Appendix F Calculations and theory
Page F.4
Equation F.1#3b
: V.O.S. of the measured gas (pure of composition) for S.G. method
Using:
()
¸
¸
¹
·
¨
¨
©
§
+−
=
C
G
G
G
C
K
C
CK
C
*
1
*
1
1
τ
τ
Where:
G
C = V.O.S. of the measured gas (in m/s)
C
C = V.O.S. of the calibration gas (in m/s)……………………..……..{See Equation F.1#2}
τ
= Periodic time of density transducer output signal (in μs)
K = Density transducer VOS constant
= 2.10 * 10
4
for a 7812 Gas density transducer
= (1.35 * 10
4
for a 7810 Gas density transducer)
= (2.62 * 10
4
for a 7811 Gas density transducer)
And:
1G
C =
()
»
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»
¼
º
«
«
«
¬
ª
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¸
¸
¹
·
¨
¨
¨
©
§
»
¼
º
«
¬
ª
+
−
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¼
º
«
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¹
·
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+
+
gc
t
SGSG
K
K
273*293*
*1
004
3
λλρ
Where: t = Calibration temperature
SG = Specific gravity
[ ]
c
= For calibration gas
[ ]
g
= For measured gas
0
γ
= Low pressure ratio of specific heats (or ‘Gamma’)……………… (See notes below)
And:
3
K and
4
K are constants that must be SET into the 795x……….………(See notes below)
Notes:
• K
3
and K
4
are normally taken from the calibration certificate that was issued with the gas density transducer.
Alternatively, the following table has typical values that can be used.
• ‘Ideal’ values for Specific Gravity can be taken from Table F.2. In practice, the live Specific Gravity
measurements may be more appropriate.
• For a measured
pure gas, a value for
0
γ can be taken from Table F.2.
• For a measured
composition of gas, a value for
0
γ can be taken from Table F.2 but needs to modified in
proportion to the volumetric fraction (percentage) of each gas component.
Table F.3: K3 and K4 Values
Gas Composition Density K
3
K
4
Nitrogen-Methane 10 to 60 kg/m
3
830.222 59.006
Nitrogen-Methane 60 to 200 kg/m
3
1389.4 205.455
Argon-Methane 60 to 200 kg/m
3
2186.01 310.079