* Converting 4 to 20mA Linear Signal to Square
Root Extraction Output 4 to 20mA Linear Signal
to Square Root Extraction Output *
Some pressure measurements are used to indirectly derive another
type of measurand. One of these is the Rate of Flow of a gas or
liquid. 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. In order to optimise the resolution of
flow measurement the output on some differential pressure transmitters can
be altered so that it is directly proportional to the flow rate rather than the
differential pressure.
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)
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):
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
Use this website www.clabberhead.com you will need to know the bore of the
orifice plate you are measuring the DP across. The internal diameter of the pipe, you
will find this from ppipe table by comparing it to the pipe specification, normally
marked on the PID's.
Basically the DP is equal to the (square of the mass
flow)/((square of (pipe CSA X square of beta ratio))x
density).