Sierra INNOVA-MASS 241-VTP - Manual (Page 75)

Appendix C Fluid Calculations Series 24-HP Instruction Manual
C-2 IM-24-HP
Calculations for Gas (“Real Gas” and “Other Gas”)
Use this formula to determine the settings for “Real Gas; Gas” selections
and “Other Gas” selections entered in the Fluid Menu. The calculations
for gas were taken from Richard W. Miller, Flow Measurement Engi-
neering Handbook (Second Edition, 1989).
Density
The density for real gases is calculated from the equation:
f f
f Air w
T R Z
p GM
0
, = ρ
Where G is the specific gravity, Mw is the molecular weight of
air, pf is the flowing pressure, Z is flowing compressibility, Ro is
the universal gas constant, and T is the flowing temperature.
The specific gravity, and Ro are known and are stored in a table used by
the Vortex meter.
The hard coefficient to find is the compressibility, Z. Z is found using the
Redlich-Kwong Equation (Miller page 2-18).
The Redlich-Kwong Equation uses the reduced temperature and pressure
to calculate the compressibility factor. The equations are non linear and
an iterative solution is used. The Vortex program uses Newton’s Method
on the Redlich-Kwong equations to iteratively find the compressibility
factor. The critical temperature and pressure used in the Redlich-Kwong
equation are stored in the fluid data table with the other coefficients.
Viscosity
The viscosity for real gases is calculated using the exponential equation
for two known viscosities. The equation is:
n
K cP
aT
= μ
Where a and n are found from two known viscosities at
two temperatures.
) / ln(
] ) /( ) ln[(
1 2
1 2
K K
cP cP
T T
n
μ μ
=
and
n
K
cP
T
a
1
1
) (
μ
=