244LVP Intelligent Buoyancy Transmitter for ... - Foxboro Eckardt

26 244LVP MI EML1710 A-(en)
11 DIMENSIONING OF DISPLACER
CALCULATING WEIGHT FORCES (also see VDI/VDE-Guideline 3519, sheet 1)
Displacer length = measuring range
Measurement type
Liquid level
( � = negligible )
2
Interface
( � = not negligible)
2
Density
( � = min. density,
2
� = max. density )
1
Measurement type
Liquid level
( � = negligible )
2
Interface
= not negligible)
( � 2
1)
1)
Lower range value
= 0 % output signal
F = F
0 G
F =
0
F G -V · ·
g
Displacer length > measuring range
(without elevation)
Measurement type
Interface
= not negligible)
( � 2
Lower range value
= 0 % output ssignal
F = F
0 G
F = F -V
0 G
Displacer length > measuring range
(with elevation)
· ·
g
Lower range value
= 0 % output signal
�
2
�
2
Liquid level
h
1)
( � = negligible) ·
� 0
F = F -V
0 G · g 1
2 L
F 0
h 0
L-h 0
= F -V
G · g ( � + � )
1
L 2 L
FG [ N ] Weight force of displacer in atmosphere
F0 [ N ] Weight force action on suspension point of
displacer at lower range value
F100 [ N ] Weight force action on suspension point
of displacer at upper range value
FA [ N ] Buoyancy force of displacer (FA =F0 -F100)
V [ m³ ] Displacer volume (specified on data label in
cm³!)
Attention: 1 kg generates a force of 9.807 N
Weight forces
Upper range value
= 100 % output signal
F = F -V · g ·
100 G
Weight forces
Upper range value
= 100 % output signal
F 100 = F G -V · g ·
F
100 = F -V
G · g (
h
� b
+
1
L
Weight forces
Upper range value
= 100 % output signal
F 100
F =
100
= F G -V · g
� 1
�
1
· �
1
h b
L
h + h
0 b
L
�
2
L-h b
h + h L-h -h
( � 0 b
b 0
F -V · g
+ �
)
G 1
2
L
L
L
)
L=h b
L
h
b
0%
0%
0%
� 2
� 1
�
2
�
1
�
2
�
1
ρ1 [ kg/m³ ] Liquid density
ρ2 [ kg/m³ ] Density of gas or lighter liquid
g [ m/s² ] Local acceleration due to gravity
( e.g. 9.807 m/s²)
L [ m ] Displacer length
h0 [ m ] Lower range value
hb [ m ] Measuring span
1) ρ2 is negligible if ρ2 = gas at atmospheric pressure
or with ratio ρ2 : ρ1 less than 0.5 %.
L
h
h 0
b
100 %
L=h b
L
h
b
100 %
100 %
L
h
h 0
b
� 2
� 1
�
2
�
1
�
2
�
1