Combining Multi-Function Displays with Liquid FLO

Combining Multi-Function Displays with Liquid FLO
Industry: University
Technical Bulletin APP011
January 2007
McMillan Corporate Headquarters:
Post Office Box 1340
Georgetown, TX 78627-1340
United States of America
Toll-Free: 800.861.0231
Direct: 512.863.0231
Fax: 512.863.0671
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Combining Multi-Function Displays with
Liquid FLO-SENSORS for Exceptional Accuracy
A research & development laboratory requires a liquid flow system with extreme precision to monitor
liquid flow rates in the 13 mL/minute up to 10 L/minute range.
Any Model 10x Liquid FLO-SENSOR (101, 102, 104, 106, 108)
Model 220 Rate Meter/Totalizer or Model 25x Multi-Function Display (250, 251)
This article describes a method of obtaining linearity better than ±0.5% of full scale (FS) for
McMillan Liquid FLO-SENSORS with pulse output, or a combination of analog and pulse
output. Generally, the pulse output specifications are ±3% FS. Analog outputs are typically
±1% FS. It is reasonable to expect accuracy as good as ±0.3% FS because of the excellent
repeatability of ±.2% FS. However, a steady, repeatable reading requires that the flow be free
of pulsations and the FLO-SENSOR not be damaged in any way.
If a multi-function display is used such as the Model 250 or 251, or a data acquisition system
with multi point correction, then linearization and accuracy has already been accomplished.
Accuracy can be ±0.5% or ±0.3% FS depending on the method of calibration. For a user with
a simpler rate meter or frequency meter, an alternate method can give a significant
improvement in accuracy. The data sheet supplied with the FLO-SENSOR documents three or
four data points, each point giving a frequency for a corresponding flow. This response is
nearly linear but not perfect due to friction in the sensor of water molecules, bearings, and
viscosity effects which cannot be eliminated entirely. This results in a response curve that
deviates somewhat from an ideal, straight-line response and is usually linear to ±1% FS bestfit straight line that does not cross through zero, but it is repeatable (see Figure 1). So, if the
FLO-SENSOR is repeatable to ±0.2% FS, and the data sheet gives 3 or 4 points of frequency
vs. flow, then the stated ±3% FS pulse accuracy can be narrowed to at least ±0.5% FS or
The response curve is exagerated for
series 1 = response curve
series 2 = ideal straight line response
Frequency Hz
Flow Rate mL/min
Assuming that the response is repeatable at all points, then the frequency output should be
repeatable to ±0.2% FS at any flow. If a full scale frequency is 200 Hz, and the full scale flow
is 200 mL/min, then the scaling is:
200mL / 200Hz = 1mL / 1 Hz.
If the frequency is 190Hz, then flow is:
190Hz x 1 mL / Hz = 190 mL / min.
…Or is it?
Taking the data from a typical 101-5T flow sensor pulled from the records, the recorded data
of flow vs. frequency is as follows:
500 mL/min
Frequency (Hz)
Slope mL/Hz
The fourth column is added to indicate the changing response of the flow (slope of the curve,
Flow / Frequency) at each data point. If the slope is taken at full scale and applied as a factor
to the frequency obtained at various flow rates, it can be seen that there will be error for flow
rates at other than full scale. For example, the slope at full scale is 1.305 mL/Hz. Using that
ratio to calculate the flow at a frequency of 195 Hz will be
195 x 1.305 = 254.48 mL/min.
That is an error of 0.90% as calculated by flow. The actual flow at 195 Hz is 250mL.
254.48 – 250 / 500 x 100 = 0.90%
Using this full scale ratio applied against the frequency of any flow in a simple rate meter will
give an indication of flow rates within the ±3% rating. We can use each data point with its own
slope value but that would improve accuracy only at that data point and error would increase
at flow rates between those points. If we have an indicated frequency of 200Hz, for example,
what is the flow?
We can calculate by the following method:
The error at 195 Hz is +0.91%. This is close to 200 Hz so the slope of the curve at 195 and at
200 Hz will be nearly identical.
383Hz X 0.91% = 4.55Hz (to calculate error in Hz at 195 Hz)
So taking the full scale factor of
1.305 X 200 mL = 261.00mL.
Subtracting the error gives:
261.00 mL – 4.55mL = 256.45 mL/min
The offset of 4.55 mL was subtracted from the flow rate because the error at 250 mL was
positive. Notice that if the frequency would be near the middle of the data points, the actual
error would be different.
Find the 2 data points nearest to 200 Hz and use those data points of 500mL/minute at 383
Hz and 250mL/minute at195Hz.
(500 – 250 mL ) ÷ (383 – 195Hz) = 1.330 mL/Hz (slope)
200 – 195 Hz = 5 Hz (frequency above lower point)
5 x 1.330 = 6.65 mL
6.65 mL + 250.00 mL = 256.65 mL/min
Another method is proposed that will allow relatively easy calculation of flow at any indicated
frequency, utilizing the chart and trend functions of Microsoft EXCEL program.
STEPS (see chart below for example)
1. Access the EXCEL program
2. Enter the data from the flow sensor data sheet with the frequency in column A and
flow rates in column B.
3. Choose > Chart Wizard
XY (scatter)
chart sub-type = curved lines connecting dots
4. Chart will be displayed:
Right click on trend line
Add trend line
Polynomial (2nd order)
Options: check box “display equation on chart”
The equation for the curve is displayed near top of the chart.
The equation developed from the previous data is:
y = 0.0002x2+ 1.2334x + 4.0689
Where y = desired flow rate, x = frequency
y = (0.0002 x 2002)+ (1.2234 x 200) + 4.0689
+ 4.07
256.75 mL/min
y = 0.0002x + 1.2234x + 4.0689
Flow Rate mL/min
It would take careful actual flow measurements to determine the true flow rate but as seen, the
3 methods differ by a maximum of 0.30 mL/min or 0.06% of full scale.
Due to the limitations of each of these methods to absolutely predict the actual flow rate
because of the small vagaries of the response curve, maximum limits of error will be the
±0.2% repeatability of the sensor plus the difference between the value generated by the
equation and the actual flow rate that generally would not exceed ±0.1%. Be aware of the
sign of the components of the particular equation, whether they are + or -.
Methods of obtaining accuracy:
A system that will give an accuracy of ±3% FScan be a flow sensor with a Model 220 display
or pulse output to a data acquisition system scaled for the full scale mL/Hz ratio.
A system with an accuracy of ±0.3 to 0.4% FS can be achieved by using a frequency counter
(such as the Model 220 programmed for Hz /sec.) and performing the hand calculations
previously described. This can be useful if ±3% accuracy is sufficient for most if the time but
occasional higher accuracy is needed.
A system with an accuracy near the ±0.2% FS spec can be achieved with the Model 251 MultiFunction Display programmed with up to 9 data points directly from flow rates at those points.
The error between the multiple adjacent data points will not be significant. It is recommended
that this system be calibrated at the factory to achieve multipoint generated accuracy. A Model
251 calibrated for the 3 or 4 data points listed on the data sheet can be expected to be
accurate to ±0.5% FS. A Model 251 Display can be added at any time by programming the
Model 251 for the 3 or 4 data points and then hooking up the display to the FLO-SENSOR.
There is also the option of a linearized analog output and relay outputs for alarms and process
Note: A Model 250 Multi-Function Display calibrated against the analog response of a FLOSENSOR is also a viable option.
A McMillan microturbine Liquid FLO-SENSOR combined with a Model 251 Multi-Function
Display will give an accurate, reliable system at a very competitive price.
The above information is derived from data from a typical flow sensor response calibrated for
DI water. Absolute accuracies are not guaranteed due to differences in characteristics of
different liquids and other influences that cannot be accounted for here. However the above
methods will improve the accuracy of data as applied to the output generated by the flow
For more information on the excellent repeatability, reliability, and long life of the McMillan
pelton wheel flow sensors, see the article Turbine Flow Sensors….The Best Choice For Liquid
Flow Measurement, by R.D. McMillan.
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