Square Root To The 3Rd Power; Square Root To The 5Th Power; Custom Linearization Curve; Bidirectional Flow - ABB 266 HART Series Operating Instruction

8.15.3 Square root to the 3rd power

The x3 Square root Transfer function can be used for open
channel (see figures on the right) flow measurement using ISO
1438 rectangular weirs (Hamilton Smith, Kindsvater-Carter,
Rehbock formulas) or trapezoidal weirs (Cippoletti formulas) and
ISO 1438 Venturi flumes. In these types of devices the relationship
between the flow and the developed head h (the differential
pressure measured by the transmitter) is proportional to h3/2 or
square root of h3.
Other types of Venturi or Parshall flume do not follow this
relationship. Using this function, the output is proportional to the
square root of the third power of the input signal in % of the
calibrated span: the instrument gives an output proportional to the
rate of flow calculated using the above mentioned formulas.
Figure 52: Tanks (respectively rectangula weir, trapezoidal weir and
V-notch weir)

8.15.4 Square root to the 5th power

The x5 Square root Transfer function can be used for open
channel flow measurement using ISO 1438 Vnotch (triangular)
weirs (see figure on the right) where the relationship between
the flow and the developed head h (the differential pressure
measured by the transmitter) is proportional to h5/2 or square
root of h5.
Using this function, the output (in % of the span) is proportional
to the square root of the fifth power of the input signal in % of
the calibrated span: the instrument (it gives an output
proportional to the rate of flow calculated using the Kingsvater-
Shen formula).
58 OI/266/HART-EN Rev. M | 2600T Series Pressure transmitters

8.15.5 Custom linearization curve

The custom linearization curve transfer function it is used
typically for volumetric level measurement in tanks with an
irregular shape. It can be registered to a freely identifiable
transfer function with a maximum of 22 base points. The first
point is always the zero point, the last is always the final value.
Neither of these points can be altered.
A maximum of 20 points can be freely entered in between.
These points have to be defined by extrapolating the tank filling
table data and reducing them to 22 points.Once identified the
22 points they will need to be uploaded into the device by
either using an HART hand held terminal or a proper
configuration software like Asset Vision Basic.
8.15.6 Bidirectional Flow (to be used when the transmitter

is connected to a bidirectional flow element)

The bidirectional function, applied to the transmitter input (x)
expressed in percentage of the calibrated span, has the
following form:
Output = ½ + ½ sign (x) ∙ x ½
where "x" and "Output" should be normalized in the range 0 to
1 for calculation purpose, with the following Output meaning:
— Output = 0 means Analog out 4 mA;
— Output = 1 means Analog out 20 mA.
This function can be used for flow measurement purpose when
the flow is in both the directions and the primary elements are
designed to perform this type of measure.
As an example, if we have a bidirectional flow measurement
application with the following data:
Max reverse flow rate: -100 l/h
Max flow rate: +100 l/h
The differential pressure generated by the flow primary is for the
maximum flow rate 2500 mmH2O, for the max reverse flow rate
2500 mmH2O.
The transmitter will have to be configured as follows:
Calibrated span: 4mA
20mA = URV = +2500mmH2O
Transfer function:

Bidirectional flow

Once configured as above the transmitter will deliver:
flowrate 100 l/h reverse:
no flowrate:
Flow rate 100 l/h:
8 Operation
= LRV = -2500mmH2O
output= 4 mA
output= 12 mA
output= 20 mA