1. Measurements in Fluid Mechanics 058:180 (ME:5180) Time & Location: 2:30P - 3:20P MWF 3315 SC Office Hours: 4:00P – 5:00P MWF 223B-5 HL Instructor: Lichuan Gui lichuan-gui@uiowa.edu Phone: 319-384-0594 (Lab), 319-400-5985 (Cell) http://lcgui.net

2. 2 Lecture 6. Measurement uncertainty

3. Probability density function: f(x) Mean value:  3 Measurement errors Physical property: x True value: x true Measured value: x i, i=1,2, ,N Absolut error:  x i =x i -x true Relative error:  x i /x true Standard deviation:  Bias (fixed or system) error:  =  - x true  Precision (random) error:  i =x i -  ii Normal (Gaussian) distribution

4. 4 Accuracy and uncertainty Accurate measurement: |  |<< | x true | and  << | x true | Inaccurate measurement: - Precise but biased, i.e.  << | x true | but |  | relatively large - Unbiased but imprecise, i.e. |  | << | x true | but  relatively large - Biased and imprecise, i.e. both |  | and  relatively large Measurement uncertainty: Bias limit b signifies that the experimenter is 95% confident that |  |<b Precision limit p signifies that, for every single repeat measurement x i, the mean value  would fall within the interval [ x i -p,x i +p ] 95% of the time. b k – individual bias limits of totally K sources

5. 5 Uncertainty of derived properties Derived property: Uncertainty: Bias limit: Precision limit: Precision limit of mean value of repeat number N: Propagation of uncertainty:

6. 6 Homework - Questions and Problems: 2 on page 53 - Read textbook 3.1-3.4 on page 45-53 - Due on 09/05

7. 7 Start to write a Matlab program Write a Matlab program to - read a digital image image01.bmp available at http://lcgui.net/ui-lecture2012/hw/00/image01.bmp - display the image - determine size of the image - read gray values at the center and 4 corners of the image - find location of maximal gray value –Simplest Matlab program A=imread('image01.bmp'); imshow(A); [M N]=size(A); A(1,1) A(1,N) A(M,1) A(M,N) A(M/2,N/2)......

8. 8 60 49 45 51 44 49 37 45 50 35 54 47 57 41 39 40 44 52 38 52 50 22 23 48 48 43 49 50 42 40 33 47 36 29 40 50 47 26 26 54 56 38 45 42 32 46 40 38 62 48 38 40 51 36 48 58 47 40 48 48 43 43 51 43 30 35 39 34 34 50 36 51 49 38 44 50 52 59 56 46 51 32 43 43 43 45 21 33 35 41 45 33 43 41 52 49 46 37 37 37 49 36 39 50 42 42 44 26 12 25 26 30 47 41 33 53 53 40 50 59 40 33 41 45 39 37 36 29 28 35 44 32 26 44 34 38 35 24 67 53 50 46 49 23 33 46 47 39 36 63 36 33 25 34 55 44 38 28 28 28 30 43 39 27 39 44 39 39 58 37 34 34 48 37 15 38 36 35 36 51 36 60 38 35 40 47 35 53 53 27 30 48 33 47 34 38 35 37 30 40 41 36 50 34 33 53 39 30 34 46 53 52 41 43 41 44 54 41 53 44 34 39 16 24 32 53 50 30 29 57 33 36 56 48 44 56 33 34 37 46 45 54 41 30 24 14 29 39 40 39 46 51 36 39 35 31 51 47 56 57 54 43 50 32 54 46 27 32 28 34 27 34 42 40 39 47 44 36 33 61 30 47 48 59 45 46 38 53 52 28 32 41 52 29 36 36 35 45 36 39 35 22 36 21 24 50 46 54 41 37 27 27 31 23 33 31 33 21 26 34 28 43 40 32 42 50 27 32 44 54 51 60 58 43 31 43 48 40 61 39 36 32 41 35 44 33 50 44 29 37 35 33 55 56 75 85 60 39 40 52 33 50 39 36 23 37 12 21 22 23 55 41 26 27 26 49 68 103 255 167 73 36 12 12 30 28 46 37 19 29 28 30 27 48 43 43 29 40 51 57 84 184 149 63 29 20 5 28 31 47 46 28 35 26 37 35 46 26 37 35 32 39 41 47 59 50 54 48 31 22 21 30 38 37 37 48 20 38 35 33 37 23 27 44 48 59 37 44 42 47 50 36 41 24 37 28 48 35 41 22 50 47 51 32 38 28 41 45 48 55 42 34 38 27 42 22 31 19 24 46 38 44 39 55 44 56 38 40 40 31 33 34 36 32 25 39 19 19 25 27 14 10 54 34 22 43 50 54 52 36 38 21 34 18 46 46 44 52 38 24 30 23 32 45 15 26 48 38 44 32 49 46 47 37 29 47 40 21 47 36 40 38 26 27 31 34 37 35 24 36 31 43 42 31 38 47 40 28 21 30 36 54 47 32 31 41 27 30 36 25 31 25 28 44 image01.bmp A(i,j) for i=1,2,3 , M; j=i=1,2,3 , N Start to write a Matlab program Understand digital image file and Matlab matrix i – number of lines j – number of columns >> A(1:10,1:5) ans = 60 49 45 51 44 48 48 43 49 50 40 38 62 48 38 50 36 51 49 38 43 41 52 49 46 53 53 40 50 59 67 53 50 46 49 43 39 27 39 44 40 47 35 53 53 30 34 46 53 52