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3098 Technical Manual Performance Optimisation
A-3
VELOCITY OF SOUND EFFECT
The velocity of sound effect on the sensor is such that:
ρρ
τ
=
i
K
c
1
3
2
−
§
©
¨
·
¹
¸
()
A1
Where:
ρ
= The line density.
ρ
i
= The indicated density assuming infinite VOS.
K
3
= The VOS coefficient, typically 4.41x10
8
τ
= The sensor periodic time, typically 515μs.
c = The velocity of sound in the gas in metres per second.
The velocity of sound in a gas can be determined as follows:
c
P
=
γ
ρ
A2
Where:
γ
= The ratio of specific heats.
P = The line pressure in bars.
ρ
= The line density.
For an ideal gas at 20°C, equation A2 can be simplified to:
c
M
= 1562
γ
A3
Where: M = The molecular weight of the gas.
Therefore, substituting into equation A1 and simplifying:
()
ρρ
γ
=
i
M
x1 6 95 10
4
−
ª
¬
«
º
¼
»
−
.
where the term
()
1 6 95 10
4
−
−
M
x
γ
. can be referred to as the velocity of sound factor, V
F
, i.e.
ρ
ρ
=
iF
V A4
It follows that the VOS factor is substantially related to the molecular weight or base density, the main additional influence
being due to unrelated differences in the specific heat ratios. From equation A1, the VOS factors (V
F
) for the calibration
gases and sample gases can be calculated and tabulated, see the example illustrated in Table A2.