1. ME 322: Instrumentation Lecture 4
January 26, 2016
Professor Miles Greiner
Lab Guidelines and grading, pressure gages, Manometers, Instrument sensitivity

2. Announcements HW assignments, reading and Labs on Website
Turn in HW 1 now
Use ME 322 student number, Not name
HW 2 due Monday 2/1/2015
Use ME 322 student number and Lab Day to make it easier to return in lab, if necessary.
Joseph Young will hold office hours
9-10:50 AM (right after this class) on the Monday, Wednesday, of Friday before HW is due in ME Kitchen
This Friday
Go to PE 2 for lab this week
Lab 2 - Statistical Analysis of UNR Quad Measurements
Download and read instructions Lab 2 Instructions and Lab Guidelines

3. Lab Grading Participation Grade Assigned by lab assistant, based on:
Working in 2-person lab groups (assigned in lab)
Being on time (responsibility to lab partner and TA)
Being prepared (read lab instructions, in future labs bring prepared Excel and LabVIEW files)
Participating and interacting with your partner in setting up experiment, acquiring data, checking consistency, retaking data if necessary, writing report, and cleaning up.
Being professional and patient (treat partner and TA’s well)
Report Grade Assigned by grader, based on:
Following directions and answering questions
Calculation results (based on your measurements), and
Clear tables and plots (formatting)

4. Plots Formats Bad  Good  Clear Engineering Communication
Variable name, symbol and [units] on axes
Make plot, labels and symbols big enough to see clearly
Avoid redundant frames that make the plot smaller
These features are graded

5. Tables Good  Bad  Font size, variable name, symbols, units
Average
Standard Deviation L
464 81 S
135 23 A
64000
20000 C
1110
350
Average
Standard Deviation
Long Side Length, L [ft]
464 81
Short Side Lenth, S [ft]
135 23
Area, A [ft2]
64000
20000
Cost, C [$]
1110
350
Font size, variable name, symbols, units
Grids, centered
Clarity, simplicity

6. Pressure Generally can’t see it Need gages (gauges) to
Qualitatively know when it changes
Quantitatively measure it
Units: Force per area
[Pa] = [N/m2]; [kPa] = [1000 Pa]; [MPa] = [106 Pa]
[psi] = [lbf/in2], [1 atm] = kPa
Gage Pressure
Amount a vessel’s pressure is above its surrounding’s
PGAGE = P – PATM P
PATM

7. Some Gages Bourdon Tube Diaphragm Manometers Vertical Inclined
Water Head, h

8. Instrument Transfer Function
Sometimes call Calibration curve
Relationship between the instrument Reading R (h or output) and its Measurand M (pressure or quantity being measured)
Not always linear

9. U-Tube Manometer 𝑃= 𝑃 1 + 𝜌 𝑠 𝑔ℎ= 𝑃 2 + 𝜌 𝑚 𝑔ℎ
∆𝑃= 𝑃 1 − 𝑃 2 = 𝜌 𝑚 − 𝜌 𝑠 𝑔ℎ
𝐼𝑓 𝜌 𝑠 << 𝜌 𝑚
𝑇ℎ𝑒𝑛: ∆𝑃= 𝜌 𝑚 𝑔ℎ
𝑃 1
𝑃 2
Sensed
Fluid Density
Manometer
Fluid Density
Reading
Measurand
Reading
Fluid Height
when DP = 0
Fluid
Air (1 ATM, 27°C)
Water (30°C)
Hg (27°C)
𝝆 𝒌𝒈 𝒎 𝟑
1.774
995.7
13,565 𝑃
The reading can be given in units of inches or cm of water column [in WC] or [cm WC]
Or inches or cm of mercury or alcohol (manometer fluid)
Transfer function ℎ= ∆𝑃 𝜌 𝑚 𝑔 (Reading ℎ versus Measurand ∆𝑃, linear)

10. Transfer Function ℎ= ∆𝑃 𝜌 𝑚 𝑔 Low rm (alcohol) High rm (mercury)
ℎ= ∆𝑃 𝜌 𝑚 𝑔
Low rm
(alcohol)
High rm
(mercury)
Instrument sensitivity describes how much the Reading changes for a small change in the measurand
𝑆= 𝜕𝑅 𝜕𝑀 =𝑠𝑙𝑜𝑝𝑒= 1 𝜌 𝑚 𝑔
Increases as 𝜌 𝑚 decreases (small change in P produces larger h)

11. Inclined-Well Manometerh1 h2
DP = 0 AT AW R q P1 P2
ℎ= ℎ 1 + ℎ 2
ℎ 2 =𝑅𝑠𝑖𝑛𝜃
ℎ 1 𝐴 𝑤 =𝑅 𝐴 𝑡
ℎ 1 = 𝐴 𝑡 𝐴 𝑤 𝑅
ℎ= 𝐴 𝑡 𝐴 𝑤 𝑅+𝑅𝑠𝑖𝑛𝜃=𝑅 𝐴 𝑡 𝐴 𝑤 +𝑠𝑖𝑛𝜃
By measuring R we can find h. Generally 𝑅>ℎ
Use a scale on the measuring tube to measure 𝑅 directly

12. Transfer Function Sensitivity 𝑆= 𝜕𝑅 𝜕𝑀 =𝑠𝑙𝑜𝑝𝑒= 1 𝜌 𝑚 𝑔𝑠𝑖𝑛𝜃
∆𝑃= 𝑃 1 − 𝑃 2 = 𝜌 𝑚 𝑔ℎ= 𝜌 𝑚 𝑔𝑅 𝑠𝑖𝑛𝜃+ 𝐴 𝑡 𝐴 𝑤
∆𝑃= 𝜌 𝑚 𝑔 𝑠𝑖𝑛𝜃+ 𝐴 𝑡 𝐴 𝑤 R
If 𝜃≈30°,
And 𝑠𝑖𝑛𝜃≈ 1 2 ≫ 𝐴 𝑡 𝐴 𝑤
𝑇ℎ𝑒𝑛: ∆𝑃= 𝜌 𝑚 𝑔𝑅𝑠𝑖𝑛𝜃
𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛: 𝑅= 1 𝜌 𝑚 𝑔𝑠𝑖𝑛𝜃 ∆𝑃
Sensitivity 𝑆= 𝜕𝑅 𝜕𝑀 =𝑠𝑙𝑜𝑝𝑒= 1 𝜌 𝑚 𝑔𝑠𝑖𝑛𝜃
S increases as 𝜌 𝑚 and 𝜃 decreases
Easy to vary instrument sensitivity

13. Inclined Manometer Transfer Function
𝑅= 1 𝜌 𝑚 𝑔𝑠𝑖𝑛𝜃 ∆𝑃
Small q
Large q

14. General “Linear” Instrument Characteristics
𝑅 𝑚𝑎𝑥
∆𝑅 𝑚𝑖𝑛
𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦:
𝑆= 𝜕𝑅 𝜕𝑀
𝑀 𝑚𝑎𝑥
∆ 𝑀 𝑚𝑖𝑛
𝑅 𝑚𝑎𝑥 ≡Maximum Reading (i.e. tube length)
∆𝑅 𝑚𝑖𝑛 ≡Readability (smallest change in reading that can be detected, i.e. tick mark, digit)
𝑀 𝑚𝑎𝑥 = 𝑅 𝑚𝑎𝑥 𝑆 ≡Instrument Range (Maximum measurand for which instrument can be used)
∆ 𝑀 𝑚𝑖𝑛 = ∆ 𝑅 𝑚𝑖𝑛 𝑆 ≡Instrument Resolution (smallest detectiable change in measurand)

15. Sensitivity affects both Resolution and Range
In general, it is not hard to change sensitivity, i.e.
Increasing S improves resolution
But decreases range
Resolution as a fraction of Range
𝑆= 𝜕𝑅 𝜕𝑀 = 1 𝜌 𝑚 𝑔𝑠𝑖𝑛𝜃
∆ 𝑀 𝑚𝑖𝑛 = ∆ 𝑅 𝑀𝐼𝑁 𝑆
𝑀 𝑚𝑎𝑥 = 𝑅 𝑀𝐴𝑋 𝑆
∆ 𝑀 𝑚𝑖𝑛 𝑀 𝑚𝑎𝑥 = ∆ 𝑅 𝑚𝑖𝑛 𝑆 𝑅 𝑚𝑎𝑥 𝑆 = ∆ 𝑅 𝑚𝑖𝑛 𝑅 𝑚𝑎𝑥 ≡% of full scale that can be detected.

16. Instrument Repeatability
Will an instrument give the same reading every time it is exposed to the same Measurand?
Why not?
Transfer function may drift with time. So at a later time the readings may shift to consistently higher (or lower) values than before.
Referred to as Systematic or Calibration Error
Random variations of uncontrolled inputs (such as RF (radio frequency) noise, orientation of instrument, humidity, hysteresis), may lead to Random variations of the Reading.
Referred to as Random Errors or Imprecision
Calibration Drift
Hysteresis

17. General Instrument Instrument Desired Input (Measurand M)
i.e. length, pressure
temperature
Instrument
Output Reading R
(deflection, number
of steps, needle angle)
Controlled
i.e. temperature,
orientation
Uncontrolled
i.e. RF frequency, Average
walking stride length, Value
approved from above or below
Undesired Inputs
x1, x2, x3, x4, x5,…

18. General Transfer Function
Reading R = fn(M, x1, x2,…, xn)
How to find the Transfer Function?
Theory:
good for simple device (manometer)
Done in other classes
Only includes the effects you model (at best)!
Calibration:
Controlled measurement process
Measure reading (R) while exposing instrument to a range of measurands (M) that are being measured by a reliable standard (used to determine M).
Includes affects you don’t anticipate

19. Calibration Correlation
“Expected” Transfer
Function
Measured Data
“Best Fit” Line
Instrument
Under Test
Standard
Expose instrument to a range of Measurands M that are measured by a reliable standard. Record Standard output M and Instrument output Reading R
Correlate Reading R with Measurand M (least squares fit)
May not be linear
Uncontrolled inputs can cause R to have undesired variations of the same M!
The size of the variation is a measure of the instrument impression
random, inconsistent output
Systematic errors can be removed using calibration, but random errors cannot!

20. How to reduce Measurement Imprecision?
Improve the control of undesired inputs, and/or
Use a different instrument that is less sensitive to uncontrolled inputs

21. Lab 3 Pressure Transmitter Calibration
Proximity Sensor or
PHI
PLO
Dwyer Series 616 Pressure Transmitter
Measurand: Pressure difference between HI and LO ports,
DP = PHI – PLO
Power must be supplied to pins 1 and 2 (10-35 VDC)
Sensor: diaphragm with a strain or proximity gage
Output may be affected by orientation due to gravity (undesired)
The Output or “Reading” is current, IT [mA], measured by a Digital Multimeter (DMM), pins 3 and 4

22. End 2016

23. Transmitter Characteristics
See Lab 3 website, ~$150
Use different diaphragm thickness or flexibilities to get different sensitivities to vary Full Scale (FS) range and resolution
Output Signal: 4 to 20 mA (h = 0 to FS, linear)
Accuracy: 616: ±0.25% F.S.
Stability: ±1% F.S./yr.
Two models in lab:
616-1: FS = 3 in WC; Accuracy = *3 = ± in WC
616-4: FS = 40in WC; Accuracy = *40 = ±0.1 in WC
What does this accuracy mean (what is its confidence level)?

24. Manufacturer’s Inverted Transfer Function
Output Signal: 4 to 20 mA (h = 0 to FS, linear)
Measurand vs Reading
Needed to use the gage
Pressure head:
ℎ=𝐹𝑆 𝐼−4𝑚𝐴 16
Pressure Difference:
Δ𝑃= 𝑃 𝐻𝐼 − 𝑃 𝐿𝑂 = 𝜌 𝑤 𝑔ℎ
= 𝑘𝑔 𝑚 𝑚 𝑠 2 𝐹𝑆 𝑐𝑚 𝑖𝑛𝑐ℎ 1 𝑚 100 𝑐𝑚 𝐼−4𝑚𝐴 16
What is the confidence level (probability) that the real pressure head is within the interval h ± Accuracy?
this is what we will determine in Lab 3
Manufacturer’s Transfer Function (R vs M)
𝐼= 16 𝑚𝐴 𝐹𝑆 ℎ+4 𝑚𝐴
We will try to confirm this in Lab 3

25. Calibration Transfer Function
Data
Correlate
Scatter – Uncontrolled inputs instrument

26. Lab 2 Plots and Table Average Standard Deviation
Average
Standard Deviation
Long Side Length, L [ft]
430
110
Short Side Lenth, S [ft]
120 30
Area, A [ft2]
56,000
19,000
Cost, C [$]
980
330

27. Lab 2 Questions Is stride length F “highly correlated” with height, H?
Does the distribution of the cost estimates look the way you expect?
Do any of the cost estimates look “out of place?”
How can you interpret the sample mean and standard deviation of the cost estimates in terms of the distribution?
Are the measured values of L and S “highly” correlated?
Should they be? What does this mean?
If you budget the amount of your cost estimate, then
You are only 50% sure to have enough to cover quad (be above the average value, which we assume is the most accurate estimate)
How much money should you budget to be 90% sure to have enough

28. Transfer Function Plot
Actual Outputs
Best fit line