ABB SM2000 User Manual Supplement page 15

...2.10.1 Liquid Flow – Fig. 2.12
Math1 Math2
Math2 Math3 Math4 Math5 Math6
Equation
29.9
29.9—
29.9–a2
29.9–a2*
29.9–a2*1.01
29.9–a2*1.01+
29.9–a2*1.01+1
Math1 Math3
Math2 Math3 Math4 Math5 Math6
Equation
a1
a1/
a1/m2
V
Q = k√h
1+(t
Mass Flow Correction
Derived density
correction
Qmd =
Qc x Dd
Mass Flow
--->
Reference
Temperature, t
Actual
Temperature, t
(Input a2)
Coefficient
of expansion
--->
Linearized
volume flow
Raw measured variables
h
Square root linearization
(Sometimes implemented
in the transmitter)
Q
Temperature Compensation
–t )a
r b
Qc
Measured
Average density
density correction
correction
Qma =
Qc x Dm
Qc x Da
Qm
Fig. 2.12 Temperature and Density Compensation
Mass Flow Calculation – Average density correction
The average density over a given temperature range is usd to
calculate the mass flow as follows:
Qma = Qc x Da,
where Qc is the temperature compensated flow and Da
r
(a constant) is the average density.
This is implemented as follows:
a1xDa
m3 =
m2
where a1 and m2 are the linearized flow and temperature
b
compensation from the previous example:
Math1 Math2 Math3 Math3
Equation
a1
a1*
a1*1.99
a1*1.99/
a1*1.99/m2
Where
V
h
Q
Qc
Qm
*
K
t
r
t
b
a
Da
Qmm =
Dd
Dm
2 MATH CONFIGURATION...
Math4 Math5 Math6 --->
= Linear volume flow
= Differential pressure head
= Uncorrected volume flow
= Corrected volume flow
= Mass flow
= Scaling constant
= Reference temperature
= Base or actual temperature
= Coefficient of expansion for a given
liquid (a constant).
= Average density over operating
temperature range
= Density derived from preset
temperature vs density curve
= Density meter input
Linearized
volume flow
Average
Density
Constant
Temperature
Compensation
13