected for the pressure drop through the
meter (AP ) as follows:
V = V Pb " APm [32]
9 m PK
V = Volume of gas being measured
y
V = Volume indicated by meter
m
Pb = Barometric pressure, mm Hg
AP = Pressure drop through meter, mm Hg
Whenever it is desired to convert the measured volume (V ) to the volume
at a standard temperature (25°C; 298°K) and pressure (760 mm), then:
-------
51
Pa . Tstd V = 0.392 ^a_ V
where P and T are the meter, or actual, temperature and pressure of V .
a a Q
SECONDARY STANDARDS
Secondary standard gas-flow measurement devices are generally cali-
brated with a primary or intermediate standard. They are extensively
used in the field as well as the laboratory. Very often they form an
integral part of instruments used for sampling and analyzing industrial
process and waste gases as well as the ambient air. These devices in-
clude flowrate meters such as rotameters, orifice meters, and critical
orifices, mass flowmeters, such as thermisters and thermocouples, and
mechanical flowmeters, such as anemometers, velometers and magni-heliguages.
Rotameters
Rotameters are an extensively used form of variable area rate-of-
flow meters. They are used for both gas and liquid volume flow measure-
ments. They generally consist of a vertical transparent glass or plastic
tapered tube containing one or two floats of differing densities [Figures 14,
15]. Tube sizes vary from one-sixteenth inch for low flowrates to as much
as twelve inches for high flowrates. The velocity of the fluid (gas or
liquid) moving up the tube decreases due to the increasing annular space
between the tapering walls and the float. The floats rise until the
gravitational forces equal the combined buoyant and drag forces of the
moving fluid. The height of the float at its equilibrium position is a
-------
52
AIR
FLOAT
TAPERED GLASS TUBE
FLOAT STOP
AIR
Figure 14.
Cross-sectional View of a Variable Area Rotameter
-------
53
Float reading
taken her*
D
U
T
a.
b.
c.
d.
e.
a. Dual floats such as glass and stainless-steel spheres
b. Plumb-bob float
c. Viscosity-stable float
d. Ultra viscosity stable float
e. T-shaped float
f. Combination float
Figure 15.
Various Types of Rotameter Floats
-------
54
measure of the flowrate which is read either directly from a scale on
the tube or from a calibration curve. The height is always taken at the
widest dimension of the float [Figure 15].
The scale may be linear, non-linear, or logarithmic depending on
the flowrate range covered and the taper of the tube. Mechanical, mag-
netic, or electrical float height indicators are used for fluids that
are not transparent or when metal tubes are used. The floats may be made
of glass, ceramics, or metals of various densities. A combination of
a glass and stainless steel float in the same tube is often used. The
second float wtth the greater density conveniently extends the range of
the flowmeter.
The flowmeter range of a single rotameter tube covers approximately
10 to 100 times the smallest flow unit (i.e. 1-10 or 1-100 ml/min.,
cfm etc.). The range of a rotameter can be extended by the use of sup-
plementary tubes having a wider or narrower bore. A full set of rota-
meters can measure gas flowrates from 1 ml/min to 9 m /min. Rotameters
have been used at pressures up to 300 psig and temperatures of -50 to
400°F. They can be accurate to 1 to 2% if carefully manufactured and
calibrated, but are often used to give rapid, visual indication of the
flowrate. They suffer from float oscillation with pulsing, or rapidly
changing flowrates. Surge bottles generally will correct such oscilla-
tions if placed upstream of the rotameter for pressurized sources and
downstream for vacuum induced flow. Vapors in the gas may condense and
contaminate the rotameter if they are near their dew points.
Calibration of rotameters for gas flowrates may be accomplished by
the use of any of the standard or intermediate standard devices. In
general, it is best to calibrate the rotameter with the gases and under
the conditions of use. Figure 16 schematically shows how a rotameter is
calibrated for measuring the air flowrate passing through a midget
-------
MANOMETER r
ROOM_
AIR "
THERMOMETER
WET TEST
METER
MANOMETER
20ml
I 0»l
IMP/NGER
TRAP
TO
VACUUM
PUMP
_L/ROTAMETER
Figure 16.
Calibration of a Rotameter with a Wet Test Meter
(Note that other measuring or sampling methods may be calibrated in this manner)
en
en
-------
56
impinger. Note that the wet test meter is placed at the front of the
sampling train so that the volume of entering air is measured directly.
A glass wool trap is placed after the impinger to catch any mist or
spray which might coat the rotameter ball and tube and give erroneous
results due to increased weight, smaller annular space or friction with
the sides. The glass wool is loosely packed to prevent unnecessary and
possibly interfering pressure drops. The advantage of the system shown
in Figure 6 is that the effect of the pressure drop through the impinger
is automatically included in the calibration curve. Any other sampling
device (fritted bubbler, filter head, etc.) may be substituted for the
impinger. Conversely, any other flow measuring device (fixed or criti-
cal orifice, hot wire anemometer, etc.) may be calibrated in the place
of the rotameter. In addition, the wet test meter can be replaced with
any primary or secondary calibration device.
The calibration curve for the rotameter will hold in the field
within +4% if the temperature and pressure do not vary from the calibra-
tion temperature and pressure by no more than +10°C (18°F) and +30 mm Hg
pressure. If there is a greater difference, or if greater accuracy is
possible and desired, the following approximate correction may be
applied:
[34]
Q = Actual flowrate during sampling
3
Qc = Observed flowrate obtained from calibration curve
prepared in the laboratory
P = Pressure of calibration air, mm Hg
T = Temperature of calibration air, °K or °R
P = Pressure of air in field, mm Hg
a
T = Temperature of air in field, °K or °R
3
-------
57
Orifice Meters
Orifice meters have been used extensively in industry for many
years. They furnish a convenient and accurate method for measuring
fluid (gas or liquid) flow in a pipe. They operate on the principle
that as a fluid passes through a constriction in the diameter of a
pipe the velocity of the fluid increases while its pressure drops
[Figures 17, 18]. A measure of the pressure drop gives a measure of
the flowrate of the fluid. The pressure drop depends on the type and
amount of constriction but generally is one to two orders of magnitude
greater than the differential pressure measured by a pi tot tube. If the
physical properties of the fluid and the dimensions of the pipe and its
constriction are known, the theoretical flowrate can be calculated. In
practice, however, the flowrate is never equal to the theoretical rate
and an overall coefficient of discharge (a) for each type of orifice
must be determined.
There are three general types of orifice meters: venturi, nozzle,
and plate. The first two are similar; they require more careful design
and installation and cannot be easily varied to cover a wider range
of flowrates and fluid types. However, if properly designed, abrupt
flow disturbances are avoided, energy loss is minimized, and the co-
efficient of discharge is usually near unity making mathematical calcu-
lation of the flowrate possible.
Thin Plate Orifice Meters. The plate orifice is more popular for
measuring wider ranges of flowrates and fluid composition. The orifice
plates are relatively easy to manufacture, install and change, and the
orifice requires less pipe length and space [Figure 18]. Equation 35
indicates the factors involved in the calculation of the flowrate
through the orifice.
-------
58
A. Inlet section
B. Throat section
C. Outlet section
D. Upstream Pressure tap
E. Downstream pressure tap
Figure 17.
Venturi Meter
-------
59
MJJ JUlf IJ JJH1H.I. ... • l.ll" , . >!,! | , , ,,,,,, j ,.,,,,. ......!.
a. Upstream pressure tap
b. Downstream pressure tap
Figure 18.
Thin Plate Orifice Meter
-------
(P '
2P1vr1 r2' . / Y -
60
2/Y
Q« = oA°GV '-2 i
Q = Weight rate of flow
W
a = Coefficient of discharge of the orifice (usually deter
mined experimentally)
A = Area of the orifice opening
G = Force of gravity
Pi = Density of gas upstream of orifice
P! = Upstream gas pressure
P2 = Downstream gas pressure
m = Ratio of pipe diameter to orifice diameter
Y = Ratio of specific heat at constant pressure to that at
constant volume, C /C
* = Ratio of downstream pressure to upstream pressure
The second square root term of equation 35 adjusts the equation for the
compressibility of the flowing fluid. It can be replaced by a single
term, E, the compressibility factor, to render a general equation:
n r « ^ I 1X 1 2' nfil
Qw = EaAQG ,/ [36]
For incompressible fluids or for gases near normal atmospheric pres-
sures, the compressibility factor, E, is essentially one and may be
ignored.
Orifice meters may be calibrated experimentally with any of the
primary or intermediate standards. The flowrates for a given orifice
meter are within limits proportional to the square root of the pressure
drop. A plot of the flowrate versus the square root of the pressure
drop should give a straight line for flowrate ranges covering pressure
drops of several inches of water. A plot of flowrate versus pressure
drop would give a usable but curved line.
-------
61
For atmospheric measurements, a laboratory calibration curve would
hold within +4% for atmospheric pressure changes of +30 mm Hg and
temperature changes of +10°C (18°F). For greater changes or for a more
accurate approximation, the flowrate may be calculated from equation
36. However, by assuming that only the density of the air (pp in
equation 36 changes and that all other parameters remain essentially
constant, an approximate correction may be obtained by equation 34.
When sampling power plant stacks or other types of gases, the
molecular weight of the gas can differ from the "molecular weight" of
air. If the orifice has been calibrated with air then an additional
term should be introduced into equation 34 to compensate for the effect
of the molecular weight (or gas composition) change on the gas density,
i.e.:
. T3 HW r,,n
_c . _a_ . _c [37]
P. T. MW_
a C a
Q = Sampling flowrate in field
cl
Q = Flowrate obtained from calibration chart
P = Pressure of calibration air, mm Hg
P = Pressure in field, mm Hg
cl
T = Temperature of calibration air, °K or °R
T = Temperature in field, °K or °R
3
MW = "Molecular Weight" of calibration air (Equation 9)
MW = "Molecular Weight" of gas being measured (Equation 9)
3
Capillary Orifice Meters. In many laboratories, orifice meters
are constructed from small bore glass tubing combined with a U-tube
manometer [Figure 19]. For gas velocities up to near the speed of
sound, the flowrate is a function of the pressure drop and the length
-------
62
Control volve
Mercury manorneter-
Orific.
~T
__L
Filling porll
Figure 19.
Typical Capillary Orifice Meter and Calibration Curve
-------
63
of the tubing (or capillary). This type of orifice meter may be cali-
brated directly by any of the primary or intermediate methods described
above. The flowrate may also be calculated by the following equation if
the kinetic effects at the beginning and ending of the tube or capillary
can be neglected.
[38]
Q = Volumetric gas flowrate
PI = Upstream gas pressure
P2 = Downstream gas pressure
r = Internal capillary radius
u = Viscosity of gas
L = Length of capillary tube
Table 5 gives viscosity data for a number of common gases, and
Table 6 shows the variation of the viscosity of air with temperature.
Except for low and very high pressures, the viscosity of air is rela-
tively independent of the pressure.
Critical Orifices. Critical orifices are popular for use in situ-
ations where a constant air flowrate is desired. They are easily con-
structed from hypodermic needles, capillary tubing, and polyethylene or
Teflon rods. They are also easily calibrated with any of the primary
or intermediate standards as described above [Figure 20].
-------
64
Table 5
GAS-VISCOSITY DATA3
Gas
Air
Carbon dioxide
Carbon monoxide
Chlorine
Ethane
Ethyl ene
Helium
Hydrogen
Hydrogen chloride
Hydrogen sulfide
Methane
Nitric oxide
Nitrogen
Nitrous oxide
Oxygen
Propane
Sulfur dioxide
Xenon
Temperature
(°C)
18
20
21.7
20
17.2
20
20
20.7
18
17
20
20
27.4
26.9
19.1
17.9
20.5
20
Viscosity
(micropoises)
182.7
148.0
175.3
132.7
90.1
100.8
194.1
87.6
142.6
124.1
198.7
187.6
178.1
148.8
201.8
79.5
125.4
226.0
a From Chemical Rubber Co. Handbook
-------
65
Table 6
VARIATION OF VISCOSITY OF AIR WITH TEMPERATURE3
Temperature
°C
-194
-104
0
18
40
74
Viscosity
(Micropoises)
55
113
171
183
190
210
a From Chemical Rubber Co. Handbook
-------
MANOMETER -
ROOM_
AIR
THERMOMETER
WET TEST
METER
0)=^
- MANOMETER
30 Ml
20 ml
10 ml
HYPODERMIC
NEEDLE
MEMBRANE
FILTER
IMP/NGER
TRAP
Figure 20.
Calibration of a Critical Orifice with a Wet Test Meter
RUBBER
SEPTUM
TO
•VACUUM
PUMP
en
en
-------
67
The air flowrate through the orifice becomes critical when its
velocity is equal to that of sound. This occurs when the downstream
pressure is reduced to 53% or less of the upstream pressure. The air
velocity becomes constant and independent of any excess vacuum on the
downstream side. Thus a constant and known flowrate can be maintained
by merely taking the precaution to keep a vacuum of 53% or more of
the upstream pressure [Figure 21] on the downstream side of the criti-
cal orifice.
The theoretical treatment of the flowrate is quite complex. The
following relationship has been derived for a perfect gas:
= Maximum flowrate, mass per unit time
a = Discharge coefficient of critical orifice
Ap = Cross-sectional area of critical orifice
P, = Upstream gas pressure
G = Gravity force constant
Y = Ratio of specific heats C /C
MW = Molecular weight of gas
R = Gas constant
T = Gas temperature, absolute
Equation 39 shows the various factors that affect the maximum
flowrate of a critical orifice. They include a discharge coefficient,
a, which is an empirical factor to account for physical aberrations in
the orifice. It can change with slight changes in the surface or dia-
meter of a critical orifice and with changes in the Reynolds number of
the flowing gas stream. The molecular weight of the gas, its tempera-
ture and pressure, and the specific heat ratio (i.e. C /C ) are also
-------
zao
180
E
v»
1
if 140
ro
01
E
100-
60-
426
326
1.0
0.8 0.6 0.4 o.2
Downstream to Upstream Pressure Ratio, ?«/?.
Figure 21.
Variation of Volumetric Flowrate Through a No. 27 Gauge Hypodermic
Needle as a Function of Downstream (P2) to Upstream (P,) Pressure Ratios
CD
-------
69
of importance. Any changes of any of the above factors would affect
the flowrate as indicated by equation 39.
For air, many of the variables of equation 39 are known or can
be estimated (K), and the following simplified equation may be used.
Qmax = K . ex . [40]
max -
In this case, Q is a direct function of the physical structure
iTlaX
(K, a, and A2) of the critical orifice as well as the upstream pressure,
P.|. The flow is also inversely proportional to the square root of the
absolute temperature. From equation 40 it follows that for a given
critical orifice calibrated in a laboratory and then used in the field,
the following equation may be used for obtaining the critical flowrate
in the field from the critical flowrate obtained in the laboratory.
where "a" and "c" indicate the field (or actual) and calibration values,
respectively. If the sampling device (filter, impinger, or other) is
placed before the critical orifice, Pa (or P,) is equal to the barometric
3 I
pressure minus the pressure drop caused by the sampling device.
In practice, a difference of +25°C (45°F) in temperature causes
an error in the order of +4%. A pressure variation of +25 mm Hg (1 inch
Hg or 13.6 in H20) would also cause an error of approximately +4%. The
errors would be additive if the pressure and temperature changes were
in the same direction. They would offset each other if the changes
were in the opposite direction, i.e. if one increased while the other
decreased.
-------
70
Table 7 shows the range of flowrates that can be obtained with
hypodermic needle critical orifices varying in size from gauge number
13 through 25 and in length from 1/2 to 3-1/2 inches. It also shows
that manufacturing uniformity for a given batch of needles gives flow-
rates reproducible to a relative standard deviation of less than 10%
and more usually less than 5% for the larger gauge and longer length
needles. The flowrate decreases slightly with the number of times
the needles are used. A small percentage of needles plug on first
use, and the percentage of plugging increases with reuse. To prevent
serious plugging, the orifice needs the protection of a membrane, or
equivalent, filter between it and the sampling device [Figure 20].
Since calibration is rapid once the apparatus has been set up, it is
suggested that the needles be calibrated frequently. In cases where
greater accuracy is desired, the calibration should be conducted before
and after each use.
HEAT TRANSFER ANEMOMETERS
The movement of air can be measured by its ability to absorb
heat from a heated probe. The probe may be in the form of a wire,
thin metal film, thermistor, or thermocouple. Equation 42 below,
gives the theoretical relationship for the rate of heat loss from a
wire maintained at a fixed temperature above that of the flowing gas.
H = ke + (2TTkCvpdv)%e
H = Rate of heat loss per unit length of wire
k = Thermal conductivity of gas
6 = Number of degrees above temperature of gas
C = Specific heat at constant volume of gas
p = Density of gas
d = Diameter of wire
v = Velocity of gas
-------
71
Table 7
Flowrate (liters/min) as a
Function of Needle Gauge and Length
(Measured at 630 mm Hg. Each flow rate is the mean for 12
Becton-Dickenson (B/D) needles. Values in ( ) are the
percent relative standard deviations of flow rates.
Gauge
13
15
17
IS
10
20
21
22
23
24
2i
3'A 3
12 2(2)
8 9(1)
2.15(7)
.59(15)
2'A
o
3
2
1.67(5) 1
1
2
.59(1)
77(3)
37(5)
75(1)
.23(2)
.GS(-J)
.42(2)
.19(5)
-Needle Length,
1'A
4 1 (3)
2.43(5)
1.83(3)
1.32(3)
.80(3)
.49(4)
.29(3)
I'A
2.5S(3)
1 97(1)
1.3S(2)
.76(6)
.54(2)
.40(3)
1
4.45(2)
1 97(2)
1.47(3)
.59(3)
.54(0)
.42(5)
.26(4)
•A
.69(6)
.45(4)
31(3)
V.
.61(5)
.50(5)
31(6)
'/.
.63(5)
.51(4)
.34(9)
Reprinted from APCA Journal, Vol. IS, No. 4, April, 1968
-------
72
As can be seen from equation 42 a number of factors affect the
rate of heat loss (H) by a given probe. In addition to the tempera-
ture and diameter of the wire, the thermal conductivity, specific heat,
and density of the moving gas as well as its velocity are of importance
in removing heat. Changes in any of these factors would change to a
proportionate degree the output of the sensor.
In practice, two probes are used [Figure 22]. One does the actual
sensing while the second is partially or entirely shielded from the gas
flow and is used as a reference for the first. The electronic circuitry
of the unit controls the current to the sensors and maintains a fixed
voltage and/or current across the two probes. The output generally is a
DC voltage proportional to the heat loss which in turn is proportional
to the mass flowrate of the gas.
The advantages of heat transfer anemometers is that the output is
in actual mass flow units directly convertible to standard temperature
and pressure gas flowrates. The output is not linear but can be with
proper electronic circuitry. Accuracies of +0.5% with repeatabilities
of +0.1% are common. For well-designed and calibrated units accuracies
of +2% are obtainable with changes of as much as +30°C (+54°F) in tem-
perature and 1/3 to 3 atmospheres in pressure.
There are some disadvantages. The heated wires or probes can
react with corrosive, flammable, or reactive gases causing possible
calibration changes or explosive situations. Particulate or foreign
matter can also collect on the probes and give erratic results. Some
units have self-cleaning circuits to prevent such contamination. The
resistance-temperature coefficient of a thermistor is inverse to but
much greater than that of a heated wire; however, at lower temperatures
the coefficient changes rapidly and non-1inearly at very low pressures.
In general, the cost of heat transfer units is relatively high. The
electronic circuitry necessary for ease of calibration, linearized out-
put, output stability, etc. is relatively difficult to manufacture.
-------
73
»
Inlet screens
Measuring s«
Fcxx-elem«nt
bridge circuit
Shielded reference tenser
Figure 22.
Cross-section of a Temperature-compensated Gas Flow Anemometer
-------
BIBLIOGRAPHY
Ower, E., and Pankhurst, R.C. "The Measurement of Air Flow," Pergamon
Press, 1966.
Nelson, G.O. "Controlled Test Atmospheres," Ann Arbor Science, Ann Arbor,
Michigan, 1971.
"Fluid Meters: Their Theory and Application," Sixth Edition, ASME
Research Committee on Fluid Meters, H.S. Bean, Ed., American Society
of Mechanical Engineers, New York, 1971.
"Atmospheric Sampling," Institute for Air Pollution Training, Environ-
mental Protection Agency, Research Triangle Park, N.C. 1972.
Brenchley, D.L., Turley, C.D., and Yarmac, R.F. "Industrial Source
Sampling," Ann Arbor Science, Ann Arbor, Michigan, 1973.
Perry, R.H. and Chilton, C.H. "Chemical Engineers' Handbook," 5th Edition,
McGraw Hill, New York, 1973.
McCabe, W. L. and Smith, J.C. "Unit Operations of Chemical Engineering,"
Third Edition, McGraw Hill, New York, 1976.
"Guide to Rotameter Application," Technical Bulletin No. T-022 Revision E,
Brooks Instrument Division, Hatfield, Pa., 1977.
FIGURE CREDITS
The figures used in this document were taken wholly or in part
from the following sources. Figures 6 - 9, 16 and 20 from various
EPA documents; 2, 5, 10, 11, 19 and 22 from Nelson; 17 and 18 from
McCabe and Smith; 12 and 13 from manufacturer's literature; and 1
from A. H. Strahler "The Earth Sciences," 2nd Ed, Harper and Row,
1971.
------- |