ABB 266 Operating Instruction page 11

Square root to the 3rd power
The x Square root Transfer function can be used for open channel (see figures on the right) flow measurement using ISO 1438
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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 (in % of the span) 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.
Square root to the 5th power
The x Square root Transfer function can be used for open channel flow measurement using ISO 1438 Vnotch (triangular) weirs
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(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).
Bidirectional Flow
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:
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:
Transfer function: Bidirectional flow. Once configured as above the transmitter will deliver: flowrate 100 l/h reverse:
Cylindric lying tank
This function is used to measure the volumetric level into a cylindrical horizontal tank with flat ends. The transmitter calculates the
volume from the measured filling level.
Spherical Tank
This function is used to measure the volumetric level into a spherical tank. The transmitter calculates the volume from the measured
filling level.
Figure 47: Tanks (respectively rectangula weir, trapezoidal weir and V-notch weir)
Max reverse flow rate: -100 l/h
Max flow rate:
4mA = LRV = -2500mmH2O
20mA = URV = +2500mmH2O
no flowrate:
Flow rate 100 l/h:
2600T Series Pressure transmitters | OI/266/FF/ADD-EN Rev. B 11
+100 l/h
output= 4mA
output= 12mA
output= 20mA