-- Orifice Meter Mass Flow Rate Calculations for Dry Air
-- Larry Meyn, e-mail: meyn@cruzio.com

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The orifice meter equations for flange taps were derived from
ÒFluid Meters, 6th ed.Ó; H. Bean; pp. 165, 251; American Society of
Mechanical Engineers; New York; 1971.  These equation are only valid
for unchoked flow through the orifice.

Input values

D1   - Pipe diameter in inches
beta - Ratio of orifice diameter to pipe diameter, D2/D1
T1   - Inlet temperature in Rankine
P1   - Inlet pressure in psia
DP   - Pressure drop across the orifice plate in psi


Calculated Values

D2   - Orifice diameter in inches
Z1   - Compressibility factor of the incoming flow
FA   - Thermal expansion factor of the orifice plate material
VIS  - Absolute vicosity of the incoming flow (lbm/ft-sec)
RHO  - Density of the incoming flow (lbm/ft^3)
Y    - Expansion factor
C    - Discharge coefficient
RE   - Reynold number
M    - Mass flow rate (lbm/sec)

-- About the Compressibility Factor Table for Air

The compressibility factor, Z, is defined by the relation,Z =
(PV)/(RT). For an ideal gas, Z is equal to one.  However, for
temperatures and pressures far from ambient conditions, real gas
effects result in compressibility factors that differ significantly
from one.  Unfortunately,  no single equation currently exists that
accurately gives Z as a function of pressure and temperature over a
very wide range of conditions.  Reference 2 gives a table of
coefficients for an accurate equation of state for air, but the
coefficients change with temperature and the equations are in terms
of specific volume, so an iterative procedure would be required to
find Z for a specific temperature and pressure.  The most practical
solution is to use a lookup table of Z for various temperatures and
pressures.  The method used to generate this table is described here.

The tabulated data in the files Òz_air.*Ó was derived from three
sources that are listed as references 1, 2, and 3.  For pressures
from 1 atm to 300 atm and temperatures from 140 ¡K to 380 ¡K,
tabulated specific volume data from reference 1 was used to determine
values of Z.  For pressures from 1 atm to 100 atm and temperatures
from 380 ¡K to 1000 ¡K, tabulated compressibility factor data from
reference 2 was used.  Reference 2 was also used for compressibility
factor data at a pressure of 0.7 atm.  For pressures from 100 atm to
300 atm and temperatures from 380 ¡K to 1000 ¡K, figure II-III-31-2
of reference 3 was used to determine values of Z.  The figure in
reference 3 gives the compressibility factor for gases in terms of
reduced pressure and reduced temperature.  The reduced pressure for
air was calculated using a critical pressure of 37.21 atm and a
critical temperature of 132.47 ¡K.  These values are the average of
the two sets of critical constants for air given in reference 1.

The data from the three sources described above was combined into a
single table with pressure given in psia and temperature in ¡R.  The
data from references 2 and 3 was interpolated where necessary to fill
out the table.    The error in the values of Z in the lookup table is
estimated to be less than 0.5% for the worst case and in the range of
most likely use, the error should be less than 0.05%.

If measuring the mass flow rate other gases is desired in the future,
one possibility would be to create a lookup table of Z  values as a
function of reduced temperature and pressure from figure II-III-31 in
reference 3.  This table could then be used for several different
gases as long as values for the critical temperature and pressure of
the gas are provided.

References:

1	"Thermodynamic Functions of Gases: Volume 2"; F. Din; pp.
39,46-49; Butterworths; London; 1962.

2	"Tables of Thermodynamic and Transport Properties"; Hilsenrath,
Hoge, Beckett, et. al.; pp. 27-32, 74; Pergamon Press; 1960.

3	ÒFluid Meters, 6th ed.Ó; H. Bean; pp. 165, 251; American Society
of Mechanical Engineers; New York; 1971.

LEGAL NOTICE: Use of this program and the accompanying data is at
the user's own risk.
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