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 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

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

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 PGAGE = P – PATM P 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) Not always linear

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)

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)

Inclined-Well Manometer h1 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

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

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

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)

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.

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 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,…

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

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!

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 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= 𝑃 𝐻𝐼 − 𝑃 𝐿𝑂 = 𝜌 𝑤 𝑔ℎ = 998.7 𝑘𝑔 𝑚 3 9.81 𝑚 𝑠 2 𝐹𝑆 2.54 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

Calibration Transfer Function Data Correlate Scatter – Uncontrolled inputs instrument

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

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

Transfer Function Plot Actual Outputs Best fit line