EPA-AA-TEB-87-01
USE OF HEATED CRITICAL FLOW VENTURI SAMPLE PROBES
          TO MAINTAIN  PROPORTIONAL FLOW
                       by


               Walter Andrew Adams
                  February 1987
           Test  and Evaluation  Branch
      Emission Control  Technology Division
            Office of Mobile  Sources
      U.S. Environmental  Protection Agency

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                            Abstract
     The   Notice    of    Proposed   Rule-Making    (NPRM)    for
raethanol-fueled vehicles proposes using sample  probes  heated to
235°F when sampling  for  methanol  or  formaldehyde.   When using a
critical  flow  venturi   constant  volume  sampler  (CFV-CVS)   to
measure exhaust flow, critical  flow  venturi  (CFV)  sample probes
must  be  used  to  obtain  a  constantly  proportional  exhaust
sample. The gas temperature  at  the sample CFV  must  be the same
as that of the bulk stream for the sample flow  to  be constantly
proportional  (when  a  heat  exchanger  is  not  used to  control
dilute exhaust temperature).   Tests conducted with  a sample  CFV
heated  to  235°F indicated that  the  gas  temperature  at  the  CFV
was not the same  as  the bulk steam temperature.  This caused a
measurable  (approx.  3%) change  in  flow  through the  CFV.   The
conclusion is  that a heated  CFV may  not be  able  to maintain
constantly proportional  flow if  the  temperature of  the dilute
exhaust stream  varies.   There are viable  alternatives  to  this
approach,   such  as  using  a  heat  exchanger  in  the  CVS  or
insulating the venturi from the heated sample line.

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                            Foreword
     The   Notice    of    Proposed   Rule-Making    (NPRM)    for
methanol-fueled vehicles (ref. 1) requires:

     1.  Proportional  sampling  of dilute  exhaust  for  methanol
and formaldehyde,  and

     2.  Using  heated  probes  (235 +_  15 F)  when  sampling  for
these  two  pollutants.   If  a critical  flow  venturi  constant
volume  sampler  (CFV-CVS)   is  used,  the NPRM suggests  simply
heating standard CFV sample probes.

     In CFV-CVS  units  which  do  not  use  a  heat  exchanger  to
control dilute  exhaust  temperature  (as is  the  case  with  most
light-duty CVS units),  critical  flow  venturi  sample  probes  are
used  to  obtain a  constantly proportional  exhaust  sample.   If
applying heat to the venturi causes a change  in the temperature
of  the gas  flowing  through  it,  the flow  through  the  venturi
will no longer  be  constantly proportional  to that of  the  bulk
stream,  as  is  required  by  the  NPRM.   Testing  was  needed  to
determine  if  a  CFV could  be  heated  without  affecting  the
temperature  of  the  gas  flowing  through it.   This  report  gives
the  results   of  the testing,  documents  the  difference,   and
recommends ways to  obtain  a  heated,  constantly  proportional
exhaust sample.
                             Summary


     The  test  results  indicate  that  heating  a  critical  flow
venturi  (CFV)   does  change  the   flow  characteristics  of  the
venturi (other than  those  due to  thermal expansion).   The  data
obtained  indicate  that  a sample CFV cannot  be  used to maintain
constantly  proportional   flow  if   it   is   heated   (without
temperature  control  of   the  bulk   stream),   and  that  other
alternatives will  have  to be  explored  if we wish  to  heat  the
probes used for methanol and formaldehyde sampling.

     The most  viable alternatives  are:

     1.   Using  a  heat  exchanger  in  the  CVS.   This  would
eliminate the  need for CFV's in the sample lines.

     2.  Not heating the critical flow venturi  and  insulating
it from the heated  sample  line.   Sample losses  should not occur
at the venturi  due to the high gas  velocity.

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I.     Introduction and Theory

       Exhaust    from    methanol-fueled    vehicles    contains
significant amounts  of  methanol and  formaldehyde.   EPA  wishes
to  regulate  emissions  of  these  two  pollutants  for  vehicles
running on blends of 50% or more methanol.  Current  exhaust  gas
sampling  systems used  for testing  gasoline  vehicles are  not
equipped to measure methanol or formaldehyde.

       The NPRM published in August 1986  outlines  equipment  and
procedures required  for methanol and  formaldehyde  sampling.   In
each case,  one  of  the  requirements   is  that   sample  collection
lines  and  probes  (including  venturies)  be  heated to  235°F  in
order to avoid losses in the collection equipment (reference 1).

       The  theory   of   operation   of  critical   flow  venturi
constant  volume  samplers  (CFV-CVS)   requires   that   the  gas
temperature at  the  inlet to  all  venturies be  the  same  unless
the temperature  of  the  dilute  exhaust stream is controlled (see
Appendix  C   for  theory  of   operation   of   constant   volume
samplers).  The  question this  report  addresses is:   "Will  the
gas  temperature  at  the  orifice of  the  sample  venturi  be  the
same as  at the  bulk stream  venturi   if  the  sample venturi  is
heated?"  If it is not,  the sample  obtained will no  longer be a
constantly proportional sample, which  the NPRM requires.


II.    Apparatus and Procedure

       It  is   very   difficult   to  accurately  measure  the  gas
temperature at   a  critical flow  orifice  without  altering  the
flow conditions.  It  is  much  easier  to simply measure  the flow
through  the orifice when heated and unheated.   A  change  in gas
temperature through the orifice can be seen as a change in flow.

       The apparatus used  for  testing  the probe in  an unheated
condition is  shown  in Figure  1.   A 20 CFH  smooth  approach CFV
was attached to  the inlet of  a Metal   Bellows  Pump  Model  MB-158
(standard equipment  used  for  drawing  bag  samples at MVEL) .  The
pump outlet  was  connected  to a  laboratory  wet  test  meter.
Instrument connections were made using 1/4"  316 stainless steel
tubing  and Swagelok fittings.

       The  apparatus used  for testing  the   heated  probe  was
identical except  for the addition of  a  95VAC  heat  tape  and an
Athena   temperature  controller  set   at   235°F.    A  type  "J"
thermocouple was  attached to  the outside  surface  of the  probe,
with the heat  tape wrapped  over  it,  to  supply   the  feedback
signal  to  the  controller.  Other  temperature  measurements were
made using a fine tip "J" thermocouple and digital readout.

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                                   Digittl B*rom«Ur
                  ViJidyu
              Prwrun Trwuductr
           20CFH
         Critical Flow
   MB-158
  2.3 SCFM
Cipwity Pump
                                                       Vtt T«t
                                                        Mtt«r
                         FIGURE 1.  Unheated Test Configuratioi
    LA5T 2 mCKIS OJ
    VTHTUII VEAJJZD
    wrnt 95 VAC
    HZAT TAJZ
szz
    A.TKZHA. PBOIOBTBOHAJ.
        TZMIZBA.TUIZ
        COHTBOIIZB
                                                                                to
                                                                        AtmospLtrt
                                                                   ZZZDBA.CK
                                                                   TKZBMOCOUTLZ
                                                            KZAT TA1Z (NOT SKOWK)
                                                            WBAJPZD OVZB LAST
                                                            TWO IHCHZS OZ PBOBZ
                                                   riNZ-TII J T/C
                                                   FOB BZADIKO
                                                   VTNTUBI ZA.CZ
                                                   TEMPZBA.TUBZ
                                            U JT/C
                                       ZOB BZADIKC
                                       IBOBZ SUB7ACZ
                                       TZMIZBATUBZ
                        FIGURE 2. Hea^d Test Configuration

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       The  sample  pump  was  started  approximately  20  minutes
before  any  data  was  collected  and  allowed  to   run  for  the
duration   of  the   experiment   (approximately   75   minutes).
Experimental  runs  were  performed by  simultaneously taking  an
initial  wet  test meter  reading  and  starting  the  stop  watch,
followed by stopping the watch and taking a final  reading.

       There are three main  differences  between the test set-up
and the way a sample would really be collected in  a  CVS:

       1.  The temperature  of the bulk  steam would be  20-30°F
higher  than  ambient temperature  and would  fluctuate  (in  this
experiment the  ambient  air  from  which  the sample  is  drawn  is
analogous to the bulk stream),

       2.  The  bulk  steam  would  be  moving  very  fast,  rather
than not at all as in the test set-up,

       3.  The  sampling  systems  to  be  heated will  have  flow
rates  on  the order of  2  to  10  CFH,  not 20 CFH as  in  the test
set-up.

       These  differences  are  unimportant  for  the  purpose  of
this test,  which  was to determine if heating  the  probe  changed
the gas temperature at  the probe  inlet.   The  apparatus  used was
sufficient for this purpose.
Ill.    Presentation and Discussion of Results

       A seguence of  nine  tests  were run as follows:   tests  1,
2, and 3 were  conducted with an unheated probe; tests  4,  5 and
6 followed immediately using a heated probe; finally,  runs  7,  8
and  9  were  made  with  an  unheated  probe  as   a  check  for  any
unforeseen changes in the equipment or surroundings.

       The  results  for  all  runs  are   contained   in  Table  1.
There  appears  to  be  a  significant  difference   in  flow  for
unheated and  heated  configurations.  The  results  from  Table  2
confirm this;  there  is a difference  in  flow of  about  3 percent
between  heated and  unheated  runs,   while  the  coefficient  of
variance is on the order of 0.1 percent.

       Could  the  difference  in  flow be due to  anything  other
than a change  in  gas  temperature?   The only other  effect  that
could cause  a  change  in flow is  thermal expansion  of  the  probe
during heating.  Calculations contained  in  Appendix B  show that
the  inside  radius of  a cylinder  increases as  the temperature
increases for  materials with positive  coefficients of  thermal

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expansion.   This would  cause  the  area  available  for  flow  to
increase  and,  therefore,  the  flow would tend  to  increase  as
well.  Since the  flow  decreased when  the orifice was heated,  it
must be concluded that the change in flow was  not  the  result  of
thermal expansion of the probe.

       A  further  check  on the  consistency  of  the  data  is  to
calculate  the  temperature  of  the  gas  flowing  through  the
venturi  during  heated  runs.    This  calculation  is  shown  in
appendix B;  the  gas temperature was  about  103°F for  runs 4-6.
This correlates very well  with the observed face temperature of
the probe which was about 105°F (data  in App.  A).


Table 1.   Flow through CFV in Heated and Unheated Configurations
       RUN

        1
        2
        3
        4
        5
        6
        7
        8
        9
                   PROBE
                  HEATED?

                    NO
                    NO
                    NO
                    YES
                    YES
                    YES
                    NO
                    NO
                    NO
                               FLOW
                              (SCFH)

                               18.255
                               18.188
                               18.215
                               17.625
                               17.664
                               17.629
                               18.124
                               18.130
                               18.145
         Table  2.   Statistical  Analysis  of  CFV Flow Data
RUNS

1-3
4-6
7-9
HEATED?

  NO
  YES
  NO
 MEAN
 FLOW
(SCFH)

 18.219
 17.639
 18.133
SDEV

0.027
0.017
0.009
                                  C.O.V,
                                    o, '
0.150
0.099
0.048
         % CHANGE
           FROM
           RUNS 1-3
-3.18
          % CHANGE
           FROM
           RUNS 6-9
-2.72
     In concluding  this discussion,  I  feel I  should  address  a
question posed  by several engineers  when  told of this problem,
which is:   "How  can  a gas moving at  sonic  velocity (1000 ft/s)
have  time  to  heat  up  as  it  moves   through  the  venturi?"

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It did  not  seem to  make intuitive sense at  the  time,  although
it  does if  we  think of  this  as a  classical  heat  transfer
problem.  The pertinent heat transfer  equation here is:

     q/A= h(twai 1 - tgas)

where q is  the rate  of  heat transfer  (BTU/hr),  A is  the  heat
transfer  area  (ft2),   and   h   is  the  local   heat   transfer
coefficient   (BTU/hr-ft2-F) .    h   is   a   function  of   fluid
properties  only;  a  typical  correlation for  predicting  h  is
Dittus-Boelter (see reference 4), which is:

                  Nu = .023 Re' 8Pr "4

                  Nu = hd.  Re = pvd, Pr = joCp
                       k         y         k

                  then h= .023 /vd\ 8 /CP\ "4 k
                                               d
where
                                       /
                                       \

                       h=.023(pv) • 8 /CP\ -4
     Re = Reynolds number, dimensionless
     Nu = Nusselt  number, dimensionless
     Pr = Prandtl  number, dimensionless
     h  = heat transfer coefficient,    BTU
                                     hr-ftz-°F
     d  = diameter, ft
     k  = thermal conductivity,   BTU
                               ft-hr-°F
     p  = density, Ib
                   ft3
     v = velocity, ft
                •   hr
     jj = viscosity,  Ib
                    ft-hr
     Cp = heat capacity, BTU
                        lb-°F
     This correlation  says that  the heat  transfer  coefficient
is proportional to velocity to the 0.8 power.  In other  words,
h  is  almost  directly  proportional  to  the gas velocity,  which
reaches a maximum at the venturi.   It is not surprising  at  all
that  the  gas  temperature  changes significantly  before  it  can
move through the venturi because of this effect.

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Recommendations

     There appear to be  three  ways  to circumvent  the problem of
sampling proportionally without using a heated CFV.

     1.  Use  a  Heat   Exchanger  in  the  CVS  -  Using   a   heat
exchanger to  hold  the  temperature of  the dilute  exhaust  stream
constant eliminates the need for CFV  sample  probes,  so  sampling
can  be done  at a  constant  flow  rate  using  a  heated  static
probe.   Appendix C gives  the  physical relationships  that  prove
the validity of this  method.

     2.  Do not  heat  the CFV  -  Heat the sample  line up  to the
dilution tunnel, but  don't heat the  CFV  sample  probe.   Sampling
losses   should  not  occur  within the  probe  because  of  the  high
gas  velocity,   and  also  because  the  temperature   within  the
dilution   tunnel   is   high   enough  to   ensure   that   water
condensation will  not  occur within  the  probe.    (Absorbtion  by
condensed water  is thought  to be  the main source  of  methanol
sampling losses.  Formaldehyde  losses  are  thought to occur due
to both absorption by  condensed  water as well as  polymerization
in the  presence of  liquid water.)

     3.  Use feedback control  - By putting  a  flow controller in
the  sample  line which gets  its set  point  from the  CVS  flow
computer,  proportional  flow can be  maintained as  long as the
response  time  of  the   controller  is  very   fast.   This  method
requires some modification  of  existing equipment, as well  as  a
mass flow  controller  or equivalent  flow control  device for the
sampling system.  It is  also  not  a true proportional method in
the strictest  sense,  since there will always be some  lag time
between a  change of  flow  through  the bulk  stream   venturi and
the  controller's  response  to  that  change.   However,  for  a
controller with relatively  fast  response (95% of  full  scale in
one  second  or  less  is  typical for  a  good  quality mass  flow
controller),  the lag  time should be negligible.

     Of the three  alternatives listed  above,  the first  one is
the most technically sound; it would also meet all  requirements
in  the  NPRM  as  it   is  now  written.    The  only  unresolved
technical question is  whether or  not a heat  exchanger affects
methanol and  formaldehyde  emissions.    It  is  unlikely that  a
heat   exchanger  would  have   an   effect  unless   there   were
condensation  occurring  within   the  heat   exchanger   due  to
inadequate dilution of  the raw exhaust.

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                          10
                      References
NPRM-Methanol Fueled Vehicles, ECTD, QMS, Summer 1986,
     Sec. 86.109-88.  Published in Federal Register,
     August 29, 1986, Vol. 51, No. 168.

Paulina, Carl. "Non-Proportional Sample Rates in a
     Critical Flow Venturi Constant Volume Sampler." EPA,
     QMS, EOD, TPB, January, 1982.

Perry, Robert H.  Perry's Chemical Engineers' Handbook.
     New York: McGraw-Hill, 1984, p.5-14

Bennett, Carroll  O., and Myers, John E., Momentum, Heat,
     and Mass Transfer.  New York: McGraw-Hill, 1982,
     p.384.

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                               11
       Appendix A.   Raw Data  Inputs  and Calculated Outputs
     PROBE
RUN  HEATED?
1
2
3
4
5
6
7
8
9
NO
NO
NO
YES
YES
YES
NO
NO
NO
     VI
   (CU FT)
   V2
 (CU FT)
16
18
19
32
33
35
38
39
40
.500
.000
.400
.300
.800
.500
.100
.300
.800
17
19
20
33
35
39
39
40
41
.500
.300
.900
.600
.400
.200
.200
.700
.800
189
247
285
255
313
216
210
267
191
.86
.72
.42
.64
.94
.26
.35
.64
.01
        WET TEST
        METER TEMP
        (PEG F)

          73
          73
          73
          73
          73
          73
          73
          73
          73
            VENTURI
            FACE TEMP
            (PEG F)

             73
             73
             73
            105
            105
            105
             73
             73
             73
 PROBE
SURFACE
(PEG F)

   73
   73
   73
  182
  182
  182
   73
   73
   73
DELTA P
(IN H20)
  0
  0
  0
  0
  0
  0,
  0
  0
  0.1
  PI
(IN HG)
ABSOLUTE

 29.078
 29.078
 29.078
 29.078
 29.078
 29.078
 29.078
 29.078
 29.078
  P2
(IN HG)
GAUGE

-13.0
-13.0
-13.0
-13.0
-13.0
-13.0
-13.0
-13.0
-13.0
 P2/P1*
ABS PRESS
  RATIO

  0.553
  0.553
  0.553
  0.553
  0.553
  0.553
  0.553
  0.553
  0.553
FLOW
(SCFH)
18
18
18
17
17
17
18
18
255
188
215
625
664
629
124
130
18.145
*According  to  fluid mechanics  textbooks,  the critical pressure
ratio,  PC,  required  for  sonic  flow of  air  is  0.528 or  less
(ref.  3).   However,  this  is  really the ratio  required  for  an
orifice; the ratio  can  be  much hiqher for  a  venturi,  depending
on the  venturi design.   For the  sample  venturies  used at MVEL,
PC is about 0.6 ,  a number arrived  at  by experimentation  with a
margin  of  safety  included  (see reference 2).  A PC of 0.553 is
well below  the ratio  required  to  maintain sonic  flow for this
type of venturi.

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                               12


                    Appendix B. Calculations

     1.  Thermal Expansion of Heated Probe

     Calculation of  the change  in size  of  the  sampling  probe
orifice  due  to  thermal  expansion would   require  a  detailed
equation  based on  probe  geometry, material,  and  temperature
change.   Unfortunately,  equations  available  for  calculating
thermal expansion of solids are limited  to  the  linear  case.   In
order  to  more  accurately  predict  the  effect of  heating  under
the conditions  of  the  test,  a  simplified  model  was  developed
which  attempted to take  into account  the  cylindrical geometry
of  the orifice.  The  derivation  is  long  and  arduous, and it
goes beyond the scope  of this report to present it here.  There
were two important results that pertain to the problem at hand:

     a. The formula  for calculating the  change  in  radius  of a
cylinder is:

     r2 = r,(BAt + 1)

where    rt = old radius
         r2 = new radius after heating
         0  = thermal expansion coefficient
         At = temperature change

     This is the same  equation one would arrive  at  by assuming
that the radius expands linearly with temperature.

     b.  If  At and  B  are  both  positive,  r2  will  always be
greater  than   r(.   The  orifice   size  will  always  increase as
temperature  increases.   This  means that  the  decrease  in   flow
seen when  the  probe  was  heated  could  not  have  been due to
thermal effects, since  the  orifice had to increase in size  upon
heating.

     What  was   the  maximum  change  in  orifice   size  for   this
experiment?  Since

     Atmax = 235 - 73 = 162 deg F
     B     = 9.6E-6 deg F"'
     ri    = .016  inches

     r2    = .016((9.6E-6)(162) + 1)
     r2    = .0160248 inches

     The maximum % change in area available for flow would be

     %AAF = (irr| - -rrr2 )/(irr2)
     %AAF = (.01602482  - .0162)/.0162

     %AAF = .3113%

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                               13
     2.   Calculation of  Gas  Temperature at  Venturi for  Heated
Runs

         For  a  CFV  at  a  given  upstream  pressure  and  gas
composition, the mass flow rate through the venturi will be

     m = K

     Where n = mass  flow rate,  Ib/hr

           K =  proportionality constant based on gas
                temperature and venturi design,

           T = absolute gas temperature
     Subscripts:   1 = unheated
                  2 = heated

     (1)  mi  = K           (2)  mz  = K
     Dividing eqn.  (1)  by eqn.  (2),

mt = K
mz  Jf
         JT1
             *  1   =fTl
           \    K    JT,

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                          14
Since

m = Qp

where Q = volumetric flow rate, SCFH
      p = density of air at standard conditions

substituting for m in the previous equation yields
Q2p
fli =
Qz  JT,

Qi = 18.133 SCFH (runs 7-9)
Q2 = 17.639 SCFH (runs 4-6)
T! = 73°F = 533°R
T2 =?
18.133 =  T
17.639  >J533

T2 = 563.3°R

T2 = 103.3°F

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                                   15
                    Appendix C.  Theory of Operation
                       of Constant Volume Samplers
         Constant volume  samplers (CVS)  use one  of  two methods  to
    measure  dilute  exhaust  flow  and   obtain   sample  at  a  rate
    proportional to the dilute exhaust  flow.   These two  methods are
    described below:

         1.   Critical Flow Venturi.   A sketch of  a CFV-CVS is shown
    in  Figure  3.    As  the  raw  exhaust   flow   rate  varies,   the
    temperature and pressure of the dilute exhaust stream changes.
                                                                 VMK
                DILUTION
                  AIR

                   1
RAV EXHAUST
DILUTE EXHAUST
Ts-J
                                           BAG SAMPLE
             Fif ore 3. Critical Flov Yenturi Constant Volume Sampler

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                               16
The  equation  for  flow  of an  ideal
orifice is (see references 2 and 3):
                                       gas  at  a  critical  flow
     Q = CA
           \
gck RT
                           \k-
t. +/k-i\B2]
  \—)  J
P-'
V t 1
\ J\. J.
where    Q  =  Volumetric flow rate (ftVsec)
         C  =  Coefficient of discharge (dimensionless)
         A  =  Cross-sectional area of orifice (ft2)
         gc =  gravitational constant (32.2 ft/S2)
         k  =  ratio of specific heats (dimensionless)
         R  =  ideal gas constant (1545 ft-lbf/°R-mol)
         M  =  Molecular weight of gas (Ib/lb-mol)
         T  =  Absolute gas temperature (°R)
         B  =  ratio of orifice diameter to pipe diameter
                 (dimensionless)

     For  values  of  B  less  than  0.2  (the  usual  case),  the
bracketed  term  on the  right  is  approximately equal  to  unity.
For a  given orifice  and  pipe size. A, B,  and C are constants.
For a given gas, k and M are constants.

     The only  variable left  in the  equation is  T;  therefore,
for a  given gas  and  orifice  (or venturi),  this equation takes
the form
             Q =
     where  K  is  a  dimensional
and venturi properties.
                                 constant  that  incorporates  gas
     For the  venturies in the  CFV-CVS,  the flows  through each
would be
             Qb = K

             and Qs = KsNJT?

     where  the subscripts  (b
sample streams, respectively.

         Dividing, we get
                                and s)  refer  to the  bulk  and
             Q
                = Kb
                  KS
then
     If the  venturies  are  located  near  each  other,  Tb  = T.
                = 1

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                                         17
               and Qb = Kb = a constant
                   Q,   Ks

               Since  the  ratio  Qb/Qs  is  a  constant,  the  flows  through
           the  sample  and  bulk   stream   venturies   will   be  constantly
           proportional to  one another as  long as  the gas  temperatures at
           each venturi are equal.

               Notice  that if  the temperatures  of  the bulk and  sample
           streams  remain  constant,  it  is no  longer necessary that  the
           temperatures of the two  streams  be  equal.   The flow will remain
           constantly  proportional  because all  terms on  the right  hand
           side of the equation will be constant.

               2.  Positive Displacement Pump.   A sketch  of  a PDP-CVS is
           shown  in  Figure  4.   Dilute  exhaust  passes  through  a  heat
           exchanger  and  reaches  a constant  temperature  before  entering
           the  PDP.   The  unit   is  designed  to  maintain  a  relatively
           constant  pressure  at  the  pump inlet.   Since  T  and  P  are
           constant,  sampling of  the dilute  exhaust can be done with  a
           static probe at a constant flow  rate.
                DILUTION
                  AIR

                   I
                                                                        VMK
RAV EXHAUST
                     WATTS W  (r) (p)
                     —M-I-
DILUTE EXHAUST
                                        WATER OUT
                                                                 PDP
                                                   BAG SAMPLE
              Figure 4. Positive Displacement Pump Constant Volume Sampler

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