1. ME 322: Instrumentation Lecture 13: Exam Review February 18, 2015 Professor Miles Greiner

2. Announcements/Reminders Labs – This week: Lab 6 Elastic Modulus Measurement – Next Week: Monday only: Lab 6 No lab on the other days – In two weeks: Lab 6 Wind Tunnel Flow Rate and Speed Only 4 wind tunnels (currently constructing one more) Sign-up for 1.5 hour slots with your partner this week in lab Tesla – Looking to hire ~330 interns this summer – Many of them will be ME majors – http://www.teslamotors.com/careers/university http://www.teslamotors.com/careers/university

3. Starts Today, Evening with Industry, next Wednesday Career Fair next Thursday

4. Midterm 1 Friday Open book, plus bookmarks, plus one page of notes – If you have an e-book, you must turn off internet 4 problems, some have parts – each part like HW or Lab calculations – Remember significant figures, uncertainty, units, confidence level Be able to use your calculator – sample average and sample standard deviation – linear regression Y FIT = aX + b Review Session – Marissa Tsugawa, this evening, 7-9 pm in PE 113, see WebCampus Handout: last year’s midterm problems – These problems will not be on the exam – Neither Marissa nor I will not provide answers or solutions for this See me after class today regarding special needs

5. Multiple Measurements of a Quantity Do not always give the same results. – Affected Uncontrolled (random) and Calibration (systematic) errors, as well as Measurand. Patterns are observed if enough measurements are acquired – Bell-shaped probability distribution function – The sample may exhibit a center (mean) and spread (standard deviation) Statistical analysis can be applied to this “randomly varying” process Quad Area [m 2 ]

6. Statistics

7. Example Problem

8. “Typical” Problems Find the probability the next value is within a certain amount of the mean (symmetric) Find the probability the next value is below (or above) a certain value If one more value is acquired, what is the likelihood it is above the mean? – How much must be added to the next measurement so the sum will have a specified-likelihood to be above the mean?

9. Instrument Calibration

10. To use the calibration

11. Stand. Dev. of Best-Fit Slope and Intercept

12. Propagation of Uncertainty

13. Statistical Analysis Shows

14. General Power Product Uncertainty

15. Instruments

16. U-Tube Manometer Measurand Reading Power product? Fluid Air (1 ATM, 27°C) Water (30°C) Hg (27°C) 1.774 995.7 13,565  P = 0

17. Inclined-Well Manometer

18. Strain Gages

19. Wheatstone Bridge Output Voltage, V O R3R3 + + - -

20. Quarter Bridge R3R3 + + - - Undesired Sensitivity

21. Half Bridge R3R3 + + - -

22. Beam in Bending: Half Bridge ε3ε3 ε 2 = -ε 3

23. Beam in Bending: Full Bridge 3 1 2 4 R3R3 + + - - =  3 =  3 = -  3 =  3

24. Tension Configuration (HW) ε 1 = ε 3 ε 4 = ε 2 = -υ ε 3 23 41 R3R3 + + - - What would happen if all four were parallel?

25. Beam Surface Strain Neutral Axis σ y W L T F F

26. Fluid Speed V (Pressure Method) V PSPS PSPS P T > P S

27. How to Find Density

28. Water Properties (Appendix B of Text) Be careful with header and units

29. Volume Flow Rate, Q Variable-Area Meters Venturi Tube Nozzle Orifice Plate

30. To use

31. Discharge Coefficient Data from Text

33. Student T If N >30 use student t Correlation Coefficient