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IM-P198-05 MI Issue 2 127
 =
GM
w
,
Air
P
f
Z
f
R
0
T
f

cP
= aT
K
n
n =
1n [( 
cP
)
2
/ ( 
cP
)
1
]
1n(T
K2
/ T
K1
)
a =
( 
cP
)
1
T
K1
n
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 Engineering Handbook (Third Edition, 1996).
Density
The density for real gases is calculated from the equation:
r =
GM
w
,
Air
P
f
Z
f
R
0
T
f
Where G is the specific gravity, M
w
is the molecular weight of air, p
f
is the flowing pressure, Z
is flowing compressibility, R
0
is the universal gas constant, and T is the flowing temperature.
The specific gravity, and R
0
are known and are stored in a table used by the Turbine 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
Turbine 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:
m
cP
= aT
K
n
Where a and n are found from two known viscosities at two temperatures.
n =
1n [( m
cP
)
2
/ ( m
cP
)
1
]
1n(T
K2
/ T
K1
)
and
a =
( m
cP
)
1
T
K1
n
 =
GM
w
,
Air
P
f
Z
f
R
0
T
f

cP
= aT
K
n
n =
1n [( 
cP
)
2
/ ( 
cP
)
1
]
1n(T
K2
/ T
K1
)
a =
( 
cP
)
1
T
K1
n
 =
GM
w
,
Air
P
f
Z
f
R
0
T
f

cP
= aT
K
n
n =
1n [( 
cP
)
2
/ ( 
cP
)
1
]
1n(T
K2
/ T
K1
)
a =
( 
cP
)
1
T
K1
n
 =
GM
w
,
Air
P
f
Z
f
R
0
T
f

cP
= aT
K
n
n =
1n [( 
cP
)
2
/ ( 
cP
)
1
]
1n(T
K2
/ T
K1
)
a =
( 
cP
)
1
T
K1
n
 =
GM
w
,
Air
P
f
Z
f
R
0
T
f

cP
= aT
K
n
n =
1n [( 
cP
)
2
/ ( 
cP
)
1
]
1n(T
K2
/ T
K1
)
a =
( 
cP
)
1
T
K1
n