The modern solution to this problem is to incorporate square-root signal characterization either inside the transmitter or inside the receiving instrument e.
Either way, the square-root function must be implemented somewhere in the loop in order that flow may be accurately measured throughout the operating range. Note :With so many modern instruments being capable of digitally implementing this square-root function, one must be careful to ensure it is only done once in the loop. I have personally witnessed flow-measurement installations where both the pressure transmitter and the indicating device were configured for square-root characterization.
This essentially performed a fourth root characterization on the signal, which is just as bad as no characterization at all! Like anything else technical, the key to successful implementation is a correct understanding of how the system is supposed to work. In the days of pneumatic instrumentation, this square-root function was performed in a separate device called a square root extractor. The Foxboro model left and Moore Products model 65 right pneumatic square root extractors are classic examples of this technology:.
Note : This is outdated, we are no more dealing with special need of square root extractors in industries. Pneumatic square root extraction relays approximated the square-root function by means of triangulated force or motion. In essence, they were trigonometric function relays, not square-root relays per se.
However, for small angular motions, certain trigonometric functions were close enough to a square-root function that the relays were able to serve their purpose in characterizing the output 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:.
As you can see from the table, the square-root relationship is most evident in comparing the input and output percentage values. At an input signal pressure of 10 PSI When graphed, the function of a square-root extractor is precisely opposite inverted of the quadratic function of a flow-sensing element such as an orifice plate, venturi, or pitot tube:.
Although analog electronic square-root relays have been built and used in industry for characterizing the output of mA electronic transmitters, a far more common implementation of electronic square-root characterization occurs in DP transmitters designed with the square-root function built in. Note : We are using square root extraction function which is available inside the transmitter software configuration. Continuously run a timer. On a new pulse rising edge , divide the time base by the accumulated time, then reset the timer.
For faster pulses , count the pulses in a fixed time period, and multiply that by a time multiplier and the volume per pulse multiplier. If the pulses are coming more often than once every two scans, this will require a high-speed counter DI which counts pulses and reports the count per scan to the processor since the processor would miss pulses just looking at the raw DI. In this example, you might program the processor to count pulses every second.
Totalized flow is an important value for most flow meters. If your flow meter is attached via HART or some other communication protocol, you may be able to read the flow total from the meter. Otherwise, you will need to calculate it in the controller using an accumulator.
If you calculate a total for one hour, a work shift, or a day, then roll that into a previous register, a standard totalizer will work. A float has a precision of about 1 part in 16,, If you add 1 to 16,, into a float, the result will be 16,, as expected. So, a totalizer will quit accumulating altogether after 16,, scans and will have been inaccurate for a while before that.
The grand total will always be those two registers added together. Sign up for our newsletter to get industry trends, educational content, and product updates, the way you want to receive them. Download our latest W9. All rights reserved Privacy Policy Terms of Use. Web Design by Drum Creative. Skip to content.
Hose and Fittings. Products Services Locations. Mobile Systems Integration. Process Solutions. Precision Measurement. Process Equipment. Process Services. The following table shows values for linear to square root extraction 4 to 20 milliamp current loop signal.
Convert any linear measurement to sqrt extraction mA signal. The formula for converting a square root extraction mA signal to a linear one is:.
The following table shows values for square root extraction to linear 4 to 20 milliamp current loop signal. Simply put, the narrow throat causes the fluid to accelerate from a lower velocity to a higher velocity.
However, we also know that the total energy at any point in the fluid stream must remain constant, because no energy is added to or taken away from the stream in this simple fluid system. Therefore, if kinetic energy increases at the throat, potential energy must correspondingly decrease to keep the total amount of energy constant at any point in the fluid.
Since this venturi tube is level with the ground, there cannot be a height change to account for a change in potential energy. Therefore, there must be a change of pressure P as the fluid travels through the venturi throat. The Laws of Mass and Energy Conservation invariably lead us to this conclusion: fluid pressure must decrease as it travels through the narrow throat of the venturi tube.
To simplify our task, we will hold to the following assumptions for our venturi tube system:. Now we will algebraically re-arrange this equation to show pressures at points 1 and 2 in terms of velocities at points 1 and Factoring v 2 2 out of the outer parentheses set:.
We are only one step away from a volumetric flow equation here, and that is to convert velocity v into flow rate Q. Velocity is expressed in units of length per time feet or meters per second or minute , while volumetric flow is expressed in units of volume per time cubic feet or cubic meters per second or minute.
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