ABB LMT Series Operating Instruction page 41

L M T 1 0 0 A N D L M T 2 0 0 | M A G N E TO S T R I C T I V E L E V E L T R A N S M I T T E R S | F F O I/ L M T 1 0 0/ 2 0 0/ F F - E N R E V. A
Figure 30 Tank Volume Calculation
When volume is a linear function of the level, the Level can be
isolated as result of a factorization In these cases, the accuracy
of the calculated volume could be considered as equal to the
accuracy of the level measurement
Cylindrical tanks are very common The type described in
Figure 29 typically requires only two linearization points,
because the volume is a linear function of the measured level
Typically, the volume can be easily implemented from the
formula: AL = πR , V = AL x Level The exception is when internal
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features of the tank affect the relationship between the volume
and the measured level, causing the accuracy of the volume
calculation to move outside of the acceptable range Such
features may include pipes running through, agitators, entry
ports, nozzles, etc These features can either decrease or
increase the calculated volume
Calculating the volume of liquid in a partially filled tank is
sometimes a challenge For many applications, the use of
linearization tables overcomes this challenge However, in some
cases the calculation requires the use of complex formulas and
must be deferred to the Control System
A cylindrical tank in a horizontal position is also very common in
the industry, but unlike its vertical counterpart the volume is
not a linear function of the measured level Figure 29 shows an
example of calculating partial volume in such a tank:
Figure 31 Tank Volume Calculation
Figure 30 shows the chart for the plot of Level (mm) vs Volume
(m3) for the tank in figure 29
Diameter = 1000 mm & Length = 2500 mm
The plot in blue shows the ideal characteristic as calculated for
an infinite number of points The plot in red shows the Volume
output from a transmitter using a 2-point (1-segment)
linearization/strapping table with linearization points at 0 mm
and 1000 mm The plot in green shows an output characteristic
using a 6-point (5-segment) linearization/strapping table with
linearization points at 0 mm, 200 mm, 400 mm, 600 mm, 800
mm and 1000 mm
Figure 32 Level vs Volume - 2 Point Strapping
Figure 33 Level vs Volume - Multi-Point Strapping
From Figure 31 we can see the following:
• The accuracy of the linearization increases with the number of
points More points, more accuracy
• The characteristic of the volume vs level measured gets closer
to linear in the center of the tank Choosing the points
strategically can improve the accuracy of the measurement
For example, we could set most of the points closer to the
bottom and top of the tank as follows: 0 mm, 100 mm, 200
mm, 800 mm, 900 mm and 1000 mm
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