- What is square root extraction in flow measurement?
- What is a square root extractor?
- Why flow rate is directly proportional to the square root of ?p?
- Why square root is used in the flow transmitters?
- Where is square root extraction performed?
- Square root extraction formula:
- Square root extraction table:
- Where Should you Apply Square Root Extraction in Transmitter or Control System?
- Square Root Extraction in Smart Transmitters
- Troubleshooting Errors in Square Root Flow Measurement
- What does a square root extractor do in instrumentation?
- What does a square root extractor do?
- Why is square root extraction used in flow transmitters?
- What is the output signal from a square root transmitter?
- When should square root extraction be applied?
- Differential pressure measurement is a commonly used method to measure the flow across an obstruction.
- Differential pressure is in direct proportion to the square of the flow.
- The square root relationship is applied only for DP-type flow measurements.
- These DP sensors or DP transmitters can measure differential pressure across various obstructions made in the flow channel or in a flow line.
- This differential pressure is developed by the use of primary elements such as an orifice plate, venturi tube, etc.
- But, differential pressure is not proportional to the flow rate across the orifice.
- The above relation is not a linear relationship or it is called the square root relation because the differential pressure measured has nonlinear relation with flow through the pipeline.
- The graphical relationship between differential pressure (?P) & flow rate (Q) is the quadratic parabola.
- A miserable significance of this quadratic relationship is that a flow rate is not directly sensed when a pressure-sensing instrument is connected to a flow sensor. But the pressure sensing instrument will sense the square of the flow rate.
- The square root function should be implemented in the loop for accurate measurement of flow throughout the operating range.
- The square root extractor converts the measured differential pressure into the rate of flow.
- Almost 50% of all flow-measuring applications use the differential pressure method to derive the flow rate. The relation between Differential Pressure (DP) and flow rate is given as
Where
Q = flow rate.
DP = differential pressure.
K = is a constant that depends on various factors such as the diameter of the pipe, orifice diameter, and so on.
What is square root extraction in flow measurement?
- A square root extractor is a type of signal conditioner.
- It is easy to use indicators, recorders, and controllers to register linearly with the flow velocity.
- Square root extraction in flow measurement is an arithmetic conversion applied to a linear measurement scale to convert it into a nonlinear square root scale.
- The square root scale is generated by considering the square root of the ratio between measurement reading and full span.
- Square Root Extraction is sometimes called square root scaling. And it is a fundamental step in considering the flow rate from a differential pressure measurement.
What is a square root extractor?
- A square root extractor converts a linear differential pressure signal to a nonlinear flow rate.
- The square root extractor is an electronic or pneumatic instrument that generates a corresponding linear flow signal from the flow transmitter.
- Usually, the flow transmitter signal is in the form of a square root.
Why flow rate is directly proportional to the square root of ?p?
- According to Bernoulli’s principle “the square root of DP is directly proportional flow rate. It means if the pressure is high, then the flow rate increases and vice versa.
- The flow rate in the pipe is equal to the velocity multiplied by the cross-section because the pressure comes from only one end of the pipe.
- Flow element creates a pressure change by accelerating a fluid stream in differential pressure based flow meter.
- The pipeline is intentionally narrowed to create a low-pressure region.
Why square root is used in the flow transmitters?
Generally, the flow transmitter is configured in square root because a small change in differential pressure on the lower end results in a large change in flow.
If the square root is considered in the controller, the large change in flow makes it extra sensitive to electrical noise on the mA signal.
Where is square root extraction performed?
- Almost modern smart differential pressure transmitters allow the DP to square root conversion to be calculated within the transmitter.
- But, all SCADA and DCS systems have inbuilt square root extraction function blocks to configure inputs from DP transmitters.
- All square root extractions are performed in one or other of these locations.
- So, the instrument and control system engineer has an option of where to have the signal conversion.
Square root extraction formula:
A. To convert a given linear 4 to 20mA signal to a square root signal the following relation is adopted.
B. And to convert a square root signal to a linear 4 to 20mA signal use this formula:
Square root extraction table:
The table shows values for both a linear to square root conversion and a square root to linear conversion.
| Linear (mA) | Square root (mA) | Square root (mA) | Linear (mA) |
| 4 | 4.00 | 4 | 4.00 |
| 5 | 8.00 | 5 | 4.06 |
| 6 | 9.66 | 6 | 4.25 |
| 7 | 10.93 | 7 | 4.56 |
| 8 | 12.00 | 8 | 5.00 |
| 9 | 12.94 | 9 | 5.56 |
| 10 | 13.80 | 10 | 6.25 |
| 11 | 14.58 | 11 | 7.06 |
| 12 | 15.31 | 12 | 8.00 |
| 13 | 16.00 | 13 | 9.06 |
| 14 | 16.65 | 14 | 10.25 |
| 15 | 17.27 | 15 | 11.56 |
| 16 | 17.86 | 16 | 13.00 |
| 17 | 18.42 | 17 | 14.56 |
| 18 | 18.97 | 18 | 16.25 |
| 19 | 19.49 | 19 | 18.06 |
| 20 | 20.00 | 20 | 20.00 |
Where Should you Apply Square Root Extraction in Transmitter or Control System?
You can use square root extraction in either the differential pressure transmitter or the control system (DCS/PLC/SCADA). The choice depends on the needs of the application and the design of the system.
Apply square root extraction in the transmitter when:
- YYou wish to reduce the effect of noise on the 4-20 mA signal.
- You are sending signals over huge distances.
- We require local diagnostics and linear flow readings right from the field equipment.
Apply square root extraction in the control system when:
- you need raw DP data for diagnostics or more complicated math.
- You need a central place to control scaling and converting signals.
- In the control room, there are several flow computations or compensation strategies in use.
Don’t do square root extraction in both places, as this could cause readings to be wrong.
Square Root Extraction in Smart Transmitters
Smart transmitters like HART, Foundation Fieldbus, or Profibus typically contain built-in features that let them take the square root of a number. You can set these transmitters to send out either:
- A straight signal (that shows the difference in pressure)
- A square root signal shows the flow rate.
Benefits of using smart transmitters:
- Better precision thanks to integrated digital signal processing
- Remote configuration using handheld devices or software tools
- Extra pay for the density, temperature, and pressure of the fluid
- Diagnostics and status notifications on board
Troubleshooting Errors in Square Root Flow Measurement
Common issues to watch for:
- Double extraction: Taking the square root in both the transmitter and the control system gives you wrong (over-compensated) values.
- No extraction used: If you neglect the square root extraction step, the flow readings will be nonlinear and not useful.
- Incorrect signal scaling: If HMI or SCADA displays assume linear input but get square root data instead, they may present the wrong results.
- Sensitivity to electrical noise: If square root extraction is done in the controller, low-end flow numbers can be messed up by noise in the mA loop.
What does a square root extractor do in instrumentation?
You can use a square root extractor to turn a differential pressure (DP) signal into a flow signal. This device makes it easier to read and use in control systems by turning a linear DP measurement into a nonlinear signal that is proportional to flow rate. This is because flow rate is proportional to the square root of differential pressure, according to Bernoulli’s equation..
What does a square root extractor do?
A square root extractor, whether it’s electronic or pneumatic, takes the linear output from a differential pressure transmitter and changes it into a signal that shows the actual flow rate. This lets you get accurate flow measurements in systems where flow comes from DP readings, like orifice plates, venturi tubes, or flow nozzles.
Why is square root extraction used in flow transmitters?
The flow rate has no direct relationship to the difference in pressure; it is proportional to the square root of the change in pressure. If the transmitter does square root extraction, it makes the system less sensitive to noise, especially when the flow rate is low. Setting up the square root extraction at the transmitter level makes the signal more stable and accurate by making it less affected by electrical noise in the 4-20 mA loop.
What is the output signal from a square root transmitter?
A square root transmitter gets its input straight from a DP sensor and sends out a 4–20 mA signal that is proportional to the flow rate that was calculated. This device linearizes the output signal to match the real flow profile by applying the square root function to the observed differential pressure.
When should square root extraction be applied?
When measuring flow indirectly with differential pressure, you should always utilize square root extraction. This happens a lot when using primary flow devices like venturi tubes or orifice plates. Using the square root makes sure that the output signal accurately shows how flow and pressure are not related in a linear way.
