Treadmill User Manual

7ML19985GE01 SITRANS LC 500 – INSTRUCTION MANUAL Page 91
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Appendix E
Applications Examples
Generic Application Calculations
The capacitance expected in a cylindrical tank with a probe centrally mounted is
estimated using the following formula:
(L in meters) or (L in feet)
Examples (using dimensions above):
Capacitance in air:
Dimensions in meters:
Dimensions in feet:
Capacitance in oil:
If the same vessel is filled with oil, relative dielectric constant for oil (2) replaces the
relative dielectric constant for air (1), and the resulting calculation is:
(dimensions in meters)
or
(dimensions in feet)
The initial capacitance value at 0% (probe in air) is 12.7 pF, and the capacitance value for
100% (tank filled with oil) is 25.4 pF.
C ε
24 L×
Log D d⁄()
--------------------------
pF=
SITRANS LC 500
0.25 m (0.82’)
L = 0.95 m
(3.12’)
D = 1.0 m
(3.28’)
d = 16 mm
(0.05’)
Where:
C = capacitance value in pF
ε
r
= relative dielectric constant
L = active measurement length
D = internal tank diameter
d = electrode diameter
24 = a K constant for dimensions in meters
7.32= a K constant for dimensions in feet or inches
ε
r
= 1 (air)
ε
r
= 2 (oil)
C ε
7.32 L×
Log D d⁄()
--------------------------
pF=
C
air
ε
air
24 0.95×
Log 1 0.016⁄()
-----------------------------------
pF 12.7pF==
C
air
ε
air
7.32 0.82×
Log 10.06⁄()
--------------------------------
pF 12.7pF==
C
oil
ε
oil
24 0.95×
Log 1 0.016⁄()
-----------------------------------
pF 25.4pF==
C
o
il
ε
oil
7.32 3.12×
Log 3.28 0.05⁄()
----------------------------------------
pF 25.4pF==