Square Root Extraction of 4-20mA Instruments

[MorphuisOGrady]

Finally I got access to the BBL PLC. Here is the logic for the Square Root Extraction: Does this make sense to anyone?

Value = SQRT(Scaled_Input) * SQRT(Span)

Value= Derived Flow
Scaled_Input = Scaled 4-20mA Signal i.e 0-1cum/s
Span - Range of signal = 1

 

[danw]

To calculate flow rate: square root of percentage of pressure = percentage of max design flow

Example: design max flow = 1200mm (wc) DP pressure drop at 1,000 lpm

100% of 1200mm pressure = 1200mm; Sq rt of 1.00 = 1.00; 100% of max flow = 1,000 lpm

81% of 1200mm pressure = 972mm; Sq rt of 0.81 = 0.900; 90% of max flow = 900 lpm

50% of 1200mm pressure = 600mm; Sq rt of 0.50 = 0.707; 70.7% of max flow = 707 lpm

25% of 1200mm pressure = 400mm; Sq rt of 0.25 = 0.500; 50.0% of max flow = 500 lpm

20% of 1200mm pressure = 240mm; Sq rt of 0.20 = 0.447; 44.7% of max flow = 447 lpm

16% of 1200mm pressure = 192mm; Sq rt of 0.16 = 0.400; 40.0% of max flow = 400 lpm

10% of 1200mm pressure = 120mm; Sq rt of 0.10 = 0.316; 31.6% of max flow = 316 lpm

5% of 1200mm pressure = 60mm; Sq rt of 0.05 = 0.223; 22.3% of max flow = 223 lpm

1% of 1200mm pressure = 12mm; Sq rt of 0.01 = 0.100; 10.0% of max flow = 100 lpm

The quick check points I remember are:
25% of max pressure = 50% flow rate
50% of max pressure = ~ 70% flow rate

 

[Tom Jenkins]

DanW's math is right. I think the formula in the PLC is wrong.

The original programmer skipped the step of converting the input to actual differntial pressure. This works fine, although I don't like to do it that way for trouble shooting purposes. DanW's method of taking the square root of the percentage accomplishes the conversion nicely.

Taking the square root of the span is wrong. The original programmer gets away with it because the square root of 1 is 1! However, if you apply the same formula to a transmitter with a different span, say 20 l/s, you will get the wrong answer.

 

[MorphuisOGrady]

Great. Some of them have a span of 0-2.4cum/s

So the flows are wrong for about 20 years...Lovely