Videographic Recorders
SM1000 and SM2000
2 Math Configuration
16
IM/SM2000ADV
Issue 7
Mass Flow Calculation – Average density correction
The average density over a given temperature range is used to
calculate the mass flow as follows:
Qma = Qc x Da,
where Qc is the temperature compensated flow and Da (a
constant) is the average density.
This is implemented as follows:
where a1 and m2 are the linearized flow and temperature
compensation from the previous example:
Reference Temperature, t
r
Actual Temperature, t
b
(Input a2)
Coefficient of Expansion
Linearized Volume Flow
m3
a1
Da
×
m2
-------------------
=
Linearized Volume Flow
Average Density Constant
Temperature Compensation
Fig. 2.12 Temperature and Density Compensation
h
V
Q
1+(t
r
t
b
)a
Qma =
Qc x Da
Qmm =
Qc x Dm
Qmd =
Qc x Dd
Qc
Derived density
correction
Where
V
= Linear volume flow
h
= Differential pressure head
Q
= Uncorrected volume flow
Qc
= Corrected volume flow
Qm
*
= Mass flow
K
= Scaling constant
t
r
= Reference temperature
t
b
= Base or actual temperature
a
= Coefficient of expansion for a given
liquid (a constant).
Da
= Average density over operating
temperature range
Dd
=
Density derived from preset
temperature vs density curve
Dm
= Density meter input
Q = kÖh
Raw measured variables
Square root linearization
(Sometimes implemented
in the transmitter)
Temperature Compensation
Mass Flow Correction
Average density
correction
Measured
density correction
Qm
Mass Flow
