ME 322: Instrumentation
Lecture 4
January 26, 2016
Professor Miles Greiner
Lab Guidelines and grading, pressure
gages, Manometers, Instrument
sensitivity
Announcements
• HW assignments, reading and Labs on Website
•
http://wolfweb.unr.edu/homepage/greiner/teaching/MECH322Instrumentation/
• 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
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)
Plots Formats
Good 
•
•
•
•
•
Bad 
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
Tables
Bad 
Good 
Standard
Average
Deviation
Average
Standard
Deviation
Long Side
Length, L [ft]
464
81
L
464
81
Short Side
Lenth, S [ft]
135
23
S
135
23
Area, A [ft2]
64000
20000
A
64000
20000
Cost, C [$]
1110
350
C
1110
350
• Font size, variable name, symbols, units
• Grids, centered
• Clarity, simplicity
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] = 101.3 kPa
• Gage Pressure
– Amount a vessel’s pressure is above its
surrounding’s
P
– PGAGE = P – PATM
PATM
Some Gages
• Bourdon Tube
• Diaphragm
• Manometers
– Vertical
– Inclined
– Water Head, h
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)
Reading
– Not always linear
Measurand (quantity being measured)
U-Tube Manometer
Sensed 𝑃1
Fluid Density
𝑃2
Manometer
Fluid Density
Reading
𝑃 = 𝑃1 + 𝜌𝑠 𝑔ℎ = 𝑃2 + 𝜌𝑚 𝑔ℎ
∆𝑃 = 𝑃1 − 𝑃2 = 𝜌𝑚 − 𝜌𝑠 𝑔ℎ
𝐼𝑓 𝜌𝑠 << 𝜌𝑚
𝑇ℎ𝑒𝑛: ∆𝑃 = 𝜌𝑚 𝑔ℎ
Measurand
Fluid Height
when DP = 0
𝑃
Reading
𝝆 𝒌𝒈 𝒎𝟑
Fluid
Air (1 ATM, 27°C) 1.774
Water (30°C)
995.7
Hg (27°C)
13,565
• 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
𝜌𝑚 𝑔
(Reading ℎ versus Measurand ∆𝑃, linear)
Transfer Function
Reading, h [cm]
Low rm
(alcohol)
High rm
(mercury)
∆𝑃
ℎ=
𝜌𝑚 𝑔
Measurand, ∆P [kPa]
• Instrument sensitivity describes how much the Reading
changes for a small change in the measurand
– 𝑆=
𝜕𝑅
𝜕𝑀
= 𝑠𝑙𝑜𝑝𝑒 =
1
𝜌𝑚 𝑔
– Increases as 𝜌𝑚 decreases (small change in P produces larger h)
Inclined-Well Manometer
AW P1
DP = 0
h1
h2 q
AT
P2
R
ℎ = ℎ1 + ℎ2
ℎ2 = 𝑅𝑠𝑖𝑛𝜃
ℎ1 𝐴𝑤 = 𝑅𝐴𝑡
𝐴𝑡
ℎ1 =
𝑅
𝐴𝑤
𝐴𝑡
𝐴𝑡
ℎ=
𝑅 + 𝑅𝑠𝑖𝑛𝜃 = 𝑅
+ 𝑠𝑖𝑛𝜃
𝐴𝑤
𝐴𝑤
• By measuring R we can find h. Generally 𝑅 > ℎ
• Use a scale on the measuring tube to measure 𝑅 directly
Transfer Function
𝐴𝑡
∆𝑃 = 𝑃1 − 𝑃2 = 𝜌𝑚 𝑔ℎ = 𝜌𝑚 𝑔𝑅 𝑠𝑖𝑛𝜃 +
𝐴𝑤
∆𝑃 = 𝜌𝑚 𝑔 𝑠𝑖𝑛𝜃 +
If 𝜃 ≈ 30°,
1
And 𝑠𝑖𝑛𝜃 ≈ ≫
2
𝐴𝑡
𝐴𝑤
R
𝐴𝑡
𝐴𝑤
𝑇ℎ𝑒𝑛: ∆𝑃 = 𝜌𝑚 𝑔𝑅𝑠𝑖𝑛𝜃
1
𝑇𝑟𝑎𝑛𝑠𝑓𝑒𝑟 𝐹𝑢𝑛𝑐𝑡𝑖𝑜𝑛: 𝑅 =
∆𝑃
𝜌𝑚 𝑔𝑠𝑖𝑛𝜃
• Sensitivity 𝑆 =
𝜕𝑅
𝜕𝑀
= 𝑠𝑙𝑜𝑝𝑒 =
1
𝜌𝑚 𝑔𝑠𝑖𝑛𝜃
• S increases as 𝜌𝑚 and 𝜃 decreases
– Easy to vary instrument sensitivity
Inclined Manometer
Transfer Function
1
𝑅=
∆𝑃
𝜌𝑚 𝑔𝑠𝑖𝑛𝜃
Reading, R [cm]
Small q
Large q
Measurand, ∆P [kPa]
General “Linear” Instrument Characteristics
𝑅𝑚𝑎𝑥
Reading
∆𝑅𝑚𝑖𝑛
𝑆𝑒𝑛𝑠𝑖𝑡𝑖𝑣𝑖𝑡𝑦:
𝜕𝑅
𝑆=
𝜕𝑀
Measurement
𝑅𝑚𝑎𝑥 ≡ Maximum Reading (i. e. tube length)
∆𝑀𝑚𝑖𝑛
𝑀𝑚𝑎𝑥
∆𝑅𝑚𝑖𝑛 ≡ Readability (smallest change in reading that can be detected, i.e. tick mark, digit)
𝑀𝑚𝑎𝑥 =
𝑅𝑚𝑎𝑥
𝑆
∆𝑀𝑚𝑖𝑛 =
≡ Instrument Range (Maximum measurand for which instrument can be used)
∆𝑅𝑚𝑖𝑛
≡ Instrument Resolution (smallest detectiable change in measurand)
𝑆
Sensitivity affects both Resolution and Range
• In general, it is not hard to change sensitivity, i.e.
𝜕𝑅
1
𝑆=
=
𝜕𝑀 𝜌𝑚 𝑔𝑠𝑖𝑛𝜃
– Increasing S improves resolution
– But decreases range
𝑀𝑚𝑎𝑥
∆𝑀𝑚𝑖𝑛
𝑅𝑀𝐴𝑋
=
𝑆
• Resolution as a fraction of Range
∆𝑅𝑚𝑖𝑛
∆𝑀𝑚𝑖𝑛
∆𝑅𝑚𝑖𝑛
𝑆
=
=
𝑅
𝑀𝑚𝑎𝑥
𝑅𝑚𝑎𝑥
𝑚𝑎𝑥
𝑆
≡ % of full scale that can be detected.
∆𝑅𝑀𝐼𝑁
=
𝑆
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
General Instrument
Desired Input
(Measurand M)
i.e. length, pressure
temperature
Controlled
i.e. temperature,
orientation
Instrument
Undesired Inputs
x1, x2, x3, x4, x5,…
Output Reading R
(deflection, number
of steps, needle angle)
Uncontrolled
i.e. RF frequency, Average
walking stride length, Value
approved from above or below
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
Standard
Instrument
Under Test
M (units) R(Units)
--------------------------------
Reading, R (units)
Calibration Correlation
Measured Data
“Best Fit” Line
“Expected” Transfer
Function
Measurand, M (units)
• 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!
How to reduce Measurement
Imprecision?
• Improve the control of undesired inputs, and/or
• Use a different instrument that is less sensitive to
uncontrolled inputs
Lab 3 Pressure Transmitter Calibration
Proximity Sensor
or
IT
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
End 2016
Transmitter Characteristics
• See Lab 3 website, ~$150
• Use different diaphragm thickness or flexibilities to get
different sensitivities to vary Full Scale (FS) range and
resolution
• Output Signal: 4 to 20 mA (h = 0 to FS, linear)
• Accuracy: 616: ±0.25% F.S.
• Stability: ±1% F.S./yr.
• Two models in lab:
– 616-1: FS = 3 in WC; Accuracy = 0.0025*3 = ±0.0075 in WC
– 616-4: FS = 40in WC; Accuracy = 0.0025*40 = ±0.1 in WC
– What does this accuracy mean (what is its confidence level)?
Manufacturer’s Inverted Transfer Function
• Output Signal: 4 to 20 mA (h = 0 to FS, linear)
• Measurand vs Reading
– Needed to use the gage
• Pressure head:
– ℎ = 𝐹𝑆
𝐼−4𝑚𝐴
16
• Pressure Difference:
– Δ𝑃 = 𝑃𝐻𝐼 − 𝑃𝐿𝑂 = 𝜌𝑤 𝑔ℎ
𝑘𝑔
𝑚
2.54 𝑐𝑚
1𝑚
𝐼−4𝑚𝐴
= 998.7 3 9.81 2 𝐹𝑆
𝑚
𝑠
𝑖𝑛𝑐ℎ
100 𝑐𝑚
16
• What is the confidence level (probability) that the real pressure head is
within the interval h ± Accuracy?
•
this is what we will determine in Lab 3
• Manufacturer’s Transfer Function (R vs M)
16 𝑚𝐴
– 𝐼=
ℎ + 4 𝑚𝐴
𝐹𝑆
– We will try to confirm this in Lab 3
Calibration Transfer Function
M (units) R(Units)
-------------------------------Scatter – Uncontrolled inputs
instrument
Correlate
R (units)
Data
Uncertainty
M (units)
Lab 2 Plots and Table
Average
Standard
Deviation
Long Side
Length, L [ft]
430
110
Short Side
Lenth, S [ft]
120
30
Area, A [ft2]
56,000
19,000
Cost, C [$]
980
330
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
Manometer Reading Rm
Transfer Function Plot
Actual Outputs
Best fit line
Manufacturer
Specified
Performance
Applied Pressure hT