Appendix A
Series 810 Instruction Manual
Number of Atoms in the Gas Molecule
N
Monatomic
1.040
Diatomic
1.000
Triatomic
0.941
Polyatomic
0.880
The mass flow rate, m, can also be written as:
m =
P
Q
( 3 )
Where:
P
= The gas mass density at standard conditions (g/l);
P
is given
in the tables (at 0°C, 760 mm Hg).
Furthermore, the temperature difference,
A
T, is proportional to the
output voltage, E, of the mass flow meter, or
A
T = aE
(4)
where:
a = A constant.
If we combine equations (3) and (4), insert them into equation (2),
and solve for Q, we get
Q = (bN/
P
C
r
)
(5)
where:
b = H/aE = a constant if the output voltage is constant.
For our purposes, we want the ratio of the flow rate, Q
1
, for an
actual gas to the flow rate of a reference gas, Q
2
, which will produce
the same output voltage in a particular mass flow meter or controller.
We get this by combining equations (1) and (5):
Q
1
/Q
2
= K
1
/K
2
= (N
1
/
P
1
C
p1
)/(N
2
/
P
2
C
P2
)
(6)
Please note that the constant b cancels out. Equation (6) is the fundamental
relationship used in the accompanying tables. For convenience, the tables give
“relative” K-factors, which are the ratios K
1
/K
2
, instead of the K-factors
themselves. In the tables, the relative K-factor is
K
actual
/KN
2
where the
reference gas is the commonly used gas, nitrogen (N
2
).
The remaining
columns give Cp and
P
, enabling you to calculate
K
1
/K
2
directly
using Equation
(6). In some instances,
K
1
/K
2
from the tables may be different
from that which
you calculate directly. The value from the tables is preferred
because in
many cases it was obtained by experiment. Sierra calibrates every
transducer
with primary standards using the actual gas or a molecular equivalent
reference gas. The calibration certificate accompanying the transducer cites the
reference gas used.
A-2
IM-81
