What is square root extraction in flow measurement?

Square Root Extraction is a mathematical process which is applied to a linear measurement scale to convert it to a non-linear square root scale. For example the flow of a gas or liquid through a closed pipe is proportional to the square root of the differential pressure.

How do you calculate square root flow?

Logic for Taking the Square Root in the Controller But the root of a number from 0-1 is larger: √0.5 = 0.707. So if you have a 12 mA signal from the DP cell, that’s 50% DP, but 71% flow rate. Multiply the resulting square rooted signal (still 0-1) by the flow scale span to get flow rate in engineering units.

Why flow square root extraction is required?

Why use square root extractor for DP transmitter? Differential pressure developed by a venturi, orifice plate, pitot tube, or any other acceleration-based flow element is proportional to the square of the flow rate. The square root extractor is used to convert the measured differential pressure into flow rate.

How do you calibrate a square root extractor?

In order to calibrate, you should simply move the first calibration point a bit higher than 0% of the input range. If the first calibration point is at 5 – 10% of the input range, you are already out of the steepest part of the curve and you can get reasonable readings and error calculation.

How do you convert square roots to linear equations?

Example:

1. Convert 50 % linear to square root.
2. Square root % = √X*10.
3. = √50*10.
4. = 70.71%

Why do we calculate square root in flow?

The flow rate along a closed pipe is directly proportional to the square root of the pressure drop or differential pressure between two points. Since the relationship is non-linear, there is a greater change in flow at low pressures compared to higher ones.

What is square root in transmitter?

What is the transmitter square root function and why you should use it? It is a function on differential pressure (DP) transmitters that calculates the process flow using differential pressure readings.

How to convert square root extraction to linear extraction?

The reverse formula for converting a square root extraction output to a linear one is: The following table shows values for linear to square root extraction and vice versa (please note all conversion values are rounded to 2 decimal places):

How to convert linear output to square root output?

The following formula can be used for converting a linear 4-20mA current loop output to a square root extraction type: [Output Sq Rt] = 4mA + (4 x Square Root of ([Output Linear] – 4mA)) The reverse formula for converting a square root extraction output to a linear one is: [Output Linear] = 4mA + (([Output Sq Rt] – 4mA)^2 / 16)

What is the function of a square root extraction relay?

Pneumatic square root extraction relays provide a square-root function that the relays were able to serve their purpose in characterizing the output flow signal of a pressure sensor to yield a signal representing flow rate. The following table shows the ideal response of a pneumatic square root relay:

How does the square root function work in a DP transmitter?

When we connect the output of the DP transmitter to the input of Square Root Extractor, the square-root function applies to the output signal – the result is an output signal that tracks linearly with flow rate (Q). An instrument connected to the square root relay’s signal will, therefore, register the flow rate as it should.